Large unidirectional spin Hall and Rashba−Edelstein magnetoresistance in topological insulator/magnetic insulator heterostructures

The recently discovered unidirectional spin Hall magnetoresistance (USMR)^1,2 is very interesting from both scientific and engineering perspectives. In a bilayer structure consisting of a ferromagnetic (FM) layer and a non-magnetic (NM) heavy metal layer, the USMR originates from interactions between the spin-polarized electrons at the interface generated by the spin Hall effect (SHE) in the NM layer and spin conduction channels in the FM layer; its strength is proportional to the projection of the magnetization in the FM along the direction of spin polarization at the FM/NM interface. From an engineering perspective, the USMR is particularly interesting for spin–orbit torque (SOT) switching devices since it possesses a unique symmetry that is sensitive to 180° magnetization changes. The standard approach to designing SOT devices involves a three-terminal geometry. Two of the terminals are used for writing by switching the magnetization state of a FM via a current through the spin Hall channel.³ The third terminal is a full magnetic tunneling junction (MTJ) structure, which serves as the means to read the magnetization state of the SOT device.³ Although the physical processes underlaying USMR are similar to those responsible for the spin Hall magnetoresistance^4,5 and the Rashba–Edelstein magnetoresistance,⁶ the USMR is in a separate category due to its electrical nonlinearity and unique unidirectional symmetry. The USMR effect enables the simpler design of SOT devices that only needs two terminals.

Despite these advantages, prior measurements of USMR have yielded signals that are still too small to be practical. In a FM/NM system, the amplitude of the USMR peaks at the NM thickness of about a few times of the spin diffusion length^1,7 and is ultimately limited by the spin Hall angle of the NM, which characterizes the capability of converting a charge current into a transverse spin current. Topological insulators (TIs) are a class of materials that have evoked great interest in this context. While the bulk is ideally electrically insulating, the surfaces conduct spin polarized charge currents due to “spin-momentum locking” (SML).^8–11 In order to reflect the fact that the spin generation relies partially on the topological surface states and exhibiting the Rashba–Edelstein effect,¹² the term unidirectional spin Hall and Rashba−Edelstein magnetoresistance (USRMR) is used in systems involving TIs.¹³ Thanks to the TI's high efficiency in converting surface and bulk charge currents into a spin current even at room temperature,^14,15 it is natural to expect that the USRMR in FM/TI systems may be much larger than the USMR in FM/NM heterostructures. Indeed, recent measurements of Bi₂Se₃ (BS)/CoFeB demonstrate this expectation.¹³ However, the metallic FM layer in such heterostructures shunts most of the injected current. The current flowing in the TI is, thus, small and fails to generate significant spin accumulation at the interface. In this work, we demonstrate the USRMR effect in a device that avoids current shunting by using a magnetic insulator (MI)/TI bilayer consisting of an insulating ferrimagnetic thin film substrate (yttrium iron garnet, Y₃Fe₅O₁₂, YIG) on which we grow a TI thin film (Bi₂Se₃, BS).¹⁶ Our work presents the first observation of the room-temperature USRMR in the MI/TI system. At 150 K, we observe a record amplitude of the USRMR per current density per total resistance, about five times larger than that in the metallic CoFeB/Bi₂Se₃ system¹³ and an order of magnitude larger than the highest values reported in all-metal Ta/Co bilayers.¹ Notably, this is a large effect even in non-ideal TI films (Bi₂Se₃) with both bulk and surface conduction.¹⁷ 

In addition, we show how the observation of USRMR in MI/TI devices leads to a useful device functionality. Extensive studies have explored the paths to achieve current-induced magnetization switching with TIs in a variety of materials combinations: TI/FM bilayers,^18,19 TI/conductive ferrimagnet bilayers,²⁰ magnetic TI/TI bilayers,²¹ and NM/perpendicular MI bilayers.²² In this paper, we demonstrate a prototype memory device wherein current-induced magnetization switching in TI/MI bilayers, aided by an Oersted field, is read out electrically via USRMR. This could be a first step toward implementing a spin switch concept that was proposed based on TI materials.²³ 

The phenomenon of the USRMR in a YIG/BS bilayer is sketched in Fig. 1. In the presence of a charge current j in the BS layer, spin-polarized electrons are generated at the YIG/BS interface due to the SML as well as spin–orbit coupling (SOC) in the bulk. The magnetization of YIG at YIG–TI interface alters the scattering of the spin polarized electrons generated by the TI. Depending on the relative directions between the spin polarization of electrons at the interface and the magnetization in the YIG, different resistance is induced because of spin-dependent scattering. The USRMR switches state when either magnetization is reversed (as shown in Fig. 1), or electrical bias polarity is reversed (not shown). We observed the USRMR effect at temperatures between 70 and 300 K in YIG(30 nm)/BS(t)/Al(4 nm) structures with t = 6, 8, and 15 quintuple-layer (QL). The YIG layer is first deposited on a single-crystal (111) gadolinium gallium garnet (Gd₃Ga₅O₁₂, GGG) substrate in an ultrahigh vacuum sputtering system at room temperature and is then annealed in situ in O₂ at 800 °C. Following the YIG deposition, the BS layer and the Al capping layer are grown in turn by molecular beam epitaxy (MBE). The thin film stacks used in this work and their characterizations are nearly identical to those in the work by Liu et al.²⁴ Hall bars with nominal length L = 50 μm and width W = 10 or 20 μm are fabricated by standard photolithography processes and tested with harmonic measurements in both longitudinal and transverse resistance configurations. For simplicity, we will refer to all samples as YIG/BS(t = 6, 8, or 15).

Figure 2(a) shows the longitudinal resistance measurement setup and the definitions of the coordinates and rotation planes. Note that the sample in this figure is “inverted” relative to the sketches in Fig. 1. The “+” and “−” signs and the arrow of j indicate the relative polarities of current source outputs and lock-in amplifier (LIA) inputs. Zero angles are at the +x, +z, and +z directions for the xy, zx, and zy rotations, respectively. The rotation directions for increasing angles are indicated by the arrows in the center area of the Hall bar. An external field of 3 T is applied and is rotated in the xy, zx, and zy device planes, while the first order resistance R_ω and the second harmonic resistance R_2ω are recorded using a sinusoidal AC with a frequency of ω/2π = 33 Hz and a peak amplitude of 707.1 μA. Figures 2(b) and 2(c) show the angle dependence of R_ω and R_2ω, respectively, of the YIG/BS(8) sample measured at 150 K for L = 50 μm and W = 20 μm. One can see that R_ω exhibits a behavior that differs from both the conventional anisotropic magnetoresistance and the spin Hall magnetoresistance since it varies only when the angle between the +z direction and the applied field changes. This is a result of the positive magnetoresistance in the TI.^25,26 In stark contrast, R_2ω varies with the angle between the +y direction and the magnetization, similar to the behavior observed previously in NM/FM bilayers.¹ One can clearly see that in Fig. 2(c), R_2ω varies with a period of exactly 360° for the xy and zy rotations but shows a flat response for the zx rotation. The amplitude of R_2ω is about 13.66 ± 0.14 mΩ at an average current density of 0.4419 MA cm⁻². Figure 2(d) shows the R_2ω vs magnetic field applied along the y direction, B_y. The R_2ω does not change significantly further up to 3 T once the magnetization of YIG is switched around a few mT. This is an indication that the R_2ω signal observed is likely not the unidirectional magnetoresistance (UMR), which was discovered in magnetic TI/TI bilayer systems, since UMR decreases rapidly at high field due to the decrease in magnon population^27,28 (more discussion in the third paragraph following this paragraph). This field dependence of R_2ω also allows us to exclude the bilinear magnetoelectric resistance discovered in a single TI layer, which is proportional to the magnetic field.²⁹ Note that during the measurements, R_2ω is read from the Y-channel of the LIA at a frequency of 2ω. Due to the nature of the harmonic measurement scheme and LIA, the reading is, in fact, −1/2 of the actual resistance change that would have been observed directly with a DC. In other words, R_2ω < 0 and R_2ω > 0 represent higher and lower resistances, respectively, under a forward current bias (j > 0) (see the supplementary material Note 2).

Figure 3(a) shows the Hall resistance measurement setup. The transverse Hall resistance is measured while the external field is rotated in the xy plane. Figure 3(b) presents the second-harmonic Hall resistance $R2ωH$ vs angle responses measured with the external fields of different strengths, as indicated. The amplitude of $R2ωH$ is much smaller than that of R_2ω. The measurements of the second harmonic Hall signal help to extract the contribution of thermoelectric effects in the second harmonic longitudinal signal. Due to Joule heating in the device while passing current for testing, both the anomalous Nernst effect (ANE) and the spin Seebeck effect (SSE) contribute to the R_2ω signal. To separate their contributions (denoted as $R2ωΔT$⁠) from the USRMR contribution, we carried out a series of measurements of $R2ωH$ for the xy-plane rotation in various external field strengths. The $R2ωH$ contains contributions from not only the ANE and the SSE but also the magnetization oscillations of YIG induced by field-like (FL) and damping-like (DL) SOTs. The contributions from the ANE, the SSE, and the DL SOT are all proportional to $cosφ$ while that from the FL SOT is proportional to $cos 3φ+cos φ$ (Ref. 30), where $φ$ is the angle of magnetization from the +x direction in an xy-plane rotation and follows the direction of increasing angle indicated in Fig. 3(a). Since the DL SOT and the FL SOT contribute to $R2ωH$ by perturbing the magnetization in the YIG, their effects diminish when the external field is very large. Figure 3(b) shows that the data measured with external field B_ext = 375 mT contain a dominant $cos φ$ contribution and a small $cos 3φ$ component, while with B_ext = 3 T, the data exhibit almost no angle dependence. We first obtain $R2ωH, ΔT$ by fitting the angle dependent data, allowing us to extract the amplitudes of the $cos φ$ and $cos 3φ$ components. The FL SOT contribution can then be easily determined and separated. This leaves the contributions of ANE/SSE and DL SOT. We plot the data corresponding to these contributions vs the reciprocal of total field, as shown in Fig. 3(c). In this figure, B_demag–B_ani is the demagnetization field minus the perpendicular anisotropic field of the MI layer, which is about 176 mT (Ref. 16) (also see the supplementary material Note 4 and Fig. S3). Since the effect of the DL SOT will diminish at infinite field, the intercept of the fitted line is the contribution of ANE/SSE to the second order Hall resistance. Then, the contribution of ANE/SSE to the longitudinal resistance R_2ω, $R2ωΔT$⁠, is obtained by scaling that from the Hall resistance, $R2ωH, ΔT$⁠, with a factor of the device's aspect ratio. Finally, the USRMR is determined once the ANE/SSE contribution is subtracted from the total R_2ω signal.

Figures 3(d) and 3(e) show the R_2ω, $R2ωΔT,$ and $R2ωUSRMR$ of the YIG/BS(6) sample and the YIG/BS(8) sample, respectively, at various temperatures. The current densities used are 1.0607 and 0.4419 MA cm⁻² at 300 K and other lower temperatures, respectively. The dimensions of the Hall bars for all data points in Figs. 3(d) and 3(e) are L = 50 μm and W = 20 μm, except for the one of the Hall bar tested of YIG/BS(8) at 300 K being L = 50 μm and W = 10 μm. The error bars in Figs. 3(d) and 3(e) indicate uncertainty bounds with 95% confidence (see the supplementary material Note 5). At lower temperatures, both YIG/BS(6) and YIG/BS(8) samples show very little thermoelectric effects and the USRMR contributes the most to the total R_2ω signal. While at 300 K, the thermoelectric effect is still weak in the YIG/BS(6) sample but becomes much more prominent in the YIG/BS(8) sample. This is possibly due to the 8 QL BS layer having larger resistivity, more volume and generating more heat than the 6 QL BS layer at 300 K with the same current density [see the supplementary material Note 1 and Fig. S1(a)].

The USRMR values after the removal of contributions of thermoelectric effects may still contain UMR, which originates from magnon-electron scattering. If the measured nonlinear magnetoresistance was UMR, the $R2ωH$ signals should be expected to be 1/3 of the amplitude of the R_2ω under the same external field strength in the xy rotation.²¹ However, based on the results shown by Fig. 3(b), the amplitude of the $R2ωH$ signal is much smaller than 1/3 of the amplitude of the R_2ω. Additionally, as mentioned previously, the UMR is expected to decay rapidly at high magnetic field. This is different than the USMR where it shows constant amplitude at high field. Our measurements of R_2ω [Fig. 2(d)] match better with the USMR picture. Furthermore, we attempt to analyze our R_2ω field dependency data with the methods developed by Avci et al.,³¹ which separates the contributions of both the magnon-electron-scattering UMR and the spin-dependent USMR. Although the sensitivity of fitting is poor due to the almost constant field dependency data, the fitting indicates that the UMR might be only a small portion (∼1/5) of the observed nonlinear magnetoresistance. Based on the above three qualitative and/or quantitative observations, we believe that our results may contain some of the magnon-electron-scattering contribution of UMR, but its contribution is only a small portion at most, and the USMR picture is dominant in our experimental results.

Figure 4 shows the USRMR per current density per total resistance (⁠$RUSRMR/R/j$⁠) and the sheet USRMR per current density (⁠$RsUSRMR/j$⁠) of all three samples as a function of temperature. The error bars indicate uncertainty bounds with 95% confidence (see the supplementary material Note 5). Note that $RUSRMR$ is defined as the amplitude of USRMR: $RUSRMR=12R±M,±j−R±M,∓j$ and $RsUSRMR$ is $RUSRMR$ normalized by device aspect ratio. We also would like to point out that the USRMR obtained by harmonic measurements, $R2ωUSRMR$⁠, is half of the $RUSRMR$⁠, by the nature of LIA and harmonic measurements. The sheet USRMR, $RsUSRMR$⁠, is also doubled from the harmonic measurement results, $Rs, 2ω USRMR$ (see the supplementary material Note 2). The $RUSRMR/R/j$ and $RsUSRMR/j$ provide more meaningful figure-of-merit for comparisons of USRMR across different thin film systems regardless of their testing currents and lateral dimensions. As shown in Fig. 4, these two values show very similar temperature dependent trends for the YIG/BS(6) and YIG/BS(8) samples. The largest $RUSRMR/R/j$ is found in the YIG/BS(8) sample at 150 K of 23.56 ± 0.48 ppm MA⁻¹ cm², and it is about an order of magnitude larger than the largest USRMR reported in the Ta/Co system¹ (also see the supplementary material Note 10 and Table S1 for more information). The largest $RsUSRMR/j$ is found in the YIG/BS(6) sample at 150 K of 27.31 ± 0.38 mΩ sq⁻¹ MA⁻¹ cm². This is about five times larger than that in the metallic CoFeB/Bi₂Se₃ system¹³ and an order of magnitude larger than the highest values reported in all-metal Ta/Co bilayers¹ (also see the supplementary material Fig. S7). The difference of $RsUSRMR/j$ between the YIG/BS(6) and YIG/BS(8) samples is almost constant across all temperatures despite the substantial change in their absolute values.

To better understand the temperature dependence of our YIG/BS systems, we characterize a thin film sample with a thicker 10 nm Bi₂Se₃ layer using polarized neutron reflectometry (PNR) to obtain the chemical composition and temperature-dependent magnetization at different fields as a function of depth. The thin film sample that we use for PNR is identical to samples utilized for USRMR measurements in terms of growth and has representative electrical transport properties (supplementary material Note 8). Additional information regarding the measurements and PNR data can be found in the Methods section, supplementary material Note 9 and Fig. S6. As shown in Fig. 5(a), the complex nuclear scattering length density (SLD) vs sample depth confirms that the thicknesses are near nominal values and display low interfacial roughness at the top surface of the YIG, Bi₂Se₃, and Al layers.

We find a thin transitional growth region (with a reduced structural density) at the bottom of the Bi₂Se₃, which was previously identified in electron microscopy characterization of nearly identical samples.³² As shown in Fig. 5(b), there is a weak proximity-induced magnetization near the YIG–BS interface, which is antiparallel to the YIG magnetization at low temperature, and decreases in magnitude to effectively zero at 300 K. This observation is consistent with earlier reports.^25,33–35 Such a proximity layer at the YIG–BS interface agrees with the USRMR picture. Analysis of the PNR shows that the interface between the GGG substrate and YIG film is heavily inter-mixed and requires a 2.5 nm intermediary layer to fit key features of the PNR data, consistent with previous reports detailing effects of Ga and Gd diffusion.^36–38 In addition to the field-dependent paramagnetic contribution from the GGG substrate, the magnetic SLD profile in Fig. 5(b) shows that the intermediary layer between GGG and YIG exhibits a strongly field and temperature dependent magnetization that is decoupled from the majority of the YIG film. At 50 K, the magnetization of the GGG–YIG intermediary layer is large and aligns antiparallel to that of the YIG and to the field. At 150 K, the magnetization of the intermediary layer is nearly zero, and at 300 K, it is aligned parallel to the bulk of the YIG with a reduced magnitude. This observation of a low temperature antiparallel magnetization in the intermediary layer at GGG–YIG interface was also described in prior studies.^36–38 

Our observation of temperature-dependent coupling from the intermediary region could help to understand the temperature dependence of the USRMR (Fig. 4), in particular the decrease in the USRMR with temperature below 150 K. The BS layer generates a pure spin current flowing into the YIG. The spin current can further propagate through the YIG reaching the GGG–YIG interface due to magnon-mediated spin transport. This interface can reflect some spin current back through the YIG to the BS–YIG interface. The amount of reflected spin current can alter the spin accumulation at the BS–YIG interface and, therefore, modify the USRMR. The magnetic intermediary layer at the GGG–YIG interface can act as a spin sink and relax the incoming spin current and reduce the reflected spin current. Since this intermediary layer magnetization is modulated by temperature, the spin accumulation at the YIG–BS interface and the resulting USRMR can also be expected to change with temperature. This could be a possible explanation for the observed non-monotonic temperature dependence of the USRMR with a peak at 150 K. Additionally, the TI's charge-spin conversion and the resulting total spin generation decrease at higher temperature.^39–41 This, along with the PNR observation that the proximity magnetization at the YIG–BS interface significantly decreases at 300 K, may further explain why the USRMR becomes small at 300 K. Also note that the dependency of the magnon-mediated spin transport on both external field⁴² and temperature⁴³ is expected to be insignificant for such short distance across the film thickness direction. Finally, YIG could have reduced spin current transport at lower temperature, which is indicated by reduction of spin pumping and increase in damping^44,45 (also see the supplementary material Note 4 and Fig. S3). Therefore, this could work together with the above-described mechanism of spin transport being modulated by the intermediary region magnetization, resulting in decreased USRMR at temperature below 150 K.

Recent studies have demonstrated current-induced magnetization switching with TIs in a variety of materials combinations: TI/FM bilayers,^18,19 TI/ferrimagnet bilayers,²⁰ magnetic TI/TI bilayers,²¹ and NM/perpendicular MI bilayers.²² However, current-induced magnetization switching of a MI using a TI has not yet been reported. Here, with the convenient aid of the USRMR, we demonstrate such magnetization switching with Hall bar devices. Figure 6(a) shows the testing sequence of the current switching and USRMR reading experiment. A switching pulse with an amplitude of I_write and a width of 0.2 ms is applied to the device. Then, a moderate AC I_read (1.1312 mA amplitude) is applied to allow the LIAs for reading the USRMR of the device, which tells the magnetization state. This cycle is repeated multiple times to complete a current switching hysteresis sweep. Figure 6(b) shows the R_2ω vs I_write of the YIG/BS(8) Hall bar sample of L = 30 μm and W = 20 μm at 150 K. At large negative current, the USRMR (R_2ω) is high, while at large positive current, the USRMR (R_2ω) is low. At I_write = 0, the USRMR (R_2ω) maintains two separate stable levels. This indicates that the magnetization of the YIG layer is manipulated by the charge current (more testing is done to rule out any temperature effect and time-dependent effect, see the supplementary material Note 6 and Fig. S4). The figure also indicates a critical switching current density smaller than 5.0 MA cm⁻² at 150 K, which is lower than the current density required to switch perpendicular MI, thulium iron garnet, with Pt at room temperature.²² It is comparable to or about one order of magnitude larger than that needed to switch a FM with a TI at room temperature¹⁹ and a perpendicular ferrimagnet with a TI at room temperature.²⁰ However, the coercivity of the device along the y-direction is much lower, being about 0.75 mT originally and at worst 0.35 mT after degradation (see the supplementary material Note 7 and Fig. S5). The Oersted field with 5.0 MA cm⁻² current density is about 0.25 mT. Therefore, although the experiment shows current-induced magnetization switching, the Oersted field contributes a sizeable portion of the switching. Note that the signal fluctuations seen in the maximum 8.0 mA (bluish green diamonds) curve in Fig. 6(b) is likely attributed to minor magnetic domain motions in the YIG layer of the Hall bar device.

In summary, we observed a nonlinear magnetoresistance that is sensitive to the magnetization component projected in the in-plane direction transverse to the current direction in MI/TI (YIG/Bi₂Se₃) heterostructures. The USRMR in this YIG/Bi₂Se₃ system was observable with a much lower current density compared to all metallic NM/FM bilayers. The large USRMR was attributed to the absence of current shunting by the insulating magnetic layer and better charge current utilization in the TI channel. Furthermore, the temperature stability of the YIG makes the USRMR even present at room temperature, which is crucial for future applications. The largest USRMR is observed at 150 K and is about an order of magnitude larger than the best USMR reported in the metallic Ta/Co system. The PNR study reveals an intermediary layer at the GGG substrate–YIG interface, of which the magnetization and its coupling to YIG magnetization are strongly temperature dependent. These observations help to explain the temperature dependence of the USRMR. Finally, a prototype Hall bar memory device with the YIG/Bi₂Se₃ bilayer, where its magnetization is switched by current and read by USRMR directly, was demonstrated. The large USRMR observed in the YIG/BS system would shed light on many new material systems that will potentially be good candidates for practical two-terminal SOT switching devices that can be read out by USRMR.

See the supplementary material for additional information.

This work was supported in part by C-SPIN, one of six centers of STARnet, a Semiconductor Research Corporation program, sponsored by MARCO and DARPA. This work was currently being supported in part by SMART, one of the seven centers of nCORE, a Semiconductor Research Corporation program, sponsored by the National Institute of Standards and Technology (NIST) and by the UMN MRSEC program under Award No. DMR-1420013. Parts of this work were carried out in the University of Minnesota Nanofabrication Center, which receives partial support from NSF through NNCI program and in the Penn State Two-Dimensional Crystal Consortium-Materials Innovation Platform (2DCC-MIP) under NSF Grant No. DMR-1539916. The work at CSU was also supported by NSF (Nos. ECCS-1915849; EFMA-1641989). The authors would also like to thank Timothy Peterson for his help on the usage of PPMS.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The YIG films were grown on GGG(111) substrates by RF magnetron sputtering at room temperature and then in situ annealed at 800 °C for 2 h under the oxygen pressure of 1 Torr, with a heating rate of 10 °C/min and a cooling rate of 2 °C/min.

After exposure to air, the YIG films were then transferred to either an EPI 620⁴⁶ MBE system or a Scienta Omicron EVO50⁴⁶ MBE system for the Bi-chalcogenide deposition. In the EPI 620 chamber, Bi₂Se₃ films were grown from high purity (5N) Bi and Se evaporated from Knudsen cells at a beam equivalent pressure flux ratio of 1:14. For Bi₂Se₃ films grown in the EVO50, the growth conditions were kept similar to those used in the EPI 620, but the Se was evaporated from a two stage cracker cell with the second stage of the cracker cell kept at 500 °C. The substrate temperature according to a radiatively coupled thermocouple was 325 °C (pyrometer reading of 250 °C), and the growth rate was 0.17 nm/min. The films have a root mean squared (RMS) roughness of approximately 0.7 nm over a 25 μm² area measured by atomic force microscopy (AFM). Film thickness was measured by x-ray reflectivity and crystal quality by high-resolution x-ray diffraction rocking curves of the (006) crystal plane. The latter show a full width half max (FWHM) of approximately 0.28°. A 4-nm-thick capping layer of Al was grown before each sample left the MBE chambers.

The thin film stacks were then fabricated with a standard photolithography process followed by an ion milling etching step to define the Hall bars. Then, a second photolithography process and an e-beam evaporation followed by a liftoff step were performed to make electrode contacts.

The devices were tested in a Quantum Design physical property measurement system (PPMS),⁴⁶ which provides temperature control, external field, and rotation. A sinusoidal AC of 33 Hz was supplied by a Keithley 6221⁴⁶ current source. A Stanford Research SR830⁴⁶ or an EG&G 7265⁴⁶ LIA together with an EG&G 7260⁴⁶ LIA was used to measure the first and second harmonic voltages, respectively, and simultaneously. For USRMR vs switching current measurements, each acquisition of data point consists of a switching stage in which the LIAs are broken from the device by a Keithley 7001⁴⁶ switch box and a rectangular current pulse is fired, and a reading stage, in which the LIAs are closed back to the device while a mild sinusoidal AC is applied, and device voltage is read back. In the reading stage, the LIAs continuously recorded readings every 0.2 s during the period of between the 10th second and 20th second since the application of the sinusoidal AC. Then, the mean and standard deviation of reading samples are used for plots.

Polarized neutron reflectometry measurements were carried out using the Polarized Beam Reflectometer instrument at the NIST Center for Neutron Research (NCNR). The incident neutrons (λ = 4.75 Å) were spin polarized parallel or antiparallel to the applied in-plane magnetic field ranging from 250 mT to 3 T. The temperature was varied in situ using a closed cycle refrigerator allowing for measurements between 50 and 300 K. The non-spin flip scattering cross sections (R⁺⁺ and R⁻⁻) were measured as a function of the momentum transfer (Q) normal to the surface of the film. The data were reduced with the REDUCTUS⁴⁷ software package and simultaneously model-fit using the REFL1D program.^48,49 The depth profiles of the nuclear and scattering length density were used to calculate the expected reflectivity, and the layer thickness, interfacial roughness, and complex nuclear and magnetic scattering length densities were fit to minimize χ². An intermediary layer between the GGG and YIG was included, where the magnetic scattering length density was fit and allowed to align parallel and antiparallel to the applied field, as suggested by previous works.^36,37 A transition growth region at the bottom of the Bi₂Se₃ layer was also included, consistent with prior characterization of similar samples.³² The nuclear SLD profile was constrained to be invariant with temperature and field, whereas the magnetization of each layer was allowed to vary. Finally, a 3 nm interfacial region of the Bi₂Se₃ near the YIG was allowed to be weakly magnetic in the model-fitting.