Highly Efficient Spin Transport in a Paramagnetic Insulator at Room Temperature

The exploration of new materials exhibiting excellent spin transport properties, particularly those capable of efficiently transmitting pure spin currents at room temperature, is a crucial aspect of spintronics. This work reports the observation of room‐temperature spin transport in a paramagnetic insulator Gd3Ga5O12 (GGG). By measuring the longitudinal spin Seebeck voltage, spin Hall magnetoresistance, and anomalous Hall resistance in a Y3Fe5O12 (YIG)/GGG/Pt heterostructure at room temperature, the spin current is found to propagate in GGG up to a distance of 7 nm through the paramagnons, which are the collective excitations of the local spin within the paramagnet. Remarkably, this spin propagation phenomenon occurs at a small magnetic field and irrespective of whether the spin current injected into GGG is thermally induced from YIG or electrically generated through the spin Hall effect of Pt. Moreover, the inclusion of a thin GGG spacer layer increases the thermal spin current from YIG to Pt by 31%. Calculations based on the diffusive magnon transport model indicate high spin conductance at the GGG/Pt interface. These findings highlight the potential of a wide range of paramagnetic materials in facilitating spin transport and advancing the development of spintronic devices.


Introduction
Spin currents, defined as the movement of the spin angular momenta, have been the central topic in spintronics due to their rich DOI: 10.1002/apxr.202300073physical connotations and application prospects.Generally, two distinct types of spin currents can be identified: one is carried by conduction electrons, and the other is mediated by magnetic excitations in the form of spin waves or magnons.Notably, the latter type can convey spin information without the need for electron migration, resulting in lower energy dissipation and offering an ideal platform to investigate pure spin current phenomena. [1]][13] However, most studies exploring the transport of magnon spin currents have focused on ferromagnetic or antiferromagnetic materials, limiting the selection of materials for the spintronics community.Consequently, it is highly desirable to explore new materials with exceptional magnon excitation and transport performance.
which challenge the conventional models that posit the necessity of magnetic ordering for magnon generation.][21] But to date, the reported paramagnonic spin currents generation and transport are observed at low temperatures (< 100 K) and under high magnetic fields. [14,18]This limitation poses challenges for practical applications, as the working conditions involved are not conducive to real-world implementations.
In this study, we report the efficient room-temperature spin transport in a paramagnetic insulator Gd 3 Ga 5 O 12 (GGG), commonly employed as the substrate for the epitaxial growth of the ferrimagnetic insulator Y 3 Fe 5 O 12 (YIG).By measuring the LSSE in the layer structures of YIG/GGG/Pt, where the thermalinduced magnon spin currents are generated from the YIG, transmitting through the GGG layer and are detected by the inverse spin Hall effect (ISHE) of the Pt layer.We discover robust spin propagation mediated by the paramagnons within the GGG layer, at room temperature and under a weak magnetic field (within ±3 Oe), with a propagation distance of up to 7 nm.Furthermore, we observe a 31% increase in thermal spin currents locally injected from YIG into Pt by incorporating a thin GGG spacer layer.In addition, we discover that the spin currents generated by the spin Hall effect in Pt can penetrate the GGG layer and undergo reflection at the YIG/GGG interface.Utilizing the diffusive magnon transport model, we find a high spin transfer efficiency at the GGG/Pt interface.This study underlines GGG as an exceptional spin conductor at room temperature, holding promise for integration into a variety of spintronic devices.

Material Characterization and PNR Measurement
We used RF magnetron sputtering to fabricate epitaxial YIG/GGG multilayer films on (111)-oriented GGG substrates with a thickness of 0.5 mm.For clarity, the GGG substrate is denoted as GGG(sub) to distinguish the nanometric epitaxial GGG layer.Figure 1a illustrates the XRD 2/ pattern of the GGG(sub)/YIG(30 nm)/GGG(7 nm) film.It showcases a distinct and well-defined GGG (444) peak corresponding to the substrate, accompanied by a relatively weaker additional YIG/GGG(444) film peak on the left side.Notably, clear Laue oscillations are also evident.The film thickness (T) can be calculated from these additional satellite peaks by using the equation T = /2Δcos, [22] where  = 1.542Å is the wavelength of the Cu K 1 , Δ ≈ 2.3 × 10 −3 rad is the peak separation of the Laue oscillations,  = 0.443 rad represents half of the Bragg diffraction angle of the additional peak.The calculated value of T is 37.1 nm, consistent with the total thickness of the YIG and GGG layers.This consistency confirms the epitaxial growth of both the YIG and GGG films, as well as a sharp interface for GGG(sub)/YIG and a smooth surface for the GGG layer.The atomic force microscopy image profile demonstrates a root-mean-square roughness value of 0.18 nm over a scanning area of 5 μm × 5 μm for the same sample, as shown in Figure 1b.This result again verifies the smooth surface of both YIG and GGG layers.Next, we deposited a Pt layer of 5 nm onto the garnet bilayer film for the microstructural characterization.The High-angle annular dark-field (HAADF)scanning transmission electron microscope (STEM) image of the GGG(sub)/YIG(30 nm)/GGG(7 nm)/Pt(5 nm) sample is shown in Figure 1c.The YIG and GGG single-crystal structures are clearly discernible in the image.Additionally, enlarged images of the GGG(sub)/YIG and YIG/GGG interface, taken from selected areas indicated in marked panels are presented in Figure 1d,e, respectively.These enlarged images provide conclusive evidence that the YIG and GGG layers are epitaxially grown on the GGG substrate, featuring an atomically sharp interface.
To further evaluate the quality of the YIG and GGG films, as well as the GGG(sub)/YIG and YIG/GGG interfaces, we conducted polarized neutron reflectivity (PNR) measurement to investigate the depth-dependent nuclear and magnetic neutron scattering length density (SLD N and SLD M ) of the GGG(sub)/YIG/GGG/Pt.The SLD N and SLD M increase with the nuclear and magnetization scattering potential, respectively.Figure 2a displays the experimental and fitted non-spin-flip neutron reflectivity curves (R ++ and R − ) as a function of the scattering vector Q under an in-plane field of 10 kOe.The spinasymmetry (SA), calculated as SA = (R ++ − R − )/(R ++ + R − ), serves as a sensitive indicator of film magnetization.The inset of Figure 2a presents the experimental and simulated SA as a function of the scattering vector Q.By employing the GenX software to fit the reflectivity curve, we achieved a good fit using a six-layer model for the multilayer structure.This model consists of the interface layer between GGG(sub) and YIG, the bare YIG layer, the interface layer between YIG and GGG, the bare GGG layer, the interface layer between GGG and Pt, and the Pt layer.
As depicted in Figure 2b, SLD N exhibits a sharp gradient from the GGG(sub) extending into the YIG film, indicating negligible element interdiffusion between the GGG substrate and the YIG layer.Besides, The SLD M profile does not provide any indications of an induced magnetic moment within the GGG(sub) layer.The GGG(sub)/YIG interface region is estimated at ≈2.6 nm, which is thinner than reported values in other studies. [23,24]n order to make an accurate characterization for the element diffusion near the garnet interface region, we performed STEMelectron energy loss spectrum (EELS) analyses of the spatial distribution of elements in the spectrum line profile across the GGG(sub)/YIG and the YIG/GGG interfaces from Figure 1c, in which simultaneous collection of O, Ga, Gd, Y, Fe, and Pt element signals was performed.For regions across the GGG(sub)/YIG interface, the Ga and Gd signals are only present in the GGG substrate and are not detected in the YIG layer within the detection limit.The Y and Fe peaks, on the other hand, are exclusively detected in the YIG layer, as shown in Figure 2c.This result further confirms that element intermixing near the GGG(sub)/YIG interface is negligible.SLD N results indicate a thickness of 3.6 nm for the YIG/GGG interface.STEM-EELS analyses in Figure 2d suggest observable interdiffusion of Ga and Fe atoms at the YIG/GGG interface, resulting in a non-negligible interface layer between YIG and GGG.It is important to note that no ferromagnetic signals are detected in the region of the YIG/GGG interface LSSE thermal voltage V th in YIG/GGG(t GGG )/Pt is measured as a function of the applied field H, t GGG is fixed at b) 0 nm, c) 1 nm, d) 1.5 nm, e) 3 nm, f) 7 nm, g) 10 nm, respectively.h) Spin Seebeck coefficient S as a function of the t GGG , the solid line shows the fitting result based on the diffusive magnon transport model, the magnon spin diffusion length caused by the thermal gradient  ∇T mag is determined as 1.7 nm.Inset shows the t GGG dependent S in the logarithmic scale, the straight lines are the exponential fits, from which the spin decay lengths  dec is obtained as 1.8 nm.
layer or the bare GGG layer according to the PNR results.These findings indicate that no ferrimagnetic garnet phases, such as Gd 3 Fe 5 O 12 and Gd x Y 3-x Fe 5 O 12 , [25,26] or exchange coupling [27] are formed at the YIG/GGG interface.Besides, there is no indication of a magnetic proximity effect at the Pt interface, which is in consistence with the case in YIG/Pt [28] and Ho 3 Fe 5 O 12 /Pt [29] heterostructures at room temperature via the PNR measurement.Thus, it is safe to conclude that all the regions between the YIG and Pt layers are paramagnetic, and the spin transport properties of the paramagnetic GGG will be discussed below.

Room-Temperature Spin Transport in GGG Through Thermal and Electrical Spin Injection
To investigate spin transport in GGG, we conducted LSSE measurements on GGG(sub)/YIG(30 nm)/GGG(0-10 nm)/Pt(3 nm) samples at room temperature with a lateral size of 0.5 mm × 3.4 mm.The thickness of Pt is selected as 3 nm to obtain a considerable ISHE signal.As shown in Figure 3a, we applied an out-ofplane temperature gradient ∇T to the multilayers, which allows for the injection of a magnon spin current j s from the YIG layer into the upper GGG layer.The direction of j s is determined by the ∇T.The YIG magnetization and the injected spin polarization direction  are aligned along the short-axis direction of the samples by applying an external magnetic field (H).As a result, the magnon spin currents can penetrate through the GGG layer into the Pt layer and generate an electric field in the direction of  × j s via ISHE, accompanied by a thermal voltage V th along the long-axis direction of the samples.Figures 3b-g present the V th versus H curves for samples with different thicknesses of GGG (0, 1, 1.5, 3, 7, and 10 nm).The insulating nature of the YIG and GGG films is confirmed through electrical measurements.The LSSE result for YIG/Pt is displayed in Figure 3b, showing an ISHE voltage V ISHE = [V th (H = − 10 Oe) − V th (H = 10 Oe)]/2 of 1.94 μV.It is worth noting that YIG exhibits an extremely soft magnetic property, with a coercivity of ≈1 Oe and a saturation field smaller than 3 Oe.Surprisingly, when 1-2 nm thick GGG layers are inserted between the YIG and Pt layers, a significant enhancement of the ISHE signals in Pt is observed: V ISHE = 2.39 μV for 1 nm GGG insertion Figure 3c and V ISHE = 2.55 μV for 1.5 nm GGG insertion Figure 3d.
GGG is a geometrically frustrated magnet that displays shortrange magnetic order at extremely low temperatures. [30]At room temperature, the spins in GGG are locally correlated and allow for the propagation of magnons even in the absence of any long-or short-range magnetic order.This excitation mode of magnons in such a thermally fluctuating magnetic system is called paramagnons. [19,20]A very recent study proposed an alternative mechanism to explain spin transport in GGG through a Pt/GGG/Pt nonlocal geometry. [14]This mechanism suggests that spin diffusion in GGG is influenced by long-range dipole interactions.However, to generate spin diffusion through dipole interactions, a strong magnetic field (>10 kOe) and low temperature (≤100 K) are required to generate magnetic order in GGG via the Zeeman interaction. [14]In our experiment, spin transport in GGG was measured around the switching field of YIG at room temperature, which is close to zero.This indicates that the enhancement of LSSE in the YIG/GGG/Pt structure is primarily attributed to the excitation of paramagnons in GGG by the thermal spin current injected from YIG.
When the GGG spacer layer exceeds 3 nm [Figure 3e], the V ISHE in the YIG/GGG/Pt structure becomes smaller compared to YIG/Pt and decreases rapidly with GGG thickness.A noticeable ISHE voltage of 0.07 μV can still be detected with a 7 nm GGG insertion [Figure 3f], but no ISHE voltage is observed in the YIG/GGG(10 nm)/Pt sample [Figure 3g].To provide a meaningful comparison with other studies, we use the spin Seebeck coefficient S = V ISHE /L∇T to characterize the spin-to-charge conversion efficiency in our system, where ∇T = 26 K mm −1 and L = 3.4 mm.[33] To assess the reproducibility of the acquired spin Seebeck coefficient, we have conducted multiple rounds of testing on YIG/Pt samples featuring identical structures.Our investigations revealed that spin Seebeck coefficient exhibited fluctuations within a controlled range of 5%. [3,34]This observation indicates that, for our specific measurement method, the influence from the variation in thermal contact resistance for the samples is negligible.This level of control ensures that our method provides a reliable and repeatable comparison of spin Seebeck coefficient for different GGG thicknesses with a high confidence.
Figure 3h shows the dependence of transverse thermopower on GGG thickness.Initially, the transverse thermopower exhibits a sharp increase, reaching a 31% enhancement with a 1.5 nm GGG insertion compared to the YIG/Pt bilayer.However, after reaching a peak, S decreases exponentially with increasing GGG thickness, indicating diffusive spin transport in the GGG layer.The inset of Figure 3c presents a linear relationship in the semilog plots, allowing us to obtain the spin decay length  dec of GGG by fitting the equation S(t GGG ) = ke −t GGG ∕ dec , where k is a constant parameter.The fitting result yields  dec = 1.8 nm for GGG (excluding the data point for t GGG ≤ 1.5 nm from the fitting).This value is larger than that measured by FMR-SP (0.7 nm) in the same structure. [19]This variation in  dec suggests that different spin injection methods (microwave or dc thermal excitation) may lead to different spin current propagation processes in the paramagnetic insulator.In the LSSE measurement, the thermal paramagnons in GGG have a spatial dependence with a nonequilibrium distribution, which exhibit a broader spectrum distribution and larger wave numbers compared to their coherent microwave counterparts in spin-pumping measurements. [35,32]onsequently, the paramagnons can experience longer spin relaxation through thermal spin injection.
To gain further insights into the spin transport characteristics of GGG, we also conducted measurements of the spin Hall magnetoresistance (SMR) in the YIG/GGG/Pt structure, which allow us to examine the spin transport properties of GGG when subjected to electrical spin accumulation induced by Pt.In the conventional SMR model of the YIG/Pt bilayer, when an electric current (j c ) is passed through the nonmagnetic metal Pt, an electrical spin current is generated due to the spin Hall effect in Pt.The spin current density (j YIG∕Pt s ) at the YIG/Pt interface is determined by the spin-mixing conductance and the spin accumulation, which depends on the magnetization orientation (m) of the YIG layer [36] ej YIG∕Pt where e is the elementary charge,  s is the spin accumulation corresponding to the spin current polarization , G r and G i are the real and imaginary parts of the spin mixing conductance, respectively, and G s is the interface spin conductance.The m-dependent boundary conditions of the spin current density at the YIG/Pt interface, in conjunction with the ISHE of Pt, lead to magnetoresistance in the system, which exhibits maximum value at m⊥ and minimum at m∥.As sketched in Figure 4a, by rotating a magnetic field (3500 Oe) that is large enough to align the YIG magnetization in the x-y plane with angles  relative to the electric current (x-axis), the resistance was measured as a function of .
Figure 4b illustrates the  dependent magnetoresistance results of YIG/GGG(t GGG )/Pt.All the curves exhibit a cos 2 () behavior and reach the maximum resistance at  = 0°(corresponding to the configuration where m⊥), and the minimum resistance at  = 90°(corresponding to m∥).These observations align with the expectations of the SMR model, indicating that the electrical spin currents generated by Pt can propagate through the GGG layer and undergo reflection at the YIG/GGG interface.Note that the magnetoresistance contribution arising from the magnetic proximity effect in Pt [37,38] and spin-dependent scattering at the GGG/Pt interface are not expected due to the paramagnetic nature of GGG.Therefore, the SMR results suggest that GGG is capable of transmitting spin currents through electrical spin injection.The GGG thickness dependence of the SMR ratio (  = 0 )∕ 0 is shown in Figure 4c, where x and  0 represent the resistivity at  = 0°,  = 90 ○ and zero magnetic field, respectively.SMR is observable for t GGG less than 10 nm but decreases monotonically across the entire thickness range.This behavior differs from the LSSE results, which exhibit a peak at t GGG = 1.5 nm before

Theoretical Analysis Based on Diffusive Magnon Model
A phenomenological model, based on magnon excitations at the interface between the ferromagnetic insulator and the normal metal, along with diffusive magnon transport within the ferromagnetic insulator, provides a quantitative description of the observed dependence of SMR on the GGG thickness. [7,39]According to this model, SMR in the YIG/GGG/Pt system as a function of GGG thickness can be described by the following equation: where h is the Planck constant,  SH ,  sf ,  Pt , and t Pt are the spin Hall angle, spin diffusion length, resistivity, and thickness of the Pt layer, respectively.The effective spin mixing conductance G YIG∕GGG∕Pt eff takes into account the combined impact of the interface spin conductance G GGG∕Pt s , the bulk magnon spin conductivity  mag of GGG, and the real part of the spin mixing conductance at the YIG/GGG interface G YIG∕GGG r .It can be expressed as follows: Here, the magnon spin transport within GGG is described as a diffusion process with a magnon spin diffusion length  mag . [11]he detailed derivation of the above equation can be found in Supporting Information S3.
By substituting the expression for G YIG∕GGG∕Pt eff obtained from Equation 3 into Equation 2, we can fit the SMR ratio shown in Figure 4c.Certain parameters are fixed to values relevant to our experiment, such as  SH = 0.16, [40] t Pt = 3 nm,  sf = 1.5 nm, and  Pt = 100 μΩ cm.The best fit is achieved with the following parameter values:  mag = 1.6 × 10 4 S m −1 ,  mag = 3.1 nm, G GGG∕Pt s = 4.5 × 10 13 Sm −2 , and G YIG∕GGG r = 8.8 × 10 12 Sm −2 .The obtained value of  mag is lower than that measured in the Pt/GGG/Pt structure ( mag = 7.3 × 10 4 Sm −1 ) using the nonlocal geometry at low temperature (5 K). [14] This suggests that the degree of spin correlations in GGG, increasing with reduced temperature, significantly influence the magnon spin conductivity.Stronger spin correlations result in more efficient magnon spin diffusion in GGG.Most striking, the interface spin conductance of GGG/Pt in our work (4.5 × 10 13 Sm −2 at 300 K) is found to be much larger than that measured at low temperature (G GGG∕Pt s = 1.8 × 10 11 Sm −2 at 5 K). [14]Interestingly, the ratio of G GGG∕Pt s at 300 K to G GGG∕Pt s at 5 K is roughly equivalent to (300/5) 3/2 , which follows the spinwave approximation.In addition, the obtained G GGG∕Pt s value is even larger than that in the YIG/Pt sample at room temperature (G YIG∕Pt s = 1.5 × 10 13 Sm −2 ). [41]This suggests that the GGG/Pt interface is highly efficient for spin transport, which can lead to an enhancement of the LSSE signal in YIG/GGG/Pt trilayers compared to YIG/Pt bilayers under specific conditions.
The magnon diffusion length value ( mag = 3.1 nm) determined by SMR is ≈1.7 times the spin decay length ( dec = 1.8 nm) in the LSSE results.To validate the value of the magnon diffusion length obtained from the SMR measurements and the diffusive magnon model, we conducted an anomalous Hall effect (AHE) measurement on the same serials of YIG/GGG/Pt samples.The AHE measurement involves sweeping a magnetic field perpendicular to the film plane and measuring the Hall voltages in the Pt layer, as shown in Figure 4d.It is worth noting that the AHE in this system shares the same underlying mechanism as the SMR, with the difference being that the AHE is sensitive to the z-direction component of the magnetization and the imaginary part of the interface spin mixing conductance. [36]he thickness-dependent AHE results are shown in Figure 4e, demonstrating a similar decreasing trend with GGG thickness as the SMR results.The AHE resistivity ( AHE ) can be calculated us-ing the formula , where  H (H + Sat ) and  H (H − Sat ) are the Hall resistivities at positive and negative saturation fields, respectively.By utilizing the magnon spin diffusive model mentioned earlier, the  AHE in the YIG/GGG/Pt structure can be expressed as [36] The effective spin mixing conductance of the YIG/GGG/Pt structure in the AHE measurement, denoted as G and  mag to obtain the best fit to the GGG thickness dependence of the AHE data shown in Figure 4f.The fitting yields  mag = 3.4 nm and G YIG∕GGG i = 1.4 × 10 12 Sm −2 .The obtained value of  mag from the SMR and AHE measurements is nearly the same, confirming that electrical spin accumulation in GGG leads to a longer magnon spin diffusion length (referred to as  J mag = 3.1−3.4nm) compared to the thermal counterpart in the LSSE measurement (referred to as  ∇T mag = 1.7 nm, which we derived from fitting the LSSE results based on the magnon spin diffusion model, see Supporting Information S3).
On the other hand, the obtained , which is in agreement with theoretical calculations.This result indicates that the real part of the spin mixing conductance between the insulator interface is much larger than its imaginary counterpart. [42]For comparison, we extract the spin mixing conductance values for YIG/Pt (G as well as the Pt spin conductance.In the LSSE experiment, the observed enhancement in a spin current injection of YIG/GGG/Pt can be attributed to a larger spin conductance at the GGG/Pt interface and a comparatively smaller spin conductance at the YIG/Pt interface.However, in the case of SMR and AHE experiments, it is found that the spin mixing conductance at the YIG/Pt interface exhibits a higher value, consistently surpassing the effective spin mixing conductance of the YIG/GGG/Pt system (see Supporting Information S2 and S3).This discrepancy ultimately leads to a monotonic decrease in spin current transport across the entire range of GGG thickness for the YIG/GGG/Pt.

Conclusion
In summary, we have demonstrated robust paramagnonmediated spin transport in GGG up to a distance of 7 nm at room temperature.The thermal-induced spin current from YIG into Pt can be enhanced by inserting a thin epitaxial GGG spacer, which is attributed to the highly efficient spin conversion at the GGG/Pt interface, as supported by the theoretical analysis based on the diffusive magnon model.In addition, the magnon spin diffusion length in GGG is found to vary depending on the spin injection method employed, such as microwave, thermal gradient, or spin Hall effect.This indicates the unique nature of paramagnon spin transport that warrants further investigation.One notable advantage of paramagnetic insulators is their immunity to magnetic after-effects and Barkhausen noise, [43] which are typically associated with materials exhibiting magnetic order.The availability of room-temperature paramagnetic insulators with excellent spin transport properties opens up a wide range of possibilities for exploring spintronics in the paramagnetic materials family.

Experimental Section
The YIG films with a thickness of 30 nm were grown on (111)-oriented Gd 3 Ga 5 O 12 (GGG) substrates by using an ultrahigh vacuum off-axis sputtering system (4 × 10 −6 Pa), then the GGG films with a slight lattice mismatch were grown on YIG.All the garnet films were deposited at room temperature.The working gas is high pure Ar (5N) at a pressure of 1.0 Pa, and the sputtering rate was ≈0.029 nm −1 s for YIG and 0.035 nm −1 s for GGG with an RF power of 50 W.The as-deposited YIG and GGG films were amorphous.In order to obtain high-quality garnet films with epitaxial growth, all films were annealed at 800 °C for two hours and then cooled down to room temperature in a quartz tube furnace, the oxygen pressure was 500 Pa, and the flow rate was 45 SCCM.Pt films were deposited on the crystallized garnet films via a physical mask for the spin transport measurement.
Sample crystalline structure was characterized using a Bruker AXS D8-Discover diffractometer with Cu K 1 radiation.The microscopic crystalline and interfacial structure of the heterostructures were revealed by a JEM-ARM200F scanning transmission electron microscope (STEM) fitted with a double aberration corrector.High-angle annular dark-field (HAADF) imaging was performed in thin specimen regions, and STEM-electron energy loss spectrum (EELS) line scanning with the atomic resolution was performed vertically throughout the interfaces.The polarized neutron reflectivity (PNR) measurements were carried out on a Multipurpose Reflectometer at the China Spallation Neutron Source (CSNS). [44]The neutron reflectivity curves are recorded as a function of the scattering vector Q = 4sin/, where  and  are the incident angle and wavelength of the neutron beam, respectively.The depth dependence of the neutron scattering length density (SLD) profile is obtained by fitting the reflectivity curve through the software of GenX.
The LSSE of the samples was investigated in a self-built magnetothermal-transport measurement system.The temperature gradient is normal to the film plane, and the temperature difference between the top of the films and the bottom of the substrates is ≈13 K.The lateral dimen-sions of samples for LSSE-ISHE measurements were fixed at 0.5 mm × 3.4 mm.The placement of electrical contact points was confined to the cross-section of the samples.A four-probe technique was adopted for SMR and AHE measurements in a rotational magnetotransport measurement system.All the measurements mentioned in this work were performed at room temperature.

Figure 2 .
Figure 2. PNR and STEM-EELS characterization of the GGG(sub)/YIG(30 nm)/GGG(7 nm)/Pt(5 nm) sample.a) Room-temperature PNR results under an in-plane magnetic field of 10 kOe.Black and red symbols correspond to the experimental data, while the black and red solid lines show the fitted curves.Inset: The experimental and fitted SA curves as a function of the scattering vector Q. b) The fitted nuclear and magnetic SLD N and SLD M profiles for the sample.STEM-EELS analyses of the spatial distribution of the elements across the c) GGG(sub)/YIG and the d) YIG/GGG interface, the elements of O, Ga, Gd, Y, Fe, and Pt signals are collected simultaneously.

Figure 3 .
Figure 3. Room-temperature spin transport in GGG through thermal spin injection.a) Schematic of thermal spin transport measurement in the GGG.LSSE thermal voltage V th in YIG/GGG(t GGG )/Pt is measured as a function of the applied field H, t GGG is fixed at b) 0 nm, c) 1 nm, d) 1.5 nm, e) 3 nm, f) 7 nm, g) 10 nm, respectively.h) Spin Seebeck coefficient S as a function of the t GGG , the solid line shows the fitting result based on the diffusive magnon transport model, the magnon spin diffusion length caused by the thermal gradient  ∇T mag is determined as 1.7 nm.Inset shows the t GGG dependent S in the logarithmic scale, the straight lines are the exponential fits, from which the spin decay lengths  dec is obtained as 1.8 nm.

Figure 4 .
Figure 4. Room-temperature spin transport in GGG through electrical spin injection.a) Schematic of SMR measurement.The magnetic field H is applied in the xy plane with angle  relative to the electrical current directions (x-axis).b)  dependence of the longitudinal resistivity ratio (  x −   = 90 • x )∕ 0 in the YIG/GGG(t GGG )/Pt.  x and   = 90 • x are measured at the 3500 Oe field,  0 is the zero-field longitudinal resistivity.c) GGG thickness dependence of the SMR ratio.The solid line is the best fitting according to the diffusive magnon transport model, d) Schematic of AHE measurement.The magnetic field H is swept along the z-axis, which is perpendicular to the film plane.e) The measured Hall resistivity  Hall as a function of H in the YIG/GGG(t GGG )/Pt.f) GGG thickness dependence of the AHE resistivity  AHE .The solid line is the best fitting according to the diffusive magnon transport model.
the imaginary part of the spin mixing conductance at the YIG/GGG interface.Keeping all other parameters the same as the SMR fitting results, we varied the parameter G YIG∕GGG i = 3.15 × 10 11 Sm −2 .It is important to note that the SMR ratio and AHE value of the YIG/Pt bilayer is predominantly influenced by the spin mixing conductance of YIG/Pt and Pt spin conductance.In contrast, in YIG/GGG/Pt trilayers, the SMR and AHE results are governed by G