Field‐Free Switching and Enhanced Electrical Detection of Ferrimagnetic Insulators Through an Intermediate Ultrathin Ferromagnetic Metal Layer

Perpendicularly magnetized ferrimagnetic insulators offer great potential for the development of fast and energy‐efficient spintronic devices. However, a major challenge for these devices is the requirement of an auxiliary magnetic field to achieve spin‐orbit torque (SOT)‐driven magnetization switching, along with the extremely small electric read‐out signal from the adjacent heavy metal layer. In this work, an approach by introducing an ultrathin Co layer primarily with in‐plane magnetization at the interface of the Tm3Fe5O12/Pt bilayers, which enables field‐free deterministic switching of the perpendicular Tm3Fe5O12 layer is demonstrated. Meanwhile, it is observed that a large anomalous Hall resistance readout signal from the coupling‐induced perpendicular component of the interfacial Co, which is nearly two orders of magnitude larger than that observed in Tm3Fe5O12/Pt bilayers. The crucial role played by the Co layer in modifying the SOT is elucidated. This research represents a significant step toward the practical implementation of ferrimagnetic insulator devices.


Introduction
The electric manipulation and detection of magnetic states of ferromagnetic (FM) or ferrimagnetic (FiM) films are central issues in the field of spintronics, driven by their potential applications in magnetic memory and logic devices.In recent DOI: 10.1002/admi.2023006323][4] The SOT originates from the spin Hall effect (SHE) [5][6][7] in the HM layer and/or the Rashba-Edelstein effect [8][9][10] resulting from the symmetry breaking at the interface.In the case of the SHE, an in-plane electric current (J c ) applied in the HM layer generates a pure spin current (J s ) along the out-of-plane direction, with its spin polarization  perpendicular to both J s and J c . [1]However, achieving deterministic switching of a perpendicular magnetic layer through SOT typically requires an external magnetic field in the current direction to break the symmetry, which severely hinders practical applications. [1]To realize field-free electric manipulation of magnetization, several approaches have been proposed in all-metallic HM/FM structures.These include exploiting lateral structure asymmetry, [11] engineering interface, [12,13] introducing tilted magnetic anisotropy, [14] leveraging the effective field provided by exchange bias [15,16] or interlayer exchange coupling, [17,18] harnessing gradient-driven Dzyaloshinskii-Moriya interaction. [19]n comparison to metallic FM films, FiM insulator films such as rare earth iron garnet (REIG) films offer fascinating prospects for fast and energy-efficient spintronic device applications.The insulating nature of REIGs can eliminate part of Jouleheating-related dissipation. [20]Additionally, their low magnetic damping [21,22] and high-frequency magnetization dynamics [23] are desirable for ultra-fast domain wall motion and SOT-induced switching.To date, SOT-induced switching has been successfully demonstrated in various REIG heterostructures with PMA, including Tm 3 Fe 5 O 12 (TmIG), [24,25] Y 3 Fe 5 O 12 (YIG), [26] Tb 3 Fe 5 O 12 (TbIG), [27] Gd 3 Fe 5 O 12 (GdIG), [28] Ho 3 Fe 5 O 12 (HoIG), [29] and Tm substituted YIG (Y 1-x Tm x IG) [30] films with a HM overlayer of either platinum (Pt) or tungsten (W).However, achieving fieldfree switching of FiM insulators remains unexplored.Nonetheless, the electric detection of insulator magnetization previously relied on the extremely small anomalous Hall resistance, [31,32] which arises from the magnetic proximity effect [33] and/or the nonequilibrium SHE [34] in the HM layer.This readout signal is even 2-3 orders of magnitude smaller than the anomalous Hall effect (AHE) observed in transition FM metals.Additionally, a small room temperature tunneling magnetoresistance (TMR) was found in the magnetic tunnel junctions (MTJs) consisting of nonmagnetic metal (NM)/FiM insulator/FM metal.This TMR, originating from the spin filter effect of the insulating FiM, [35][36][37] directly reflects the magnetic states of the insulating ferrimagnet.Alternatively, if a proper coupling between a FiM insulator and an FM metal is established, the TMR using conventional MTJs hybridized with a FiM insulator could be also utilized to monitor the magnetic state of the FiM insulator.However, for either MTJs, there are numerous problems that will be encountered in the growth of the FiM insulator/FM metal heterostructures with appreciable TMR, including large lattice mismatch, and extremely different growth conditions.Undoubtedly, the lack of sufficient large electrical readout signal from FiM insulator heterostructures presents an additional challenge for their potential applications in spintronic devices.
In this study, we have successfully achieved field-free switching of the perpendicularly magnetized TmIG layer together with a significantly enhanced anomalous Hall resistance readout signal by incorporating an ultrathin in-plane anisotropic Co layer at the interface of the TmIG/Pt heterostructure.The substantial anomalous Hall signal in response to the TmIG switching originates from the small perpendicular magnetization component of the Co layer due to the interfacial coupling.Moreover, the broken symmetry for the spin-orbit torque via the hybrid structure enables magnetization switching of the TmIG layer without the need for an external magnetic field.When the switching current was applied along the easy axis of the Co layer, the polarity of field-free switching in the TmIG perpendicular magnetization was determined by the in-plane magnetization orientation of the Co layer.On the other hand, when the current was orthogonal to the Co easy axis, both the TmIG perpendicular magnetization and the Co in-plane magnetization underwent simultaneous switching in the absence of an external field.The hybrid heterostructure presented in this work opens up new possibilities for effectively manipulating and detecting the magnetization states of magnetic insulators through the all-electric method, providing a promising pathway toward the development of practical spintronic devices based on magnetic insulator materials.

Results and Discussion
The TmIG films were epitaxially grown on (111)-oriented Y 3 (Sc 2 Ga 3 )O 12 (YSGG) substrates, as detailed in the Experimental Section. Figure 1a presents a representative 2/ scan X-ray diffraction spectrum of a 10 nm TmIG film.Apart from the sharp (444) peak originating from the substrate, a distinct TmIG (444) peak is observed (with a full XRD scan shown in Figure S1 in the Supporting Information).The inset of Figure 1a displays the rocking curve of the TmIG (444) peak, exhibiting a small full width at a half maximum value of 0.028°.In Figure 1b, a highresolution X-ray reciprocal space mapping (RSM) around the (486) diffraction peak of the same sample is presented, which shows well alignment of the film peak with the substrate peak.These results highlight the high-quality crystalline structure of the fully strained TmIG film.The perpendicular and in-plane magnetic hysteresis loops of the 10 nm TmIG film are displayed in Figure 1c.The PMA is evident for the TmIG film, with an effective PMA field of ≈2.5 kOe.The saturation magnetization (M S ) of the 10 nm TmIG film is determined to be ≈90 emu cm −3 , slightly lower than the room-temperature bulk value of 110 emu cm −3 .Figure 1d exhibits the surface morphology of the TmIG film captured through atomic force microscopy (AFM).The image reveals a smooth surface with a root-mean-square (RMS) roughness value of 0.19 nm over a scanned area of 4 × 4 μm 2 .
The obtained TmIG films with PMA were transferred to an ultrahigh vacuum magnetron sputtering chamber for the deposition of Co and Pt overlayers.During deposition, a static field of ≈300 Oe was applied parallel to an edge of the substrate, denoted as the x-axis.For electric measurements, the TmIG/Co/Pt trilayer stacks were patterned into Hall bars with dimensions of 20 × 100 μm 2 using conventional lithography and ion milling, while film's normal direction was defined as z-axis.Figure 2a   z that is anti-parallel to the TmIG magnetization (M TmIG ) in the small perpendicular field regime.It is important to emphasize that, overall, the coupling between the Co and TmIG layers is ferromagnetic, as demonstrated by the minor loop shift of the perpendicular magnetization curve and x-ray magnetic circular dichroism (XMCD) measurements (refer to Figures S2 and S3 in the Supporting Information).
To elucidate the origin of the negative R rem H behavior, a series of TmIG(10)/Co(t Co )/Pt(3) samples with different Co thicknesses (t Co ) were systematically investigated.It was found that all these samples with t Co ranging from 0.4 nm to 1.8 nm exhibited appreciable negative R rem H with varying magnitude.The full AHE loops for each sample are provided in Figure S4 of the Supporting Information, and the |R rem H |∕|R sat H | ratios are summarized in Figure 2d.Note that |R rem H |∕|R sat H | ratio gradually decreases from a large value of 0.48 for the 0.4 nm Co sample to 0.03 at t Co = 1.8 nm, indicating an interfacial effect.Based on the aforementioned results, a simple description of the moment orientations in the heterostructure is proposed and depicted in the inset of Figure 2d.There is an interfacial perpendicular Co sublayer that is strongly antiferromagnetically coupled with TmIG.The rest of the Co layer, namely the Co bulk part, is preferentially magnetized in the film plane but slightly tilted up or down due to weak magnetostatic coupling with TmIG.From the |R rem H |∕|R sat H | ratios, the interfacial Co sublayer could have an effective thickness ≈2 Å.It could correspond to the interfacial intermixing region due to the TmIG roughness together with the complicated crystal structure of TmIG which has a large unit cell (a = 12.376 Å) with 160 atoms. [38]These partially buried Co atoms are antiferromagnetically coupled with TmIG through super-exchange interaction and thus contribute a large negative R rem H . On the other hand, the bulk Co part with primarily in-plane anisotropy contributes a smaller positive R rem H .Both contributions collectively account for the observed |R rem H |∕|R sat H | results.Above speculation about the interfacial and bulk Co moment orientations is also supported by the in-plane anomalous Hall effect measurement (refer to Figure S5 in the Supporting Information).Further investigation to gain a deeper understanding of the microscopic origin of the interfacial magnetism would require additional experimental methods, With measurement geometry shown in Figure 3a, currentinduced TmIG magnetization switching was examined in the TmIG(10)/Co(1.3)/Pt(3)sample.Here current pulses and assistant field were parallel to the in-plane easy axis of Co layer (xaxis).Switching current pulses with a width of 1 ms and varying amplitude were applied.Following each current pulse, a sensing current of 0.1 mA was applied, and the large Hall resistance was recorded to acquire the corresponding magnetization state of the TmIG layer.Figure 3b illustrates typical current-induced magnetization switching loops at different assistant fields (H x ).The magnetization switching occurs when the current exceeds a threshold value with |H x | ranging from 10 Oe to 200 Oe.The polarity of the switching loop changes signs as the direction of H x reverses, confirming that SOT is the driving force of the magnetization switching.The critical switching current at H x = 10 Oe is ≈14 mA, corresponding to a current density of ≈1.63 × 10 7 A cm −2 assuming for simplicity that the current den-sity is uniform throughout the Co/Pt bilayer.This value is comparable to the switching result obtained in the TmIG(10)/Pt(3) bilayer under the same conditions. [30]Remarkably, deterministic switching of the TmIG magnetization induced by current under a zero field was achieved in the TmIG(10)/Co(1.3)/Pt(3)sample, as displayed in Figure 3c.In this case, the in-plane magnetization of the Co layer was preset at ±x-axis by applying a field of 1000 Oe or -1000 Oe, which was then decreased to zero.When the Co layer was preset along the +x direction, positive current pulses favored the "up" state (and negative current pulses favored the "down" state), resulting in an anti-clockwise switching polarity, the same as the switching polarity observed with positive assistant H x applied.Conversely, when the Co layer was preset along the -x direction, opposite switching polarity was induced by the current.It should be pointed out that the SOT-driven switching has a smaller Hall resistance variation ΔR SOT H in comparison with the field-induced Hall resistance variation ΔR H .This phenomenon is rather common in the current-induced switching.Such an incomplete switching is probably due to the insufficient effective in-plane field. [39]With an appropriate assistant field, the SOT-induced switching ratio ΔR SOT H /ΔR H becomes larger (refer to Figure S6 in Supporting Information).Similar field-free magnetization switching phenomena were also observed in the TmIG(10)/Co(t Co )/Pt(3) trilayers with t Co = 1.2 nm and 1.5 nm.For the samples with a thinner Co layer, deterministic switching of the TmIG magnetization requires an assistant field H x , with two orders larger Hall readout signal when compared with TmIG(10)/Pt(3).On the other hand, the SOTdriven switching, either with or without the in-plane field, is blocked when the Co thickness exceeds 1.5 nm because the transmission of spin current from the Pt layer to the TmIG/Co interface exponentially decays with the Co thickness.Without a doubt, the SOT symmetry is broken in the TmIG/Co/Pt trilayer, leading to the observed Co moment-dependent field-free switching at the appropriate Co thickness range.The breaking of SOT symmetry in such a trilayer could originate from various factors, including the Co-modified spin current from the Pt layer, spin current involved with AHE, and anisotropic magnetoresistance (AMR) effect of the Co/Pt layers, [40] as well as the interface effect. [41]ield-free switching induced by such spin currents has been demonstrated in CoFeB/Ti/CoFeB [42] and CoFeB/Mo/CoFeB [43] trilayers.Additionally, the contribution of magnetostatic coupling fields or orange peel coupling [44] between the TmIG and Co layers cannot be excluded.The lack of field-free switching for the extremely thin Co samples could be caused by the insignificant overall interfacial coupling and other effects listed above because of the discontinuous Co layer.Considering the complexity of the coupling between a FiM insulator and an FM metal, it is challenging to determine the specific contribution of each possibility mentioned above.Further investigations are necessary to clarify these aspects in future research endeavors.
We also examined the current-induced magnetization switching with current pulses and assistant field applied along y-axis, which is orthogonal to the in-plane easy axis of the Co layer.The measurement geometry is depicted in Figure 4a.It should be parenthetically pointed out that the Co layer of the patterned samples maintains the in-plane easy/hard direction at x/y-axis, demonstrated by AMR measurement (refer to Figure S7 in the Supporting Information).When the current and field are aligned at the Co in-plane hard axis, the switching behavior is found to be quite different.Figure 4b shows the current-induced switching loops of the TmIG(10)/Co(1.3)/Pt(3)sample with an assisted field H y of ±100 Oe and 0 Oe.The TmIG magnetization switches under sufficient large current at both H y = ±100 Oe and 0 Oe.The switching polarities at H y = ±100 Oe are consistent with the case of the current and field along the x-axis.However, at zero field, the switching polarity no longer depends on the history of the Co magnetization state.In fact, the zero-field switching polarity coincides with the negative field switching polarity, suggesting the presence of a negative effective field along y-axis.This negative effective field would be canceled out at an appropriate positive assistant field H y , leading to the absence of the SOT-induced switching.The magnetization switching loops with H y varying from 10 Oe to 50 Oe were measured, and SOT-switching was consistently observed at a sufficiently large current.Representative results are shown in Figure 4c.Note that with the increase of H y , the switching loop shrinks gradually until the switching polarity undergoes a complete reversal, rather than experiencing an abrupt change in polarity.This observation implies the existence of two competing SOT-induced switching mechanisms, as discussed below.
When the switching current is applied along the y-axis, the polarization of spin current induced by the SHE of the Pt layer is aligned along the x-axis, which is parallel to in-plane easy axis of Co layer.It is well known that an in-plane magnetic layer can be switched under the generated field-like effective field (H FL ) along its in-plane easy axis. [2]This switching process is understood as the transfer of spin angular moment from the spin current to the magnetization of in-plane magnetic layer.In our case, the inplane switchable Co layer plays a crucial role in breaking the SOT then facilitating the deterministic switching of the perpendicular TmIG layer.On the other hand, when the applied external field H y is sufficiently large (e.g., 100 Oe) to fix the Co in-plane magnetization, although the switching of the Co layer through H FL is blocked, the perpendicular TmIG layer can still be switched through damping-like torque due to the limited coupling between the TmIG layer and the main part of the Co layer.Considering that the current-induced magnetization switching in the micrometer-sized sample is eventually completed via reverse domain nucleation, domain-wall depinning, and propagation, the competition between Co-layer-assisted switching under the field-like torque and the damping-like torque-dominated switching at a small positive H y will lead to the coexistence of the up and down domains, corresponding to a superposition of their individual loops with different weights, as observed in Figure 4c.
To provide direct evidence for the simultaneous switching of the TmIG perpendicular magnetization and the Co in-plane magnetization i zero fields with current pulses applied along the y-axis (hard axis), the unidirectional spin Hall magnetoresistance (USMR) [45,46] is determined through the second harmonic measurements of the longitudinal resistance in the patterned TmIG(10)/Co(1.3)/Pt(3) sample.As is known, the USMR is a nonlinear magnetoresistance that is sensitive to in-plane magnetization components transverse to the current direction.It reflects the modulation of the longitudinal resistance caused by the interaction between the SHE-induced interfacial spin accumulation and the magnetization as depicted in Figure 5a.The USMR measurement geometry is schematically drawn in Figure 5b.An AC current with an amplitude of 1 mA and a frequency (/2) of 1333 Hz was injected along the y-axis, and the longitudinal second harmonic resistance (R 2 ) was recorded while sweeping the magnetic field along the x-axis, parallel to the easy axis of the Co layer.Figure 5c shows the corresponding R 2 as a function of magnetic field H x .It reveals an ≈2 mΩ difference in R 2 for the Co layer aligned in the +x and -x directions.Additionally, besides the expected USMR at low fields, R 2 gradually changes back with a sign reversal at high fields.This change is likely due to the magnetothermal contributions, including the anomalous Nernst effect and the spin Seebeck effect. [47]From the R 2 -H x loop, the in-plane coercive field of the Co layer is determined to be ≈30 Oe, which agrees well with magnetic measurements.Next, the dependence of R 2 on the current pulse I y in the absence of an external field was measured, and the results are shown in Figure 5d.After each I y pulse, R 2 was recorded with an AC current of 1 mA in amplitude.By comparing R 2 -I y with the R 2 -H x loop, the switching of the in-plane magnetization of the Co layer in x direction by current along y-axis was identified.The normalized R 2 -I y loop and R H -I y loop are directly compared in Figure S8 (Supporting Information).The two switching loops are coincided with each other.These results convincingly demonstrate the synchronous switching of the perpendicular magnetization of TmIG and the in-plane magnetization of the Co layer without the need for an external magnetic field when a current is applied along the in-plane hard axis of the Co layer.

Conclusion
In conclusion, our study has successfully demonstrated the fieldfree switching of the FiM insulator TmIG film and significantly enhanced the electrical read-out signal of the TmIG switching through a hybrid heterostructure TmIG/Co/Pt.The interfacial coupling-induced anomalous Hall signal can serve as a sensitive detection for the perpendicular magnetization of the insulating garnet layer.Meanwhile, the incorporation of a metallic Co layer with uniaxial in-plane anisotropy leads to two distinct types of field-free switching behavior.Under zero external field, the switching polarity depends on the history of the Co magnetization when a current is applied along the easy axis of the Co layer.On the other hand, when the current is applied along the hard axis, both the TmIG perpendicular magnetization and the Co in-plane magnetization undergo simultaneous switching in the absence of an external field.Our findings highlight that a thin Co inserter facilitates the field-free switching in the most studied TmIG/Pt bilayer and enables the highly efficient electrical detection of the TmIG magnetization state.This discovery enables the design of functional spintronic devices that combine FiM insulators with FM metals, holding potential for next-generation information storage and processing technologies.

Experimental Section
Sample Preparation: The TmIG films were deposited on (111) Y 3 (Sc 2 Ga 3 )O 12 (YSGG) single-crystal substrates using an off-axis magnetron sputtering system (4 × 10 −6 Pa) at room temperature.The working gas was high pure Ar (5 N) at a pressure of 1.0 Pa.The as-sputtered TmIG films were annealed at 800 °C for 2 h in a quartz tube with a pure oxygen pressure of 8 × 10 3 Pa under a flow rate of 45 SCCM.Then the postannealed TmIG films were transferred into another high-vacuum magnetron sputtering chamber (8 × 10 −6 Pa) to deposit the metallic overlayers.The metallic films of Co and Pt were grown by DC magnetron sputtering at room temperature.The Ar pressure was 0.5 Pa.The thickness of each layer was controlled by the deposition time based on the growth rate, which was calibrated using X-ray reflectivity measurements.
Structure Characterization: The crystalline structure and strain distribution of the TmIG films were examined by X-ray diffraction (XRD) 2/ scan, rocking curve, and reciprocal space mapping (RSM) using Cu K a radiation on a Bruker AXS D8-Discover diffractometer.
Device Fabrication: For current-induced magnetization switching measurement, the TmIG/Co/Pt and TmIG/Pt stacks were patterned into Hall bars devices with a channel width of 20 μm using standard optical lithography and Ar ion etching.Subsequently, electrode pads made of Ti(5 nm)/Au(50 nm) were formed at the ends of Hall cross using DC sputtering and a lift-off process.When used only for AHE measurement, the Hall bar devices are fabricated by using a metal mask on the TmIG films to deposit the Co and Pt overlayer.
Magnetic Measurement and Transportation Characterization: The magnetic properties of films were determined by using SQUID-VSM (Quantum Design).The electric transport properties were measured by four-wire mode using a Keithley 2400 source meter and Keithley 2182 voltmeter with an electromagnet.The AHE loops at a high field (5 T) of TmIG/Co/Pt were measured with a Physical Property Measurement System (PPMS, Quantum Design).All measurements were performed at room temperature.
Synchrotron Study: X-ray magnetic circular dichroism (XMCD) measurements were conducted on a TmIG(10)/Co(1.5)/Pt(2) sample at Beamline BL07U of the Shanghai Synchrotron Radiation Facility (SSRF).The absorption spectra were collected at an incident angle of 90°from the surface of the film at room temperature.The TmIG(10)/Co(1.5)/Pt(2) sample was pre-magnetized along the out-of-plane direction using an external magnetic field of 0.5 T. Subsequently, X-ray absorption spectra (XAS) were acquired at the Fe L 2,3 and Co L 2,3 absorption edges through total electron yield (TEY) measurements under zero external magnetic field conditions.
illustrates the schematic of a TmIG(10)/Co(1.3)/Pt(3) stack and the optical microscope image of a Hall device.The numbers in parentheses indicate the individual layer thicknesses in nanometers.In Figure2b, the magnetic curves of the TmIG(10)/Co(1.3)/Pt(3)blanket sample under magnetic fields along the x, y, and z axes are presented, including the full loops and the zoomed-in details.These M-H curves demonstrate that the TmIG layer maintains PMA.Simultaneously, the Co layer is preferentially magnetized in the film plane with a small in-plane uniaxial anisotropy along the growth field direction (x-axis).The AHE measurement further revealed the subtle interplay between the Co and TmIG layers.The full AHE loop of TmIG(10)/Co(1.3)/Pt(3) is shown in the upper panel in Figure 2c.Since the TmIG layer is insulating, the AHE signal of the trilayer primarily originates from the AHE of the conducting Co/Pt bilayer, with negligible contribution from the non-equilibrium spin Hall-induced AHE (referred to as SH-AHE).The measured anomalous Hall resistance (R H ) thus reflects the z-component of the Co magnetization (m Co z ).It is noteworthy that R H approaches saturation at a field of ≈2 T, coinciding with the large saturation field of the perpendicular M-H curve.Remarkably, there is an inverted sharp switching behavior around the zero field, where the sign of the anomalous Hall resistance in the remanent state

Figure 1 .
Figure 1.Structural and magnetic characterization of (111)-oriented YSGG/TmIG(10 nm) film.a) X-ray diffraction 2/ scan of the TmIG film.Inset shows the rocking curve of TmIG (444).b) The reciprocal space mapping (RSM) of high-resolution XRD around the (486) diffraction of TmIG films.c) Perpendicular and in-plane magnetic hysteresis loops of the 10 nm TmIG film.The perpendicular loop is scaled in the bottom x-axis, whereas the in-plane loop is scaled in the top x-axis.A diamagnetic contribution from the YSGG substrate has been subtracted.d) Atomic force microscopy image of the 10 nm TmIG film.

Figure 2 .
Figure 2. Magnetization and Hall resistance measurements of TmIG/Co/Pt trilayers.a) Schematic of YSGG/TmIG(10)/Co(1.3)/Pt(3)stack and the Hall cross-device with a channel width of 20 μm fabricated by conventional lithography and ion milling.b) Magnetic hysteresis loops of TmIG(10)/Co(1.3)/Pt(3) blanket film along x, y and z axes.The inset shows full M-H loops at high field.c) Anomalous Hall resistance of the TmIG(10)/Co(1.3)/Pt(3)sample and TmIG(10)/Pt(3) control sample with magnetic field sweeping along z-axis.The upper panel shows the full AHE loop of the TmIG(10)/Co(1.3)/Pt(3)sample at a high field.The bottom panel shows zoomed-in details of the AHE for both the TmIG(10)/Co(1.3)/Pt(3)sample and TmIG(10)/Pt(3) control sample.The AHE for TmIG/Pt is enlarged 100 times for ease of viewing.d) The ratio of |R rem H |∕|R sat H | as a function of the Co layer thickness for TmIG(10)/Co(t Co )/Pt(3) samples.

Figure 3 .
Figure 3. Current-induced switching in TmIG(10)/Co(1.3)/Pt(3) sample with current applied along the x-axis.a) Schematic of the measurement geometry for SOT-switching.b) SOT switching curves of the sample under different in-plane magnetic field H x .c) Current-induced magnetization switching at zero external magnetic fields.The magnetic moment of Co layer is preset along x-axis in either the positive (+x) or negative (-x) direction using a magnetic field of ±1000 Oe before SOT measurements.

Figure 4 .
Figure 4. Current-induced switching in TmIG(10)/Co(1.3)/Pt(3) sample with current applied along the y-axis.a) Schematic of the measurement geometry for SOT switching.b) SOT switching curves of the sample with external magnetic fields H y of ±100 Oe and 0 Oe.c) SOT switching curves of the sample with the field H y increasing from 10 Oe to 50 Oe.

Figure 5 .
Figure 5. Demonstration of current-induced in-plane magnetization switching of the Co layer in TmIG(10)/Co(1.3)/Pt(3) sample by USMR.a) Schematic illustration of the unidirectional spin Hall magnetoresistance.SHE-induced spin accumulation at the interfaces of Co/Pt modulates the longitudinal resistance depending on the magnetization direction parallel or anti-parallel with the spin polarization.b) Schematic of the measurement geometry for USMR.c) The longitudinal second harmonic resistance with a magnetic field sweeping along x-axis.d) The longitudinal second harmonic resistance with switching current sweeping along y-axis under zero field.