Investigation of Magnetoresistance Tuned by Interface States of YIG/Pt Heterostructures

Transcription

1 Technische Universität München Fakultät für Physik Walther-Meiÿner- Institut für Tieftemperaturforschung Master's Thesis Abschlussarbeit im Masterstudiengang Physik Investigation of Magnetoresistance Tuned by Interface States of YIG/Pt Heterostructures Saki Matsuura Supervisor: Dr. Matthias Althammer Primary Reviewer: Prof. Dr. Rudolf Gross Garching, September 29, 2017

2 Erstgutachter (Themensteller): Prof. Dr. Rudolf Gross

3 Contents 1 Introduction 1 2 Theory Spin currents in normal metal/ferromagnetic insulator heterostructures Spin current in metals Spin current in ferromagnetic insulators Spin Hall eect and inverse spin Hall eect Spin Hall magnetoresistance Magnetoresistance Hanle magnetoresistance Magnon mediated magnetoresistance Fabrication of YIG/Pt heterostructures YIG/Pt bilayers with in-situ interface YIG/Pt bilayers with ex-situ interface Fabrication of Hallbar structure and mounting on chip carriers Spin Hall magnetoresistance in YIG/Pt heterostructures Experimental procedure measurement longitudinal and transverse resistivity Rotation conguration of ADMR ADMR measurements of YIG/Pt bilayers temperature dependence of MR MR in OOPT rotation MR in IP rotation Summary of ADMR measurement Magnetotransport experiments as a function of external magnetic elds Experimental setup for FDMR measurements Field dependence of longitudinal MR as a function of temperature Transverse magnetotransport and dependence on external magnetic eld Measurement setup and data evaluation iii

4 5.3.2 Experimental results of the spin Hall anomalous Hall eect Conclusion to eld dependence of MR as a function of temperature Summary and Outlook Summary Outlook A Interface optimization for magnetoresistance by Ar-etching bombardment 73 Bibliography 80 Acknowledgments 81 iv

5 Chapter 1 Introduction In 2017, due to the advent of new technologies, the industrial world faces a tumultuous time. The realization of electric vehicle has become a common theme for the automotive industry, and due to the concept of Internet of Things (IoT) [1] a multitude and variety of physical devices with embedded small computers start to be connected with the internet. Therefore, the rise of electronics and the technology of IC (Integrated circuits) naturally has never shown a sign of slowing down, even now an advancement of these elds is more and more desired. However on the other hand, Moore's law is about to end, which is that the density of transistors in semiconductor industry increases exponentially year after year [2]. Roughly speaking, thanks to the development of micro-fabrication nanotechnology, IC chips with a higher and higher density of transistor have been realized, but are closing in on to the physical limitations of solid state physics. Here, the level of miniaturization is comparable to the scale of the leakage charge current of silicon. Therefore, an important task is the research for new devices replacing conventional charge current devices, that are controlled by the on and o states represented by electrical charges. As one of the technologies playing a role in this new age, spintronics has been rapidly gathering attention [35]. Spintronics aims to realize innovative devices by combining charge, which is the star in conventional electronics, with the spin of electrons. The history of spintronics is dating back to the discovery of the giant magnetoresistance (GMR) by Albert Fert [6] and Peter Grünberg [7] in 1987, which was awarded with the Nobel Prize in Physics in Since the GMR eect is not only a signicant discovery from the viewpoint of fundamental research, but also achieved practical applications, like a hard-disc read-head in computer in an instant, spintronics has become an active area of research in both of the academic and industrial world. Thus, the history of spintronics is short and it is still a developing research eld for both fundamental research and application sides. The investigation of a current of spin (called a pure spin current) and physical phenomena related to pure spin currents, e.g. spin Hall eect (SHE) [8, 9], inverse spin Hall eect (ISHE) [1012], spin Seebeck eect (SSE) [13, 14] and many more represent a new paradigm in the world of 1

6 spintronics. In the eld of pure spin currents, the ow of pure spin currents across an interface plays an important role for many eects. Investigating the role of such interfaces on the pure spin current transport thus is of great importance for future device applications and to advance fundamental research. In this work, we investigate one of the eects related to pure spin currents, which was experimentally discovered in 2013 [15, 16], the spin Hall magnetoresistance (SMR) which contributes to determine some important parameters related to pure spin current physics. However, there are still some unsolved issues concerning the interpretation of experiments in terms of the SMR mechanism, which can stem from the dierence of sample preparations and measurements conditions. To this end, we present the investigation of the magnetoresistance related to pure spin currents in YIG/Pt bilayers systems, which were fabricated through dierent sample preparation techniques in this thesis. By using dierent sample preparation techniques, we can generate several dierent interface states between YIG/Pt bilayers samples. The main purpose of this study is to systematically investigate the magnetoresistance modulated by the dierent interface states with respect to the SMR and other magnetoresistance eects. This thesis is organized as follows. The theoretical background of phenomena related to pure spin currents will be introduced in Chapter 2. At rst, we begin with the denition of a pure spin current. Subsequently, the SHE and ISHE, and the magnetoresistance due to the combination of the SHE and ISHE eect, i.e. the SMR, are introduced. In the end of this Chapter we give a brief description of additional new types of magnetoresistance; Hanle magnetoresistance and magnon-mediated magnetoresistance. In Chapter 3 we will present the fabrication processes of the YIG/Pt bilayers samples, which we used in this work. The six YIG/Pt bilayers samples were fabricated by preparing two types of YIG thin lms and using two dierent Pt-deposition processes, i.e. electron beam evaporation and sputter deposition. The experimental procedure and measurement results are summarized in Chapter 4 and Chapter 5. In Chapter 4 the temperature dependence of magnetoresistance in the samples, with dierent fabrication techniques are investigated and we discuss the possible causes of the observed temperature dependence of the magnetoresistance. Moreover, we investigate the magnetoresistance in the samples as a function of an external magnetic eld strength in Chapter 5. In this chapter we also discuss the possible causes leading to the observed eld dependence of the magnetoresistance. The summary and an outlook are given in Chapter 6 to conclude this thesis. Some additional experiments are proposed in this chapter about open issues, which remain unsolved in this work. 2

7 Chapter 2 Theory The theoretical background of phenomena related to pure spin currents is summarized in this Chapter. We start with a denition of pure spin currents in metals in Sec and in insulators in Sec Then we will give a brief overview of phenomena for the generation and detection of pure spin currents via the spin Hall eect (SHE) and the inverse spin Hall eect (ISHE) in Sec After that, we introduce magnetoresistance phenomena induced by spin current physics. Combining the concepts of the SHE and the ISHE for a FMI/NM bilayer leads to the spin Hall magnetoresistance (SMR) (Sec ). Finally, in Sec. 2.2 we will introduce the other magnetoresistance eects recently reported, Hanle magnetoresistance and magnon mediated magnetoresistance. 2.1 Spin currents in normal metal/ferromagnetic insulator heterostructures Spin current in metals electron up-spin ( ) down-spin ( ) An electron has two properties, namely, a negative charge ( e) and a spin angular spin momentum (Fig. 2.1). According to -e quantum mechanics, a spin is an internal chrage degree of freedom and it has two types of eigen states, namely, up-spin and Figure 2.1. Sketches of electron and spins. down-spin. Electrons with up-spin and down-spin have spin angular momentum s = 2 and 2, respectively, with a magnetic moment µ = µ s B, where µ B is called Bohr magneton of the electron [17]. A charge current is a directed ow of charge. Specially, in a non-magnetic metals (NM) exhibiting an equal amount of electrons with and states, electrons propagate without a net current of spin angular momentum (Fig. 2.2(a)). In contrast, Fig. 2.2(b) shows a spin 3

8 2.1 Spin currents in normal metal/ferromagnetic insulator heterostructures (a) charge current (b) spin current q up spin q current of charge q down spin current of spin angular momentum Figure 2.2. (a) In a pure charge current, the same number of spin-up and spin-down electrons propagate in the same direction. This leads to a ow of charge, but no net ow of spin angular momentum. (b) Assuming that electrons with and propagate in the opposite directions leads to a net transport of spin angular momentum, but no net charge current contribution. This case is called a pure spin current. current, which is a ow of spin angular momentum. In the situation of two electrons with opposite spin orientation propagating in opposite directions, only a ow of spin angular momentum exists because the net ow of charge is canceled out. In a two spin channel model, the charge current of electrons with can be denoted as j and the charge current carried by electrons with as j. Thus, the total charge current j q and the total spin current j s can be expressed as j q = j + j, (2.1) j s = 2e (j j ). (2.2) In our notation, a positive spin current is dened as the propagation direction of particles. Figure 2.2(a) and (b) show the cases of pure charge current (i.e. j q 0 and j s = 0) and pure spin current (i.e. j q = 0 and j s 0), however, the case that both charge and spin information are transported can be of course assumed, and it is called a spin-polarized current. This case can be found in materials with an imbalance of spin-up and spin-down charge carriers at the Fermi level, like in ferromagnetic conductors. At rst glance, there is no big dierence between the concepts of charge current and spin current in metals. However, the spin is not a conserved transport quantity and will vanish after propagating a certain length, which is known as spin relaxation length λ in metals Spin current in ferromagnetic insulators In the previous section, we described a pure spin current in a metal, namely the spin current propagated by conduction electrons. However, the spin current can be carried not 4

9 Chapter 2 Theory (a) spin Hall effect (SHE) (b) inverse spin Hall effect (ISHE) up down NM up V NM down Spin accumulation Figure 2.3. Schematics of the spin Hall eect (a) and inverse spin Hall eect (b). j q, j s, and σ denote as the charge current, the spin current, and the spin polarization direction of the spin current in NM, respectively. (a) Spin Hall eect: Due to SOI a trajectory of electrons are deected dependent on the spin orientation ( or ), and j s is generated along the direction of both perpendicular to j q and σ. (b) Inverse spin Hall eect as a reciprocal process of SHE. j s is converted to j q along both perpendicular to j s and σ, and it can be detected electrically. only by conduction electrons in metals but also by spin waves in magnetically ordered systems. Here, a spin wave means an oscillation of the localized magnetic moments. A quantized spin wave is called a magnon, which can be considered an analogy of the phonon, which is the quantization of lattice oscillation. Magnons can be excited both in metals and insulators as long as it is a magnetically ordered system. Therefore, this mechanism enables the propagation of spin current in ferromagnetic (or ferrimagnetic) insulators (FMI) Spin Hall eect and inverse spin Hall eect In the previous section we introduced the concept of spin currents. However, how is a spin current generated? The generation and detection of pure spin currents are also the essential questions for spintronics, since the development of electronics has been supported by the established technology of the generation and detection of charge currents. The phenomena widely used as the way to generate and detect a pure spin current in a metal is the spin Hall eect (SHE) and the reciprocal process, the inverse spin Hall eect (ISHE), and these enable ones to generate and detect a spin current electrically. In this section, we briey discuss the SHE and the ISHE. The SHE is the phenomenon that a charge current j q owing in a NM conductor is converted into a spin current j s along the direction perpendicular to both j q and spin polarization vector σ caused by the spin-orbit interaction (SOI) as shown in Fig. 2.3(a), 5

10 2.1 Spin currents in normal metal/ferromagnetic insulator heterostructures and it is described using the spin Hall angle θ SH as j s = 2e θ SH (σ j c ), (2.3) where θ SH describes the eciency of a charge current to a spin current conversion. As a result of the SHE, the converted spin current causes a spin accumulation at the edge of the conductor. The rst observation of SHE was in GaAs semiconductor by Kato et al. in 2004 [8] and Wunderlich et al. in 2005 [9]. The mechanisms of SHE can be understood from the view points of extrinsic and intrinsic scattering processes. While the above-mentioned SHE is due to extrinsic scattering: skew scattering and side jump scattering [1820], the intrinsic SHE is related to the Berry curvature [21, 22] and caused by the band structure of the material. The reciprocal process of SHE is called the inverse spin Hall eect (ISHE), which is the phenomenon that electrons with up-spin and down-spin in the spin current owing in a conductor are deected to the same direction perpendicular to both j s and σ due to SOI. Therefore, the ISHE leads to a conversion from a spin current into a transverse charge current (Fig. 2.3(b)) described as Spin Hall magnetoresistance j c = 2e θ SH (σ j s ). (2.4) As we mentioned in the last section, the SHE occurs when a charge current ows in the NM and leads to a generation of spin accumulation on the surface of NM layer due to the SOI. Now as a denition of coordinates, the direction of an applied charge current owing in the NM is j, the surface normal is n, and the direction perpendicular to both j and n is t. In this case, the spin polarization vector σ of the spin current owing along n which is induced by the SHE is oriented along t because of Eq. (2.3) such that σ t. Within the length scale of the spin diusion length, namely in the range where spin information is conserved, the spin current polarized to σ ( σ) accumulates at the top (bottom) of NM as shown in Fig. 2.4(a). This spin accumulation leads to a gradient in the spin-dependent etectrochemical potential µ σ=,. In short, the spin accumulation µ = µ µ is a potential to ow a spin current along µ as if a voltage for a charge current. Thus, the spin accumulation leads to a generation of a back-ow spin current js back into n (see in the left panel of Fig. 2.4(a)). This js back is converted a charge current along j via the ISHE in Eq. (2.4) as shown in Fig. 2.4(a). In the range of nano-scale, the eect of this ISHE-induced charge current is nite, therefore a spin accumulation is involved in a charge current owing in NM with a strong SOI. Let's consider the case that a ferromagnetic insulator layer is adjacent to the NM layer 6

11 Chapter 2 Theory (a) j n t SHE Spin accumulation ISHE n µ σ j s -j q j s back NM (b) (c) t -n -j t -n -j FMI NM FMI NM STT V V (d) (e) hi I lo V trans hi lo n E trans t ρ long High hi lo V long E long FMI NM j Low Figure 2.4. (a) Schematic of a combination of the SHE and the ISHE in NM. The SHE generates a spin accumulation at the surface of NM. This spin accumulation leads to a gradient in the spin-dependent electrochemical potential µ σ, and then raise a back-ow spin current js back. js back is converted to a charge current via the ISHE. (b) and (c) illustrate the SMR mechanism in two cases. m denotes a magnetization in FMI and σ is a spin polarized vector. When m σ as shown in (b), no angular momentum transfer into FMI is possible. However if m σ, it is possible to transfer angular momentum via the STT eect. This leads to a decrease of a spin accumulation, js back, and nally the ISHE-induced j q. (d) Denition of the coordinate system dened by j, t, and n. (e) Longitudinal resistivity in NM as a function of (m, σ). Due to the SMR, ρ m σ > ρ m σ. 7

12 2.1 Spin currents in normal metal/ferromagnetic insulator heterostructures as shown in Fig. 2.4(b). Since there is no conductivity in FMI, FMI does not directly aect the electrical conduction in the NM layer. However, properties related to magnetization can be aected. As shown in Fig. 2.4(b) when the magnetization m in FMI directs parallel to σ, spin accumulation at the interface of FMI/NM is not aected by m and the charge current j q should be identical with the case of Fig. 2.4(a). This intrinsic resistivity in NM denotes ρ 0. However as shown in Fig. 2.4(c), if m is not parallel to σ, it is possible to transfer spin angular momentum from the spin accumulation at the surface of NM onto the m in FMI via the spin transfer torque (STT). The STT should be maximum when m σ. This results in a dissipation of spin accumulation and nally it can lead to a decrease of js back and the ISHE-induced j q because js back is generated by the spin accumulation which works as a voltage for a spin current. Therefore, a resistivity ρ in NM at m σ can be larger than ρ at m σ, i.e. ρ m σ > ρ m σ. This phenomenon that the resistivity in NM can change depending on the relative angle between σ in NM and m in FMI via the SHR and ISHE is called spin Hall magnetoresistance (SMR). For a quantitative understanding of the SMR, the theoretical study of the SMR was performed in Ref. [23], and so far the SMR has been experimentally conrmed by many groups [15, 16, 2426]. transverse resistivity are described as: According to the theoretical SMR model, the longitudinal and ρ long = ρ 0 + ρ 1 (1 m t 2 ) (2.5) ρ trans = ρ 2 m n + ρ 3 m j m t (2.6) where ρ 1 = ρ 3. The amplitude of ρ 1 /ρ 0 indicates the SMR eect as shown in Fig. 2.4(e). Following the calculations detailed in Ref. [23], the relative magnitude of the SMR eect is given by the ratios ( ) 2λG r tanh 2 dn ρ 1 = θsh 2 λ 2λ ( ) (2.7) ρ 0 d N dn σ N + 2λG r coth λ ( ) ρ 2 = 2σ Nλ 2 θsh 2 G i tanh 2 dn 2λ ( ( )) ρ 0 d 2 (2.8) N dn σ N + 2λG r coth λ Here, λ the spin diusion length in the NM, σ N the electrical conductivity in the NM, d N the thickness if the NM, and G r the real part and G i the imaginary part of the spin-mixing interface conductance. From Eq. (2.5), the longitudinal resistivity as a function of (m, σ) is given as in Fig. 2.4(e) and the amplitude of the SMR eect is determined by several parameters described in Eq. (2.7). 8

13 Chapter 2 Theory The SMR originates from the simultaneous action of the SHE and ISHE in NM, and both of SHE and ISHE result from the spin-orbit interaction (SOI). The anisotropic magnetoresistance (AMR) has been known for long time as an other phenomena driven by the SOI in ferromagnetic metals. The AMR causes the change of resistivity in a ferromagnetic metal depending on the relative angle between the charge current j and the magnetization m in the ferromagnetic metal. In a theoretical picture, the longitudinal and transverse resistivities modulated by AMR are given as [27]: ρ long = ρ 0 + ρ AMR m 2 j (2.9) ρ trans = ρ 2 m n + ρ AMR m j m t. (2.10) At rst glance, AMR and SMR in ρ long appear very similar, but the eect by AMR is proportional to m 2 j not m 2 t. This becomes a crucial dierence when one performs ADMR measurements which we will mention below (see in Sec ). In this section we presented the theoretical introduction to the spin Hall magnetoresistance. Recently other new magnetoresistance phenomena related to spin current have been reported. In the following section, we will give a brief description of them. 2.2 Magnetoresistance Recently, new types of MR related to spin current have been reported besides the SMR. This section we will give a brief of Hanle magnetoresistance [28, 29] and magnon-mediated magnetoresistance [30, 31] Hanle magnetoresistance A theoretical work was performed by Dyakonov [28] and he predicted the Hanle magnetoresistance eect in metals with strong spin-orbit coupling (SOC). Let's think of a NM layer where a charge current is owing. As we mentioned in Sec , a spin accumulation orienting σ is created at the top and bottom surface of the NM layer by the SHE. When an external magnetic eld µ 0 H is applied along the direction perpendicular to σ, the spins start to precess around µ 0 H and dephase via the Hanle eect as shown in Fig. 2.5(a). This destroys the spin accumulation at the interface and reduces an ISHE-induced charge current. Therefore, the resistivity in the NM layer can increase as with the SMR mechanism, and this is the Hanle magnetoresistance (HMR). The HMR exhibits the same angular dependence as SMR; no ρ long change is observed at µ 0 H σ and an increase of ρ long is obtained at µ 0 H σ. However, the HMR can occur without a FMI, as this is an intrinsic phenomenon in the NM layer. Moreover, the dierent point 9

14 2.2 Magnetoresistance NM spin accumulation Figure 2.5. Schematic of spin precession at the surface of NM layer. Since spins orienting σ start to precise around an external magnetic eld µ 0 H applied perpendicular to the sample, a spin accumulation at the interface is destroyed. This can lead to a reduce of an ISHE-induced charge current in NM. with the SMR eect is that the dissipation of spin accumulation in the HMR is induced by the spin precession by the external magnetic eld. Thus, the spin accumulation can be more destroyed by the stronger µ 0 H, and this suggests that HMR can depend on not only the direction but also the strength of the external magnetic eld Magnon mediated magnetoresistance Recently, the magnon-mediated magnetoresistance (MMR) has been experimentally discovered as a non-local magnetoresistance eect in the YIG/Pt heterostructures [30]. This eect is the phenomenon that an electrical signal is transmitted via a magnon transportation in YIG lm from an injector to a detector made by Pt stripes as shown in Fig. 2.6(a). At the injector side, spin accumulation is created at the interface of YIG/Pt from an applied charge current by the SHE. If the magnetization m in YIG is collinear to σ in Pt, spin angular momentum is transferred to the YIG via the exchange interaction at the interface, and a magnon is created in the YIG as shown in Fig. 2.6(b). At the detector side, the reciprocal process leads to the creation of spin accumulation from the diusing magnon at the interface. This created spin accumulation leads to a generation of charge current in the detector Pt stripe via the ISHE. In conclusion, a voltage induced by a non-local charge current is detected via the SHE, magnon transportation, and the ISHE. Therefore, this eect is called a non-local magnetoresistance or magnon-mediated magnetoresistance [31]. In the process of this mechanism, the spin accumulation at the injector side is destroyed by spin-ip scattering, thus this may result in the resistivity change in the Pt stripe at m σ where nothing should be observed in the SMR frame. 10

15 Chapter 2 Theory (a) detector (b) injector Pt Pt + V - Spin accumulation metal (Pt) Spin-flip scattering I YIG GGG µ 0 H M YIG magnet (YIG) magnon Figure 2.6. (a) Illustration of the magnon-mediated magnetoresistance (MMR). An applied charge current owing in a injector made by Pt stripe generates a spin accumulation at the interface of YIG/Pt via the SHE. Through a spin-ip scattering explaining in (b), spin angular momentum is transferred into YIG and this creates magnons in YIG. The magnons then diuse towards the detector Pt strip and a spin accumulation is created through the reciprocal process of (b) induced by the diusing magnons at the YIG/Pt interface of the detector side. Finally, the spin accumulation is converted to a charge current via the ISHE. Figure (a) and (b) are taken from [30]. This concludes the theoretical introduction related to the phenomena induced by spin current; spin Hall and inverse spin Hall eect, spin Hall magnetoresistance, Hanle magnetoresistance, and magnon-mediated magnetoresistance. In the following chapter, we present an overview of the samples used in our experiments. 11

16

17 Chapter 3 Fabrication of YIG/Pt heterostructures To investigate how the dierence of interface states between FMI/NM bilayers aects the spin Hall magnetoresistance (SMR), we prepared several types of samples with dierent interface states. A basic sample structure is a Hall bar mesa structure made by Pt as the normal metal (NM) deposited on yttrium iron garnet (Y 3 Fe 5 O 12, YIG), as ferrimagnetic insulator (FMI) on gadolinium gallium garnet (Gd 3 Ga 5 O 12, GGG) substrate as shown in Fig. 3.3(a). Figure 3.1. Crystalline structure of YIG taken from [32]. Yttrium iron garnet has a complicated cubic crystal structure as shown in Fig The lattice constant is Å and YIG is a ferrimagnet with two magnetic sublattices. Three of the ve Fe ions are on one magnetic sublattice and two are on the other. Then the net magnetic moment is due to one Fe ion which is not canceled, and consequently YIG shows ferrimagnetism [33]. YIG has been widely used in spintronics because of the unique properties, like good insulator, low-damping magnetic material, and exhibiting linear and nonlinear spin wave dynamics [3337]. This chapter provides a brief overview on the sample fabrication. In this study, we used several dierent methods in depositing Pt and fabricating YIG which leads to six samples dierent with dierent interface states. At rst we explain the fabrication of YIG/Pt bilayers samples with in-situ interface and with ex-situ interface. In addition, the reference bilayer samples consisting of Pt on SiO 2 substrate were prepared for comparison with the YIG/Pt bilayers. The thickness of the Pt layer for all samples was kept constant to approximately 3.5 nm to ensure a high spin Hall magnetoresistance value [15]. 13

18 (a) in-situ sample prepara on 1. YIG produced by PLD 2. Pt deposited 3. photolithography by EVAP (i.e. insitu1) or by spu ering (i.e. insitu2) resist YIG in-situ transfer Pt YIG substrate YIG (GGG) Pt substrate Pt PLD-YIG (GGG) substrate Pt PLD-YIG (GGG) 4. Ar-ion etching to make Hall bar-shape Pt Ar 5. remove resist 6. YIG/Pt heterostructure substrate Pt Pt PLD-YIG (GGG) substrate Pt PLD-YIG (GGG) substrate Pt PLD-YIG (GGG) (b) ex-situ sample prepara on 1. YIG produced by PLD or LPE method YIG YIG YIG 2. photolithography resist 3-1. surface cleaning by Ar-ion etching Ar substrate (GGG) substrate YIG (GGG) substrate YIG (GGG) 3-2. nothing 4-1. Pt deposited by EVAP on LPE-YIG (i.e. exsitu1) or on PLD-YIG (i.e. exsitu3) 5. Li off process 6. YIG/Pt heterostructure Pt Pt Pt substrate (GGG) YIG 4-2. Pt deposited by spu ering on LPE-YIG (i.e. exsitu2) or on PLD-YIG (i.e. exsitu4) substrate Pt YIG (GGG) substrate Pt YIG (GGG) Figure 3.2. Flowcharts of YIG/Pt bilayers samples fabricated in-situ (a) and ex-situ (b). Details are described in the text and Table

19 3.1 YIG/Pt bilayers with in-situ interface Chapter 3 Fabrication of YIG/Pt heterostructures As an in-situ YIG/Pt bilayer structure sample, we prepared two types of samples as shown in Fig. 3.2(a). First YIG layers were fabricated by pulsed laser deposition (PLD) on a (100)-oriented GGG substrate at a substrate temperature of 360 C in an oxygen atmosphere (p = 25 µbar) and an energy uence at the target of 2.0 J/cm 2. After the YIG deposition, a Pt layer was deposited in-situ on the YIG substrates by means of electron beam evaporation (EVAP) (sample ID: insitu1 ) and sputtering (sample ID: insitu2 ) in ultrahigh vacuum without breaking the vacuum to ensure a clean interface between these two layers. By means of optical lithography a Hall bar structure was formed by Ar-ion etching. 3.2 YIG/Pt bilayers with ex-situ interface For the ex-situ YIG/Pt bilayer structure samples, we prepared four types of samples as shown in Fig. 3.2(b). At rst, two types of YIG layers were prepared which were fabricated by the PLD method (i.e. PLD-YIG) and by liquid-phase epitaxy (LPE) method (i.e. LPE-YIG) on GGG substrates, and Hall bar-shape masks were made on the YIG layers by photolithography. Then, a Pt layer was deposited by sputtering on a LPE-YIG substrate (sample ID: exsitu2 ) and a PLD-YIG (sample ID: exsitu4 ), respectively. On the other hand, a Pt layer was deposited by EVAP on LPE-YIG substrate (sample ID: exsitu1 ) and PLD-YIG layer (sample ID: exsitu3 ). Immediately before the Pt deposition by EVAP, the surface of both LPE-YIG and PLD-YIG layers were cleaned by Ar-ion bombardment for 14 minutes in vacuum ( p = mbar ) in order to enhance SMR value as we show in App. A. The sample preparation details are summarized in Table 3.1. Sample name Substrate of Pt deposition Interface Ar-ion etching on YIG process states YIG substrate insitu1 PLD-YIG EVAP in-situ x insitu2 PLD-YIG sputtering in-situ x exsitu1 LPE-YIG EVAP ex-situ for 14 minutes exsitu2 LPE-YIG sputtering ex-situ x exsitu3 PLD-YIG EVAP ex-situ for 14 minutes exsitu4 PLD-YIG sputtering ex-situ x Table 3.1. Summary of the details of YIG/Pt bilayers samples fabricated in this study. 15

20 3.3 Fabrication of Hallbar structure and mounting on chip carriers (a) (b) hi I lo n t W V trans n hi lo E trans t 14 mm j L = 600 µm V long hi lo V long L d substrate E long FMI NM j copper electrode W = 80 µm V trans Figure 3.3. (a) A schematic illustration of the YIG/Pt Hallbar mesa structure, which was used in this study. The distance L of electrodes for V long is 600 µm and the distance W for V trans is 80 µm. (b) A picture of a chip carrier with a mounted sample and an optical microscope image of a typical YIG/Pt bilayer sample. Black lines in the optical image are Al bond wires connecting electrodes with copper contacts of the chip carrier. SiO 2 /Pt bilayers As reference samples to consider the intrinsic eects from a Pt layer, we prepared three types of SiO 2 bilayers samples. One Pt layer was deposited by EVAP without any pretreatments, another one was deposited by EVAP after Ar-ion bombardment, and the third one was deposited by sputtering Pt on SiO 2 substrates, respectively. 3.3 Fabrication of Hallbar structure and mounting on chip carriers A sketch of the fabricated YIG/Pt bilayer samples with the Hallbar mesa structure is shown in Fig. 3.3(a). To measure a longitudinal voltage V long and a transverse voltage V trans, samples were mounted on a chip carrier and connected to the copper contacts of the chip carrier by aluminum wire bonding as shown in Fig. 3.3(b). The length L of the Hallbar structure is 600 µm and the width W is 80 µm, and the thickness d of Pt is 3.5 nm. 16

21 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures In the previous chapter, we described the preparation of the six YIG/Pt bilayers samples fabricated in dierent processes. In the following, we discuss the magnetoresistance (MR) of the fabricated YIG/Pt bilayers samples. To measure the spin Hall magnetoresistance (SMR), the sample was rotated in xed external magnetic eld, while the longitudinal and transverse voltages were recorded with respect to the applied charge current. These angle-dependent magnetoresistance (ADMR) measurements were performed at several temperatures and magnetic eld strengths to study the temperature dependence and magnetic eld dependence of the samples. We will start with describing the experimental procedure and the rotation conguration of ADMR measurements in Sec Then we will discuss the results of ADMR measurements of the six YIG/Pt bilayers samples and the temperature dependence of magnetoresistance with respect to the six samples in Sec Experimental procedure of the angle-dependence magnetoresistance (ADMR) measurements measurement longitudinal and transverse resistivity It is known that electrons diuse along a temperature gradient [38] as well as a gradient of electric potential. To exclude thermal eects, the voltage was recorded while a charge current j c is applied with positive (V + ) and negative polarity (V ), respectively. As the sign of the voltage induced by the temperature gradient V therm from Joule heating is unchanged for a positive current or a negative current, while the sign of the voltage induced by a resistive response V res is inverted, the V therm and V res are calculated as V therm = V ++V 2, and V res = V + V 2. For each data point we repeated this measurement scheme three times and took the average of V res and V therm. We thus can exclude any thermal contribution to 17

22 4.1 Experimental procedure 2 V + Voltage (u.a.) V V therm V res V therm -2 V res -100 µa 0 A 100 µa Applied charge current Figure 4.1. Schematic of recording voltage. Recording the voltages upon applying both a positive and a negative charge current leads to the measurements of the voltage induced by a resistivity without the thermal eect. V res. In the following we will use V long for the longitudinal V res and V tr for the transverse V res response of the sample. As a next step we calculated the longitudinal resistivity ρ long and a transverse resistivity ρ tr of Hallbars as ρ long = V long I c ρ trans = V trans I c W d Pt L W d Pt W (4.1) (4.2) where the length L = 600 µm, the width W = 80 µm, the thickness d Pt = 3.5 nm of the NM (Pt) layer, and I c denotes the magnitude of an applied charge current (typically 100 µa) Rotation conguration of ADMR In this section we explain the rotation conguration of the ADMR measurements which is performed in this study by using Moria which is the measurement system for physical properties used in our group. Figure 4.2(a) illustrates the rotation congurations of ADMR measurements in three rotation planes; IP (a-1) means that the external magnetic eld µ 0 H (= µ 0 Hh) is applied rotating in a sample's plane, OOPJ (a-2) and OOPT (a-3) mean the external magnetic eld is applied rotating in the plane always perpendicular to j-axis and t-axis, respectively. Note that a charge current j c is applied along j-axis (j c j) and a spin current j s ows along n-axis (j s n), therefore the spin polarization vector σ is oriented along the t-axis (σ t). The rotation angles of the external magnetic eld α, β, γ, start from j, n, n 18

23 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures (a-1) (a-2) (a-3) IP OOPJ OOPT β h γ h α h (b-1) SMR and AMR can be observed (b-2) no AMR due to constantly (b-3) no SMR due to constantly SMR ρ long ρ SMR ρ AMR AMR (c-1) ρ long (nωm) ρ ρ L α β γ (c-2) (c-3) insitu1 T = 300 K µ 0 H = 7 T α β γ Figure 4.2. (a) Rotation congurations of ADMR measurements for three rotation planes: the external magnetic eld h rotates in a sample plane (IP, (a-1)), in the plane normal to j-axis (OOPJ, (a-2)), and in the plane normal to t-axis (OOPT, (a-3)). The initial positions of h for the IP, OOPJ, OOPT congurations are j, n, and n, respectively. (b) The simulations of the longitudinal resistivity in ADMR measurements corresponded the above three rotation congurations. The signals from the SMR and AMR eects are shown by green and orange sine function, respectively. In IP (b-1) conguration, the longitudinal resistivities from both of SMR and AMR eects are observed. In OOPJ (b-2) conguration, only the SMR should be observed as h, i.e. m is always perpendicular to j, while in OOPT (b-3) conguration, only the AMR should be observed as h, i.e. m is always perpendicular to t. (c) ADMR measurement data of the insitu1 sample with an external magnetic eld strength of 7 T at T = 300 K. The signal in IP (c-1), OOPJ (c-2), and OOPT (c-3) are in very good agreement with the simulations of SMR (green lines) shown in (b-1), (b-2), and (b-3). 19

24 4.2 ADMR measurements of YIG/Pt bilayers directions in IP, OOPJ, and OOPT, respectively. The simulations of the longitudinal resistivity signals which should be observed in ADMR measurements in IP, OOPJ, and OOPT congurations are shown in Fig. 4.2(b). As we discussed in Sec , the longitudinal resistivity changes depend on the angle of the external magnetic eld with respect to the sample. Taking SMR and AMR eects into account, the resistivity change induced by both SMR and AMR in ADMR rotations can be expressed as [15]: ρ SMR long = ρ 1 ( 1 mt 2 ) (4.3) ρ AMR long = ρ AMRm j 2 (4.4) where m i=j, t, n is the component of a magnetization orientation m ( m = m j 2 + m t 2 + m n 2 = 1) in the YIG layers and ρ 1 and ρ AMR indicate the SMR and AMR eects. Here m is assumed to be parallel to h as the applied magnetic eld strength is large enough to saturate the magnetization of the YIG layers. We now discuss the expected angle dependence for the three dierent rotation planes. In IP rotation, the signals from the SMR and AMR eects show the same angle dependence as shown in Fig. 4.2(b-1) as 1 m t 2 can be recalculated to m j 2 due to m n = 0. On the other hand, the resistivity change in OOPJ rotation should be induced by only the SMR because the external magnetic eld is always normal to j, i.e. m j = 0, then it leads to no AMR eect (Fig. 4.2(b-2)). In contrast, the resistivity change in OOPT rotation should be induced by only the AMR because the external magnetic eld is always normal to t, i.e. m t = 0, then it leads to no SMR eect (Fig. 4.2(b-3)). The point here is that performing ADMR measurements in these three orientations enables ones to distinguish between the SMR and the AMR eects. These ADMR measurements were performed at a wide range of temperatures from 5 K to 300 K. The charge current of 100 µa was applied by a Keithley K2400 sourcemeter along the j-direction of the Hallbar mesa-structure and the longitudinal V long and transverse V trans voltages were measured with a Keithley K2182A nanovoltmeter (Fig. 3.3(a)). The rotating angle of the external magnetic eld was swept from 20 to 380 in 10 steps and back from 380 to 20 in 20 steps to check the reproducibility and possible hysteresis eects. 4.2 ADMR measurements of YIG/Pt bilayers In this section we will show the results of ADMR measurements explained in the last part. Figure 4.2(c) shows the ADMR measurement of insitu1 with the external magnetic eld strength µ 0 H = 7 T at T = 300 K. In IP (Fig. 4.2(c-1)) and OOPJ (Fig. 4.2(c-2)) 20

25 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures ρ long (nωm) T = 300 K IP OOPJ OOPT T 5 T 3 T 1 T 0.5 T T = 5 K α insitu1 Figure 4.3. ADMR measurements of insitu1 at T = 300 K (red background color) and at 5 K (blue background color) in three orientations. The color dierences in the plots represent the dierence of the external magnetic eld strengths. The angles of α, β, and γ correspond to the denition shown in Fig. 4.2(a). β γ rotations the longitudinal resistivity changes with the angle of α and β, respectively, and they show a cos 2 angle-dependence, while in OOPT (Fig. 4.2(c-3)) rotation any changes are observed. Therefore, we can say these results are in good agreement with the SMR theory (see Sec ). However, the ADMR signals become more complicated with decreasing the temperature. Figure 4.3 shows the ADMR measurement of insitu1 at T = 300 K (red back color) and 5 K (blue back color) with several magnetic eld strengths. Compared with these two results, dierences are obvious; the resistivities in IP and OOPJ rotations at T = 300 K behave regardless of the magnetic led strength, while the resistivity at T = 5 K apparently depends on the magnitude of the external magnetic eld. In addition, focusing on the results in OOPT rotation, while the resistivity at T = 300 K shows a constant value, an angle-dependent signal at T = 5 K is observed, which shows a maximum in ρ long at γ = 0 (m n), and a minimum in ρ long at γ = 90 (m j). Since these additional signals at low T can not be explained in the SMR model, the temperature and/or magnetic eld strength dependence indicate that other additional eects beyond the SMR model play a role. In order to investigate the additional eects from the temperature and magnetic eld strength in more detail, we calculated the MR for all the six samples in the three rotation planes. The MR is calculated as the change of resistivity ρ divided by the reference 21

26 4.2 ADMR measurements of YIG/Pt bilayers (longitudinal) resistivity ρ L0 (Fig. 4.2(c-1)): MR = ρ = ρ θ=0 ρ θ=90 ρ L0 ρ θ=0 (4.5) here we used ρ L0 as the longitudinal resistivity at θ = 0 (θ = α, β, γ) and ρ as the dierence between ρ θ=0 and ρ θ=90. To calculate the MR, we extracted the ρ L0 and ρ by tting the following function to the results of the ADMR measurements, ρ long = ρ L0 + ρ sin 2 (θ θ c ) (4.6) where θ and θ c denote the respective angles and a possible phase shift which results from a misalignment of the Hallbars with respect to our measurement geometry. At rst, we will show and discuss the temperature dependence of magnetoresistance for the six YIG/Pt bilayers samples temperature dependence of MR Figure 4.4 shows the MR plotted against the temperature from T = 5 K to 300 K for the three rotation planes (IP, OOPJ,and OOPT) for all six samples. The solid circle, open inverted triangle, and open star symbols in Fig. 4.4 represent the MRs in IP, OOPJ, and OOPT rotations, respectively, and the color dierences show the applied external magnetic eld strengths for 0.5 T µ 0 H 7 T. To begin with, we will discuss the OOPJ signals to investigate the pure SMR phenomena. Focusing on the MR in OOPJ of insitu1 (Fig. 4.4(a)), the MR rapidly decreases with decreasing the temperature for 0.5 T µ 0 H 7 T, and the µ 0 H dependence property of MR is smallest of the other ve samples. On the other hand, the other ve samples show a similar temperature dependence, i.e. the MRs vary drawing a rainbow curve with decreasing the temperature. In addition, worthy of attention here is that the ve samples apparently exhibit a µ 0 H dependence of the MR, although to varying degrees. Though we will discuss the magnetic eld strength dependence of MR later (in Chap. 5) in more detail, in principle in the SMR frame, the SMR amplitude (ρ 1 /ρ 0 ) is independent of the amplitude of the external magnetic eld after the magnetization of the FMI layer is saturated by the external magnetic eld. Therefore, in order to exclude the eect of the dierence of µ 0 H in the following, we focus on the results at µ 0 H = 1 T. In this case, the MR in OOPJ ( MR OOPJ ) is regarded as the SMR amplitude, i.e. MR OOPJ = ρ ρ L0 = ρ 1 ρ 0 = SMR. 22

27 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures (a) insitu1 (PLD, EVAP) (b) insitu2 (PLD, Sputter) MR (x10-4 ) 8 4 IP OOPJ OOPT 7 T 5 T 3 T 1 T 0.5 T 8 4 MR (x10-4 ) 0 0 (c) T (K) exsitu1 (LPE, EVAP) T (K) (d) exsitu2 (LPE, Sputter) MR (x10-4 ) MR (x10-4 ) (e) T (K) exsitu3 (PLD, EVAP) T (K) (f) 16 exsitu4 (PLD, Sputter) 12 MR (x10-4 ) MR (x10-4 ) T (K) T (K) 0 Figure 4.4. Temperature dependence of MR ( ρ/ρ 0 ) in YIG/Pt measured in three rotations (IP, OOPJ, and OOPT) between 5 K to 300 K with the external magnetic eld strength for 0.5 T µ 0 H 7 T. The solid circle, open inverted triangle, and open star symbols represent the MRs in IP, OOPJ, and OOPT rotations, respectively. In-situ samples; (a) insitu1, (b) insitu2. Ex-situ samples; (c) exsitu1, (d) exsitu2, (e) exsitu3, (f) exsitu4. 23

28 4.2 ADMR measurements of YIG/Pt bilayers (a) 500 ρ L0 (nωm) µ 0 H = 1 T (b) 16 MR OOPJ (x10-4 ) insitu1 insitu2 exsitu1 exsitu2 exsitu3 exsitu4 µ 0 H = 1 T T (K) T (K) Figure 4.5. Temperature dependence of (a) the intrinsic electrical resistivity ρ L0 of Pt and (b) the magnetoresistance in OOPJ rotation (MR OOPJ ) in YIG/Pt at the external magnetic eld µ 0 H = 1 T for the six samples. The color code represents the respective samples. The lines are guides to the eye. Figure 4.5 shows (a) the resistivity ρ L0 of Pt and (b) the MR OOPJ at µ 0 H = 1 T for the six samples for 5 K T 300 K, respectively. The color codes represent the respective samples. In Fig. 4.5(a) we observe the dierence of ρ L0 among the six samples, which is attributed to the nite roughness of the YIG/Pt interfaces due to the dierent process of the sample preparations. Upon decreasing the temperature from T = 300 K to 5 K, ρ L0 decreases by 20%. The MR OOPJ of insitu1 in Fig. 4.5(b) corresponds reasonably well with the results published in Ref. [39] by Meyer et al.. This similarity seems to be because insitu1 was basically fabricated in the same process performed in Ref. [39]; the Pt layer was deposited in-situ on a PLD-YIG layer by EVAP with the same machine. In Ref. [39] the authors attributed the temperature dependence of MR to a decrease of the spin Hall angle θ SH with decreasing temperature. Thus, we attempt to evaluate the temperature dependence of MR OOPJ from the view point of the temperature dependence of θ SH by calculating θ SH with the same parameters used in Ref. [39], since the sample used in Ref. [39] is nearly identical with insitu1. As we mentioned in the SMR theory section (see Sec ) the 24

29 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures (a) θ SH insitu1 µ 0 H = 1 T G r = 4.0 x Ω -1 m -2 λ = 1.5 nm d n = d Pt = 3.5 nm T (K) (b) G r (x10 14 Ω -1 m -2 ) insitu1 insitu2 exsitu1 exsitu2 exsitu3 exsitu4 10 K T (K) Figure 4.6. (a) Temperature dependence of the spin Hall angle θ SH of insitu1 at µ 0 H = 1 T, which was calculated by Eq. (4.7) with G r = Ω 1 m 2, λ = 1.5 nm, and d N = d Pt = 3.5 nm. ρ 1 /ρ 0 and σ ρ 1 L0 were taken from the experimental values shown in Fig. 4.5(a) and Fig. 4.5(b). (b) Simulations of the temperature dependence of the spin mixing conductance G r for Pt with respect to the six samples. The values for G r were estimated as the relative change to that of insitu1 by Eq. (4.7) as θsh Pt is assumed to be identical for all the six samples used in this study. SMR amplitude is given as ρ 1 ρ 0 = θ 2 SH λ d N ( ) 2λG r tanh 2 dn 2λ ( ) (4.7) dn σ + 2λG r coth λ where σ is the electrical conductivity of Pt and is taken as σ ρ 1 L0. Since σ is dened from experimental values, Eq. (4.7) has three tting parameters, θ SH (T ), λ(t ), and G r (T ). The θ SH as a function of temperature is shown in Fig. 4.6(a) calculated by Eq. (4.7) with the same parameters in Ref. [39]; G r = Ω 1 m 2 and λ = 1.5 nm. The thickness of NM (Pt) layer is d N = d Pt = 3.5 nm. The estimated θ SH is comparable to the result in Ref. [39] in size. This result leads to the expectation that the temperature dependence of MR OOPJ of insitu1 is caused by the temperature dependence of θ SH. Moving on to the other ve samples in Fig. 4.5(b), the MR OOPJ of the four samples (i.e. insitu2, exsitu1, exsitu2, and exsitu3 ) have peak positions for 5 K T 300 K as reported in earlier SMR experiments [40], though the exsitu4 sample shows a relatively similar trend as the insitu1 sample. On the assumption that MR OOPJ shown in Fig. 4.5(b) remains within the SMR frame, they should be reproduced by Eq. (4.7) on an equality with 25

30 4.2 ADMR measurements of YIG/Pt bilayers insitu1, thus, we attempt to explain the results by Eq. (4.7). In the previous evaluation, we count G r and λ as independent of the temperature, namely, G r and λ are constant 5 K T 300 K. However we can no longer explain the temperature dependence of MR for all ve samples (except for the insitu1 sample) with a constant G r and λ as studied in Ref [39]. Thus we choose G r and λ as free parameters. Due to Eq. (4.7), it is not possible to determine G r and λ independently as both inuence the MR for a xed d Pt. Accordingly, we assume two cases; in one scenario G r varies with temperature while λ is constant, and the other is λ changes for T with constant G r. Here, we assumed that θ SH is identical for all samples due to the following reasons; θ SH is an intrinsic parameter depend on the material. Since the NM layers of all the samples in this study were fabricated by the same Pt-target material, they should have the identical Pt characteristics. Therefore, Pt layers fabricated in this study should have the same physical properties and this leads to the identical θ SH for all six samples. However, due to the dierent resistivityies of the sample θ SH may also be sample dependent to a certain extent, which we will neglect in the following discussion. Simulation of G r as a function of temperature At rst, we investigate the case that G r varies as a function of temperature. The simulation of G r from Eq. (4.7) with ρ(t ) from Fig. 4.5(a), θ SH (T ) from Fig. 4.6(a), and λ = 1.5 nm is shown in Fig. 4.6(b). Obviously G r of the samples decrease with increasing temperature for all samples except for insitu1, and in particular, G r of the four samples (insitu2, exsitu1, exsitu2, and exsitu3 ) show similar behavior. They decrease rapidly after 50 K, and then they seemingly saturate at a certain value below 200 K. On the other hand, G r of exsitu4 shows a dierent behavior from the other samples. The change of G r is modest and, if anything, the behavior is close to that of insitu1. Considering this simulation of G r, the absolute values of G r calculated in Fig. 4.6 are unreliable because they were performed on the assumption that λ = 1.5 nm is constant as a function of temperature. However, a relative comparison between the samples is valid. From this, one can conclude that sample insitu1 has the largest G r for all temperatures investigated. Samples exsitu2 and exsitu4 have values which are lower than insitu1, but are larger thant the rest of the samples. For the samples insitu2, exsitu1 and exsitu3 we nd the lowest calues from all samples. This nding suggests that for in situ sample preparation EVAP processes should be preferred, while for ex situ processes deposition via sputtering in desirable, if large calues of G r, and thus a large interface transparency for pure spin currents [23] are the goal. The observed temperature dependence may originate from the interface of thermal uctuations of the magnetic order parameter [41]. One should keep in mind that our 26

31 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures (a) λ (nm) insitu1 insitu2 exsitu1 exsitu2 exsitu3 exsitu4 (b) λ (nm) 0.5 G r = G r (300 K) fitting by 1/T G r = G r (10 K) T (K) T (K) Figure 4.7. Simulations of the temperature dependence of λ for Pt given by solving Eq. 4.7 with G r at (a) T = 300 K and (b) T = 10 K in Fig. 4.6(b). Other parameters are ρ(t ) in Fig. 4.5(a), θ SH (T ) in Fig. 4.6(a). There are some empty spaces in the plots since the results show only real solutions. The solid lines in (b) represent ts to the data below 50 K using the function of 1/T. data analysis started by using the same θ SH temperature dependence, such that a real quantication of this eect is very problematic. If thermal uctuations are the main cause for the temperature dependence of G r, one would expect to also observe a temperature dependence for insitu1, which we have excluded by taking G r as a constant value for extracting θ SH fromour data. In summary a more quantitative analysis of the temperature dependence of G r for our samples is currently not possible and would require further experiments. Simulation of λ as a function of temperature Next, we look into the scenario that λ varies for 5 K T 300 K. In Ref [40] the temperature dependence of MR was attributed to the increase of λ with decreasing temperature due to the Elliot-Yafet spin dephasing mechanism [42] which should exhibit a 1/T temperature dependence. Following this case we calculated λ from Eq. (4.7) with ρ(t ) from Fig. 4.5(a), θ SH (T ) from Fig. 4.6(a), and a constant G r, and show the obtained results in Fig Since in this case it is impossible to set a constant G r for all samples, we use G r at T = 300 K (Fig. 4.7(a)) and T = 10 K (Fig. 4.7(b)) gained from the simulation in Fig. 4.6(b). While solving Eq. (4.7) with G r at T = 300 K leads to no real solution of λ at some temperatures for four samples except for insitu1 and exsitu4 as shown in Fig. 4.7(a), for G r at T = 10 K we can calculate solutions for all samples and temperatures except for 27

32 4.2 ADMR measurements of YIG/Pt bilayers exsitu4 between 75 K and 175 K as shown in Fig. 4.7(b). For four samples except for the insitu1 and the exsitu4, λ above 50 K behave along the function of 1/T which tting results are represented with solid lines in Fig. 4.7(b), and this result corresponds to the analysis in Ref [40]. At low temperatures (T 50 K) the extracted λ seems to saturate at values close to 1.5 nm, which shows that a temperature independent spin-dephasing mechanism dominates the spin diusion length. This could originate from some anisotropic exchange mechanism like Dzyaloshinsky-Moriya interactions [43, 44] mediated by spin-orbit coupling. At higher temperatures scattering of charge carriers is increased and the Elliot-Yafet mechanism starts to dominate the spin diusion length λ. In this section we investigated the temperature dependence of MR of the six samples. In the SMR frame, MR can be described by Eq. (4.7), thus the temperature dependence of MR should result from the parameters θ SH (T ), λ(t ), ρ(t ), and G r (T ). In this study θ SH and ρ as a function of temperature could be reasonably estimated from our experiments. It is again important to emphasize that our analysis only allows a qualitative extraction of the parameters. Due to the inter linking of λ and G r for a single NM thickness it is impossible to really quantify the values of λ and G r separately. Clearly, further experiments are required to fully address this issue, but also would require a lot of time as for each thickness d Pt all temperature and elds have to be measured, which is beyond the scope of this thesis MR in OOPT rotation Next, we discuss the signals observed in OOPT rotation in Fig In principle, as we mentioned in the theory part of SMR, no angular dependence is expected and thus no MR in OOPT rotation. Thus, we always assume σ M in OOPT rotation. However, with decreasing the temperature down to 5 K, a nite MR signal arises in OOPT rotations like shown in Fig Moreover, it it interesting to note that the sign of the MR in OOPT (MR OOPT ) can change among the six samples in Fig. 4.4, namely, MR OOPT except for insitu1 shows a negative sign, while MR OOPT of insitu1 shows a positive sign. In addition, the eld dependence is also dierent among the samples investigated. To illustrate the temperature dependent changes in the OOPT conguration, we show in Fig. 4.8 the ADMR results at T = 5 K r the samples insitu1 and exsitu1 as well as the temperature dependence of the MR OOPT extracted from ADMR experiments. For additional comparison we also included results obtained from a bare Pt layer, which was deposited onto a SiO 2 substrate by EVAP without any surface treatment (SiO 2 /Pt wo ). The comparison of the ADMR results for the three samples yields the following interesting results. At rst sight, the position of maxima and minima for the exsitu1 sample is shifted by 90 with respect to the insitu1 and SiO 2 /Pt wo samples. From this we can 28

33 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures (a-1) (a-2) h -j h n exsitu1 0 ρ long (nωm) MR oopt (x10-4 ) -2 OOPT γ h (b-1) ρ long (nωm) insitu1 h -j h n 7 T 5 T 3 T 1 T 0.5 T γ γ T = 5 K (b-2) MR oopt (x10-4 ) T (K) OOPT 7 T 5 T 3 T 1 T 0.5 T T (K) (c-1) h -j h n (c-2) ρ long (nωm) MR oopt (x10-4 ) 8 4 MR oopt (x10-4 ) T (K) 50 SiO2/Ptwo γ T (K) Figure 4.8. Comparison of the ADMR measurements at T = 5 K (left panels) and the temperature dependence of MR OOPT in (a) insitu1, (b) exsitu1, and (c) SiO 2 /Pt wo. The inset in (c-2) shows the low temperature range 5 K T 50 K. 29

34 4.2 ADMR measurements of YIG/Pt bilayers conclude that the MR OOPT has the same (positive) sign for insitu1 and SiO 2 /Pt wo and a inverted (negative) sign for exsitu1 (and all other YIG/Pt samples investigated). The eld dependence for the three samples on also very dierent, while for the exsitu1 and SiO 2 /Pt wo the amplitude of the angle dependent oscillation increases with larger external magnetic eld, for the insitu1 ample we only observe a very weak eld dependence. From there ndings we conclude that even this Pt layers itself exhibits a MR in the OOPT direction, which has already been observed by Ref. [45]. However, for Pt on YIG the MR in the OOPT direction can not be fully accounted for by only the standard MR of a bare Pt layer. At least one more additional eect needs to contribute to the MR OOPT, which should have a negative sign. This additional eect would bellow to explain the sign inversion of MR OOPT for the exsitu1 sample and the low eld dependence for insitu1. This statement is further conrmed by the temperature dependence of MR OOPT for the three samples. While the bare Pt layer shows only a sizable MR OOPT at T 25 K with a strong increase for lower T, the YIG/Pt samples all show a nite MR OOPT even for T 300 K. In addition, the insitu1 sample exhibits a MR OOPT = for T = 5 K and µ 0 H = 7 T, which is in absolute values smaller than the MR OOPT = obtained for the exsitu1 sample. Moreover, the MR OOPT temperature dependence in Fig. 4.8(a-2) of the exsitu1 sample has a stronger magnetic eld dependence than the insitu1 sample in Fig. 4.8(b-2). From this investigation we can conclude that additional eects need to be considered that can lead to a MR in the OOPT conguration. We classied them into experimental eects (errors) due to the YIG/Pt interface. We will discuss these dierent contributions in more detail in the following. Tilt in rotation plane We rst consider the case that the mounting of the samples on the chip carrier can lead to a misalignment and tilting of the sample with respect to our j, t, n coordinate system. For the OOPT conguration this will lead to t-component m t of the magnetization in YIG is no longer zero but nite. This will cause a nite MR in the ADMR measurement in OOPT rotation because a nite m t leads to a nite SMR according to Eq. (4.3). We show the possible misalignments of the Hallbar occurring for m t 0 in Fig While the situations in Fig. 4.9(a)-(c) illustrate the ideal cases with m t = 0 for the OOPT conguration, in the situation of Fig. 4.9(d) and Fig. 4.9(e) a rotation in the jt-plane around the z-axis causes a nite m t as shown in Fig. 4.9(g). In addition, in the case of Fig. 4.9(f), the jt-plane of the sample tilts towards the y-axis because of the glue used to mount the samples on the chip carriers. This also leads m t 0 as shown in Fig. 4.9(h). Although we assume the 30

35 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures Ideal cases (a) t-axis (b) µ 0 H ext µ 0 H ext t-axis (c) y -x z γ h y Error cases z (d) t-axis θ OOPT µ 0 H ext x µ H (e) µ 0 H Glue 0 ext ext (f) θ t-axis or Chip carrier φ µ 0 H ext (g) (h) γ h γ h Figure 4.9. Schematics illustrating possible misalignments of Hallbar mesa-structures for a OOPT rotation. (a)-(c) show the ideal cases of a sample alignment with m t = 0. (d) and (e) show the error cases that jt-plane tilts at θ to t-axis by a sample misalignment. (d) and (e) result in the nite m t when the external magnetic eld µ 0 H ext rotates around y-axis as shown in (g). (f) shows the error that jt-plane tilts at φ to n-axis, and this also leads to the nite m t when the external magnetic eld µ 0 H ext rotates around y-axis as shown in (h). Red semicircles in (g) and (h) illustrate the trajectory of µ 0 H ext in the error cases. 31

36 4.2 ADMR measurements of YIG/Pt bilayers (a) (b) insitu1 T = 5 K µ 0 H = 1 T 1.0 Calculation 0.8 insitu1 ρ long (nωm) MR oopt (x10-4 ) exsitu γ T (K) Figure (a) ADMR measurements of insitu1 simulated by Eq. (4.10). The blue-full and red-broken cos-curves represent the cases that jt-plane tilts at φ = +10 and 10 to y-axis, respectively. t-axis tilts at θ = 10 from y-axis. (b) Temperature dependence of MR OOPT of insitu1 (black) and exsitu1 (blue) simulated by Eq. (4.10) with θ = 10 and φ = 10 at µ 0 H = 1 T. The parameters ρ 0 (T ) and ρ 1 (T ) are used shown in Fig. 4.5(a) and (b). magnetization vector m in YIG in OOPT rotation as m(γ) = sin γ 0 cos γ the m in a tilted YIG layer as shown in Fig. 4.9(g) and (h) can be rewritten using the rotation matrices R x and R z referred in Ref. [46], R x = cos φ sin φ 0 sin φ cos φ, R z =, cos θ sin θ 0 sin θ cos θ (4.8) 32

37 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures Therefore, the m modulated by the tilt in both nj-plane and jt-plane due to misalignments is described as 1 m tilt (φ, θ, γ) = R z (θ)r x (φ)m(γ) cos θ sin γ = cos φ sin γ sin θ + cos γ sin φ cos γ cos φ sin γ sin θ sin φ = m j m t m n, (4.9) and then, the resistivity in OOPT rotation taking into account the change due to SMR can be given as: ρ long = ρ 0 + ρ 1 ( 1 m 2 t ) = ρ 0 + ρ 1 (1 ( cos φ sin γ sin θ + cos γ sin φ) 2). (4.10) The simulation results of the MR OOPT in insitu1 including the tilt errors are shown in Fig. 4.10(a) and (b). A blue-full line and a red-broken line in Fig. 4.10(a) represent the simulation results obtained for φ = 10 and 10, respectively. The simulation in Fig. 4.10(a) indicates that the sign change of MR OOPT can be reproduced by changing the tilt angle φ. The change of θ also provides a means to change the sign of MR OOPT, although the simulation is not shown here. However, the amplitude of MR OOPT in insitu1 (Fig. 4.10(b)) is not at all comparable with the values obtained in the experiment (see in Fig. 4.8(b-1)) and is by a factor of 10 lower, even if the worst case scenario of a tilt angle φ = 10 and θ = 10 is assumed. Furthermore, this simulation is not in agreement with the experimental MR in terms of the temperature behavior; while the experimental MR OOPT monotonically decreases with increasing T, MR OOPT in the simulation increases with increasing T and follows the behavior of MR OOPJ as a function of temperature (see in Fig. 4.5(b)) as both share the same origin. The temperature dependence of m t induced by a tilt must be identical with the temperature dependence of the SMR. Therefore, one can conclude that tilt errors are not dominant in our measurements because of two reasons: the amplitude of the simulated MR OOPT with tilt errors can not be made comparable with the experimental MR OOPT using reasonable tilting angles, and the temperature dependence of the simulated MR OOPT is quite dierent to the observed experimental MR OOPT. 33

38 4.2 ADMR measurements of YIG/Pt bilayers (a) ρ L0 (nωm) insitu1 µ 0 H = 1 T T ρ lowt ρ hight T ρ lowt < ρ hight T (K) (b) Lakeshore Temperature (K) 5.05 insitu1 T = 5 K exsitu mk insitu1 T = 300 K exsitu γ γ Figure (a) Comparison of the change of the basic resistivity ρ L0 in Pt ( ρ) induced by a temperature uctuation T. (b) Recorded temperatures in the proximity of samples of insitu1 (left panels) and exsitu1 (right panels) with µ 0 H = 1 T at 5 K (blue symbol) and 300 K (red symbol), respectively. Temperature uctuation during measurements The second experimental error thought as the cause of MR OOPT are temperature uctuations during measurements, since the resistivity in Pt is temperature-dependent [47]. As shown in Fig. 4.11(a), the temperature dependence is stronger at a higher temperature, and the same temperature uctuations will cause a smaller resistivity uctuation at lower T than at higher T ( ρ low T < ρ high T ). This leads to the expectation that the MR induced by the equivalent temperature uctuation ( T ) is larger at room temperature than at T = 5 K and the MR induced by a temperature uctuation should decrease with decreasing T. In fact, the uctuation width of T is larger at T = 300 K than at T = 5 K as shown in Fig. 4.11(b), which shows the recorded temperatures in the proximity of samples, while the ADMR measurements were performed, for the insitu1 and the exsitu1 sample at 5 K (blue symbols) and 300 K (red symbols). Thus, the MR induced by the temperature uctuation during ADMR measurements should be larger at T = 300 K than at T = 5 K. However, contrary to expectation, the measured MR at T = 300 K is smaller than the MR at T = 5 K for both samples, and the amplitude of MR increases with decreasing T as one can see in Fig. 4.8(a-2)-(c-2). From the above, a temperature uctuation can also not be the cause of MR OOPT. In addition to the measurements performed in the Moria cryostat, we conducted the same 1 Rotation matrices do not commute, namely R z(θ)r x(φ) R x(φ)r z(θ). Here R z(θ)r x(φ) is applied but the same procedure is also conducted for the order of R x(φ)r z(θ). However, for small values of θ and φ the dierence of a resultant value between R z(θ)r x(φ) and R x(φ)r z(θ) is negligibly small. 34

39 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures (a) IP OOPJ OOPT h γ h β α h (b) insitu1 µ 0 H = 2 T T = 300 K 0.8 nωm T = 5 K ρ long (nωm) OOPJ OOPT α, β, γ α, β, γ IP ρ long (nωm) (c) exsitu ρ long (nωm) ρ long (nωm) T = 300 K T = 5 K α, β, γ α, β, γ Figure (a) Schematics of the three rotation conguration of ADMR measurements in Chaos (see also Fig. 4.2). ADMR measurements of (b) insitu1 and (c) exsitu1 in Chaos at T = 300 K (left panels with solid symbols) and T = 5 K (right panels with open symbols). The measured longitudinal resistivity ρ long in IP, OOPJ, and OOPT are represented by black, red, and blue color symbols, respectively. 35

40 4.2 ADMR measurements of YIG/Pt bilayers Sample ID Device MR IP (x10 4 ) MR OOPJ (x10 4 ) MR OOPT (x10 4 ) insitu1 Moria Chaos exsitu1 Moria Chaos Table 4.1. Comparison of the MR IP, MR OOPJ, and MR OOPT in the insitu1 and exsitu1 sample measured bu Moria and Chaos, respectively. The external magnetic eld strength µ 0 H is 1 T in Moria and 2 T in Chaos. experiments with the dierent measurement setup (called Chaos in our group) in order to distinguish experimental errors. We observed similar results in both samples and show the ADMR measurements for the insitu1 sample in Fig. 4.12(b) and the exsitu1 in Fig. 4.12(c) at T = 300 K (solid symbols) and 5 K (open symbols) with µ 0 H = 2 T measured in the Chaos setup. The results mostly correspond to Fig. 4.3; ρ long in IP and OOPJ rotations have a cos 2 -dependence while ρ long in OOPT rotation is constant at T = 300 K in both insitu1 and exsitu1. However at T = 5 K, ρ long in OOPT in both insitu1 and exsitu1 have a cos 2 -dependence and the sign is inverted between insitu1 and exsitu1. Compared with the MR in the respective rotations in insitu1 and exsitu1 in Table 4.1, one can see that the amplitude of the MR are comparable between both setups and the MR OOPT is nite in both setups. Therefore, this result leads to the exclusion of experimental errors as the origin if the MR OOPT samples. Magnetic proximity magnetoresistance Since in the previous two sections we concluded that the experimental errors such as sample misalignments and temperature uctuations are not the dominant cause for the observed MR OOPT, in this section we will discuss intrinsic eects which occur in the materials themselves. Magnetic proximity eects [48] can be a candidate as the cause of MR OOPT. We will give a brief overview of the MPE below. For our Pt used as a non-magnetic (normal) metal layer, it is assumed that the number of up-spins and down-spins in Pt are identical, because the denition of non-magnetic is equivalent to a material without a magnetic ordering. However, it has been proven that in non-magnetic metals adjacent to ferromagnetic metals a ferromagnetic part at the interface between non-magnet metals and magnetic metals can be induced as shown in Fig. 4.13(a) [49]. This phenomena is referred to as magnetic proximity eect (MPE). For instance, since Pt and Pd have a similar electronic structure as the 3d transition ferromagnets, they can become ferromagnetic on magnetic metals by MPE [48]. Although X-ray magnetic circular dichroism (XMCD) [50] actually detected a large polarization 36

41 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures (a) (b) M non-magnetic metal feromagneticmetallic interlayer ferromagnet Lorentz force µ 0 H charge current Figure (a) Schematic of a ferromagnetic-metallic interlayer induced at the interface between a non-magnetic metal and ferromagnet layers by a magnetic proximity eect (MPE). (b) Schematic of an ordinary magnetoresistance (OMR). The longitudinal resistivity ρ long with a nite external magnetic eld µ 0 H 0 becomes lager than ρ long with µ 0 H = 0 due to a cyclotron motion of conduction electrons induced by Lorentz force. at the interface of Pt on magnetic metals [5153], studies of MPE at the interface of Pt adjacent to non-metallic magnet have been still not conclusive, for instance, XMCD studies on Pt/YIG led to conicting results [54, 55]. A ferromagnetic-metallic layer induced by MPE in a non-magnetic metal adjacent to a ferromagnet is expected to be the source of anisotropic magnetoresistance (AMR) (see in Sec ). Experimentally, some groups have reported an increasingly signicant AMR contribution in Pd/YIG [56], Ta/YIG [57], IrMn/YIG [58], Pt/YIG [58], Pt/Co 2 FeAl [59], and Pt/LaCoO 3 [60] at low temperatures and the reports indicated being due to a low temperature MPE. Here we focus on the measurement results shown in Fig. 4.4(b)-(f) of ves samples except for the insitu1, which should show no MPE at the interface of YIG/Pt as conrmed by XMCD 2. The negative MR OOPT in those ve samples was observed and they have sin 2 γ-dependence like in Fig. 4.8(a-1); a low ρ long at γ = 0 (m n) and a high ρ long at γ = 90 (m j). Thus, our results also indicate the AMR-like contribution because the AMR eect for ρ long is given as ρ long = ρ 0 + ρ AMR m 2 j and now sin γ = m j. In addition, this AMR-like contribution increases at low temperatures in agreement with previous reports [5660]. Therefore MPE could be a good candidate explaining MR OOPT. In contrast, the insitu1 sample shows a positive MR OOPT (Fig. 4.8(b)); it shows a high ρ long at γ = 0 (m n) and a low ρ long at γ = 90 (m j). Moreover, this corresponds to the MR OOPT in a SiO 2 /Pt bilayers sample (Fig. 4.8(c)), where a 3.5 nm thick Pt layer was deposited 3.5 nm by EVAP on a SiO 2 substrate without any surface treatments. In 2 As mentioned in Sec , insitu1 is assumed to be identical with the sample used in Ref. [39, 61] which were ensured no MPE by XMCD detection. 37

42 4.2 ADMR measurements of YIG/Pt bilayers SiO 2 /Pt wo we can rule out any magnetic eect arising from the substrate because a SiO 2 substrate is just an insulator. Therefore, it is assumed that the MR in SiO 2 /Pt wo arises in Pt itself and this seems to be an ordinary magnetoresistance (OMR) in Pt. The OMR appears in metals and semiconductors, and causes a change in resistivity arises an external magnetic eld is applied perpendicular to non-magnetic metal because conduction electrons are moving along curved trajectories by the Lorentz force induced by the external magnetic eld as shown in Fig. 4.13(b). Theoretically, the OMR is proportional to the square of the external magnetic eld strengths. According to Ref. [45], the OMR is always positive in Pt for thickness as d Pt above 3 nm and temperature above 5 K. This report leads to the conclusion that the sign of OMR which should be observed in our YIG/Pt bilayers samples must be identical with the sign of OMR in SiO 2 /Pt wo taking into account the conditions of our ADMR measurements (5 K T 300 K, d Pt = 3.5 nm). Therefore, we can expect that the MR OOPT observed in the ve other samples excluding the insitu1 sample are not due to the OMR, or at least the OMR is not a dominant cause. Moreover MR OOPT in the insitu1 sample is mainly caused by the OMR of Pt. In Ref. [62] the OMR in Pt grown in situ on CoFe 2 O 4 which is a room-temperature ferrimagnetic insulating oxide was rstly reported for studies on Pt/FMI, and the authors indicated that the lower resistivity ( nωm) in their in situ Pt thin lm than usual ( nωm) led to a nite OMR contribution. Since the resistivity in our Pt of the insitu1 sample is comparable to the Pt in Ref. [62], this report leads to a supporting evidence of our expectation that the MR OOPT in insitu1 is due to the OMR contribution. In conclusion, we discussed the causes of MR OOPT and suggested that MR OOPT in ve samples except for insitu1 are contributed from AMR induced by MPE enhanced at low temperatures, while MR OOPT in insitu1 is mainly related to OMR in Pt. Finally we note that there still remains open questions in the conclusions. Though the amplitude of OMR is proportional to the square of the external magnetic eld strength (µ 0 H) 2, the magnetic eld dependence of MR OOPT in the insitu1 is very low and does not scale with (µ 0 H) 2. As potential events several eects including OMR arise at in insitu1 and they compete each other. In addition to the above, since it is not possible to directly determine the existence of MPE at the interface of YIG/Pt bilayers in this thesis, other possible experiments can not be ruled out completely MR in IP rotation In the last two sections, we discussed the MR OOPJ and MR OOPT, in this section, we nally discuss the MR in the IP (MR IP ) conguration. From Fig. 4.4, we can nd that MR IP is always lager than MR OOPJ in the range of negative MR OOPT, e.g. in exsitu1 and exsitu2, while in the range of the positive MR OOPT, 38

43 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures (a) 16 insitu1 (b) 16 exsitu MR (x10-4 ) 8 IP OOPJ-OOPT MR (x10-4 ) 4 7 T 4 5 T 3 T 1 T T (K) T (K) 8 (c) m n = cosβ, cosγ β α γ ρ long ρ 1 +Ρ 2 ρ 1 +Ρ 3 -Ρ 2 +Ρ 3 ρ 1 MR OOPT MR IP MR OOPJ ρ 1, Ρ 2, Ρ 3 > 0 ρ 0 Ρ 2 > Ρ m j = cosα, sinγ Figure Comparison of temperature dependence of MR between MR IP (solid symbols) and MR OOPJ MR OOPT (open symbols) from Fig. 4.4 in (a) the insitu1 and (b) the exsitu4 samples. (c) The simulation of ADMR measurements using Eq. (4.11). ADMR measurements in the IP, OOPJ, and OOPT congurations are represented as black, red, and blue lines. Here, we assumed that the coecients of ρ 1, P 2, and P 3 are positive and P 2 > P 3. The left picture illustrates the denition of the rotation angles, α, β, and γ. 39

44 4.2 ADMR measurements of YIG/Pt bilayers MR OOPJ is bigger than MR IP like in insitu1 or around 50 K in insitu2. Moreover, with the increase in amplitude of MR OOPT, the dierence between MR IP and MR OOPJ increases below 50 K in all the six samples (except for exsitu3 ). These ndings suggest that the signal in the OOPT rotation plane has something to do with the dierence between MR IP and MR OOPJ. Thus we calculate MR OOPJ MR OOPT as a function of temperature and Fig. 4.14(a) and (b) show the comparison between MR IP with solid symbols and MR OOPJ MR OOPT with open symbols in the insitu1 and the exsitu4 samples, respectively. The MR IP and MR OOPJ MR OOPT are in very good agreement with each other. In the last section we concluded that the MR OOPJ consists of the SMR contribution, which resistivity change is given as ρ SMR = ρ 1 (1 m 2 t ), and the MR OOPT consists of the AMR-like contribution or the bare Pt-MR contribution, i.e. terms which are proportional to m 2 j (AMR) or m 2 n (Pt-MR). Now we assume that all the six samples have these three terms, namely ρ long is described as: ρ long = ρ 0 + ρ 1 (1 m t 2 ) + P 2 m j 2 + P 3 m n 2 (4.11) where P 2 and P 3 are the factor of the proportionality of the AMR-like contribution the MR-Pt like contribution, respectively. In this case, we can rewrite the resistivity dependence for each rotation plane as: ρ IP long =ρ 0 + ρ 1 (1 m t 2 ) + P 2 m j 2 =ρ 0 + (ρ 1 + P 2 )m j 2 ρ OOPJ long =ρ 0 + ρ 1 (1 m t 2 ) + P 3 m n 2 =ρ 0 + (ρ 1 + P 3 )m n 2 ρ OOPT long =ρ 0 + P 2 m j 2 + P 3 m n 2 =ρ 0 + P 2 (1 m n 2 ) + P 3 m n 2 (4.12) (4.13) =ρ 0 + P 2 + ( P 2 + P 3 )m n 2. (4.14) Therefore, the respective MR are give as (under the assumption that ρ 0 ρ 1, P 2, P 3 ): MR IP = ρ 1 + P 2 ρ 0 (4.15) MR OOPJ = ρ 1 + P 3 ρ 0 (4.16) MR OOPT = P 2 + P 3 ρ 0. (4.17) 40

45 Chapter 4 Spin Hall magnetoresistance in YIG/Pt heterostructures This leads to MR OOPJ MR OOPT = ρ 1 + P 3 ρ 0 P 2 + P 3 ρ 0 = ρ 1 + P 2 ρ 0 =MR IP. (4.18) Therefore, MR IP can be expressed as MR OOPJ MR OOPT, which is indicating that an innite amount of possible ρ 1, P 2, and P 3 exist for any given MR IP, MR OOPJ, and MR OOPT. From this we conclude that it is not possible to do a quantitative extraction of the parameters, because the equations can be fullled by an innite number of parameter sets, and only if one parameter is chosen to be zero a unique solution is possible. As we discussed in Sec , it is dicult to individually determine the contributions from m j 2 and m n 2, and to extract the coecients P 2 and P 3 in the ADMR measurements, as long as all coecients remain nite. However, the assumption above reproduces well the experimental results of MR IP and conrms the consistency of our measurements. The increase at low temperatures in MR IP is due to the enhance of MR OOPT which can be proportional to m j 2 or m n 2. The corresponding simulations are shown in Fig. 4.14(c). 4.3 Summary of ADMR measurement in YIG/Pt bilayers samples as a function of temperature In this section, we performed the ADMR measurements in the six YIG/Pt bilayers samples (insitu1, insitu2, exsitu1, exsitu2, exsitu3, exsitu4 ) which were fabricated from dierent YIG lms and Pt-deposition processes, as a function of temperature (5 K T 300 K) and with various external magnetic elds (0.5 T, 1 T, 3 T, 5 T, 7 T) in three rotation planes (IP, OOPJ, and OOPT congurations). The main goal was to investigate the temperature dependence of the magnetoresistance observed in IP, OOPJ, and OOPT conguration, respectively. The following results were found: The MR OOPJ in all the six samples have a temperature dependence. The temperature dependence in the insitu1 sample mainly stems from the temperature dependence of the spin Hall angle. The real part of spin-mixing conductance G r in exsitu1 and exsitu3 were relatively smaller than G r in insitu1. This seems to indicate that Ar-ion bombardment induces an ineective YIG/Pt interface for spin transfer torque. Under certain conditions the spin diusion length λ shows a 1/T dependence 41

46 4.3 Summary of ADMR measurement consistent with the expected Elliot Yaet relaxation mechanism for Pt. For all the six samples, the MR OOPT increases with decreasing T. The MR OOPJ in the insitu1 is shows contributions from the ordinary magnetoresistance of Pt, and those in the other ve samples are shown an AMR-like contribution induced by the a temperature MPE or other interface eects. The MR IP is in good agreement with MR OOPJ MR OOPT. Then the increase of MR IP at low temperature is due to the MR OOPT. The following topics are still unclear: Since it is impossible in this thesis to determine G r and λ at the same time, this investigation still remains in the qualitatively discussion. For quantitative understandings we need to investigate the Pt-thickness dependence of MR OOPJ. 42

47 Chapter 5 Longitudinal and transverse magnetotransport experiments as a function of external magnetic elds In the last chapter, we discussed the results of the ADMR measurements in YIG/Pt bilayers samples obtained from several dierent sample preparation processes with the focus on the temperature dependence of the ADMR. In these results (Fig. 4.3 and Fig. 4.4), we conrmed that there also exists a eld dependence of the MR in these samples. Since the SMR, in simple theory framework, is not aected by the external magnetic eld strength, this phenomenon is intriguing. In order to investigate the magnetic eld dependence of MR in more detail, we also measured the MR in all the six samples by sweeping the external magnetic eld. Hereinafter, this measurement is referred to as a magnetic eld dependent MR (FDMR) measurement. In this chapter, rst we will explain the experimental setup for FDMR measurements in Sec After that we will show the results of FDMR measurements and discuss the causes of FDMR in YIG/Pt bilayers samples. In addition to the FDMR results obtained for the longitudinal resistivity, the transverse resistivity in YIG/Pt bilayers samples is investigated with regards to the spin Hall anomalous Hall eect (SH-AHE) in the last section. 5.1 Experimental setup for FDMR measurements In the previous section (Sec. 4.1) we measured the magnetoresistance in YIG/Pt bilayers samples by applying a rotating external magnetic eld with xed magnetic eld strength, i.e. ADMR measurements were performed (Fig. 5.1(a)). For FDMR measurements, longitudinal and transverse voltages were recorded while an external magnetic eld was swept along three xed orientations: the j, t, and n axes as shown in Fig. 5.1(b). Applying a bias charge current of 100 µa along the Hallbars we measured the longitudinal and transverse voltages as a function of the external magnetic eld strength µ 0 H for 7 T µ 0 H 7 T along j, t, and n axes, respectively, at temperatures between 43

48 l l 5.1 Experimental setup for FDMR measurements (a) (b) H n V trans hi lo V trans hi lo H t hi lo V long H α substrate FMI NM hi lo V long substrate FMI NM H j ADMR measurement FDMR measurement (c) H = j H = -t H = -j H = t exsitu4 T = 300 K H j ρ long (nωm) T 5 T T 1 T 0.5 T α µ 0 H (mt) H t µ 0 H (T) Figure 5.1. Measurement geometry for (a) angle-dependent magnetoresistance (ADMR) experiments in IP conguration as dened in Sec , and (b) eld-dependent magnetoresistance (FDMR) experiments performed along a xed orientation of an external magnetic eld, H j (black arrow) H t (red arrow), and H n (blue arrow). (c) Comparison between ADMR measurements in IP conguration and FDMR measurements performed along H j (black line) and H t (red line) in the exsitu4 sample at T = 300 K. For example, the ADMR measurement at α = 0 (180 ) corresponds to the FDMR measurement where a positive (negative) µ 0 H is applied along j. Insert: low eld FDMR data. The hysteresis occurs from the magnetization rotation in YIG. 44

49 Chapter 5 Magnetotransport experiments as a function of external magnetic elds 5 K T 300 K. Figure 5.1(c) shows a comparison between ADMR in IP conguration and FDMR measurements performed along H j (black line) and H t (red line) in the exsitu4 sample at T = 300 K as an example. Since sweeping the positive (negative) external magnetic eld along j-axis is equivalent to ADMR measurements at α = 0 (180 ), the amplitudes of ρ long at α = 0 (180 ) at the respective µ 0 H should correspond to ρ long in FDMR measurements when sweeping positive (negative) µ 0 H along H j. On the other hand, since positively (negatively) sweeping µ 0 H along t-axis is equivalent to ADMR measurements at α = 270 (90 ), ρ long at α = 90 should be equal to ρ long in FDMR measurements sweeping negative µ 0 H along H t. Indeed, these assumptions are conrmed by the experiment, as indicated by the dashed arrows between the two graphs. The dips and hysteresis around zero magnetic eld in the inset in Fig. 5.1(c) stem from the magnetization reversal in the YIG thin lm. In the case of H j, for example, since the angle between a magnetization m in YIG and a spin polarization vector σ in Pt deviates from j-axis due to the magnetization reversal in the YIG, this leads to a decrease of ρ long as we can conrm from the ADMR measurements. The hysteresis is due to the coercivity of the YIG. Evaluation of FDMR measurements Focusing on the FDMR measurement at room temperature shown in Fig. 5.1(c), the resistivity along H j increases with increasing the external magnetic eld strength, i.e. it shows a positive MR, while the resistivity along H t is almost constant. However with decreasing T, the behavior of ρ long as a function of µ 0 H changes signicantly. Figure 5.2 shows the FDMR measurements at 300 K (a) and 5 K (b) in the exsitu4 sample performed for H parallel to j (black line), t (red line), and n (blue line) -axis, respectively. The slight shift in absolute value of ρ long for H t between left and right panels in Fig. 5.2 originates from the necessary remounting of the sample (see also Sec ). At T = 300 K both ρ long for H j and H n exhibit a positive MR with similar eld dependence, as can be seen from Fig. 5.2(a). However at T = 5 K, all ρ long for H j, H t, and H n decrease with increasing µ 0 H, i.e. they show a negative MR. Thus, it is worth investigating this transition in eld dependence for the FDMR measurements as a function of temperature. To summarize the results of the FDMR measurements as a function of temperature, we extracted several parameters from the FDMR measurements by tting a theoretical curve to the data. ρ long as a function of µ 0 H can be reproduced well by using a following 45

50 l 5.1 Experimental setup for FDMR measurements (a) ρ long (nωm) (b) exsitu4 H j H n H t H t T = 300 K µ 0 H (T) µ 0 H (T) H j H n ρ long (nωm) H t H t V trans hi lo H T = 5 K hi lo V long substrate FMI NM µ 0 H (T) µ 0 H (T) Figure 5.2. FDMR measurements performed along H j (black line), H t (red line), and H n (blue line) at (a) T = 300 K and (b) T = 5 K for exsitu4. The insert denes the external magnetic eld orientation along j, t, and n axes. 46

51 Chapter 5 Magnetotransport experiments as a function of external magnetic elds (a) ρ long (nωm) C = 400 nωm lager C smaller C B = 1.0 T -1 A = 2 nωm A = 1 nωm A = 0 nωm A = -1 nωm (b) ρ long (nωm) A = 1 nωm C = 400 nωm B = 1.0 T -1 B = 0.5 T -1 B = 0.3 T -1 B = 0.2 T -1 B = 0.1 T -1 A = -2 nωm µ 0 H (T) µ 0 H (T) Figure 5.3. Simulations of ρ long as a function of the external magnetic eld strength µ 0 H calculated by Eq. (5.1). (a) ρ long calculated with C = 400 nωm, B = 1.0 T 1, and various A displayed by dierent colors. In the case of larger (smaller) C, the position of ρ long (H) curve shifts upward (downward). (b) ρ long calculated with C = 400 nωm, A = 1 nωm, and various B displayed by colors dierent. equation [28, 63] ρ long = A 1 [ x 2 2(1 + x 2 ) ] C, (5.1) where x = B µ 0 H and A, B, and C are free parameters. Figure 5.3 shows the inuence of these free parameters on the functional, (a) A, (b) B, and (a) C by using a simulation based on Eq. (5.1). The parameter C corresponds to the resistivity at µ 0 H = 0 T, or the resistivity in Pt (see in Fig. 4.5(a)). Larger (smaller) C leads to a shift of ρ long (H) carve upward (downward). The sign of A determines whether a positive (A positive) or negative (A negative) MR is obtained. The magnitude of A corresponds to the strength of the MR. The parameter B describes the width of the parabolic shape of the ρ long (H) curve. For small B the width is large, while for large B the width of the parabola is small. Please note that as shown in Fig. 5.3, the eld dependence is interlinked with both parameters A and B. In the following section, we show the results of tting Eq. (5.1) to the FDMR measurements. 47

52 l 5.2 Field dependence of longitudinal MR as a function of temperature (a) A / C (x10-3 ) A / C (x10-3 ) H j H n hi lo V long V trans hi lo H n H t FMI NM H j (b) B (T -1 ) B (T -1 ) H j H n A / C (x10-3 ) 0-4 H t B (T -1 ) insitu1 insitu2 exsitu1 exsitu2 exsitu3 exsitu4 H t T (K) T (K) Figure 5.4. Temperature dependence of the parameters in Eq. (5.1) for all the samples: A/C (left-pointing triangle symbol in left column) and B (square symbol in right column) when the external magnetic eld µ 0 H is applied along H j (solid symbol with solid line in top row), H n (open symbol with dashed line in middle row), and H t (open symbol with solid line in bottom row), respectively. The inset illustrates the dierent orientations used in the experiment. 48

53 Chapter 5 Magnetotransport experiments as a function of external magnetic elds 5.2 Field dependence of longitudinal MR as a function of temperature Since C corresponds to the resistivity of Pt as mentioned above, a normalized A by C are shown in Fig. 5.4(a) to see the degree of changing ρ long toward the intrinsic resistivity, and B shown in (b) as a function of temperature. The data along H j and H n look similar, while the data along H t are quite dierent. In the both cases for H j and H n in Fig. 5.4(a), the sign of A/C in all the six samples changes to negative and decreases with decreasing T, however A/C in the insitu1 sample stays close to zero. This indicates that the eld dependence of MR in the insitu1 sample is weaker compared to the other samples. Since m is perpendicular to σ in the both of H j and H n, the phenomena related to spin current in H j and H n should show the same behavior. Therefore, the results of H j and H t look similar. A/C along H t is almost zero at room temperature in all samples, however with decreasing T it decreases monotonically and never shows a positive value. As the parameters A and B describe the eld dependence of the FDMR measurements, it is very dicult to extract exact values for A and B at T = 300 K, where the magnetic eld dependence in the FDMR data vanishes for all samples. With decreasing T the tting process allows to extract more accurate values for A and B since the eld dependence becomes more dominant. In the following we break down the possible causes of the MR and their expected behavior as a function of the magnetic eld and temperature. Hanle magnetoresistance The eld dependence of MR in YIG/Pt lms has already been investigated [29, 63] and the authors advocated the existence of Hanle magnetoresistance (HMR) in Pt. Thus, HMR could also be a possible source for our observed eld-dependence. As we mentioned in Sec , the increase of Hanle eect-induced resistance is the largest when the external magnetic eld is perpendicular to σ, in our case for H j or n, while no resistance change is expected for the parallel case, i.e. H σ (= H t). This expectation corresponds to the FDMR measurements in our samples at room temperature as shown in Fig. 5.2(a). The authors of Ref. [29] assumed that the longitudinal resistivity ρ long of the NM layer in the presence of µ 0 H is given as: ρ long = ρ L0 + ρ HMR (1 m t 2 ). (5.2) Thus, this equation Eq. (5.2) means that HMR shows the same angle-dependence as the SMR equation in Eq. (2.5). The authors attributed that the dierence of ρ long between H j and H t at small elds (µ 0 H 0), ρ SMR as shown in Fig. 5.5(a), is contributed from 49

54 5.2 Field dependence of longitudinal MR as a function of temperature ρ long (µ 0 H) (nωm) L (a) (b) exsitu4 T = 300 K H along j V trans hi lo hi lo V long ρ HMR H ρ SMR NM FMI H along t µ 0 H (T) ρ L0 8 4 insitu1 insitu2 exsitu1 exsitu2 exsitu3 exsitu T (K) Figure 5.5. (a) FDMR measurement in the exsitu4 sample for H j (black line) and H t (red line) at T = 300 K. In HMR theory [29], the dierence of ρ long along H j and H t at small eld µ 0 H 0 is due to SMR and an following increase is due to HMR. (b) The relative ( ρ/ρ L0 ) in the proximity of H 0, ρ SMR /ρ L0, in all the six samples as a function of temperature. SMR, and any subsequent increase of ρ long, ρ HMR as shown in Fig. 5.5(a), is contributed from HMR in the range of µ 0 H where the magnetization in FMI is already saturated by µ 0 H. Figure 5.5(b) shows a normalized ρ by ρ L0 in the proximity of H 0, namely ρ SMR /ρ L0, in all the six samples as a function of temperature. This graph theoretically says the same thing with MR in IP conguration at µ 0 H 0 T, therefore it looks similar with MR IP in Fig The dierence between Fig. 5.5(b) and Fig. 4.4 is probably due to the smaller µ 0 H < 0.5 T. In addition, the index of increasing ρ HMR /ρ L0 is given as [28]: ρ HMR ρ L0 = ( ρhmr ρ L0 ) H 1 [ x 2 2(1 + x 2 ) ] 1 2, (5.3) where x = Ωτ, Ω = gµ B / µ 0 H is the spin precession frequency (g is the Lande factor and is the reduced Planck constant), and τ is the eective spin life time during which the spin information is lost. This equation corresponds to Eq. (5.1) with ( ρ HMR /ρ L0 ) H = A/C and gµ B τ/ = B. In short, if we follow the HMR theory, A/C yields the degree of the HMR contribution, and from the dierence of C for H j and H t we obtain the eective SMR magnitude (compare Fig. 5.5(b)). In the following we discuss the results shown in Fig. 5.4 and Fig. 5.5(b) in terms of the HMR theory. First, let's focus on the parameter B. We calculated τ for both cases of H j and 50

55 Chapter 5 Magnetotransport experiments as a function of external magnetic elds τ T =300 K insitu1 insitu2 exsitu1 exsitu2 exsitu3 exsitu4 τ H j (ps) τ H n (ps) Table 5.1. Summary of τ for both cases of H j and H n at T = 300 K calculating from τ = B gµ B with g = 2, µ B = J T 1, = J s, and B from Fig. 5.4(b). H t at T = 300 K and the calculations are summarized in Table 5.1. Since the HMR appears in the case of σ H, τ for H t is not shown in the table. At room temperature since the FDMR measurements for H t vanishes, the FDMR measurements along H j and H n should be experimentally identical. Indeed, the τ in all six samples exhibit very identical values for H j and H t except for τ H j in the insitu1 sample. While τ in the insitu1, theexsitu2, and the exsitu4 samples are comparable to the reported value ( 0.61 ps) in Ref. [63], τ in the insitu2, theexsitu1, and the exsitu3 samples exhibit larger by a factor of 2 or more than the reported value. This extraordinary large τ in these three samples indicate that the eld-dependent MR observed in these three samples include other eects beside the HMR eect. From the dominant spin dephasing mechanism, we expect τ 1/T due to the Eliot Yaet spin dephasing mechanism, such that B should show also a 1/T dependence since B gµ B τ. However, this corresponds not to the results that we have obtained for B (see Fig. 5.4) our results are not as expected. In the temperature range where A/C is positive B increases with decreasing T, agreeing with the expected behavior, but in the temperature range of negative A/C, B decreases and shows a small value. From this discussion we can claim that the HMR model might be sucient to explain the observed eld dependence at high temperature (T > 150 K), even though the quite large values of τ might hint to additional eects not considered with HMR model at high temperatures. For low temperatures the HMR model completely fails to explain in any way the observed eld dependence. Clearly, another eect is at these temperatures the dominant contribution to the eld dependence of the MR. At T = 300 K all samples show positive MR in the case of H j and H n since A/C is positive, while A/C in H t is almost zero. This result agrees with the HMR theory. Especially, the MR in insitu1 is mostly contributed from SMR because the ( ρ/ρ L0 ) H 0 shown in Fig. 5.5(b) is very large ( ) while the HMR contribution shown in Fig. 5.4(a) is very small ( ) compared with the other ve samples. In addition, the exsitu2 sample and the exsitu4 sample also show some nite SMR contribution ( ) in Fig. 5.5(b) and a stronger HMR contribution than the insitu1 sample. The insitu2 sample, the exsitu1 sample, and the exsitu3 sample show almost no SMR 51

56 5.2 Field dependence of longitudinal MR as a function of temperature (a) MR OOPJ (x 10-4 ) SiO 2 / Pt wo 7 T 5 T 3 T 1 T 0.5 T (b) ρ long (nωm) SiO 2 / Pt wo T = 10 K H along n T (K) 907 H along t µ 0 H (T) Figure 5.6. (a) Temperature dependence of magnetoresistance in OOPJ conguration (MR OOPJ ) and (b) the FDMR measurement performed along H n with blue line and along H t with red line, respectively, in SiO 2 /Pt wo. The external magnetic eld strengths in (a) are displayed by dierent colors. contribution ( < ) and the strongest HMR contribution ( > ) except for the exsitu1 sample which A/C is almost the same with the exsitu2 sample and the exsitu4 sample. However, the conclusion that the SMR is absent in the insitu2 sample, the exsitu1 sample, and the exsitu3 sample may be to short sighted. As mentioned before, the SMR arises from the dierent orientations of m at the interface in the YIG layer and σ in Pt. Only the magnetic moments at the interface contribute to the SMR, and we use an external magnetic eld µ 0 H to align m. In other words, the SMR can not appear as far as no magnetic moment is perpendicular to σ at the interface, even if m in the bulk of YIG layer aligns already parallel to the external magnetic eld. Therefore, we can imagine the possibility that the orientation of the magnetic moments at the interface in YIG has a eld dependence dierent to the bulk YIG thin lm due to interface eects, e.g. pinning eects caused by surface roughness, which we will discuss later. Such a eld dependence of the interfacial magnetic moments can lead to the suppression of SMR at small elds in the insitu2 sample, the exsitu1 sample, and the exsitu3 sample. Since the exsitu1 sample and the exsitu3 sample were fabricated using Ar-ion bombardment, the interfaces of them are likely to be damaged compared to other samples. Moreover, a problematic point for the application of HMR theory is that A/C changes to negative with decreasing T in all samples. Although the negative A/C means the resistivity decreases with increasing µ 0 H, it is not possible to appear in the HMR frame, because the HMR theory predicts always a positive MR; the larger µ 0 H is applied, the spins start to precess with higher frequency around µ 0 H and thus the resulting larger spin dephasing 52

57 Chapter 5 Magnetotransport experiments as a function of external magnetic elds leads to a reduction of the spin accumulation and leads to an increase of resistivity in Pt. Therefore, the negative A/C indicates that additional eects are mixed with the HMR at low temperature. Another important aspect, which can not be explained by the HMR theory, is the decrease of ρ long for H t at low temperature with increasing eld. In HMR theory, nothing changes when the external magnetic eld µ 0 H is applied parallel to σ, i.e. parallel to t. However, all the six samples surely show the nite decrease of ρ long with increasing µ 0 H at low temperatures. Therefore, we need to investigate the decrease of ρ long in the case of H t. In order to see the HMR eect in pure Pt, we performed the same ADMR and FDMR measurements in SiO 2 /Pt wo and Fig. 5.6 shows (a) MR in OOPJ rotation and (b) FDMR measurements at T = 10 K in SiO 2 /Pt wo. The MR OOPJ disappears for T > 50 K in (a) although the HMR should also be present in bare Pt. Thus we expect to observe a nite MR OOPJ at T = 300 K, if HMR is really playing a role in bare Pt. Moreover from Fig. 5.6(b), the sign of ρ(h) curve remains positive in the cases of both H n and H t. So these results indicate that the HMR theory still remains imperfect and it is dicult to distinguish to what level the HMR aects on Pt. Actually in Ref. [29] which rst reported the HMR eect in YIG/Pt bilayers sample, the authors also did not observe the Hanle MR eect at 300 K in SiO 2 /Pt. In summary, the increase of ρ long with increasing µ 0 H for H j and H n at room temperature can be understood in terms of the HMR theory. However, this model still remains insucient to explain the eld dependence for H t and the eld dependence of the MR at low temperatures. Thus, we next consider the eect of Magnon-mediated magnetoresistance (MMR) onto the MR in our samples. Magnon mediated magnetoresistance The MMR can be thought of as a primal candidate to explain the resistivity change, when the external magnetic eld is applied along the t direction. As we mentioned in Sec , the MMR appears when m σ, and leads to a dissipation of the spin accumulation at the interface of NM/FMI via magnon creation or annihilation into the FMI through inelastic spin-ip scattering. Therefore the MMR can be an idea to qualitatively explain the resistivity change at m σ. The resistivity change for H t starts to appear with decreasing temperature (see the parameter of A/C shown in Fig. 5.4(a)). We try to understand this temperature dependence from the view point of a magnon density of state (DOS). The DOS shown in Fig. 5.7(a) is proportional to E in the scenario of a parabolic 3D magnon dispersion. Due to the thermal energy k B T, where k B is a Boltzmann constant, magnons on the red-broken (cyan-broken) line at T = 300 K (5 K) in Fig. 5.7(a) can be excited as a thermal excitation. 53

58 5.2 Field dependence of longitudinal MR as a function of temperature (a) (b) Energy (at T = 300 K) T = 300 K (at T = 5 K) T = 5 K ρ long µ 0 H 2 µ 0 H 1 H 1 < H 2 Higher µ 0 H DOS Figure 5.7. (a) Simulation of density of states (DOS) of magnon in three dimension with the external magnetic eld µ 0 H 1 (light-green line) and µ 0 H 2 (orange line) where µ 0 H 1 < µ 0 H 2. Due to the increase of the magnon gap by µ 0 H, the DOS can change its energy position. Red (cyan) broken line represents the maximum energy of the excited magnons by the thermal energy of k B T at T = 300 K (5 K). (b) Simulation of the ADMR measurement for the MMR model in the presence of an external magnetic eld µ 0 H. Since applying the external magnetic eld increases the magnon gap and shifts the DOS upward, the positions with µ 0 H 1 (light-green line) and µ 0 H 2 (orange line) where H 1 < H 2 is dierent as shown in Fig. 5.7(a). Therefore, the number of magnons thermally excited by k B T depends on the strength of µ 0 H, and with increasing µ 0 H it becomes tougher to thermally excite magnons. However, the µ 0 H dependence diers by temperature. According to Fig. 5.7(a), the dierence in the number of excited magnons between µ 0 H 1 and µ 0 H 2 at T = 300 K is smaller than the one for 5 K. This also means that the change in the dissipation of spin accumulation with the external magnetic eld at T = 300 K is less pronounced than at T = 5 K, since this change is related to the dierence of magnon excitations. Therefore, it can be expected that the temperature and eld dependence of MR along H t might originate via the MMR. We observed a negative MR in FDMR measurements for H t at low temperatures. As mentioned above, the number of excited magnons decreases with increasing µ 0 H due to the shift of the DOS. This also leads to the eect that the dissipation of spin accumulation with the larger µ 0 H is lower than that with a lower µ 0 H since the probability of spin-ip scattering is reduced. Therefore, one can expect that the resistivity at m σ decreases with increasing µ 0 H as shown in Fig. 5.7(b) due to the MMR. In this section, we explained a possible model for the resistivity change for H t. The magnon density of states and the MMR eect could lead to the temperature dependence 54

59 Chapter 5 Magnetotransport experiments as a function of external magnetic elds of the ρ long change for H t and a negative MR for H t at low temperatures. However, we note that this is the simplest modeling to explain the phenomena. The shape of the DOS can change drastically depending on the temperature and it is dicult to discuss it by just the simple arguments used above. In addition, it is still questionable whether the MMR at low temperature could lead to a signicant change in the MR, as it is a thermally activated process. It has been reported that a nite thermal excitation is needed to arise the MMR in Ref. [31] and the authors did not observe a nite signal due to MMR at low temperatures. Although the way of detecting signals is dierent, it is necessary to take into account these results. In the theoretical framework describing the spin current transport across the NM/FMI interface presented in Ref. [41], the spin mixing conductance G r is inuenced by the magnon population in the FMI. Therefore, applying their model to SMR theory may provide improved understanding of the MR from the perspective of MMR and magnons in the FMI. In this publication the spin mixing conductance depends on the number of magnons present in the system. Pinning centers at interface In the last two sections we discussed two possible mechanisms to explain the origin of the eld-dependent magnetoresistance. For both cases the key ingredient is a dissipation of spin accumulation at the interface between YIG/Pt, while the mechanism of SMR also results from the change of the spin accumulation at the interface of NM/FMI. In the SMR theory, the amount of a dissipation of the spin accumulation can be controlled by the orientation of magnetization in FMI layer. In the HMR scenario, the spin accumulation is dissipated via a spin precession at the interface induced by the external magnetic eld. On the other hand, in the MMR scenario, a spin-ip scattering via magnon creation or annihilation at the interface of YIG/Pt leads to the dissipation of spin accumulation. Another possible way, which causes a eld dependence of the dissipation of spin accumulation is related to interface states in YIG/Pt heterostructures. Figure 5.8 illustrates the interface situations in a YIG/Pt bilayers sample. Since the interface has some surface roughnesses and defects induced by the process for the sample preparation. The magnetic moments at the interface in YIG are exposed to these surface roughnesses and defects. This leads to an additional free energy contribution, which opposes the Zeeman energy from the external magnetic eld and leads to the fact that the magnetic moments at the interface do not align along the external magnetic eld µ 0 H. The magnetic moments are pinned at the interface. Due to the surface pinning eect, when the external magnetic eld µ 0 H low is applied to the YIG/Pt bilayers sample, the magnetic moments at the interface do not always align to H although the magnetization in the bulk part of YIG aligns following µ 0 H low as shown in (a). As a result, if the SMR appears due 55

60 5.2 Field dependence of longitudinal MR as a function of temperature (a) (b) Spin accumulation Pt Pt µ 0 H low m 1 m 3 m 2 m 1 YIG M YIG YIG µ 0 H low µ 0 H high µ 0 H high M YIG ρ long (c) Higher µ 0 H (d) ρ long (nωm) insitu2 T = 5 K H along j Higher µ 0 H µ 0 H (T) Figure 5.8. Illustrations of pinning eects of the magnetic moments in YIG at the interface of YIG/Pt bilayers sample with (a) a small external magnetic eld µ 0 H low and (b) a large µ 0 H high. Due to the surface roughness and defects, magnetic moments in YIG at the interface do not always follow µ 0 H. With the higher µ 0 H the more magnetic moments start to align to the orientation of µ 0 H. (c) Simulation of an longitudinal ADMR measurement including the eect of surface pinning, which plays a role for both cases of m σ and m σ. (d) ρ long as a function of µ 0 H for H j in the insitu2 sample at T = 5 K. µ 0 H was swept from 7 T 7 T 7 T depicted with black (forward) and gray (backward) colors. 56

61 Chapter 5 Magnetotransport experiments as a function of external magnetic elds to µ 0 H σ, the amount of spin absorption into YIG lm via spin transfer torque (STT) is smaller compared with the case if all spins are perpendicular to σ. However, one can expect that the number of spins aligning to µ 0 H increases with increasing µ 0 H, due to the fact that the Zeeman energy becomes more dominant, while the pinning energy does not change. When the stronger external magnetic eld µ 0 H high are applied to YIG/Pt, the more spins in YIG start to align along µ 0 H, perpendicular to σ, as shown in Fig. 5.8(b), and this results in an increase of the dissipation of spin accumulation at the interface for Pt, and nally leads to an increase of resistivity. Therefore, the mechanism of surface pinning could also play a role for the observed eld dependence of the resistivity. The discussion above is also applicable to the case of µ 0 H parallel to σ. Since a nite number of magnetic moments at the interface spins do not align parallel to σ under the application of µ 0 H low, a nite spin dissipation can be found. However, under µ 0 H high more magnetic moments align parallel to σ and this leads to a decrease of the amount of spin dissipation and thus leads to a lower ρ long. Therefore, the mechanism of surface pinning aects in both cases for m σ and m σ, and the expected ADMR measurement including this eect is exemplarily given in Fig. 5.8(c). Although it is not possible to know whether or not this eect actually occurs and in our samples, we found evidence for the existence of surface pinning in the FDMR measurements. We observed a large hysteresis curve in FDMR measurements in some samples (the insitu2 sample, the exsitu1 sample, and the exsitu3 sample) for low temperatures as shown in Fig. 5.8(d), while the other three samples did not show any hysteresis for all temperatures investigated. Since Pt is a paramagnet, in principle, Pt itself does not show a hysteresis. Moreover, this hysteresis also does not come from the coercivity of YIG, because we do not observe this hysteresis in all samples. Nevertheless, the resistivity is inuenced by the direction of µ 0 H. This leads to the assumption that not all magnetic moments related to the resistivity change in Pt, i.e. the magnetic moments at the interface, do follow µ 0 H. Therefore, the existence of hysteresis in our samples supports the idea of surface pinning. In this section we discussed possible candidates which can cause the eld-dependent magnetoresistance and included three mechanisms. They partly success to explain the eld dependence, although all are not perfect. To understand this issue in more detail, further investigations are required, for example, a quantitative model for the MMR contribution and investigation of surface pinning eects by scanning probe microscopy. 57

62 5.3 Transverse magnetotransport and dependence on external magnetic eld (a) 0.6 H -t V trans hi lo β H n H ADMR in OOPJ (b) V trans hi lo H H along n 0.6 ρ trans (nωm) exsitu4 T = 300 K T = 5 K substrate FMI NM 7 T 5 T 3 T 1 T 0.5 T ρ T0 substrate T = 300 K T = 5 K FMI NM H along t ρ trans (nωm) ρ trans (nωm) ρ T ρ trans (nωm) β µ 0 H (T) -0.5 Figure 5.9. Transverse resistivity in exsitu4 in (a) ADMR measurements in the OOPJ rotation and (b) FDMR measurements for H n (blue line) and H t (red line) at T = 300 K (orange back color) and 5 K (blue back color). Inserts: The conguration of ADMR and FDMR measurements for comparison. 58