The temperature and field stability of exchange biased magnetic multilayers containing a synthetic antiferromagnet

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1 Eindhoven University of Technology MASTER The temperature and field stability of exchange biased magnetic multilayers containing a synthetic antiferromagnet Deen, L.D.P. Award date: 2015 Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 13. Jul. 2018

2 Eindhoven University of Technology Department of Applied Physics Physics of Nanostructures group (FNA) The temperature and field stability of exchange biased magnetic multilayers containing a synthetic antiferromagnet L.D.P. Deen June 2015 Supervisors: Aurélie Solignac and Jürgen Kohlhepp

3 Abstract Tunnel magneto-resistance sensors are the most used sensors in the read heads of hard disks today. Now, the automotive engineering branch is looking to implement these sensors in cars, as the limits regarding the performance of regular magneto-resistance sensors that are currently used, are being reached. The conditions under which the magnetic sensors have to work properly in cars, differ a lot from the conditions in hard disk drives. The magnetic sensors consist of a pinned magnetic multilayer that needs to remain pinned, regardless of temperatures and external fields present. As the temperatures and fields are much higher in cars than in hard disks, this forms a challenge. In this study, the stability of an exchange biased multilayer combined with a synthetic antiferromagnet is investigated. Exchange bias is an effect that pins a ferromagnetic layer by linking it directly to an antiferromagnetic layer. This pinned ferromagnetic layer is used as part of a synthetic antiferromagnet. A synthetic antiferromagnet couples two ferromagnetic layers separated by a non-magnetic spacer layer antiferromagnetically via the RKKY-coupling effect. The RKKY-coupling coefficient oscillates when the interlayer thickness is varied, and in order to couple the ferromagnetic layers antiferromagnetically, the spacer layer thickness needs to be tuned. When exchange bias is combined with a synthetic antiferromagnet it results in a pinned multilayer containing no net magnetic moment. A growth study on Co/Ru/Co synthetic antiferromagnets is conducted. It is found that the sputter pressure used during the deposition of the Co layers has a large impact on the RKKY-coupling strength. Optimal growth conditions are found when depositing the Co layers at a pressure of 15 sccm and a power of 20 W. The thermal stability of synthetic antiferromagnets is investigated. The RKKYcoupling strongly depends on the thickness of the spacer layer. Magnetic multilayers are grown containing a wedged spacer layer, which showed two antiferromagnetic coupling regimes. The first regime found at spacer layer thicknesses of between 0.5 and 1.5 nm disappeared at annealing temperatures of 320 C, whereas the second antiferromagnetic regime found between nm remained stable at these temperatures. The instability of the first region is attributed to pinholes created at low spacer layer thicknesses. The field stability of magnetic multilayers containing exchange bias and synthetic antiferromagnetic multilayers is investigated via relaxation measurements. The angle of the magnetization of the exchange biased ferromagnetic layer has a large influence on the field stability effect. Decay rates of 6.3% and 27.0% were measured for applied fields of 62.5 mt and 1T, respectively. Although spin flop could induce an instability of the exchange bias when a field along the field cooling direction is applied, this was not experimentally observed. This result is promising regarding the application of these sensors in automotive environments.

4 Contents 1 Introduction Spintronics AMR-based sensors The next step: GMR/TMR based sensors This thesis: the stability of an SAF-EB system Theory Stoner-Wohlfarth Model The exchange bias effect An idealistic model Crystalline AF layers Polycrystalline AF layers The stability of the exchange bias effect against temperature and field The relaxation effect The training effect Interlayer exchange coupling Interlayer exchange coupling mechanisms The RKKY interaction between magnetic impurities The interlayer exchange coupling: a simple model Bruno s model Influence of roughness on the RKKY-coupling The thermal stability of the RKKY-coupling effect The intrinsic temperature dependence The temperature dependent disordering of the magnetic moments Extrinsic temperature dependence Theoretical magnetization curves of an SAF Combining the SAF and EB Experimental setup The sputter system The deposition process

5 3.1.2 Plasma cleaning Magnetic characterization techniques The Magneto-optical Kerr effect setup The Vibrating Sample Magnetometer - Superconducting QUantum Interference Device (VSM-SQUID) The SQUID-setup Annealing techniques The Argon oven The VSM-SQUID oven module Sample stack structure RKKY-coupled stacks EB-RKKY-coupled stacks Results Magnetic properties of an SAF Typical hysteresis loops of an SAF Extracting the oscillatory RKKY-coupling Growth studies on the Co-layers Varying the pressure and power during the Co layer deposition Investigating the thermal stability of the SAF Instability of the first transition region Interpretating the results of the SAF measurements Field stability measurements on EB-SAF coupled stacks Magnetic properties of EB-SAF stacks Investigating the stability of the exchange bias Conclusions 67 6 Outlook 69

6 In this thesis several abbreviations are used. For convenience they are listed below. GMR TMR SAF EB MOKE VSM SQUID AF FM NM Giant magneto-resistance Tunnel Magneto-resistance Synthetic antiferromagnet Exchange bias Magneto-optical Kerr effect Vibrating sample magnetometer Superconducting quantum interference device Antiferromagnetic Ferromagnetic Nonmagnetic

7 Chapter 1 Introduction Ever since the production of the first commercial cars in the early 20th century, the production, sales and usage of cars have seen a consistent increase. Today, the car is the most popular used vehicle globally, and recent figures show that the amount of registered cars within the Netherlands has seen an 18% increase in the past 15 years. Soon there will be over 8 million registered cars, averaging at 420 cars per 1000 inhabitants [1]. Comparing this to other countries, we have an average amount of cars, whereas the USA tops the chart at 845 cars per 1000 inhabitants. The current amount of cars used worldwide has been subject of debate over the past years, as oil is becoming scarce and pollution is destroying the ecological system of our planet. Therefore, the amount of pollution needs to be reduced in order to keep our planet healthy. However, it is not only the current situation which makes for concern: at the other end of the car-registration spectrum, China is found with an average of 37 registered cars per 1000 inhabitants [2]. China s economy is rising fast, and at some point the amount of car usage will start to reach western european numbers, increasing the already present pollution problem to an immense height. Solutions for these existing and upcoming problems need to be found: cars need to be smarter, less fuel consuming and less polluting. One approach to try start tackling this huge problem is to improve one of the tiniest parts of the car: the magnetoresistance (MR) sensors used in the electronic system of the car. The MR sensor technology is part of the field of spintronics. In this chapter, a brief introduction of the field of spintronics is given and the technology behind MR sensors will be explained. Afterwards the subject of the research described in this thesis will be discussed. 1.1 Spintronics Spintronics covers the research field which adresses two important properties of electrons: its charge and its spin. An important discovery within this field is the so-called giant magneto-resistance (GMR) effect, which is illustrated in figure

8 CHAPTER 1. INTRODUCTION 2 Figure 1.1: Simplified illustration of the GMR-effect for parallel and antiparallel configuration (top), and an example of the electrical resistance versus applied field for a CoPd/Ru/CoPd multilayer (bottom). Figure taken from [4]. This discovery marked the beginning of intensive spintronic research in the late 1990 s. However, long before the discovery of the GMR-effect, the ordinary and anisotropic magneto-resistance (OMR and AMR) effect were discovered. In 1856 William Thompson discovered that the resistance of a current which is sent through magnetic material varies with the direction of the magnetization within the magnetic material. He discovered that the resistance reaches it lowest value when the direction of the magnetization is parallel with the direction of the current. This effect originates from the spin scattering probability [3], which varies for different directions of the magnetization. This effect is material specific, and is still used as the main physical principle in sensor applications today. Over a century later the GMR effect was discovered by Albert Fert and Peter Grünberg, for which they received a nobel price in 2007.

9 CHAPTER 1. INTRODUCTION 3 I) θ) Magne5za5on) Figure 1.2: Simplified illustration of an AMR sensor. The resistance the current experiences depends on the angle θ between the direction of the current and the magnetization. The GMR effect is based on the fact that the electrical resistance an electron experiences when passing through two magnetic layers seperated by an non-magnetic spacer layer depends on the mutual orientation of the magnetization within these magnetic layers. Figure 1.1 shows the GMR-stack for two different orientations of the magnetization and a plot of the resistance versus the applied field. A current can be conceptually separated into two currents: a spin-up current and a spin-down current. When a current is sent through a ferromagnetic (FM) layer, electrons with a spin aligning with the magnetization of the FM layer experience less resistance than electrons with spins aligned antiparallel due to spin-dependent scattering [4]. When the current is sent through two FM layers, the resistance depends on the mutual orientation of the magnetizations of the magnetic layers. When the magnetizations are parallel, electrons with spins aligned with the magnetizations experience a low resistance while the spins that do not align with the magnetization experience a high resistance. If the magnetizations are aligned anti-parallel, all electrons experience a high resistance (either in the first or in the second layer). In the plot shown in figure 1.1 the dependence of the resistance on the mutual orientation of the two layers is clearly observed. 1.2 AMR-based sensors In the automotive industry the AMR sensor is still the most used sensor today. A simple representation of an AMR sensor is shown in figure 1.2. The resistance depends on the angle between the current and the magnetization in the magnetic material. The AMR-technology is known for over a century, and it is becoming more and more difficult to improve the AMR-sensor as the limit of its performance is being reached. A way to improve the sensors is to switch to the GMR and TMRbased sensors: the GMR and TMR-sensors are much more sensitive than the AMR

10 CHAPTER 1. INTRODUCTION 4 sensors. AMR-sensors are able to detect fields down to 10 7 Tesla, whereas GMR and TMR-sensors can detect fields down to Tesla. Nevertheless, implementing GMR and TMR-sensors in the automotive industry requires these sensors to work at high temperatures and external fields. In this thesis the thermal and magnetic field stability of magnetic multilayers used in GMR and TMR sensors are investigated. In order to describe the subject in more detail, the principle of GMR and TMR-sensors will be explained first. 1.3 The next step: GMR/TMR based sensors In a GMR/TMR-based sensor, a current passes through a stack composed of two FM layers seperated by a spacer layer. The resistance the current experiences depends on the mutual orientation of the magnetizations in the FM layers. By pinning one of the two FM layers and keeping the other FM layer rotating freely, (ultra)sensitive measurements can be done, since a small change of the magnetic orientation of the magnetization in the free layer results in a large change in resistance. In a GMRsensor, the spacer layer is a metallic layer, allowing direct flow of current through the spacer layer. In a TMR-sensor, or tunnel magneto-resistance sensor, the spacer layer consists of insulating material, allowing only flow of current through a tunneling effect. One of the biggest and most important differences between an AMR-sensor and a GMR/TMR-sensor is the use of a pinning layer. One way to pin a FM layer is to make use of exchange bias (EB): the FM layer is magnetically coupled to an antiferromagnetic (AF) layer in order to pin it. The principle behind the EB will be explained in more detail in section 2.1. Sensors combining GMR and EB are shown in figure 1.3. The configuration as shown on the left is sensitive to external fields, as the stack has a net magnetic moment: when a magnetic field is applied, a torque is exerted on the pinned FM layer. A way to prevent this is to use a synthetic antiferromagnet (SAF) : by adding an additional FM layer and a spacer layer with the right thickness, the two FM layers are coupled antiferromagnetically, resulting in no net magnetic moment when considering the pinned part of the sensor. A sensor combining GMR, EB and an SAF is shown in the right part of figure 1.3. The principle behind the SAF will be explained in more detail in section This thesis: the stability of an SAF-EB system In order for the sensor to work the pinned multilayer should remain pinned at all times, during mounting and its lifetime. Although GMR and TMR-sensors are already produced and applied in hard disk technology, applying them in the automotive industry requires different properties of the GMR/TMR-sensors. The sensors have to work properly at high external fields and high temperatures. The stability of the SAF and EB is the main subject of investigation in this thesis.

11 CHAPTER 1. INTRODUCTION 5 Free)layer) Non)magne5c)layer) Free)layer) Ferromagne5c)layer) Exchange)) bias) Spacer)layer) Ferromagne5c)layer) An5ferromagne5c)layer) Pinned) mul5layer) SAF) Exchange)) bias) Spacer)layer) Ferromagne5c)layer) An5ferromagne5c)layer) Figure 1.3: A regular GMR-based sensor (left) and a GMR-SAF sensor (right). In the regular sensor, current passes through two FM layers (green and blue) and a spacer layer (yellow). The bottom F-layer is pinned by EB, whereas the top layer is free to rotate. In the GMR-SAF sensor, an additional FM layer and spacer layer are used and are configured such that this additional layer is antiferromagnetically coupled to the other FM layer. This results in no net magnetic moment for the pinned multilayer. This thesis can be divided in two parts. First, the magnetic characteristics and thermal stability of the SAF are investigated. Later, the AF layer is added and the magnetic properties and field stability of stacks containing both EB and an SAF are investigated. Chapter 2 will start by describing the theory of EB and synthetic antiferromagnets seperately, after which a system containing both EB and an SAF will be discussed. Chapter 3 covers the experimental setups used to create and investigate both the SAF stacks and the EB-SAF multilayers. All multilayers are grown using a sputter system, and for the magnetic characterization a Magneto-optical Kerr effect (MOKE) setup and a vibrating sample measurement - superconducting quantum interference device (VSM-SQUID) are used. In order to set the exchang bias, an Argon oven as well as a build-in annealing module in the VSM-SQUID setup are used. Chapter 4 covers experimental results that are obtained during research. First, a growth study on different spacer materials is presented. Next, the thermal stability of an SAF-system is investigated. Finally, a study on the magnetic properties and field stability of an EB-SAF system is presented. Chapter 5 presents the conclusions of this study and Chapter 6 provides an outlook and recommendations for future research on EB-SAF systems.

12 Chapter 2 Theory This chapter provides the theoretical background necessary to understand the experimental results that will be described in Chapter 4. In the first section the Stoner- Wohlfarth model is introduced which can often be used to model the magnetic behavior of magnetic thin films in external fields. In section 2.2 the Meiklejohn-Bean model and the Fulcomer-Charap model describing the EB effect is introduced. The EB effect is used in the spin-valve systems to pin the magnetization of an FM layer in a prefered direction. The stability of this pinning effect is the one of the main subjects of this thesis. The stability of the EB effect is discussed in section 2.3. Next, the theory of interlayer exchange coupling is presented which is used to create the SAF based on Ruderman-Kittel-Kasuya-Yosida (RKKY)-interaction. The RKKY-interaction and a simplystic model are introduced to translate the RKKY-interaction to a system of FM layers seperated by a spacer layer. Bruno introduced a model to qualitively describe the RKKY-coupling in magnetic multilayers [5][6]. His model is briefly introduced in section 2.4. Finally, EB and the RKKY-coupling are combined to create an EB-SAF coupled stack. The magnetic properties of this stack are described in section Stoner-Wohlfarth Model When describing the reversal of magnetization in magnetic thin films, the Stoner- Wohlfarth model is often used, which is a macrospin model based on the assumption of a uniform response of the magnetization when an external magnetic field is applied. In the Stoner-Wohlfarth model, the magnetization of the thin film will rotate uniformly with the applied external field. Typical magnetic loops as described within the Stoner-Wohlfarth model are shown in figure 2.1 and

13 CHAPTER 2. THEORY 7 H) Hard)axis) easy)axis) M) M) +M F ) M) D2K F /μ 0 M F ) +2K F /μ 0 M F ) H) DM F ) M) Figure 2.1: Hysteresis loop for the Stoner-Wohlfarth model for a field applied along the hard axis. The magnetization slowly rotates towards the applied field direction, untill it completely aligns and saturation is reached. H) Hard)axis) M) M) easy)axis) +M F ) D2K F /μ 0 M F ) Hc) H) +2K F /μ 0 M F ) M) DM F ) Figure 2.2: Hysteresis loop when the field is applied along the easy axis. A minimum applied field is needed to switch the magnetization direction. When the magnetization is switched and the field is applied in the opposite direction, again a minimum field is required to switch the magnetization back. This results in magnetic behavior that depends on the field sweep direction.

14 CHAPTER 2. THEORY 8 y) x) Hard)axis) H) M) θ) β) K F ) Easy)axis) Figure 2.3: Schematic of the vectors and angles for the magnetization M, the anisotropy K F and the applied field H as defined for the Stoner-Wohlfarth model. Figure adapted from [4]. The total magnetic energy per unit area of a magnetic thin film with a uniaxial magnetocrystalline anisotropy in an applied field along the applied field direction is given by E = µ 0 Ht F M F cos(θ β) + Kt F sin 2 (β) (2.1) With H the applied field, M F the saturation magnetization, K the magnetocrystalline anisotropy of the layer and t F the thickness of the FM layer. The first term in equation (2.1) is the Zeeman energy contribution describing the effect of the applied field on the magnetization, and the second term is the magnetocrystalline anisotropy term. The angles θ and β are defined as the angles between the applied field and the magnetization respectively with the direction of the anistropy of the layer, as depicted in figure 2.3. The stable configuration of the magnetization corresponds to an energy minimization. Equation (2.1) is minimized with respect to β resulting in µ 0 Ht F M F sin(θ β) + K F t F sin(2β) = 0 (2.2) µ 0 Ht F M F cos(β θ) + 2K F t F cos(2β) > 0 (2.3)

15 CHAPTER 2. THEORY 9 When a field is applied, it is important to distinquish two directions along which the field can be applied: the easy axis and the hard axis. To explain this, assume β = 0. When applying a field along the hard axis (θ = ±π/2), the magnetization rotates gradually towards the field direction, untill it aligns completely and saturation is reached. A hysteresis loop for a field applied along the hard axis is shown in figure 2.1. When applying the magnetic field along the easy axis (θ = π) for small fields the magnetization remains aligned along β = 0 since the system is in a local energy minimum. Applying a magnetic field changes the energy landscape and in order to remove the local energy minimum state, a minimum field is required. When this field is applied, the magnetization switches and the system reaches the global energy minimum state (β = π). When the magnetic field is then reversed (θ = 0), the global energy minimum changes to β = 0, and the system needs a minimum applied field again to switch to this global energy minimum. This results in magnetic loops that depend on the field sweep direction and an example is shown in figure 2.2. The minimum field to switch the magnetization is the coercive field H c that can be obtained from (2.2) and (2.3) and is equal to 2.2 The exchange bias effect H c = ±2K F µ 0 M F (2.4) As described in chapter 1, in order for a GMR/TMR sensor to work, the magnetization of one of the FM layers needs to be pinned. One way to do this is by using the so-called EB effect. The EB effect originates from the exchange interaction between an AF layer with an FM layer at the mutual interface. Figure 2.4 shows the location of the exchange biased layer in a GMR/TMR sensor. The AF spins at the interface align with the FM spins at the interface. In order to couple these spins in a preferential uniform direction, the EB needs to be set. When the EB is set, the hysteresis loop is shifted. Figure 2.5 shows the magnetic loop before (top) and after (bottom) setting the EB. In order to set the EB, the following procedure is used: The temperature of the system is increased such that T N < T < T C A large magnetic field is applied along a prefered direction to set the magnetization direction of the FM layer The temperature is cooled down to T < T N The applied field is reduced to zero for which T N is the Neél temperature at which there is no more macroscopic magnetic ordering in the AF layer and T C is the Curie temperature at which there is no more macroscopic magnetic ordering in the FM layer.

16 CHAPTER 2. THEORY 10 Free)layer) Non)magne5c)layer) Ferromagne5c)layer) Pinned) mul5layer) SAF) Exchange)) bias) Spacer)layer) Ferromagne5c)layer) An5ferromagne5c)layer) Figure 2.4: Simplified illustration of a GMR/TMR stack with the exchange biased layers highlighted. By setting the temperature to T N < T < T C, the spins in the AF layer are disordered. By then setting the direction of the FM layer and decreasing the temperature to T < T N, the AF spins at the interface with the FM layer will experience an exchange interaction and will align with the FM spins at the interface. By decreasing the temperature even further, the orientation of the AF spins is frozen in. If then the field is reduced to zero, the FM spins will remain aligned with the AF spins due to the exchange interaction. This direction along which the AF spins at the interface are aligned is called the field cooling direction. The coupling at the interface will induce an additional anisotropy in the FM layer. Switching the magnetization of the FM layer antiparallel to the field cooling direction requires a larger field, as both the magnetocrystalline anistropy as well as the exchange coupling needs to be overcome. When the magnetization of the FM layer switches and the field is applied in the opposite direction, a smaller field is required to switch the magnetization back as the exchange coupling direction did not change and is contributing to the switching of the magnetization. This results in a shift of the hysteresis loop of the FM layer. The shift of the loop is the so-called exchange bias field H eb. EB behavior was first observed by Meiklejohn and Bean [7]. They proposed a model to describe the EB effect, which is described in the next section.

17 CHAPTER 2. THEORY 11 H) No)magne5c)) ordering) T N) <)T)<)T C ) M) +M F ) Ferromagne5c)layer) No)magne5c)) An5ferromagne5c)) ordering) layer) D2K F /μ 0 M F ) Hc) +2K F /μ 0 M F ) H) DM F ) Ferromagne5c)layer) No)magne5c)) An5ferromagne5c)) ordering) layer) H) Field)cooling)direc5on) T)<)T N ) M) +M F ) Ferromagne5c)layer) An5ferromagne5c)) layer) H EB ) 2K F t F + J eb µ 0 M F t F H C ) H C,2 ) H) H C,1 ) 2K F t F + J eb µ 0 M F t F DM F ) An5ferromagne5c)) layer) Figure 2.5: Schematic view of the hysteresis loops during the annealing process to set the EB for an ideal magnetic thin film. When the temperature is above the Neél temperature (top), there is no order in the spins of the AF layer and a regular FM hysteresis loop is found. After setting the EB, at T < T N (bottom), the AF spin orientation is frozen in. When a magnetic loop is measured, the EB results in a shift of the hysteresis loop.

18 CHAPTER 2. THEORY An idealistic model In the Meiklejohn and Bean model, a number of important simplifying assumptions are made [7][8][9] : Both the FM and AF layer are considered single domain layers (macrospins) The F layer has a uniaxial anisotropy The AF layer is blocked and is considered to have an infinite magnetocrystalline anisotropy The spins at the interface have a net magnetic moment equal to the magnetic moment of one sublattice The spins of the AF layer are completely uncompensated at the interface: The interface is atomically smooth: no imperfections or roughness is present The FM and AF layers are coupled by an interfacial exchange coupling due to the exchange interaction at the mutual interface, which is characterized by an interfacial exchange coupling energy per unit area J eb. The total magnetic energy per unit area of the system can be writen as: E = µ 0 HM F t F cos(θ β) + K F t F sin 2 (β) J eb cos(β) (2.5) in which H is the external applied field, M F is the magnetization of the FM layer, t F is the thickness of the FM layer, β is the angle between the magnetization M F and the anisotropy direction of the F layer (K F ) and J eb is the exchange energy per unit area. The first term in equation (2.5) is the Zeeman energy. The second term is the magnetocrystalline anisotropy of the FM layer and the third term is the exchange coupling resulting from the coupling at the interface of the FM and AF layers. The angles used in the Meiklejohn-Bean model are shown in figure 2.6. By minimizing the total magnetic energy with respect to β behavior of the magnetization of the FM layer versus an applied field can be calculated. The coervive field values H C,1 and H C,2 can be extracted and are equal to H c,1 = 2K F t F + J eb µ 0 M F t F (2.6) H c,2 = 2K F t F + J eb µ 0 M F t F (2.7) The coercive field of the loop H c and the displacement H eb of the magnetic loop can be calculated and are equal to H c = H c,1 + H c,2 2 = 2K F µ 0 M F (2.8)

19 CHAPTER 2. THEORY 13 y) x) Hard)axis) H) M) θ) β) K F ) Easy)axis) Figure 2.6: Schematic overview of the vectors and angles used in the Meiklejohn- Bean model. and H eb = H c,1 + H c,2 = J eb (2.9) 2 µ 0 M F t F which shows that EB results in a shift of the loop equal to H eb and does not change the coercivity field H c of the magnetic loop. The shift of the magnetic loop can be understood by considering the applied field direction as compared to the field cooling direction. When a field is applied opposite to the field cooling direction, the addional coupling has to be broken in order to rotate the FM layer and extra energy is needed. This behavior is asymmetric: when the field is applied along the field cooling direction a smaller field is required to reallign the FM layer along the field cooling direction since the coupling term favours this allignment. This asymmetric behavior leads to the shift of the hysteresis loop Crystalline AF layers The assumtions made in the previous section are idealistic. In reality, the AF layer does not have an infinite anisotropy, and experimentally it was found that the spins in the AF layer can rotate when an external field is applied, as illustrated in figure 2.7. An extra energy term for the magnetocrystalline anisotropy of the AF layer has to be introduced. The total magnetic energy per unit area is then equal to E = µ 0 HM F t F cos(θ β) + K F t F sin 2 (β) + K AF t AF sin 2 (α) J eb cos(β α) (2.10)

20 CHAPTER 2. THEORY 14 Figure 2.7: Illustration of the angles of the different magnetizations and anisotropies when a (small) rotation of the spins in the AF layer is taken into account. A rotation of α of the spins in the AF layer with respect to the initial orientation is allowed. where K AF is the anisotropy of the AF layer, t AF is the thickness of the AF layer and α is the angle between the spins of the AF layer and the anisotropy direction of the AF layer. Again, an energy minimization can be conducted with respect to α and β, leading to H sin(θ β) + sin(β α) = 0 (2.11) in which H eb Rsin(2α) sin(β α) = 0 (2.12) J eb Heb (2.13) µ 0 M F t F is the EB field value for an infinitely large anisotropy for the AF layer, and R K AF t AF J eb (2.14) is describing the ratio between the anisotropy of the AF layer and the interfacial exchange energy J eb. This ratio determines the properties of the EB system. A plot of the coercive field versus R and the EB field is shown in figure 2.8. In order to clarify the influence of this ratio, the anisotropy of the FM layer (K F ) is assumed to be zero. There are three regions of interest.

21 CHAPTER 2. THEORY 15 Figure 2.8: Plot of the ratio between the anisotropy of the AF layer and the interfacial exchange energy versus the coercive field and EB field. Figure adopted from [10]. R 1. In this region (I), the AF anisotropy is larger than the interfacial exchange coupling. This results in a limited angle over which the spins of the AF layer can rotate. A small rotation of the spins leads to a small decrease of the EB as can be seen when R=1. When R> >1, the anisotropy of the AF layer is so strong that the AF spins do not rotate anymore. At this point, the maximum EB field Heb is found. 0.5 R 1. In this region (II), the AF spins start to rotate along with the FM spins. This results in a loss of the EB. Depending on the field sweep direction, at a critical angle β of the FM spins, the AF spins will switch. This results in a hysteresis like behavior, and a coercive field is observed. R < 0.5. In this region (III), the anisotropy of the AF spins is much lower than the exchange coupling. The spins of the AF layer follow the direction of the FM spins without any jumps. For the limit if R= 0 both the coercive field and the EB field are zero. In order to pin the FM layer, it is important that EB is present and the AF spins rotate as little as possible. For this, the anisotropy of the AF layer must be large Polycrystalline AF layers The model described in the previous section assumes that the AF layer is a single domain. In reality, the AF layers are sputtered and have a polycrystalline structure.

22 CHAPTER 2. THEORY 16 In 1972, Fulcomer and Charap developed a model that accounts for this [11]. The Fulcomer Charap model considers the AF layer as an assembly of small non-interacting particles, or grains. Each grain is exchange coupled to the FM moment of the FM thin film. Figure 2.9 shows an illustration of these AF grains on a FM layer. When assuming that the system is annealed and the easy axis of the FM layer and the AF grains are aligned, the energy per unit area of a single grain is given by E AF = t g K AF sin 2 (α) cj eb cos(β α) (2.15) where t g is the thickness of the grain, α is the angle of the magnetization of the grain and the easy axis of the FM thin film and c is the contact fraction. The first term is the magnetocrystalline energy term of the grain and the second term is the EB coupling term of the grain with the FM layer. Although two grains can have the same surface area, the AF surface moment can be different due to roughness. Roughness present at the interface can lead to compensation of the EB coupling, for example when a different sublattice of the grain is in contact with the FM layer. An example is depicted in figure The coupling is significantly reduced, and the contact fraction accounts for this loss of EB coupling. For the grain depicted in figure 2.10, only 1 5 of the grain is uncompensated, so c = 1 5. When considering AF grains, the energy per unit area of the exchange biased system can be written as [12] E = µ 0 HM F t F cos(θ β) + K F t F sin 2 (β) + N [ KAF t i gsin 2 (α i ) J eb c i cos(β α i ) ] (2.16) The first term in this equation is the Zeeman energy, the second term is the magnetocrystalline energy of the FM layer, and the third term is a summation over all AF grains present in the AF layer. In order to understand the magnetic behavior of the AF grains when the magnetic moment of the FM thin film is switched, the energy diagram of an AF grain shown in figure 2.11 has to be considered. The plot shows the energy of an AF grain E AF versus the angle α when the magnetic moment of the FM layer is switched (β = π). When the magnetization of the FM layer is switched, the orientation of the magnetization of the AF grains is in a local energy minimum (α = 0). In order to reach the global minimum (α = π) the energy barrier E needs to be overcome. The barrier height E is given by ( ) ) 2 Jeb Ac E = K AF At g (1 + J eb Ac (2.17) 2K AF At g in which A is the area of a grain. i=1

23 CHAPTER 2. THEORY 17 Easy)axis) Ferromagne5c)layer) M F ) β) M AF ) α) An5ferromagne5c)grains) Figure 2.9: Illustration of the AF grains in contact with an underlying FM layer for the Fulcomer Charap model. In this model, the AF anisotropy is considered finite, and when the magnetic moment of the FM layer is rotated, the EB coupling can result in the rotation of the spins of the AF grains over an angle α. Figure adapted from [11]. Figure 2.10: Schematic representation of coupling reduction due to roughness at the interface. Roughness at the interface can result in compensation of the EB coupling due to different sublattices of the AF grain being present at the interface. In this example, 3 of the grain is coupled in the positive x-direction, while 2 of the grain is 5 5 coupled in the negative x-direction. The net contribution to the EB of this grain is 1 5 in the positive x-direction. Figure adapted from [11].

24 CHAPTER 2. THEORY 18 Field)cooling)direc5on) E 1 ) E AF) β=π) μ 0 H) Ferromagne5c)layer) )An5ferromagne5c)grain) ) E 2 ) ΔE) 0) ½)π) π) 1½)π) α) DE 2 ) Figure 2.11: Energy diagram for the orientation of the magnetization of the AF grains when the magnetization of the FM layer is switched. In order to reach a global minimum, the grains have to overcome an energy barrier E. The process of overcoming the energy barrier is a thermally activated process which means that the switching of the magnetization of the AF grains takes a certain time. The grains approach a new equilibrium distribution with a relaxation time constant equal to τ = ν 0 e E k b T (2.18) in which ν 0 is the inverse of the switching rate of the magnetizations of the AF grains. The relaxation time constant depends strongly on the temperature, and it is useful to introduce the concept of a blocking temperature T B. At low temperatures, the relaxation time is large and grains will not switch within the experimental measurement time. At high temperatures, the relaxation time is short and as soon as the magnetic moment of the FM film is switched, the grains will follow and the response seems instantly. This results in all grains switching within the experimental time. The temperature at which τ is equal to the experimental time is called T B. The switching of the grains during a measurement has great influence on the magnetic response of the system. It is important to distinguish three temperature regimes and the corresponding behavior of the grains in these regimes. At T T B the grains will not switch during the experiment, and the EB remains stable. This results in only a shift of the hysteresis loop. When the temperature is increased up to the blocking temperature grains are switching within the experimental time.

25 CHAPTER 2. THEORY 19 T B ) Figure 2.12: Plot of the EB (white circles) and the coercive field (black circles) versus temperatures close to the blocking temperature of an AFM/FM bilayer. As the temperature increases, the EB decreases since more grains become unstable. Instead, these unstable grains contribute to the coercive field, which reaches a maximum at T = T B. For T > T B grains are starting to go in a superparamagnetic state, leading to disorder and the contribution to the coercive field is lost until T T N and the grains no longer contribute to the EB or the coercive field. Figure adapted from [13]. These grains no longer contribute to the EB, but instead will switch together with the FM layer. This means that we do not only require a field to switch the FM layers, but the field needs to be large enough to switch the AF grains as well. This results in an increasing H C and leading to a maximum of H C when T = T B. When T > T N the grains are no longer antiferromagnetically ordered and no longer contribute to the EB or the coercive field. At these temperatures, only the magnetic signal of the FM layer is measured. A typical plot of H C and H eb versus T is shown in figure The stability of the exchange bias effect against temperature and field As described in Chapter 1, EB is used to pin a FM layer in a GMR/TMR sensor. In order for the GMR/TMR sensors to be applicable in the automotive industry, the GMR/TMR sensors need to function properly at high temperatures and external fields. This requires the EB to be stable at these temperatures and fields. The influence of temperature was adressed in the previous section and it was shown that thermal fluctuations can lead to the switching of spins in the AF grains, resulting in a loss of EB. In this section, the stability versus field will be discussed and two

26 CHAPTER 2. THEORY 20 The)relaxa5on)effect) Figure 2.13: Illustration of the switching of the AF grains over time when the magnetization of the FM layer is reversed. The switching of an AF grain is a thermally activated process, and the variation of size and shape of the samples results in a gradual switching of all the grains over time. When the time is sufficiently long, all grains will have switched, and the original EB is lost. This phenomenon is the so-called relaxation effect. effects will be discussed: the relaxation effect and the training effect The relaxation effect When a field is applied opposite to the setting field of the annealed bilayer, the magnetization of the FM layer switches. The torque that is then applied on the AF grains can switch the grains, as depicted in figure As the grains vary in size and shape, the time it takes to switch an AF grain varies. Small grains will switch sooner than larger grains. However, when the field is applied for a sufficient long time, the larger grains will switch as well, and a significant reduction of EB is found. As described in the previous section, this effect is a thermal relaxation effect. The probability of grains overcoming this energy barier E increases over time. If all grains are identical, this would result in a E which is equal for all grains. In reality, the grains vary, for instance in volume. A different volume leads to a different relaxation, resulting in a different E. When a grain switches, it reaches the global energy minimum, as shown in figure When a grain is switched and the magnetization versus applied field is measured, the grain will remain switched, resulting in a loss of EB. The switched grains will not rotate along with the magnetization of the FM layer, and thus do not contribute to a coercive field. When the experimental time is large enough, enough grains will switch and the EB is lost.

27 CHAPTER 2. THEORY 21 Figure 2.14: Simplified view of a GMR/TMR stack with the SAF illustrated in color. The SAF is part of the pinned multilayer in the GMR/TMR stack. By implementing an SAF in the pinned multilayer, the net magnetic moment of the pinned multilayer is zero The training effect The training effect is an effect that occurs when hysteresis loops of an exchange biased system are measured for the first time after annealing. The effect results in a change of the hysteresis loop when consecutive measurements are performed. The coercive fields and the EB decrease for increasing number of measurements. The training effect is related to the unstable state of the AF layer and the F/AF interface as prepared by the field cooling procedure. However, the exact mechanisms behind the training effect are not yet understood. It has been shown that the training effect mainly influences the first hysteresis loop [14][15] and therefore to prevent the influence of this effect, a first field sweep is conducted after the annealing process. This first field sweep is not taken into account when doing measurements. 2.4 Interlayer exchange coupling In this section, the theory behind the SAF is explained. As mentioned in the first chapter, the pinned multilayers consist of an exchange biased FM layer and an SAF. The SAF is used in order to create a pinned multilayer that has no net magnetic moment which makes it less susceptible to external fields. Figure 2.14 shows the location of the SAF within a (simplified) GMR/TMR stack. First, a general introduction on coupling mechanisms in magnetic multilayers is given. Next, the so-called Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is introduced. This interaction occurs in a system with magnetic impurities embedded in a non-magnetic metalic material, and it will be shown that these magnetic impurities can be coupled via the RKKY-interaction. In section a simplistic model is introduced to apply the RKKY-theory to magnetic multilayers to show that it is possible to couple two FM layers through a non-magnetic metallic spacer layer.

28 CHAPTER 2. THEORY 22 Figure 2.15: Illustration of the dipole-dipole interaction between two magnetic moments seperated by a distance r. Next, Bruno s model will be briefly introduced, which takes the band structure of the spacer layer into account to quantify the RKKY coupling strength. Section explains the influence of roughness at the FM/NM interfaces and the thermal stability is discussed. Finally in section the magnetic behavior of an SAF versus an applied field is discussed Interlayer exchange coupling mechanisms Two FM layers can be coupled through a non-magnetic metal spacer. Several coupling mechanisms are known to be present in FM multilayers, such as dipole-dipole interactions, direct exchange coupling through pinholes, orange peel coupling and genuine indirect exchange coupling. The dipole-dipole interaction is a long-range interaction for which the interaction energy can be written as [ ] E dip = µ 0 4π m 1 m 2 (m 1 r ) (m 2 r ) + 3 r 3 r 5 (2.19) In which r is the vector between the two magnetic moments m 1 and m 2, as shown in figure The dipole-dipole interaction falls of as 1/r 3 with increasing distance r between the magnetic moments. Bloemen calculated [16] that the dipole coupling strength of two in-plane Co monolayers at a distance d = 2Å is in the order of 10 3 mj/m 2, which is far less than the commonly observed coupling strengths ( 0.1mJ/m 2 at d = 10Å). The dipole-dipole interaction is not sufficient to explain the coupling strengths which were experimentally observed in the magnetic multilayers and is therefore neglected in this thesis. A second coupling mechanism which is present is the direct exchange interaction, which couples magnetic layers through pinholes in the spacer layer. When a spacer

29 CHAPTER 2. THEORY 23 Figure 2.16: Illustration of pinhole coupling of two FM layers. When the spacer layer is thin and inhomogeneous, direct channels of FM material between the FM layers can exist and result in a direct FM coupling of the two magnetic layers. Figure 2.17: Illustration of orange peel coupling. This coupling results from fringe fields and correlated roughness at the FM/spacer layer interface. layer seperating two FM layers is not homogeneous, pinholes can occur through which the FM layers are directly coupled as is shown in figure Pinhole coupling depends strongly on the quality of the layers and will decrease rapidly for increasing spacer layer thickness. Therefore, pinhole coupling has usually to be considered only for thin spacer layers [17]. A third coupling is orange peel coupling. Orange peel coupling is caused by fringe fields that are the result of correlated roughness at the FM/spacer layer interface, as illustrated in figure Orange peel coupling results in an FM coupling of the magnetic layers. In order to create an SAF, the FM layers need to be antiferromagnetically coupled. This is possible by considering the indirect exchange interaction. The indirect exchange interaction can couple the FM layers either parallel or antiparallel, which depends on the thickness of the spacer layer. The indirect exchange interaction bears

30 CHAPTER 2. THEORY 24 m 1 ) r) m 2 ) Co)atom)1) Co)atom)2) Distance)r)between)the)Co)atoms) ) Ferromagne5c)coupling) J) An5ferromagne5c)coupling) Figure 2.18: Illustration of the interaction strength J between two Co atoms embedded in a Cu crystal versus the distance between the Co atoms. Depending on the distance between the Co atoms, the interaction strength is either positive, governing an FM coupling, or negative, governing an AF coupling. much resemblance with the RKKY-interactions between magnetic impurities embedded in a conducting material. In the next section, the RKKY-interaction will be introduced The RKKY interaction between magnetic impurities A succesful theory behind the oscillatory exchange interaction was developed by Ruderman, Kittel, Kasuya, and Yosida in the 1960 s, after which this interaction was called the RKKY-interaction [18][19][20]. In their papers they discuss the coupling between magnetic impurities embedded in a non-magnetic metallic material. To understand the coupling mechanism, consider a Cu crystal, in which two Cu atoms are replaced by Co atoms. The coupling between the Co atoms as a function of the distance between the Co atoms is shown in figure Conducting electrons in the Cu experience a potential step when approaching the Co atom. Due to the wave properties of electrons, the scattering of electrons at the potential results in a phase shift. Since the Co atom has a non-zero magnetic moment, they will interact differently with a spin-up electron then with a spin-down

31 CHAPTER 2. THEORY 25 electron, resulting in a different phase shift for spin-up electrons as compared to spin-down electrons. The difference in interaction leads to the up and down spins not cancelling out anymore, and after a summation over all the wave vectors up to the Fermi surface this results in an oscillatory spin density. A second Co-atom, if placed not too far from the first Co atom, will experience either a net spin-up density or a net spin-down density depending on the distance between the two Co atoms and therefore is (indirectly) coupled to the first Co atom. Yoshida showed that the interaction strength J can be described by [20] : J cos(2k F r) r 3 (2.20) with k F the Fermi wave vector of a free electron gas and r the distance between the two Co atoms. When J > 0 the spins of the Co atoms are coupled ferromagnetically, and when J < 0 the spins are coupled antiferromagnetically. In order to translate the RKKY-interaction between magnetic impurities to a system of magnetic layers seperated by a spacer layer, a simple 1D model will be used [21] The interlayer exchange coupling: a simple model The 1-dimensional system is depicted in figure It contains two FM monolayers F1 and F2, seperated by a non-magnetic metallic layer. When a conducting electron in the spacer approaches the first magnetic layer it will experience a potential step due to a difference in band structure between the spacer and the magnetic material. The electron wave will partly be reflected (e r ) and partly be transmitted (e t ). The wave equations of the electron in the spacer layer ( 1d < x < 1 d) can be calculated by solving the time-independent Schrodinger 2 2 equation and results in ψ(x) = e ikxx + Re ikxx (2.21) in which k is the wavevector of the incoming and reflected electron and R is the reflection coefficient. The probability of finding an electron at a certain position x is given by ψ(x) 2 = 1 + R 2 + Re 2ikxx + Re 2ikxx = 1 + R 2 + 2Rcos(2k x x) (2.22) 2Rcos(2k x x) (2.23) when only considering the position dependent term. From this equation it can be seen that the electron density within the spacer varies due to the last cosine term: the density oscillates as a function of x with a period of π/k.

32 CHAPTER 2. THEORY 26 Figure 2.19: A schematic overview of the FM/NM/FM trilayer system. The conducting electrons in the non-magnetic layer will partly be reflected and partly be transmitted due to the potential difference at the interface. Due to the non-zero magnetic moment of the FM layer at the interface, the incoming electrons with spin up will experience a different potential than electrons with a spin down. The different potentials lead to different reflective coefficients (R and R )). The different reflective coefficients lead to two spin dependent charge density waves ψ (x) 2 2R cos(2k x x) ψ (x) 2 2R cos(2k x x) (2.24) Substracting these two standing spin density waves leads to the net spin density wave at a position x given by ψ (x) 2 ψ (x) 2 2(R R )cos(2k x x) (2.25) This is the spin charge density for only one electron, and in order to calculate the total spin density due to all electrons present in the spacer we have to integrate this over all possible k x s up to the Fermi wave vector k F, resulting in ˆk F 0 2(R R )cos(2k x x)dk x = (R R )sin(2k F x) x (2.26) The spin density has an oscillatory behavior with respect to the distance from the point of reflection, and has a period of π/k F. As the distance to the second magnetic layer increases, the sign of the spin density changes from positive to negative and back. If the total spin density is positive at a certain position, a net spin up is found and when the total spin density is negative a net spin down is found. The second FM layer placed at a certain distance from the first FM layer will experience a net

33 CHAPTER 2. THEORY 27 J RKKY (x)) d) 2d) 3d) 4d) 5d) 6d) x) Figure 2.20: Example of aliasing. The spacer layer thickness is quantified as a multiple of the interatomic distance d. This results in a larger period for the measured oscillation. spin up or net spin down density, and the magnetization of the second layer will align itself with the local spin polarization, being either parallel or anti-parallel, depending on the distance between the two magnetic layers and thus leading to an oscillatory coupling Bruno s model The model described in the previous section is a simplified phenomenological model, however it shows that two FM layers can be coupled via conduction electrons in the spacer layer. Bruno developed a more realistic model based on a bulk band structure of the spacer material and a spin-dependent reflection amplitude at the FM/NM interfaces. With this approach, he showed that the interlayer exchange coupling for large spacer layer thickness x is then given by [5] J RKKY (x) = J 0 x 2 sin(2k F x) (2.27) For a complete derivation of this formula the reader is refered to [5]. The period resulting from this theory ( λ F 2 ) is shorter than any experimentally observed period. However, it has been shown [7][8] that in this theory, the spacer thickness x is assumed to be a continuous variable and that in reality the distance between the FM monolayers is x = (N +1)d, with d the space between the atomic planes and N the number

34 CHAPTER 2. THEORY 28 of atomic planes in the spacer. This results in the fact that the interlayer distance is discrete, which leads to an effective period Λ resulting in a q vector given by 2π Λ = q n2π d (2.28) where n is such that Λ > 2d. This effect is also known as aliasing and is shown in figure Note that in this model, the magnetic layers are single monoatomic layers, and experimentally these layers are thicker. However, in his paper Bruno shows that the exchange coupling strength is in a first approximation independent of the thickness of the magnetic layers Influence of roughness on the RKKY-coupling In the past section we assumed that the layers are perfect and the location of the interface (and thus the point of reflection/transmittion) is well defined. In reality imperfections are present, such as roughness and interdiffusion. Roughness at the interface can lead to a varying thickness of the spacer layer. As the exchange coupling depends on the spacer layer thickness, this means that the net exchange coupling is an average over all the different couplings present. Another important effect of roughness at the interface is that the phase of the reflected electrons at the interface varies. The net spin density is the result of the summation over all the spin density waves of the individual electrons, and when the phases of these electrons vary widely the summation and thus the oscillating spin density will damp out quickly, resulting in a quick loss of the indirect exchange interaction. Roughness at the interface can also lead to additional coupling effects. As explained in section 2.4.1, correlated roughness can lead to orange peel coupling. Another coupling that can occur due to roughness is the biquadratic coupling which is the result of frustration between spins. The energy per unit area due to the biquadratic coupling is given by E biq = J biq cos 2 (θ) (2.29) where J biq is the biquadratic coupling strength and θ is the angle between the magnetizations of the two FM layers. The minimum energy is found when the magnetizations have an angle of 90 between eachother The thermal stability of the RKKY-coupling effect As explained in Chapter 1, in order to build a stable SAF-based spin valve system applicable in the automotive industry, the RKKY-coupling between the two FM layers must be stable at high temperatures. When the temperature is increased there are three main effects that can affect the interlayer coupling which should be

35 CHAPTER 2. THEORY 29 considered [22] : (i) the intrinsic temperature dependence, (ii) the temperature dependence deriving from the disordering of magnetic moments and (iii) the extrinsic temperature dependence The intrinsic temperature dependence As shown in the previous section, the oscillatory behavior of the exchange coupling strongly depends on the Fermi wavevector. The theory is based on a fermi distribution for the occupied states, and for non-zero temperatures the distribution of states is equal to 1 n i = e (E i/k b T ) + 1 In which E i is the energy of the specific state, k b is the boltzmann factor and T is the temperature. Finite temperatures smooth out the step function for the occupied density of states, which smooths out the oscillations of the interlayer exchange coupling J RKKY. The amplitude of the exchange coupling is thus expected to decrease for increasing temperature, while the period remains unchanged The temperature dependent disordering of the magnetic moments The interaction of the magnetization with the conducting electrons at the interface is the mechanism that creates the RKKY-coupling. Besides the intrinsic temperature dependence of the free electrons, the temperature dependence of the magnetization has to be considered as well. At finite temperatures, the magnetization will decrease due to thermal agitation. The amount of reduction is related to the temperature: for increasing temperature, the magnetization will decrease, untill the Curie temperature T c is reached. At this temperature, the magnetic ordering disappears and the system is in a paramagnetic state. Especially around T c the loss of magnetization increases rapidly and it has been shown that [23] for thicker FM layers the RKKY-coupling decays linearly and slowly with T, and for the monolayer limit the RKKY-coupling decays with T ln(t ) Extrinsic temperature dependence When an SAF is annealed at high temperatures, interdiffusion of the FM layers and the spacer layer can occur. The interdiffusion of the layers leads to a less well defined interface between the spacer layer and FM layers, thus leading to more roughness. As explained in section 2.4.5, this can result in the RKKY-coupling damping out more rapidly and additional coupling interactions such as pinhole coupling for thin spacer layers, and additional biquadratic coupling due to frustrations between spins. An additional coupling which can lead to biquadratic coupling is the so-called loose spin coupling [24]. This coupling originates from loose spins that are present in the spacer

36 CHAPTER 2. THEORY 30 layer, for instance when a FM spin is diffused into the spacer layer material due to annealing. The loose spins interact with the FM layers via the RKKY interaction, and the loose spins contribute to an effective exchange coupling between the FM films. The presence of loose spins in the spacer layer can thus effect the RKKYcoupling between the FM layers, resulting biquadratic coupling of the FM layers. 2.5 Theoretical magnetization curves of an SAF In order to understand the magnetization curves of an SAF, consider the total energy per unit area of an RKKY-coupled system which is given by [16] E = µ 0 HM F t F (cos(θ β)+cos(θ α))+k F t F (sin 2 (α)+sin 2 (β)) J RKKY cos(β α) In which the first term is the Zeeman energy term for both FM layers, the second term is the magnetocrystalline energy term of the FM layers and the third term is the RKKY-coupling term. J RKKY is the RKKY coupling coefficient which oscillates with increasing spacer layer thickness as described in the previous sections, and when the FM layers are coupled antiferromagnetically to create an SAF, J RKKY < 0. In this thesis, polycrystalline Co layers are used and the anisotropy can be considered neglegible. Minimizing the total energy with respect to α and β result in magnetization curves shown in figure The angles used in this model are shown in figure As an increasing field is applied, the magnetization will slowly align with the field. The applied field is fighting the RKKY-couping. When the applied is high enough to completely break the RKKY-coupling, the magnetizations are aligned parallel with the field. The field at which this occurs is the saturation field. The RKKY-coupling coëfficient is proportional to the saturation field and is equal to J RKKY = µ 0H sat M s t 2 (2.30) 2.6 Combining the SAF and EB As explained in Chapter 1, EB is combined with RKKY-coupling to create a pinned multilayer with no net magnetic moment as part of the GMR/TMR. This pinned multilayer is shown in figure When the SAF and EB are combined, the total energy of the system becomes E A = µ 0 HM F t F (cos(β) + cos(α)) + K F t F (sin 2 (α) + sin 2 (β)) J RKKY cos(β α) J EB cos(β) (2.31) The first term is the Zeeman energy term of the two FM layers, the second term is the anisotropy term of the FM layers, the third term is the RKKY coupling coëfficient

37 CHAPTER 2. THEORY 31 Field)cooling)direc5on) z) x) μ 0 H) M) H sat ) H sat ) H) Figure 2.20: Example of a magnetic loop of an SAF for K F =0. At zero field, the FM layers are coupled antiferromagnetically. When a field is applied, the magnetizations align gradually with the field direction, untill they are completely aligned. The field at which the magnetizations completely align is the saturation field, which is proportional to the RKKY-coupling strength. Hard)axis) Easy)axis) θ) H) M F ) α) K F ) Ferromagne5c)layer) Spacer)layer) Ferromagne5c)layer) M F ) β) K F ) Figure 2.21: Angles of the magnetizations and the field directions in an SAF system. coupling the two FM layers and the fourth term is the EB term, coupling the AF layer with the bottom FM layer. Assuming that there is no anisotropy and minimizing the total energy with respect to the angles of the magnetizations α and β results in the magnetic loops as shown in figure Combining EB with the AF RKKY-coupling results in a plateau when a small field is applied. The EB pins the magnetization of the bottom FM layer, which is

38 CHAPTER 2. THEORY 32 Ferromagne5c)layer) SAF) Spacer)layer) Exchange)) bias) Ferromagne5c)layer) An5ferromagne5c)layer) Figure 2.22: Illustration of a pinned multilayer containing an SAF and EB. Field)cooling)direc5on) z) x) μ 0 H) M) H sat,2 ) H sat,1 ) H EB ) H) H 1 ) H 2 ) Figure 2.23: Schematic representation of a magnetic loop for an EB-SAF stack. At small fields, a plateau is found. When an external field is applied opposite to the field cooling direction, the EB and the AF RKKY-coupling needs to be broken. When a field is applied along the field cooling direction, only the RKKY-coupling needs to be broken. This asymmetry results in a shift of the hysteresis loop. antiferromagnetically coupled to the top FM layer. When the field that is applied is not strong enough to either break the AF RKKY-coupling or the EB, the magnetizations will not rotate and the FM layer remains pinned. The asymmetry of the EB results in a shift in this plateau: when a field is applied opposite to the field cooling direction, the magnetization of the bottom FM layer experiences a torque. In order to rotate this layer, the field needs to be large enough to overcome both the EB

39 CHAPTER 2. THEORY 33 and the RKKY-coupling. The field required to break the EB and RKKY-coupling is equal to H 2 = J RKKY + J EB µ 0 M F t F (2.32) When a field is applied along the field cooling direction, the top layer will experience a torque. In order to rotate this layer, only the RKKY-coupling needs to be overcome. The field required to do this is equal to H 1 = J RKKY µ 0 M F t F (2.33) This asymmetry between these fields results in a shift of the loop. This shift (H 2 +H 1 ) can be measured and is the EB field. The value of the EB field can be measured over time to investigate the stability of the EB over time.

40 Chapter 3 Experimental setup This chapter describes the experimental setups used to fabricate and measure samples used in this thesis. In the first section the sputtering deposition technique is described which was used to grow all samples. In the next section the Magneto-Optical Kerr Effect (MOKE) and the Vibrating Sample Magnetometer-Superconducting QUantum Interference Device (VSM-SQUID) used to magnetically characterize the samples are introduced. The third section covers the annealing setups dedicated to set the EB and anneal the samples in order to explore the thermal stability of our samples. In the fourth and final section, the different sample stack structures are introduced. 3.1 The sputter system All samples used in this thesis were fabricated using the CARUSO sputtering system. This system is a magnetron sputtering deposition technique able to deposit subnanometer layers of materials. Samples are inserted using a load-lock system. This system is connected to the main sputter chamber which is an ultra-high vacuum chamber with a base pressure between 10 7 and 10 8 mbar The deposition process Within the main sputter chamber, 6 targets are placed which make it possible to deposit multilayer materials. The sputtering is done in a continous current process which is shown in figure 3.1. To start the deposition, an Argon gas is inserted into the chamber to increase the pressure up to 10 2 mbar. Next a large voltage is applied across the cathode and anode, creating an Argon plasma. The Argon ions are accelerated towards the (negatively charged) target where they will collide with the target atoms. Target atoms will be released from the target itself and will be deposited on the substrate. In order to increase the ionization rate of the Argon near the targets, magnets behind the targets are used to confine electrons close to the target. This increases the ionization rate of Argon near the target resulting in 34

41 CHAPTER 3. EXPERIMENTAL SETUP 35 Figure 3.1: Schematic representation of a target system for the magnetron sputtering deposition technique. An Argon ion is accelerated towards the target. When the ion hits the target, an atom is knocked of which condensates at the substrate surface. more collisions between Argon ions and target atoms which increases the deposition rate. By calibrating the deposition rate of the different target materials, control over the thickness of all the layers in complex multilayers can be obtained. In order to grow wedged samples, a wedge mask is used. During the deposition process, the wedge mask is located close to the sample surface in order to prevent shadowing. The mask protects part of the substrate from the incoming target atoms, preventing growth below the mask. By moving the mask gradually during the deposition process, a wedged sample with varying thickness can be created as shown in figure 3.2. The measurement of this wedge with local technics such as MOKE (see section 3.2) provides a fast method to study the thickness dependent effects Plasma cleaning Before depositioning the materials on a SiB substrate, the substrate is cleaned by means of plasma oxidation in the oxidation chamber. After the sample is inserted in the oxidation chamber, an O 2 gas is inserted in the chamber, increasing the pressure to mbar. A large electric field is applied, ionizing the gas and accelerating the ions towards the substrate. The ions bind with the impurities on the substrate and evaporate, removing any impurities. Since the oxidation chamber is directly connected to the main sputter chamber, in-situ cleaning is possible and the substrates will remain under high vacuum when transported to the main sputter chamber.

42 CHAPTER 3. EXPERIMENTAL SETUP 36 Figure 3.2: Illustration of the fabrication of wedged samples. The position of the wedge mask and the deposited material (blue) is shown at a) t= 0, b) 0 < t < t final to c) t = t final. 3.2 Magnetic characterization techniques In this section, the experimental setups that are used to characterize the magnetic properties of our samples are discussed. In section the MOKE setup is described. The MOKE setup is a quick and easy method to characterize the magnetic properties of a sample. However, in our setup measurements can only be done at room temperature and a maximum field of 0.4 T can be applied. For measurements at higher fields and different temperatures, the VSM-SQUID is used. This setup is explained in section The Magneto-optical Kerr effect setup The MOKE setup uses the fact that the polarisation (ellipticity and rotation) of light changes when it is reflected on a magnetic surface. By analysing the change in either ellipticity or rotation it is possible to extract the magnetic properties of the measured samples qualitively. In this section the MOKE setup will be presented. A schematic overview of the MOKE principle is given in figure 3.3. Light is linearly polarized before hitting the sample. Linear light is a combination of left- and right-handed circularly polarized light. When light hits a magnetic material, the left-handed circularly polarized light travels with a different speed through the magnetic material and has a different absorption rate as compared to right-handed circularly polarized light. The difference in absorbtion rate results in the linear light becoming elliptic and the difference in speed causes a phase difference, resulting in a net rotation. By analysing either the difference in rotation or the ellipticity of the reflected light as compared to the light before hitting the magnetic material, qualitive information about the magnetization in the magnetic material can be obtained. The MOKE principle is a very easy and fast method to measure hysteresis loops of magnetic samples. Another advantage is that due to the small laser spot size ( 300µm) the magnetization is measured locally, which is needed to analyse wedges.

43 CHAPTER 3. EXPERIMENTAL SETUP 37 Figure 3.3: Schematic representation of the MOKE principle. The change in rotation and ellipticity after linear polarized light reflects from the surface of magnetic material provides information on the magnetization in the sample The Vibrating Sample Magnetometer - Superconducting QUantum Interference Device (VSM-SQUID) In order to characterize the magnetic properties of magnetic samples at different temperatures and applied fields, the Vibrating Sample Magnetometer (VSM) - Superconducting QUantum Interference Device (SQUID) is used. With this setup quantitive information of the magnetization is obtained, and saturation and coercive field values can be extracted. Figure 3.4 illustrates a VSM-SQUID setup used during this thesis to characterize magnetic samples. As shown in the left part of the figure, a magnetic sample is placed between four detection coils. Vibrating this magnetic sample leads to a gradiant in the spatial magnetic field produced by the sample, causing a voltage over the detection coils. The voltage produced in the coils is proportional to the magnetic moment in the sample. This is used to magnetically characterize the sample. The VSM uses a multi-coil configuration, a so-called second-order gradiometer, which removes the zeroth and first spatial derivative of the magnetic field The SQUID-setup Measuring the voltage directly from the VSM using a voltmeter is possible, however to increase the sensitivity of the measurement, a SQUID-sensor is used. With this SQUID-sensor a sensitivity in the order of A m 2 can be obtained, where using regular coils a sensitivity of only 10 8 A m 2 can be obtained. As shown in the right part of figure 3.4, the SQUID is inductively coupled to the VSM-setup and consists of two superconducting regions seperated by two so-called Josephson junctions. Within the superconductor, an input current I is present. When the flux within the loop changes due to the induction field from the VSM-setup, a screening current is produced within the superconducting ring, in order to produce a screening

44 CHAPTER 3. EXPERIMENTAL SETUP 38 Figure 3.4: Illustration of the VSM-SQUID system. The VSM-setup (left) is inductively connected to the SQUID-setup (right). flux to cancel the change in flux. The superconducting properties of the ring quantize this induced screening flux as a multiple of the quantized magnetic flux φ 0. Since φ 0 is small, the resolution of a SQUID is high and the flux coming from the magnetic sample can be measured very precisely. 3.3 Annealing techniques In this section, two annealing techniques used during the annealing of samples in this thesis are presented. First, the Argon oven annealing technique is described. Secondly, the annealing of samples in the oven module of the VSM-SQUID setup is presented The Argon oven The Argon-oven is a self-build oven module used to anneal samples while applying an external magnetic field. The oven setup is depicted in figure 3.5. As shown in this figure, the sample is placed in a closed tube using a sample holder stick. The tube is filled with an Argon gas. When annealing the sample, a current is sent through a wire within the tube, heating up the sample. A thermocouple within the sample holder stick provides feedback on the temperature within the tube. The tube is placed in an electromagnet. The sample holder can be rotated, making it possible to apply fields both in-plane and out-of-plane. In this thesis, only in-plane annealing is used to set the EB. When the effect of different annealing temperatures on the

45 CHAPTER 3. EXPERIMENTAL SETUP 39 Figure 3.5: The Argon oven setup used to anneal samples. The sample is placed in a closed tube filled with Argon gas to prevent oxidation of the sample. The sample is heated through a heating wire. The electromagnet surrounding the tube allows a field to be applied during the annealing procedure which is required to set the EB in the samples. magnetic properties of the SAF is investigated, no external magnetic field is applied during the annealing process. With this setup, no magnetic measurements can be done while the sample is heated. To measure samples at different temperatures, the oven module of the VSM-SQUID setup is used, and it will be described in the next section The VSM-SQUID oven module The VSM-SQUID setup has an oven module in which samples can be annealed. With this module the sample stick holder is attached to a heating module, allowing the annealing of the sample through the sample stick. This allows measurements to be done at different temperatures. 3.4 Sample stack structure During this thesis, samples with varying layout and materials are studied. The magnetic behavior and temperature stability of the RKKY-coupling effect are studied by growing samples only containing an SAF. Other samples containing both an SAF and a F/AF bilayer are produced and magnetically characterized in order to investigate the field stability of an EB-RKKY-coupled system. Both groups of samples will be discussed in the next two sections. In this thesis, when standard growth conditions are mentioned it means that the Ta, Ru and Cr layers are grown at a pressure