Strong spin orientation-dependent spin current diffusion and inverse spin Hall effect in a ferromagnetic metal

Pure spin current transport has become the central point of the state-of-the-art spintronics. While most spin current phenomena have been extensively explored, aspects of the pure spin current injected into ferromagnetic metals are far from completely understood. The reports on a fundamental problem, i.e. the spin relaxation asymmetry with spin current polarization collinear or transverse to the magnetization of ferromagnetic metals, are quite controversial. By employing a Y3Fe5O12 (YIG)/Cu/Ni80Fe20 (Py)/Ir25Mn75 (IrMn) spin valve heterostructure with the thermal inverse spin Hall effect (ISHE) of a Py well separated from other thermoelectric transport and thermal Hall effects, we find that the ISHE signal amplitude in 10 nm Py increases by 80% when changing the relative orientation of the YIG and Py magnetization from orthogonal (⊥) to collinear (||). Moreover, the spin-diffusion length λsf and effective spin Hall angle θSHeff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta _{{\mathrm{SH}}}^{{\mathrm{eff}}}$$\end{document} of Py are also spin orientation dependent and vary from λsf⊥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _{{\mathrm{sf}}}^ \bot$$\end{document} = 1.0 ± 0.1 nm to λsf∥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _{{\mathrm{sf}}}^\parallel$$\end{document} = 2.8 ± 0.5 nm with θSHeff⊥∕θSHeff∥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta _{{\mathrm{SH}}}^{{\mathrm{eff}}}\left( \bot \right)/\theta _{{\mathrm{SH}}}^{{\mathrm{eff}}}\left( \parallel \right)$$\end{document} = 1.5, respectively. Our results demonstrate magnetization orientation-dependent spin relaxation and spin injection efficiency of a pure spin current, revealing that exchange interactions in ferromagnetic metals strongly affect the transport of the pure spin current. A method for converting quantum spin properties into electricity can be enhanced using magnetic fields. Jian-Wang Cai from the Chinese Academy of Sciences in Beijing, China and colleagues investigated how insulating magnets can transmit information via a phenomenon known as spin current generation. When heat is applied to nanoscale nickel–iron films, information about the magnet’s spin orientation moves through the alloy much like a wave through water. Placing an antiferromagnetic metal on top of the nickel–iron film enables the spin current to be captured and converted into electricity without any spurious effect. The authors’ experiments showed that spin currents could be boosted or diminished by applying external magnetic fields parallel or across the device. Analysis of this orientation dependence revealed how spin movement across interfaces may affect this new type of power generation. The authors demonstrate that the inverse spin Hall effect (ISHE) and pure spin current relaxation in Ni80Fe20 (Py) are strong magnetization orientation dependent through longitudinal spin-Seebeck effect measurement in YIG/Cu/Py/Ir25Mn75 spin valve heterostructure. With the relative orientation of the magnetization of YIG and Py varying from perpendicular (⊥) to collinear (||), it has been found that the detected ISHE amplitude in 10 nm Py increases by 80%. Besides, the spin-diffusion length λsf varies from λsf⊥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _{{\mathrm{sf}}}^ \bot$$\end{document} = 1.0 ± 0.1 nm to λsf∥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _{{\mathrm{sf}}}^\parallel$$\end{document} = 2.8 ± 0.5 nm and the effective spin Hall angle θSHeff⊥∕θSHeff∥=1.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta _{{\mathrm{SH}}}^{{\mathrm{eff}}}\left( \bot \right)/\theta _{{\mathrm{SH}}}^{{\mathrm{eff}}}\left( \parallel \right) = 1.5$$\end{document}.


Introduction
In past years, pure spin current has received considerable interest in spintronics due to its non-Joule heat properties. The ferromagnetic insulator (FMI)/nonmagnetic metal (NM) bilayer is one of the most common structures for studying pure spin current phenomena, where FMI represented by Y 3 Fe 5 O 12 (YIG) can generate pure spin current through magnetization precession or a temperature gradient while heavy NMs such as Pt with strong spin−orbit coupling (SOC) can serve as spin current detectors via the inverse spin Hall effect (ISHE) [1][2][3] . When a temperature gradient is applied perpendicular to the YIG/NM interface, a magnon spin current can be created across the whole FMI and then pumped into the NM layer because of the magnon accumulation at the YIG/NM interface, and the injected spin current in the NM is finally transformed into an electric voltage. This is the so-called longitudinal spin-Seebeck effect (LSSE) 3,4 . Although the validity of the SSE has been challenged by the parasitic thermal electric effect and thermal Hall effect, such as the anomalous Nernst effect (ANE) [4][5][6] , magnon Hall effect (MHE) 7,8 and anomalous Righi-Leduc effect (ARLE) 9, 10 , it has been verified in many YIG-based heterostructures that LSSE remains a reliable methodology to investigate pure spin current phenomena in the framework of spin caloritronics 5,11 .
Ferromagnetic metals (FMMs) have also been found to exhibit a significant ISHE 12 , and by means of LSSE [12][13][14][15] , spin pumping 16,17 and the nonlocal electrical injection and detection method [18][19][20] , the ISHE in Fe, Co, Ni and their alloys has been systematically investigated recently. Because of the presence of spin polarized electrons and spontaneous magnetization, spin relaxation in FMMs is actually much more complex than that in NMs. Early magnetotransport 21,22 and ferromagnetic resonance (FMR) 23,24 experiments showed that longitudinal and transverse spin relaxation in FMMs are governed by different mechanisms, corresponding to two different spin relaxation distances when the spin polarizationσ of the injected current (or spin current) is collinear or transverse to the magnetization of ferromagnetic metals. The ISHE can be expressed asJ c / θ SHJs σ, where θ SH is the spin Hall angle;J c andJ s represent the charge current and spin current, respectively; andσ is the polarization direction of the spin current. The variation inJ s in a material is governed by its relaxation mechanism. Thus, the ISHE of FMMs can be used as a tool to study the mechanism of spin relaxation of pure spin current in FMMs. Surprisingly, Tian et al. 25 and Li et al. 26 found that the ISHE and spin relaxation of Co are irrelevant to its magnetization direction in LSSE and FMR-spin pumping experiments, respectively. A recent study on magnon transport in a nonlocal YIG/Py hybrid structure reported that there exists a transverse spin accumulation orthogonal to the direction of the applied charge current (Ĩ) and magnetization (M) in Py. This magnetization-dependent charge/spin conversion in Py is termed the anomalous spin Hall effect (ASHE) and is assumed to have the same spin relaxation distance as the ordinary SHE/ISHE with negligible spin dephasing in Py 18 . These controversial results reflect that the effect of magnetization on the pure spin current in FMMs, one of the most fundamental issues in spintronics, remains unsettled. Parenthetically, it is important to mention that the magnetizationdependent ISHE or ASHE is different from the anisotropic spin Hall effect in nonmagnetic metals 27 and antiferromagnetic metals 28,29 , as well as the anisotropic absorption of pure spin current in pseudo spin valve heterostructures 30 , where the relevant anisotropy originates from the interaction between the spin current polarizationσ and specific crystallographic symmetries 27 or antiferromagnetic spin configurations with respect to the crystallographic axis 28,29 .
In this article, we demonstrate that the ISHE and relaxation of pure spin current in a ferromagnetic metallic permalloy (Ni 80 Fe 20 , denoted as Py) are strongly magnetization orientation dependent. By means of LSSE measurements on a YIG/Cu/Py/IrMn spin valve structure, where the spin index of the spin current is determined by the direction of YIG magnetizationM YIG , the magnetization of PyM Py is pinned by the antiferromagnetic (AFM) IrMn. We observed an appreciable increase in the thermal ISHE voltage of Py of up to 80% when the relative orientationM YIG ;M Py changed from orthogonal (⊥) to collinear ðkÞ. By systematically varying the Py thickness, we determined the spin orientationdependent spin diffusion length λ ? sf , λ k sf and the ratio of effective spin Hall angle θ eff SH ¼ J s 0 ð Þθ SH , i.e., λ ? sf = 1.0 ± 0.1 nm, λ k sf = 2.8 ± 0.5 nm, and θ eff SH ? ð Þ=θ eff SH k ð Þ = 1.5. The present results show that the magnetization of a ferromagnetic metal greatly affects the spin relaxation process and interfacial spin injection efficiency of the spin current simultaneously.

Sample preparation
The YIG films with thicknesses of 100 nm were deposited on 6 mm × 6 mm × 0.5 mm Gd 3 Ga 5 O 12 (GGG) single crystal substrate with (111) orientation by off-axis magnetron sputtering at room temperature. The base pressure of the sputtering system was better than 4 × 10 −6 Pa, and the working gas was high-purity (5N) Ar at a pressure of 1.0 Pa. The sputtering rate was approximately 0.029 nm/s with an RF power of 50 W. Samples were subsequently annealed at 800°C for 2 h in a quartz tube with a pure oxygen pressure of 450 Pa under an oxygen flow rate of 45 SCCM. Radial pattern shadow masks composed of eight 0.3 mm × 5.6 mm strip hollows were placed on the YIG films to grow the metallic multilayers by on-axis dc magnetron sputtering, and a static field of approximately 280 Oe was applied during sputtering to induce exchange bias in the Py/IrMn structure.

Magnetization and thermal voltage measurements
The magnetization of the YIG and metallic films was measured using a vibrating sample magnetometer (VSM, Model 4 HF, MicroSense LLC) at room temperature. The LSSE of the YIG-based spin valve was investigated in a customized magnetotransport measurement system with an electromagnet strength as high as 4 kOe. For the LSSE measurement with a temperature gradient ∇T z normal to the film plane, the samples (measuring 6 × 6 × 0.5 mm 3 ) are placed between two Cu blocks at two different temperatures, which are stacked symmetrically along the vertical central axis (z axis). To ensure heat contact with the two Cu blocks and samples, a thermal conductive silicon pad is taped to the surfaces of the blocks. The bottom Cu block, which is shaped as a cylinder with a height of 125 mm and a diameter of 30 mm, is placed on a horizontally rotatable stage. The top Cu block is rectangular in shape with dimensions 13 × 9 × 1.5 mm 3 and is fixed on a circular printed circuit board (PCB) (26 mm in diameter). A Pt 100-Ω heater (5 × 2 × 1 mm 3 ) (heat source) is fixed at the center of the Cu block back using silver paint, which allows the central part of the top Cu block surface to be quite uniformly heated over a large area (6 × 6 mm 2 at least). The temperature difference between the bottom of the substrate and the top of the film is approximately 13 K for the LSSE measurements as determined by two thermocouples.

Magnetic characterization and experimental configuration
The multilayer films studied have the structure GGG/ YIG (100 nm)/Cu (3.5 nm)/Py (t Py nm)/IrMn (8 nm)/SiO 2 (5 nm) with a Py thickness (t Py ) ranging from 3 to 12 nm. The top SiO 2 layer is used to protect the metallic layers from oxidation. The Cu spacer is fixed at 3.5 nm to avoid interlayer coupling between the YIG and Py, and the samples exhibit an appreciable thermal voltage with a limited shunting effect. The high-quality epitaxial YIG films used are magnetically soft and isotropic in the film plane with a very small saturation field (H s < 3 Oe) 31 . The samples are magnetically characterized using VSM. Figure 1a, b displays the hysteresis loops of a patterned sample (t Py = 10 nm) with the in-plane field applied parallel and orthogonal to the exchange bias direction, respectively. One notes thatM YIG is switched at a field smaller than 3 Oe regardless of the external field direction, whereasM Py shows a shifted loop centered at −200 Oe when the field is parallel to the exchange bias direction or slowly rotates to the field direction to a limit of ±(200−300) Oe when the field is perpendicular to the exchange bias direction. It is reasonable to say thatM Py is fixed at the exchange bias direction, while the YIG magnetization is aligned to different in-plane directions by a Schematic diagrams of c the multilayer structure and experiment configuration and d the coordinate and azimuth for magnetization orientation-dependent LSSE measurement. The metallic layers of samples are radially patterned with eight strip channels (relative alignment of 22.5°), the temperature gradient (on the z axis) is applied perpendicularly to the film plane (on the x−y plane), the external fieldH is applied along the y axis, which will align the magnetization of YIG (M YIG ) and the spin polarization (σ) of the spin current, and the thermal voltage is measured through the channel on the x axis by the two end electrodes. Here, θ means the angle betweenH and the exchange-bias direction (H EB ), changing for the different voltage measurement channels; α represents the direction of the magnetization of Py (M Py ) with respect toH. It is approximately taken that α = θ when the YIG magnetization is aligned by a small field. small external field (e.g., 3 Oe). This also holds for all other samples with different Py thicknesses because the exchange bias field of all samples exceeds 150 Oe in this study.
The schematic illustration of the multilayer structure and the angular ISHE measurement method is detailed in Fig. 1c, d. A temperature gradient ∇T = 13 K between the sample surface and substrate bottom is applied along the film normal (z axis) 13,32 , which can produce spin accumulation between the YIG and the metallic multilayers. The resultant spin current can pass through the Cu layer and be absorbed by the Py/IrMn structure. It should be pointed out that the FMM/AFM exchange bias structure has been proven to be an efficient spin sink structure 13,33 . More importantly, when a small external fieldH (e.g., 3 Oe) that exceeds the YIG saturation field is applied along the y axis,M YIG and the spin polarizationσ of spin current are also aligned along the y axis; then, one can obtain the ISHE voltage V ISHE by measuring the corresponding voltage in the strip along the x axis according tõ E ISHE /J s σ. As will be proven below, other thermal voltages entangled with V ISHE are negligible becauseM Py is fixed in the exchange bias direction during the YIG magnetization reversal at the small field. Under the same measurement conditions, the different strips of the same sample arranged in the x axis will give the corresponding V ISHE of Py with different magnetization orientations.

Magnetization orientation-modulated ISHE voltage in Py
Before presenting thermal ISHE measurement results, we would like to outline all possible contributions to the thermal voltage in a spin valve heterostructure comprising an FM insulator (YIG) and a ferromagnetic metal (Py) exchange biased by an AFM (IrMn) with the LSSE configuration. These include contributions not only from the ISHE but also from ANE and ARLE 11 and can be described by the following formulas: whereσ is the polarization direction of the injected spin currentJ s , S xy is the transverse Seebeck coefficient,M is the magnetization vector of the FMM; ΔS is the difference in the Seebeck coefficients of the metallic multilayers and contacting wires, andJ Q is the heat current in the FMM caused by the temperature gradient ∇T. By sweeping the external field, theṼ ISHE signal of the Py layer generated by the spin current from YIG will vary in response toM YIG , whereas bothṼ ANE andṼ ARLE signals will vary in response toM Py . It should be pointed out that in the spin valve heterostructure, an ISHE voltage signal in IrMn (V ISHE@AFM ) will also be induced due to the injected spin current produced by Py, but this signal is irrelevant to V ISHE of the Py and varies in response toM Py . For simplicity, we hereafter referṼ ANEÀLike for all thermal voltages in response toM Py , including conventionalṼ ANE , V ARLE andṼ ISHE@AFM . Figure 2a shows the thermal voltage loop of the sample YIG/Cu/Py (10 nm)/IrMn with an external field parallel to the exchange bias direction (θ = 0°). The well-separated magnetization reversals of YIG and Py displayed in Fig. 1a are also reflected in the thermal voltage loop except that the thermo-magnetic-electric measurement gives a slightly smaller exchange bias field (H EB ≈ 160 Oe). This can be attributed to the sample temperature increase when the temperature gradient is exerted. From Fig. 2a, we directly obtain V ISHE = 0.22 μV atM Py jjσðM YIG Þ and V ANE-Like = 0.64 μV, corresponding to the respective thermal voltage related to the YIG magnetization reversal within ±3 Oe and the shifted subloop of Py. When the external field is applied perpendicular to the exchange bias direction (θ = 90°), the thermal voltage loop displayed in Fig. 2b for the same sample also resembles its M−H counterpart as expected. Since YIG is extremely soft, with H S below one fiftieth of the Py pinning field H EB , we determine V ISHE at any θ angle as the thermal voltage difference at the fields of ±3 Oe, within which YIG magnetization reversal is just completed, whereasM Py is almost unchanged with negligible V ANE-Like involved. We thus obtain V ISHE = 0.12 μV atM Py?σ ðM YIG Þ, which is significantly smaller than the value atM Py jjσðM YIG Þ. The extended ANE voltage (i.e., V ANE-Like ) is acquired by subtracting V ISHE from the saturated total thermal voltage, which is approximately 0.73 μV, which is also quite different from the value for the parallel field case. We would like to emphasize that within the YIG switching fields of ±3 Oe, the change of V ANE-Like is estimated to be less than 0.02 μV, indeed far smaller than V ISHE , proving that the acquisition of V ISHE and V ANE-Like by the above method is reliable in the present spin valve heterostructure. To rule out other possible artifacts caused by the experiment, we also measured the ISHE voltage of a YIG (100 nm)/Pt (3 nm) sample under the same conditions. The thermal voltages of the eight Pt strips are all saturated within 3 Oe, showing that the magnetism of YIG is extremely soft and isotropic. We observed ISHE voltage fluctuations for different Pt strips, but the variation was less than 5% of the average amplitude, which seems to be caused by the tiny variation of the electrode distance due to the location error of the bonding points on the strip terminals in different measurements (for more details, see Supplementary Fig. S1a, b). We also prepared a GGG/Cu (3.5 nm)/Py (10 nm)/IrMn (8 nm)/SiO 2 (5 nm) control sample, and we note that the saturated thermal voltage is independent of the exchange bias direction except for a random small fluctuation (below 5%) for the eight strips (see Supplementary Fig. S4). It should be pointed out that the spin Hall angle of IrMn is demonstrated to be independent of the exchange bias direction by spin-torque ferromagnetic resonance (ST-FMR) measurements on Py/ IrMn 34 . Therefore, the ISHE voltage in Py is intrinsically modified significantly when the Py magnetization is changed from the parallel to the perpendicular direction with respect to the polarization direction of the injected spin current. Parenthetically, the introduction of pure spin current into the Py layer causes an additional contribution to V ANE-Like as well, and this contribution also strongly depends on the polarization direction of the pure spin current (M YIG ) with respect toM Py , althoughM Py itself is unvaried from the magnetostatic point of view.
The saturated total thermal voltage in the present spin valve heterostructure can be expressed as V total th ¼ 2V ISHEMPy jjM YIGσ ð ÞjjH high À Á þ 2V ANEÀLikeMPy jjM YIG À σ ð ÞjjH high Þj. According to Eqs.  Fig. 2f. The fraction of V ISHE in the total thermal voltage V total th decreases from 0.25 to 0.14 with θ increasing from 0°to 90°and shows a sine function dependence on θ. This reflects that the transport of the injected spin current in Py is greatly affected by the Py magnetization because of the strong exchange interaction between the injected spins and the 3d moment in Py. We would like to point out that the fraction of V ANE-Like ðV N ANEÀLike Þ in the total thermal voltage, as also shown in Fig. 2f, increases from 0.75 to 0.86 when θ varies from 0°to 90°. We have further comparatively studied the ANE-Like signals in GGG/Cu (3.5 nm)/Py (10 nm)/IrMn, and there is no recognizable variation in V ANE-Like (for more details, see the Supplementary Information Section D). The ANE-Like voltage is indeed modified in the spin-valve heterostructure due to the injected spin current with different spin polarization directions, indicative of a new approach to manipulate the spin-dependent transport in a ferromagnetic metal.
Other samples with different Py thicknesses show a similar angular dependence of V N ISHE , but the difference in V N ISHE between θ = 0°and 90°is changed. To quantitatively describe the spin orientation-dependent ISHE, we define the ratio of the angular V ISHE difference as . Figure  increases appreciably with increasing t Py and reaches a maximum of 80% at t Py = 10 nm. Assuming that t Py is much larger than the spin diffusion length (λ sf ) of Py, which is satisfied as we will prove later, V ISHE generated in Py will vary in proportion to its resistance and thus approximately in proportion to the inverse of t Py . The increasing tendency of ΔV ISHE V ISHE 90 ð Þ with increasing t Py suggests that the decay rate of ΔV ISHE caused by θ is slow than the decrease in V ISHE . Importantly, the large Ra (V ISHE ) is observed throughout the t Py range studied here, indicating that the ISHE voltage is strongly modulated by spin orientation on the nanometer scale. We would like to emphasize that because of the anisotropic magnetoresistance (AMR) for metallic ferromagnets, the resistance of the YIG/Cu/Py/IrMn strips at different θ should be different during the YIG reversal process with Py pinned in different directions, which will accordingly alter the corresponding measured thermal voltage. However, AMR in thin Py films at room temperature is rather small, below ∼1% for Py films with thicknesses less than 10 nm 35 . In fact, AMR ≈ 0.1−0.3% for GGG/Cu (3.5 nm)/Py (5-10 nm)/IrMn (8 nm)/SiO 2 (5 nm) due to the shunting effect of Cu and IrMn layers (for more details, see Supplementary Fig. S2). Therefore, the contribution of AMR to the observed angular-dependent ISHE should be negligible.

Magnetization orientation-dependent spin diffusion length and effective spin Hall angle in Py
Below, we focus on the mechanism of the magnetization orientation affecting the transport of pure spin current in ferromagnetic metals. We calculate the absolute magnitude of the thermal ISHE voltage generated in Py (denoted as V   spin valve structure compared with the single FM layer. In the present thermal ISHE measurement, the ISHE voltage is the direct detection of the spin current injected into the metals, and λ ? sf or λ J is the characteristic decay length for the transverse spin accumulation governed by the exchange interaction in ferromagnetic metals 42 . However, λ ϕ is irrelevant to the spin accumulation and diffusion in ferromagnetic metals and sets a length scale of a power law that contrasts with the exponential suppression for transverse spin accumulation 37,44,45 . Our results provide strong evidence that the spin relaxation of the pure current in Py is anisotropic and that the relaxation mechanisms between longitudinal and transverse spin accumulation in ferromagnetic metals are quite different. Finally, we would like to emphasize that the introduction of the antiferromagnetic IrMn layer helps to effectively absorb the spin current and to fix the Py moment, which greatly facilitates the exploration of spin orientation-dependent transport of pure spin current in a ferromagnetic metal.
In conclusion, by using the YIG/Cu/Py/IrMn spin valve heterostructure, we observed that the diffusion of the pure spin current and the inverse spin Hall effect in Permalloy are dependent on its magnetization. We have revealed that the spin orientation-relevant injection efficiency across the interface and spin relaxation of pure spin current in Py are the main reasons for these anisotropic spin transport phenomena. The present results provide a unified understanding of the impact of the magnetization or exchange interaction on the pure spin current transport in ferromagnetic metals.