Crossover from Positive to Negative Spin Hall Signal in a Ferromagnetic Metal Induced by the Magnetization Modulated Interface Effect

The spin Hall effect and its inverse (SHE/ISHE), describing the charge‐to‐spin interconversion, are of critical importance to the fundamental physics involving spin‐orbit coupling and the application of spintronic devices. These phenomena in nonmagnetic materials are reasonably understood after extensive studies. In ferromagnetic metals, however, the fundamental issue of generation and transport of pure spin current, especially the interplay of charge‐to‐spin interconversion and magnetization, is as‐yet poorly understood. Here, direct experimental evidence for the sign change in ISHE by injecting a spin current from Y3Fe5O12 into a Fe film via a Cu spacer is reported. The sizable negative ISHE signal (VISHE) in nanometer‐thick Fe films reverses its sign with a comparable magnitude when Fe magnetization is varied from a longitudinal to transverse orientation with respect to spin current polarization. With decreasing Fe thickness, this negative longitudinal VISHE increases rapidly to a larger positive value in magnitude. The opposite spin Hall angles for longitudinally and transversely polarized spin currents are reproduced by first‐principles transport calculations and the sign change is attributed to the anisotropic contribution at the ferromagnetic interface. This work lays a firm foundation for manipulating spin‐to‐charge interconversion with an extra degree of freedom of magnetization orientation through ferromagnetic metals.


Introduction
The spin Hall effect (SHE) and its inverse (ISHE) describe the interconversion between a charge current (j c ) and a spin current (j s ) driven by spin-orbit coupling (SOC).The conversion efficiency is characterized by the spin Hall angle ( SH ) via j s =  SH (ℏ/2e)j c ×  DOI: 10.1002/apxr.202300017 for SHE or j c =  SH (2e/ℏ)j s ×  for ISHE, with  representing the spin current polarization direction.SHE/ISHE phenomena have been extensively studied in the field of spintronics.3] which is vital for next-generation spintronic devices.
Nevertheless, whether  SH of an FM can be effectively tuned by rotating m remains an open question.Through LSSE measurements in a Y 3 Fe 5 O 12 (YIG)/Cu/Co(2 nm) stack, [34] the detected ISHE voltage using a very thin Co layer was independent of m Co ; in contrast, nonlocal measurements using YIG/Ni 80 Fe 20 (13 nm)  and YIG/Cu/Co 60 Fe 20 B 20 (7 nm) stacks [14,15] showed that both the SHE-induced spin currents and the detected ISHE signals depended on the magnetization orientation of the FM.It should be emphasized that the measured ISHE signals rely on  SH and other key parameters, [20] including spin diffusion length and spin memory loss at the interface, [35,36] where the spin current is injected.All these material parameters in principle depend on the relative angle between the magnetization orientation and the injected spin current polarization. [20]Therefore, the above seemingly contradictory results do not necessarily mean that the  SH of Co is independent of m Co , whereas the  SH for Ni 80 Fe 20 and Co 60 Fe 20 B 20 depends on their m.In addition, despite numerous experimental and theoretical studies, charge-tospin conversation analysis of FMs in these studies can be complicated by associated effects such as anomalous Hall effect, [28] anisotropic magnetoresistance, [28] planar Hall effect [37] and spin pumping. [38]Therefore, the fundamental issue of the generation and transport of pure spin current in FM is far from conclusive and awaits more direct experimental proof.
In this work, we systematically investigated the ISHE of Fe films at different magnetization alignments between Fe (m Fe ) and YIG (m YIG or ) through a spin valve heterostructure YIG/Cu/Fe/Ir 25 Mn 75 (IrMn) with spin current injected from YIG into Fe.By fixing all the experimental setups but only varying the relative orientation between m Fe and , we observed the solid experimental evidence for the m Fe -dependent ISHE signals and unambiguously demonstrated that the ISHE sign can be well tuned by the magnetization orientation and Fe thickness.First-principles calculations reveal that the observed ISHE voltage arises mainly from the interfacial contribution with opposite signs for longitudinal and transverse  SH at the Cu/Fe interface due to the modulation of Rashba SOC.This anisotropic interface  SH can be significantly suppressed by interfacial atomic intermixing.

Structural and Magnetic Characterization of the Samples
We prepared the heterostructure of YIG(100 nm)/ Cu(3.5 nm)/Fe(1.5−20nm)/IrMn(8 nm)/SiO 2 (5 nm) by using ultrahigh vacuum magnetron sputtering.Details on the sample fabrication and the multilayer microstructure characterization can be found in the Experimental Section and Figure S1, Supporting Information.The crystalline structure of the samples was examined through X-ray diffraction (XRD) 2/ scans.Figure 1a shows the XRD result of a representative sample with a 15 nm Fe layer.Apart from strong diffraction peaks from Gd 3 Ga 5 O 12 /YIG(444), the (110) peak of the Fe layer is observable, which is preferred for the body-centered cubic structure because of the close-packed (110) planes.Similarly, the Cu layer with a face-centered cubic structure should adopt (111) stacking to some extent, but no corresponding peak from the Cu layer is observed due to insufficient thickness.Magnetically, the heterostructure is characterized by a vibrating sample magnetometer.The Fe layer is strongly pinned with an exchange bias field (H EB ) of 50−320 Oe, depending on the Fe thickness, whereas the decoupled YIG layer is very soft and magnetically isotropic in the film plane with a saturation field less than 3 Oe for all samples.Figure 1b shows the in-plane hysteresis loops of a representative sample YIG(100 nm)/Cu(3.5nm)/Fe(15 nm)/IrMn (8 nm) with the field applied parallel and perpendicular to the H EB .

Angular-Dependent LSSE Signals in Fe
We performed LSSE measurements on patterned samples to study the m Fe dependence of ISHE in Fe. Figure 1c displays the schematics of the experimental setup.The samples with metallic multilayers radially patterned into eight strip channels (0.3 × 5.6 mm) with a relative angle of 22.5°are placed between two Cu blocks.The top rectangular Cu block is uniformly heated, whereas the bottom Cu block serves as a heat sink.Under the perpendicular temperature gradient (∇T), the thermal spin current generated in the YIG layer is vertically pumped into the Cu spacer, resulting in nonequilibrium spin accumulation.With negligible spin current dissipation in Cu, the spin current transmits to the pinned Fe layer and eventually converts into a charge current via ISHE.Figure 1d shows the magnetic configuration of a Fe strip in the ISHE measurement, where the injected spin current (j s ) propagating along ∇T is defined as the z-axis.The external field H is applied at the x-axis, so m YIG (or ) is aligned along the x-axis at a small field of 3 Oe.The relative angle between H EB and H (x-axis) is denoted as .Since H EB is at least an order of magnitude larger than the YIG saturation field, it is safe to say that m Fe is fixed in the H EB direction during YIG switching between the ± x directions.The corresponding voltage change measured in the Fe strip located at the y-axis reflects the ISHE signal V ISHE ∝ SH j s ×  with negligible other thermal voltage contributions.With different strips aligned to the y-axis by rotating the sample, the V ISHE signal for different m Fe is thus obtained.It should be pointed out that because of the small spin diffusion length ( sf ∼1− 2 nm) for pure spin currents in FMs, [39,40] the YIG spin current can hardly pass through the Fe layer, and the corresponding ISHE voltage induced in IrMn should be negligible for all samples (see Figure S3, Supporting Information).
Apart from the ISHE signal in response to the YIG switching at small fields, additional thermal voltages arise when the Fe magnetization is switched at larger fields under ∇T.The contributions include the voltages induced in the Fe layer by the anomalous Nernst effect (ANE) [20,21] and anomalous Righi-Leduc effect (ARLE) [41,42] as well as the ISHE voltage induced in the IrMn layer due to the injected spin current produced by Fe.For simplicity, we hereafter refer V ANE − Like to these thermal voltages in response to the m Fe switching.
Figure 2a-f shows the thermal voltage (V th ) of sample YIG/Cu/Fe(4 nm)/IrMn against the external field in different directions.When H is parallel to H EB ( = 0°), the V th -H curve displayed in Figure 2a exhibits two well-separated subloops, corresponding to the respective magnetization reversals of YIG and pinned Fe.The V ISHE value with m Fe collinear to  is significant and can be directly determined from the YIG switching subloop.When H deviates from H EB with  varying from 22.5°to 90°, as shown in Figure 2b-e, the V th -H subloops relating to Fe magnetization reversal become slanted, but the subloops of YIG switching at different  remain rather sharp within ±3 Oe due to the excellent isotropic softness of the YIG layer (see Figure S4a, Supporting Information) and the strong pinning of the Fe layer.V ISHE at different m Fe orientations are therefore extracted from these sharp narrow V th -H subloops within ±3 Oe.Comparing V ISHE in Figure 2a-e, we find that V ISHE changes monotonically with  and remarkably exhibits a crossover between opposite signs with comparable magnitude at  = 0°and 90°.With further increasing , V ISHE gradually changes back.The representative V th -H curve at  = 180°is displayed in Figure 2f, where V ISHE is the same as that obtained at  = 0°.Since the V ISHE sign is only determined by the  SH under a fixed spin current injection, it is thus unambiguously demonstrated that the effective  SH of this magnetic system is strongly dependent on its magnetization orientation. The Here, the sign of V ISHE is defined by comparing with the control samples YIG(100 nm)/Pt(3 nm) and YIG(100 nm)/Cu(3.5nm)/Pt(3 nm) (see Figure S4a  by a spin current j z sx along the z-axis with x polarization can be derived [30] after projecting  to the longitudinal and transverse directions of m Fe in the film plane.
The above expression is consistent with the measured V ISHE at different  due to unequal  ∥ SH and  ⊥ SH with opposite signs.Notably, the effective spin current j z sx in the Fe layer should be modulated, more or less, by the m Fe since the interfacial spin transparency and the  sf of bulk Fe should depend on the relative angle between  and m Fe .
From the V th -H loops in Figure 2a-f, V ANE − Like can be simultaneously determined.Since all the strips for different  have identical saturation magnetization states in the large-field limit, the saturated thermal voltage (V sat ), equal to the sum of V ISHE and V ANE − Like , is thus the same regardless of the intermediate magnetic configurations.Therefore, V ANE − Like at each  is acquired by subtracting the corresponding V ISHE from V sat and is displayed in Figure 2h.V ANE − Like exhibits an overall cos 2  dependence with a significant variation from 197 nV at  = 0°down to 102 nV at  = 90°.Parenthetically, in a patterned control sample of GGG/Cu(3.5 nm)/Fe(4 nm)/IrMn (8 nm)/SiO 2 (5 nm), the saturated thermal voltage (i.e., V sat = V ANE − Like ) is ≈200 nV, independent of  (see Figure S5, Supporting Information).The variation of V ANE − Like at different polarization directions can be attributed to the spin-transfer torque (STT) effect.In the YIG/Cu/Fe/IrMn, the pure spin current is injected from YIG into the magnetic Fe layer, which can excite the Fe magnetization precession via spintransfer torque (STT) resulting in a decrease in the magnetization of Fe, although its magnitude is unaltered from the magnetostatic point of view.The STT strongly depends on the relative angle , namely, STT is maximized at 90°and becomes minimal when m YIG is collinear with m Fe .Therefore, cos 2  is the lowestorder angular dependence of the ANE in this configuration.Thermal spin-transfer torque is an important issue unexplored yet but is beyond the scope of the present work.

Magnetization-Orientation and Thickness Dependence of Spin Hall Angle
To obtain a complete view of the ISHE of Fe films and the inherent m Fe -dependent  SH , V th -H loops at  = 0°and 90°are measured for samples with t Fe ranging from 1.5 to 20 nm.When the Fe layer is thicker than 4 nm, all samples exhibit appreciable ISHE signals with a negative/positive sign for longitudinal/transverse ISHE (LISHE/TISHE), similar to those displayed in Figure 2a,e.At t Fe < 4 nm, the LISHE voltage exhibits a transition from negative to positive as t Fe decreases.Figure 3a presents the V th -H loops at  = 0°and 90°for the representative samples with Fe thicknesses below 4 nm.The LISHE signals for t Fe = 3.5 and 1.8 nm are unambiguously negative and positive, respectively.In between, the LISHE at t Fe = 2.5 nm is too small to be detected.For TISHE, the measured signals at  = 90°are always positive.We would like to point out that, the samples with t Fe < 2 nm have a modified Fe/IrMn interface by inserting a 3 Å Cu dusting layer, with which the ultrathin Fe layers switch magnetization sharply at the cost of slightly decreased H EB .Without the dusting layer, the ultrathin Fe samples with increased roughness exhibit rather slanted V ANE − Like -H subloops together with large coercivity (not shown) to the enhanced fluctuation of local pinning at the Fe/IrMn interface, [43,44] which makes the determination of ISHE less reliable.
The LISHE and TISHE voltages generated in the Fe layers after subtracting the shunting effect of the Cu and IrMn layers are summarized in Figure 3b.V Fe TISHE decreases monotonically as t Fe increases, and it has positive values within the whole thickness range, reflecting a positive  ⊥ SH for Fe.In contrast, V Fe LISHE decreases rapidly from a large positive value to a significant negative value as the Fe thickness increases from 1.5 to 4 nm, followed by a slow decrease until t Fe = 15 nm.Finally, the large negative V Fe LISHE tends to increase with decreasing absolute value when t Fe is beyond 15 nm.The nonmonotonic variation in V Fe LISHE with the Fe thickness suggests competing mechanisms involved in the ISHE in Fe between the negative interface contribution and the positive bulk contribution (see Figure 4 below).Furthermore, the above magnetization-and thickness-induced Fe spin Hall angle reversal revealed via LSSE have been perfectly reproduced by the microwave spin pumping measurement on these exchange-biased spin valve heterostructure samples (see Figure S6, Supporting Information).

First-Principles Spin Transport Calculation and Discussion
We have performed first-principles spin transport calculations (see Experimental Section and Figure S7, Supporting Information) within the Landauer-Büttiker formalism. [45,46]To avoid introducing more complex uncertainties by quantifying the values of spin-mixing conductance, spin memory loss, and other interfacial spin transport parameters, here we explicitly compute the local longitudinal and transverse currents, which can be directly compared with the experiment.But the spin transport and dissipation at the interface are implicitly imposed in our calculation.When a charge current (j z c ) passes through a Cu/Fe bilayer along the film's normal direction (z-axis), a spin current (j y sx ) is induced as a consequence of SOC. Figure 4a shows the normalized spin current with ||m Fe ( = 0°).The calculated  ∥ SH is positive in the interior of Fe but is negative at the Cu/Fe interface for both clean (blue triangles) and disordered interfaces (red triangles).Such a negative interfacial  ∥ SH was reported in the calculation of the Au/Fe bilayer. [33]At  = 90°(⊥m Fe ),  ⊥ SH displayed in Figure 4b is positive both in bulk Fe and at the interface despite noticeable oscillations due to spin dephasing. [47]We have also calculated the charge current density j y c in response to an injected spin current j z sx , and the same conclusions about the interface and bulk contributions at  = 0°and 90°are confirmed independently.Figure 4c shows the calculated  SH of bulk Fe with continuously varying .It is always positive at both  = 0°and 90°, in agreement with the literature. [29,31]It is important to note that the sign of the spin Hall angle extracted in the LISHE does not correspond to the bulk  SH even in very thick samples (up to 20 nm).This is because the spin current can only propagate for a finite depth into the Fe, which is determined by the finite spin diffusion length.Because of the small magnitude of bulk  SH and the short propagation length of spin currents (≈ 1 − 2 nm) in FMs, [39] the positive bulk contribution saturates at sufficiently thick Fe samples and is smaller than the negative interface contribution in our LISHE case.Therefore, based on the results of the above analysis, the measured V ISHE and the sign change are dominated by the spin-to-charge conversion at the interface, where the inverse Rashba-Edelstein effect (IREE) [48,49] plays an important role in addition to the interface SHE. [47] The interface spin orientation for the majority spin in the momentum space is schematically illustrated in Figure 4d, which is the combined effect of the Rashba SOC and a much larger exchange splitting at a ferromagnetic interface. [50]At  = 0°, the injected spins exhibit polarization that is collinear with m Fe , and after being converted to a charge current, they are allowed to propagate along both the + y and − y directions.Here, spin-momentum locking is strongly suppressed by the large exchange field.At  = 90°, the injected spins along +x prefer to move along − y because the slightly lower energy induced by the Rashba spin-orbit field results in the IREE.Therefore, the negative interface SHE is compensated by the IREE at  = 90°, while it is nearly unchanged at  = 0°, resulting in a sign change in the measured V ISHE .This mechanism results in the same spin-to-charge conversion at  = 0°and 180°, as shown in Figure 2g, which is different from the symmetry resulting from spin-filtering and spin-precession effects. [32]For an ultrathin Fe film with t Fe < 2.5 nm, more structural and chemical disorders are evident at the Cu/Fe interface and Cu atoms can diffuse into the whole Fe layer.We would expect that the Rashba effect mainly due to the surface state of Fe disappears [51] and the interface SHE is significantly changed.To model this case, we calculate spin transport in a bilayer consisting of Cu and Cu 50 Fe 50 alloy, as shown by the gray circles in the insets of Figure 4a,b for  = 0°and 90°, respectively.Then, the negative spin-to-charge conversion at the interface disappears, and both cases exhibit a positive  SH .This explains the exceptional sign change in the measured V ISHE at  = 0°with varying thickness of the Fe film.
Finally, we would like to point out that current-induced SOT in FM/NM/FM trilayers [30] is an important issue for spin current phenomena and can be utilized to realize field-free magnetization switching. [19]However, it is technically difficult to directly obtain the spin Hall angle of an FM layer from the SOT in FM/NM/FM because torques arising from the anomalous Hall effect, anisotropic magnetoresistance, and many other effects are involved. [28,37,52]In addition, the undesired entanglement between the damping-and field-like torques [18,53] and the spin-pumping effect [38] will also complicate the spin current generated from the FM metal.In comparison with the SOTbased methods, including the nonlocal transport measurements and spin-transfer torque analysis, the LSSE-ISHE experimental scheme used in this work is a reliable approach to reflect the charge-to-spin conversion of the FM layer since the thermalinduced pure spin current is the spin injector, and therefore free from the aforementioned spurious effects.With the nature of the magnetization orientation-dependent charge-to-spin interconversion in the FM metal and/or at the associated interface unambiguously revealed by our direct ISHE measurement, the SOT in FM/NM/FM trilayers can be fully exploited in future studies.

Conclusion
In conclusion, we have demonstrated that the spin-to-charge conversion efficiency of Fe and even its sign can be tuned by the magnetization orientation and thickness by performing the ISHE experiment using the YIG/Cu/Fe/IrMn stack.Combined with the first-principles transport calculation, we have revealed that the strong angular dependence of the ISHE voltage observed is mainly from the interfacial contribution with opposite signs for the longitudinal and transverse spin Hall angles at the Cu/Fe interface due to modulation of the Rashba SOC.Our findings provide direct experimental evidence of the spin Hall angle, the fundamental physics involving charge-to-spin interconversion, concerning magnetization orientation in ferromagnetic metals and highlight the important role of the interface in spin transport phenomena.It offers additional degrees of freedom for exploiting and optimizing spin-orbit torques in FM/NM/FM trilayers.

Experimental Section
The spin valve heterostructure of YIG(100 nm)/Cu(3.5nm)/Fe(1.5-20nm)/IrMn (8 nm)/SiO 2 (5 nm) was fabricated by using ultra-high vacuum magnetron sputtering.The YIG films with a thickness of 100 nm were grown on (111)-oriented Gd 3 Ga 5 O 12 (GGG) substrates using an ultrahigh vacuum off-axis sputtering system (4 × 10 −6 Pa) at room temperature (RT).The working gas was high pure Ar (5N) at a pressure of 1.0 Pa and the sputtering rate was about 0.029 nm s −1 for YIG with a radio frequency power of 50 W.The as-deposited YIG films were amorphous.In order to obtain high-quality garnet films with epitaxial growth, all films were annealed at 800 °C for 2 h and then cooled down to RT in a quartz tube furnace with an oxygen pressure of 500 Pa and a flow rate of 45 SCCM.The YIG films exhibit excellent surface magnetism and enable highly efficient spin current transmission. [54,55]Then the metallic multilayers with a SiO 2 capping layer were ex situ deposited on the YIG films without any particular surface treatment by conventional multi-source sputtering with an in-plane field of about 300 Oe applied to induce the exchange bias in the Fe/IrMn structure.
The magnetization of the samples was measured using a vibrating sample magnetometer (VSM, Model 4 HF, MicroSense LLC) at room temperature.In the longitudinal spin Seebeck measurement, the patterned samples were placed between two Cu blocks through thermal conductive silicon pads.The top rectangular Cu block was uniformly heated by a Pt 100 Ω heater fixed on the back, whereas the bottom big cylindric block served as the heat sink.The whole thermal assembly was placed on a horizontally rotatable stage.The temperature difference between the bottom of the substrate and the top of the film was about 13 K, determined by two thermocouples.The metallic multilayers of Cu/Fe/IrMn deposited on the YIG films were radially patterned into eight strips (single strip dimension 0.3 × 5.6 mm) via the shadow mask.By applying the external field H along the x-axis, meanwhile placing the different strips of the same sample along the y-axis and measuring the corresponding thermal voltage by a nanovoltmeter (Keithley 2182A), the individual V ISHE values with the Fe magnetization fixed at different directions (i.e., the exchange bias field H EB direction) was obtained.To minimize the influence of this training effect, the thermal voltages were recorded after 3-5 magnetic cycles, which was found to be enough for the saturated H EB of Fe/IrMn.
First-principles spin transport calculations in a Cu/Fe bilayer were performed based on the recently developed local current scheme. [45,46]Following the XRD result, we construct Fe (110) film with the body-centered cubic (bcc) lattice constant a Fe =2.867 Å, which is attached to a Cu film along the face-centered cubic (fcc) (111).The crystalline orientation of Cu is less crucial thanks to its free-electron-like Fermi surface.Due to the different lattices and unit cells, we use a 6 √ 2 × 9 supercell bcc Fe (110) to match a rectangular 9

√
2∕2 × 3 √ 6 supercell of fcc Cu (111), where the lattice constant of Cu is stretched by 1.4%.Thermal lattice disorder is introduced into both Fe and Cu to reproduce their experimental resistivity at room temperature.In the calculation, the 2D Brillouin zone of the supercell is sampled by a 28 × 28 k-mesh and 20 random configurations of thermal disorder for the Cu/Fe bilayer in the scattering region are calculated.

Figure 1 .
Figure 1.Structural and magnetic characterization and LSSE measurement setup.a) X-ray specular diffraction pattern and b) M-H loops for the sample YIG(100 nm)/Cu(3.5nm)/Fe(15 nm)/IrMn(8 nm)/SiO 2 (5 nm) with field applied parallel (black line) and perpendicular (red line) to the exchange bias direction.c) Schematic diagram of the longitudinal spin Seebeck effect measurement geometry.d) The magnetic configuration of the sample in the ISHE measurement.
,b, Supporting Information), in which the measured V ISHE is positive for the positive  SH of Pt.The V ISHE obtained at different  for the sample YIG/Cu/Fe(4 nm)/IrMn is summarized in Figure 2g.V ISHE is approximately −50 nV with  parallel to m Fe ( = 0°) and changes to 50 nV with  perpendicular to m Fe ( = 90°).The angular dependence of V ISHE can be approximately described by a cos 2  function.It should be stressed that the radially patterned YIG(100 nm)/Pt(3 nm) gives identical V ISHE within experiment accuracy for different in-plane directions (see Figure S4a, Supporting Information).To understand the V ISHE behavior of the ferromagnet Fe, we define  ∥ SH and  ⊥ SH as the spin Hall angle for longitudinally (||m Fe ) and transversely (⊥m Fe ) polarized spin currents, respectively.The charge current j y c induced in Fe Adv.Physics Res.2023, 2, 2300017

Figure 2 .
Figure 2. Angular-dependent ISHE and ANE-Like results.Thermal voltage V th in the channel at the y-axis by sweeping H along the x-axis with H EB at angles of a)  = 0°, b)  = 22.5°, c)  = 44.5°,d)  = 67.5°,e)  = 90°, and f)  = 180°with respect to the x-axis for the sample YIG(100 nm)/Cu(3.5nm)/Fe(4 nm)/IrMn(8 nm).The variation in g) V ISHE and h) V ANE − Like as a function of ; the solid lines are the fitting results using a cos 2  function.

Figure 3 .
Figure 3. Thickness-dependent ISHE and ANE-Like results.a) Thermal voltage V th versus external field H with H EB at angles  = 0°and 90°for samples with t Fe = 3.5, 2.5, and 1.8 nm.b) Variation in LISHE and TISHE voltages generated in the Fe layer as a function of Fe thickness; the shunting effect of Cu and IrMn is subtracted.

Figure 4 .
Figure 4. First-principles spin transport calculation in a Cu/Fe bilayer.Calculated spin current with a) collinear and b) perpendicular to m Fe when a charge current passes through a Cu(111)/Fe(110) bilayer at room temperature.The blue (red) triangles represent the results for a clean (disordered) Cu/Fe interface.Two atomic layers at the disordered interface are modeled by Cu 50 Fe 50 alloy.The gray circles in the insets of a) and b) are calculated with Fe replaced by Cu 50 Fe 50 alloy.c) Calculated spin Hall angle of bulk Fe as a function of .d) Schematic of the IREE at a ferromagnetic interface.The orange arrows indicate the momentum-dependent local effective field at the 2D Fermi surface.Only the majority spin is plotted for simplicity.The green and red arrows represent m Fe and , respectively.