Current-induced switching in a magnetic insulator

In the format provided by the authors and unedited. DOI: 10.1038/NMAT4812 Current-induced switching in a magnetic insulator Can Onur Avci, Andy Quindeau, Chi-Feng Pai 1, Maxwell Mann, Lucas Caretta, Astera S. Tang, Mehmet C. Onbasli, Caroline A. Ross 2, and Geoffrey S. D. Beach 3 Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA S1. Reciprocal space mapping of a 30 nm thick TmIG film on GGG(111) The structural analysis is performed based on symmetric XRD scans (Fig. 1(a) in the main text) and reciprocal space mapping (RSM) of TmIG film grown on GGG(111). As illustrated in Fig. S1, the RSM result shows that, in case of a 30 nm-thick TmIG film on GGG(111), the respective (246) asymmetric diffraction peaks lie on one vertical line, sharing the same value for the interplanar spacing in [ 110]-direction. This can be interpreted as the TmIG being fully strained on top of the GGG substrate, leading to a rhombohedral distortion of its pseudocubic unit cell. The lattice parameter ratio of film bulk film bulk ( 444 444 ) ( 220 220 ) d / d / d / d = 0.985 is calculated using the structural data extracted from the RSM and the structural data for bulk TmIG in Ref. 1 (visualized in the figure by a red cross). 1 Current address: Department of Materials Science and Engineering, National Taiwan University, Taipei 10617, Taiwan 2 caross@mit.edu 3 gbeach@mit.edu 1 NATURE MATERIALS www.nature.com/naturematerials 1

q z // [111] (nm -1 ) DOI: 10.1038/NMAT4812 5.70 (246) diffraction TmIG 5.65 5.60 5.55 GGG 2.26 2.27 2.28 2.29 2.30 2.31 q x // [110] (nm -1 ) Figure S1 Reciprocal space map of fully strained TmIG on GGG(111). RSM around the (246) film- and substrate peaks. The dashed line is a visual guide to demonstrate that film and substrate peaks have the same q x -values. A comparison with a (246) diffraction peak of bulk TmIG is made by showing the value using a red cross in the figure. S2. Longitudinal spin Hall magnetoresistance measurements In the main text we mainly focused on the transverse measurements of the spin Hall magnetoresistance (SMR). However, the SMR does also modulate the longitudinal resistance as given in equation (1) [see main text]. In figure S2 we show the relative change in the resistance ( RR RR) when the magnetization (mm) is tilted in the zx and zy planes with an in-plane field applied along x (φφ! = 0 ) and y (φφ! = 90 ). We observe a decrease in the resistance when magnetization is tilted along the y-axis whereas the magnetoresistance is merely noticeable along the x-axis. This behavior is typical of the 2 NATURE MATERIALS www.nature.com/naturematerials 2

SMR reported in YIG/Pt system 2 and compatible with equation (1) given in the main text. Simulation based on the macrospin approximation and experimental parameters reproduce very well the angular dependence of the data expected from the SMR signal. The small increase of the resistance when the external field is applied along the x-axis can be interpreted in several ways. Due to the low signal-to-noise ratio and limitation in the applied field amplitude, it is not clear to us whether the signal saturates at higher fields or not. A non-saturating signal could indicate a field-induced Hanle magnetoresistance 3 (see further discussion in the next section). On the other hand, if the signal saturates at higher fields, proximity-induced polarization of Pt could give rise to a conventional anisotropic magnetoresistance, which would increase when m is tilted along the x-axis. Nevertheless, this set of data validates that the longitudinal/transverse resistance changes are mainly driven by the SMR as expected from magnetic insulator/normal metal systems. Figure S2 Longitudinal resistance measurements of TmIG/Pt. Relative change of the longitudinal resistance ( RR RR) is plotted as a function of in-plane field applied along 3 NATURE MATERIALS www.nature.com/naturematerials 3

(φφ! = 0 ) or across (φφ! = 90 ) the current injection direction. The resistance changes significantly as a function of mm controlled by the external field when tilted across the current direction, i.e. y axis, and it remains nearly constant when tilted along the current direction. Green curve is a simulation based on macrospin approximation and the experimental parameters. S3. Revealing the different contributions to the Hall voltage signal A convenient way to determine SMR, SMR-induced anomalous Hall effect (AHE), and the effective magnetic anisotropy field (HH! ) is to measure the transverse Hall voltage (VV! ) with a nearly in-plane field sweep at φφ! = 45, θθ! 90. Figure S3a shows such a measurement where we recognize several contributions, which we address individually. First, we recognize a small negative linear background signal, which we associate with the ordinary Hall effect (OHE, blue dashed line) due to the (unintentional) out-of-plane component of the external field. We subtract this contribution together with the sample-dependent offset (due to the misalignment of the Hall arms giving rise to a small resistance) and plot the data in Fig. S3b. Second, we observe that even after the OHE subtraction VV! is continuously increasing well above HH!. This field dependent signal identifies itself as the Hanle magnetoresistance 3 (MR) and follows approximately HH! (green curve). After subtraction of the Hanle MR we find the signal that is purely driven by the SMR and SMR-induced AHE. Due to the small out-of-plane component of the external field, mm switches between up and down states at 625±25 Oe, a value much larger than the coercivity obtained with the out-of-plane field sweep, as expected from PMA systems. When the external field is zero, mm points either up or down, and the difference in VV! (orange dashed lines) gives the AHE signal. The SMR signal indicated 4 NATURE MATERIALS www.nature.com/naturematerials 4

with the green bar is measured between the average VV! at HH = 0 and the maximum VV! after mm is fully saturated in-plane. Figure S3 Contributions to the Hall voltage signal. a, Raw data corresponding to VV! recorded during a field sweep between ±5000 Oe applied at φφ! = 45 and θθ! 90. We recognize a small linear background due to the OHE (blue dashed line). b, VV! after subtraction of OHE and a sample-dependent constant offset. We identify the Hanle MR HH! plotted in green. c, VV! after removing the Hanle MR from which we determine the AHE (orange dashed lines) and SMR (green dashed lines) contributions. The red curve shows the macrospin simulation based on the experimental parameters and the HH! value best fitting the data. By using the extracted AHE and the SMR values we performed macrospin simulations by assuming different HH! values. The red curve shows the best match to the data with HH! = 1500 Oe, which can also be approximately determined from the measured data by the field required to saturate mm in-plane where VV! shows no more variation. We note that this measurement is performed at the same current density (jj!"# = 2.1 10!! A/m 2 ) used for the second harmonic measurements and therefore HH! is considerably lower than the one reported in Fig. 2 (HH! = 2700 Oe), which was NATURE MATERIALS www.nature.com/naturematerials 5

measured at much lower current density. We conclude that the Joule heating considerably changes the magnetic anisotropy in TmIG/Pt films and one should be cautious about this when performing the second harmonic signal analysis. S4. High field behavior of the second harmonic signal and the spin Seebeck effect contribution As extensively studied in Ref. 4 the second harmonic signals can have additional contributions associated with the thermoelectric effects driven by random temperature gradients in the Hall bar device. Due to larger thermal conductivity of the GGG/TmIG bilayer with respect to the air surrounding the device, the accumulated heat from the Joule heating in Pt mostly dissipates towards the substrate creating a significant out-of-plane temperature gradient TT 4,5!. This TT! gives rise to the spin Seebeck effect (SSE) in TmIG creating a spin current jj! TT! with the polarization σσ mm. When jj! is injected into Pt a transverse voltage develops due to the inverse spin Hall effect with the symmetry VV!!" ~jj! σσ = zz mm. By assuming that TT! TT II! RR SSE is bound to generate a voltage proportional to II! and which shows up in the second harmonic signal 6 and mixes with the SOT-driven signal. The main difference between the SSE and SOT-driven signals is that the former depends only on the magnetization direction whereas the latter depends both on the magnetization direction and magnetic susceptibility to the current-induced fields. Therefore performing VV!! measurements at large fields can help to determine the origin of the second harmonic signals. 6 NATURE MATERIALS www.nature.com/naturematerials 6

Figure S4 High field behavior of the second harmonic signals. We note that VV!! is an order of magnitude larger when mm xx with respect to the signal when mm yy. This is due to the fact that the SSE dominates the signal in the former geometry and generates a much larger signal with respect to the SOT which mainly drives the signal in the latter geometry. Inset shows a zoom-in to the red curve. In Fig. S4 we compare the VV!! signals measured with a swept field of ±2300 Oe, at two different configurations. We note that this field value is considerably larger than the anisotropy value determined in the previous section (HH! = 1500 Oe), hence we expect that the SOT-driven VV!! significantly decreases at high fields. Signal at φφ! = 0 increases (decreases) with the increasing (decreasing) field and saturates at HH HH! where the magnetization is expected to be saturated in-plane. This behavior is typical of the SSE-driven thermal voltage where the SOT-driven signal is negligibly small. On the other hand the signal at φφ! = 90 (red) is relatively smaller but consistent with the SOT-driven signal (see inset for a zoom-in to the data): i) The sign changes depending on whether mm is in the up or down state, ii) The maximum signal is observed at HH 800 NATURE MATERIALS www.nature.com/naturematerials 7

Oe which is approximately half of HH! where mm has maximum susceptibility to current-induced fields, iii) at high HH the signal drops to around its value recorded at HH = 0 where no SOT-driven signal is expected. We observe an asymmetry in VV!! taken at φφ! = 90 (more visible in the inset) which we associate with a small SSE signal contribution due to the misalignment of HH with respect to the y-axis and will be discussed in more details in the following section. S5. Simulations of the second harmonic signals In order to understand the different slopes observed in second harmonic measurements which also contribute to the asymmetry reported in Fig. S4-inset we performed macrospin simulations. We therefore computed the equilibrium magnetization position by considering all effective torques acting on it, i.e. the external field (TT! ), perpendicular magnetic anisotropy (TT! ), demagnetizing field (TT!"# ) which are the static parameters, and field-like (TT!" ) and damping-like (TT!" ) torques as dynamic (current-induced) parameters. In equilibrium the sum of these torques is equal to zero: TT! + TT! + TT!"# + TT!" + TT!" = 0. (S1) At each simulation point, i.e. a different external field, we compute the equilibrium angle of the magnetization (θθ and φφ) in an iterative way, in order to satisfy the torque equation above in 3D space. Once the sum of the torques satisfies the convergence criterion for equilibrium we use the computed angles to calculate the Hall effect voltage given by Equation (2) of the main text by inserting the SMR, AHE and OHE coefficients as determined in Sect. S3. We repeat this procedure for positive and negative current by 8 NATURE MATERIALS www.nature.com/naturematerials 8

changing the sign of TT!" and TT!". The difference of these two signals computed for opposite polarity of the current gives VV!, and the sum gives VV!! due to the SOT. Finally, we add the voltage contribution from the SSE to VV!! as determined from Fig. S4. Figure S5 shows the raw data (a) and the simulations performed for two different field angle and SOT scenarios (b and c). First, we address the two SOT scenarios. The blue curves are the simulations where only the damping-like SOT is considered, whereas the red curves show the simulations when both damping-like and field-like SOT are taken into account. As discussed in the main text, we observe that the signal is dominated by HH!" even though HH!" is chosen to be as large as HH!". This result is due to the fact that the SMR coefficient is much larger than the AHE coefficient, therefore VV!! is mainly driven by the in-plane oscillations to the magnetization which is generated by HH!" in this geometry. Figure S5 Comparison between measured and simulated second harmonic signals. a, Raw VV!! data taken with the field supposedly applied along y-axis. b, Simulations by considering HH!" (blue curve) and HH!" + HH!" (red curve). We note that the signal is mainly driven by HH!" and adding HH!" to the simulations makes a difference of approx. 7% which remains within the error bar of HH!" reported in the main text. c, Simulations at slightly different in-plane angle of the applied field. We observe that a non-negligible NATURE MATERIALS www.nature.com/naturematerials 9

SSE signal gives rise to the asymmetry very similar to the raw data shown in a. Second, we discuss the influence of the in-plane field angle on VV!!. When the field is applied at φφ! = 90 the second harmonic signal is perfectly symmetric for positive and negative fields, as expected. On the other hand, when we simulate the same signal for φφ! = 89.2 (the angle is arbitrarily chosen) we obtain a slight asymmetry very similar to the raw data reported in (a). This asymmetry is due to the SSE contribution when mm has a +xx ( xx) component with positive (negative) applied field. Furthermore the simulations corresponding to VV! reproduce very well the asymmetry reported in Fig. 3b of the main text (not shown). These results further support our initial assumptions made on neglecting HH!" and the SSE origin of the different slopes in Fig.3c (main text), and validates our analysis to accurately quantify HH!". Finally we would like to comment on the quantitative comparison between the simulations and the measurement. Since the parameters used in the simulations are very similar to that measured, we expect that they are quantitatively comparable. We notice that the total amplitude of the signal in Fig. S5a and c are very close to each other within 10% of accuracy. This result corroborates with our analysis and validate the SOT quantification. S6. Switching measurement protocol and reference measurements In this section we explain in detail the switching measurements procedures and compare the switching polarity to that of a reference sample with well-known characteristics. In order to observe the switching effect we have created a measurement sequence where we apply an in-plane field (HH! ) simultaneously with the current pulse of 10 NATURE MATERIALS www.nature.com/naturematerials 10

5 ms, and then we apply a negative and positive out-of-plane field (±HH! ) which serve as reference measurements for mm!" and mm!"#$. Figure S6a upper panel shows such a sequence which takes 1 s in total. HH! shown in magenta is ramped (rather than pulsed) due to experimental limitations, and at the peak of HH! a short voltage pulse is applied to the sample along the x-axis. The system was then allowed to settle any transient discharging effects and the Hall voltage (VV! ) is averaged for 30 ms (gray region #3) just before the HH! pulses. We then applied HH! and +HH! after which we acquired VV! during 30 ms (regions #1 and #2, respectively). We finally compare VV! recorded after the pulse injection to the difference of VV! between region #2 and #1 which gives a value between 1 and 0 corresponding to switching and non-switching events, respectively. This sequence is repeated ten times for a given pulse amplitude and/or HH! to construct the data set reported in Fig. 4b and c of the main text. In Fig. S6a bottom panel we show an exemplary VV! signal recorded during one measurement sequence. We observe several interesting features. First, we recognize a very large transient signal during pulse injection which goes out of the scale of this plot. The transient signal relaxes during the next 300 ms (approx.) and by the time that the measurement is performed at 750 ms, there is no more transient signal and VV! is representative of the magnetization state driven by AHE. We note that magnetization does (does not) switch with a positive (negative) pulse. We also observe an increase (decrease) of VV! during HH! (+HH! ). This is due to the OHE contribution which disappears after removing the field. Overall, we find that for TmIG/Pt sample a positive HH! together with a positive current jj stabilizes mm!"#$ whereas opposite polarity of HH! and jj stabilizes mm!". 11 NATURE MATERIALS www.nature.com/naturematerials 11

Figure S6 Acquisition of exemplary data points for the SOT switching hysteresis loop and comparison with reference data. a, Top panel: Field and applied voltage vs. time during a single data point acquisition sequence. Bottom panel: Hall voltage measured throughout the sequence. Gray regions indicate data utilized to determine whether switching has occurred or not. Region #3 measures the effect of the pulse injection, region #1 and #2 are references for mm!"#$ and mm!", respectively. b, Similar measurements performed on Pt/Co layers, serving as reference. In Fig. S6b we show similar measurements performed in Pt/Co PMA layers in exactly the same field and pulse configurations. In this system the switching is demonstrated by several groups (see e.g. references 7,8 ) and it is know to be mediated by the torque from the spin Hall effect in Pt. Therefore this can be used as a reference measurements to confirm the switching polarity and examine whether the switching in TmIG/Pt is driven by the SHE in Pt or not. We note that due to much higher signal-to-noise ratio the measurement time is reduced to 0.5 s. We observe that the 12 NATURE MATERIALS www.nature.com/naturematerials 12

negative pulse switches mm more than 50% (red curve), whereas the positive pulse has no effect on mm (blue curve). This result is opposite to what was found for TmIG/Pt and compatible with the SHE-induced switching scenario since Pt position with respect to the magnetic layer is opposite in these two cases. S7. Estimation of Joule heating due to current injection Figure S7 Estimated temperature rise (ΔT) of Pt layer due to current injection. In order to estimate the temperature rise due to Joule heating we placed a device on a heating plate and measured the resistance by systematically increasing the plate temperature. By assuming that the heating plate and the sample are in thermal equilibrium we obtained the relation resistance versus temperature. By using the resistance versus current density data, measured independently, we obtained the direct relation between the temperature rise (ΔT) and j (see Fig. S7). We note that the temperature rise is significant (negligible) above (below) j=1x10 11 A/m 2, indicating that the Joule heating might play an important role to facilitate switching for relatively high 13 NATURE MATERIALS www.nature.com/naturematerials 13

current densities. We also note that the estimation of Joule heating is likely to be an overestimation since current spread towards the Hall branches would decrease the net current density in the central region of the Hall cross hence creating lower Joule heating in the active area of the device. References 1. Botdorf & McCarthy. XRD on TmIG. (1971). 2. Chen, Y. T. et al. Theory of spin Hall magnetoresistance. Phys. Rev. B 87, 144411 (2013). 3. Vélez, S. et al. Hanle Magnetoresistance in Thin Metal Films with Strong Spin-Orbit Coupling. Phys. Rev. Lett. 116, 016603 (2016). 4. Avci, C. O. et al. Interplay of spin-orbit torque and thermoelectric effects in ferromagnet/normal-metal bilayers. Phys. Rev. B - Condens. Matter Mater. Phys. 90, 1 11 (2014). 5. Avci, C. O. et al. Unidirectional spin Hall magnetoresistance in ferromagnet/normal metal bilayers. Nat Phys 11, 570 575 (2015). 6. Vlietstra, N. et al. Simultaneous detection of the spin-hall magnetoresistance and the spin-seebeck effect in platinum and tantalum on yttrium iron garnet. Phys. Rev. B - Condens. Matter Mater. Phys. 90, 1 8 (2014). 7. Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189 193 (2011). 8. Liu, L. Q., Lee, O. J., Gudmundsen, T. J., Ralph, D. C. & Buhrman, R. A. Current-Induced Switching of Perpendicularly Magnetized Magnetic Layers Using Spin Torque from the Spin Hall Effect. Phys. Rev. Lett. 109, 96602 (2012). 14 NATURE MATERIALS www.nature.com/naturematerials 14