Extrinsic Spin Hall Effect Research Articles

Charge-spin interconversion in nitrogen sputtered Pt via extrinsic spin Hall effect.

We experimentally investigate the charge-spin interconversion by introducing a lighter impurity, namely nitrogen (N) into Pt by varying the nitrogen gas flow rate,Qfrom 0 to 20%, and studying the Onsager reciprocity of spin Hall effect (SHE) via complementary methods of spin-torque ferromagnetic resonance and spin-pumping inverse SHE measurements, respectively. We notice a reduction in the crystalline nature of Pt upon nitrogen incorporation. We observe the influence of extrinsic side-jump scattering induced SHE by measuring the spin Hall efficiency,θSHin a wide temperature range from 10 to 296 K. This work establishes the incorporation of N in Pt by using sputtering, to enhance the SHE via extrinsic scattering as well as to observe the reciprocal effects of charge-spin interconversion.

Sign change of the extrinsic spin Hall effect in binary alloys

Sign change of the extrinsic spin Hall effect in binary alloys

Enhanced effective spin Hall efficiency contributed by the extrinsic spin Hall effect in Pt1- x Ta x /CoFeB structures

High effective spin Hall efficiency and low magnetic damping constant are essential to achieve efficient spin-charge conversion for energy-efficient spintronic devices. We report the measurements of effective spin Hall efficiency and magnetic damping constant of Pt1- x Ta x /CoFeB structures using spin-torque ferromagnetic resonance (ST-FMR) techniques. With the increase of Ta content, the spin Hall efficiency increases and peaks x = 0.15 with the value of θSHeff=0.35 , before decreases for further Ta content. This non-monotonic variation is attributed to the interaction between the contribution of the extrinsic skew scattering mechanism and the spin-orbit coupling (SOC). The weakening of the SOC in the Pt1-x Ta x layer leads to a decrease in the effective magnetic damping constant with increasing Ta concentration. High-temperature ST-FMR measurements confirm the influence of the Ta concentration on the spin Hall effect and magnetic damping mechanism. Additionally, the decrease in spin mixing conductance and the increase in spin diffusion length leads to a decrease in the interfacial spin transparency.

Investigation of spin–orbit torque performance with W/Cu-multilayers as spin current source

We study the W/Cu multilayers as a spin current source and the coherent spin–orbit torques in a Fe layer using the spin-torque ferromagnetic resonance (STFMR) technique. With increasing numbers of layers, the line shape of the STFMR signals changes from predominantly antisymmetric to predominantly symmetric. When using [W(0.5)/Cu(0.5)]5 as a spin current source, the symmetric amplitude increases by a factor of 5 compared to a single W layer. Simultaneously, the effective damping parameter also increases slightly due to enhanced spin pumping. Along with an increasing trend in the damping-like torque efficiency, this suggests that the extrinsic spin Hall effect is enhanced. Concurrently, the antisymmetric amplitude decreases significantly by a factor of 27, which indicates an increase in the field-like torque when multilayers are used as a spin current source.

Fluctuation contribution to spin Hall effect in superconductors

We theoretically study the contribution of superconducting fluctuation to extrinsic spin Hall effects in two- and three-dimensional electron gas and intrinsic spin Hall effects in two-dimensional electron gas with Rashba-type spin-orbit interaction. The Aslamazov-Larkin, Density-of-States, Maki-Thompson terms have logarithmic divergence $\ln\epsilon$ in the limit $\epsilon=(T- T_{\mathrm{c}})/T_{\mathrm{c}} \rightarrow +0$ in two-dimensional systems for both extrinsic and intrinsic spin Hall effects except the Maki-Thompson terms in extrinsic effect, which are proportional to $(\epsilon-\gamma_\varphi)^{-1}\ln\epsilon$ with a cutoff $\gamma_\varphi$ in two-dimensional systems. We found that the fluctuation effects on the extrinsic spin Hall effect have an opposite sign to that in the normal state, while those on the intrinsic spin Hall effect have the same sign.

Perpendicularly Polarized Spin Hall Effects Induced by Spin-Dependent Scattering in Ferromagnetic Metals

Spin currents in ferromagnets afford diverse functionalities. We evaluate the extrinsic spin Hall effects of magnetic impurity scattering in ferromagnetic metals. We show that spin-dependent scattering can provide a high spin current polarized perpendicularly to the magnetization direction and is a dominant mechanism in the moderate-conductivity regime. We find that the superposition of the spin-conserve and spin-flip channels causes the spin currents. These findings suggest that optimizing alloy composition is an effective strategy to control the spin Hall effect.

Enhancement of Current-Induced Out-of-Plane Spin Polarization by Heavy-Metal-Impurity Doping in Fe Thin Films

Current-induced spin polarization in magnets has recently attracted much attention because out-of-plane spin polarization is allowed, as opposed to polycrystalline nonmagnetic heavy metals. We investigate the $\mathrm{Pt}$-impurity-doping dependence of current-induced out-of-plane spin polarization in $\mathrm{Fe}$ thin films with the use of magnetocircular dichroism. Current-induced out-of-plane spin polarization is clearly observed and attributed to anomalous spin-orbit torque, in which the spin-orbit torque induced by the spin Hall effect in $\mathrm{Fe}$ acts on the magnetic moments of $\mathrm{Fe}$ at the surfaces, generating out-of-plane spin polarization. Notably, current-induced out-of-plane spin polarization is significantly enhanced with increasing $\mathrm{Pt}$ concentration. $\mathrm{Pt}$ impurities with a large spin-orbit interaction induce the extrinsic spin Hall effect of $\mathrm{Fe}$, and consequently, the anomalous spin-orbit torques are enhanced. Our results provide a guiding principle for strengthening current-induced spin polarization in magnets.

Large anomalous Hall effect and spin Hall effect by spin-cluster scattering in the strong-coupling limit

Skew scattering of electrons induced by a spin cluster is studied theoretically focusing on metals with localized magnetic moments. The scattering probability is calculated by a non-perturbative $T$ matrix method; this method is valid for arbitrary strength of electron-spin coupling. We show the scattering of electrons by a three-spin cluster produces a skew angle of order $0.1\pi$ rad when the electron-spin coupling is comparable to the bandwidth. This is one or two orders of magnitude larger than the usual skew angle by an impurity with spin-orbit interaction. Systematic analysis of the scattering probability of one-, two-, and three-spin clusters show that three spins are necessary for skew scattering. We also discuss the relation between anomalous/spin Hall effects and the spin chiralities; we find that the spin Hall effect requires three spins while it is related to the vector spin chirality defined by a pair of spins. The relevance of these results to the large extrinsic anomalous and spin Hall effects in noncentrosymmetric and/or frustrated magnets is also discussed.

Large fieldlike torque in amorphous Ru2Sn3 originated from the intrinsic spin Hall effect

We investigated temperature dependent current driven spin-orbit torques in magnetron sputtered Ru2Sn3 (4 and 10 nm) /Co20Fe60B20 (5 nm) layered structures with in-plane magnetic anisotropy. The room temperature damping-like and field-like spin torque efficiencies of the amorphous Ru2Sn3 films were measured to be 0.14 +- 0.008 (0.07 +- 0.012) and -0.03 +- 0.006 (-0.20 +- 0.009), for the 4 (10 nm) films respectively, by utilizing the second harmonic Hall technique. The large field-like torque in the relatively thicker Ru2Sn3 (10 nm) thin film is unique compared to the traditional spin Hall materials interfaced with thick magnetic layers with in-plane magnetic anisotropy which typically have dominant damping-like and negligible field-like torques. Additionally, the observed room temperature field-like torque efficiency in Ru2Sn3 (10 nm)/CoFeB (5 nm) is up to three times larger than the damping-like torque (-0.20 +- 0.009 and 0.07 +- 0.012, respectively) and thirty times larger at 50 K (-0.29 +- 0.014 and 0.009 +- 0.017, respectively). The temperature dependence of the field-like torques show dominant contributions from the intrinsic spin Hall effect while the damping-like torques show dominate contributions from the extrinsic spin Hall effects, skew scattering and side jump. Through macro-spin calculations, we found that including field-like torques on the order or larger than the damping-like torque can reduce the switching critical current and decrease magnetization procession for a perpendicular ferromagnetic layer.

Large Inverse Spin Hall Effect in Co - Tb Alloys due to Spin Seebeck Effect

Using samples of ${\mathrm{Co}}_{100\ensuremath{-}x}{\mathrm{Tb}}_{x}/\mathrm{Cu}/{\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$, we investigate the heat-to-charge current conversion phenomena in amorphous ${\mathrm{Co}}_{100\ensuremath{-}x}{\mathrm{Tb}}_{x}$ alloys. We find an enhancement of the inverse spin Hall voltage owing to the $\mathrm{Tb}$ impurity by means of the spin Seebeck effect. The spin Hall angle of ${\mathrm{Co}}_{68}{\mathrm{Tb}}_{32}$ is 3.5 times larger than that of $\mathrm{Co}$, and mainly originates from the extrinsic spin Hall effect. Meanwhile, we detect an anomalous Nernst voltage owing to the magnetic properties of ${\mathrm{Co}}_{100\ensuremath{-}x}{\mathrm{Tb}}_{x}$ alloy. The sign of the inverse spin Hall voltage is observed to be the same for all ${\mathrm{Co}}_{100\ensuremath{-}x}{\mathrm{Tb}}_{x}$ samples, whereas the anomalous Nernst voltage changes its sign around the magnetization compensation composition. Our finding proves ${\mathrm{Co}}_{100\ensuremath{-}x}{\mathrm{Tb}}_{x}$ is an efficient spin-to-charge current convertor, and it has advantages for manipulating not only the inverse spin Hall effect but also the anomalous Nernst effect by means of adjusting the $\mathrm{Tb}$ concentration.

Enhanced spin Hall conductivity in tungsten-copper alloys

We report on the enhancement of the spin Hall conductivity in tungsten by alloying with copper, measured by using the spin-torque ferromagnetic resonance technique. The alloying leads to an increase in spin-dependent scattering events and results in an enhancement of the contributing extrinsic spin Hall effects. The measured damping property shows a slight increase with higher tungsten concentration, due to spin current losses from the ferromagnetic layer into the tungsten-copper alloy. At a tungsten concentration of 60%, the spin Hall conductivity reaches a maximum of 3.68±0.68×105Ω-1m-1, corresponding to an enhancement of 120% compared to the pure tungsten sample. At the same concentration, the ratio of the spin Hall angle to the damping of the ferromagnetic layer, which offers a quick estimation for the critical switching current density, is found to be four times smaller as compared to pure tungsten.

Extrinsic spin Hall effect in inhomogeneous systems

Charge-to-spin conversion in inhomogeneous systems is studied theoretically. We consider free electrons subject to impurities with spin-orbit interaction and with spatially modulated distribution, and calculate spin accumulation and spin current induced by an external electric field. It is found that the spin accumulation is induced by the vorticity of electron flow through the side-jump and skew-scattering processes, and the differences of the two processes are discussed. The results can be put in a form of generalized spin diffusion equation with a spin source term given by the divergence of the spin Hall current. This spin source term reduces to the form of spin-vorticity coupling when the spin Hall angle is independent of impurity concentration. We also study the effects of long-range Coulomb interaction, which is indispensable when the process involves charge inhomogeneity and accumulation as in the present problem.

Impact of crystalline anisotropy on the extrinsic spin Hall effect in ultrathin films

An efficient conversion of a charge current into a spin current is a crucial point for application of the spin Hall effect in practical spintronic devices. Recently, we revealed that this goal can be achieved by using ultrathin fcc (111) and (001) noble metal films doped with Bi impurities, which possess spin Hall angles up to 80%. Here, we show that the effect can be further amplified in monolayer films with a strong crystalline anisotropy. This is demonstrated by considering noble metal films with fcc (110) geometry. Our theoretical study predicts related spin Hall angles exceeding 100% especially when the crystalline anisotropy is increased, which tunes the Fermi surface topology.

Composition dependence of spin Seebeck voltage in YIG/Pt100−XRuX, Pt100−XCuX, and Pt100−X(Cu0.5Ru0.5)X

We investigated the composition effect on spin Seebeck coefficient in YIG/Pt100−XRuX, YIG/Pt100−XCuX, and YIG/Pt100−X(Cu0.5Ru0.5)X systems. In all systems the composition of around 50 (at%) showed the maximum spin Seebeck coefficient, which is considered as the result from the extrinsic spin Hall effect improvement since the resistivity was also increased with doping Ru and Cu into Pt host. In terms of the spin Seebeck coefficient dependence on doped element, YIG/Pt100−XCuX was the largest, followed in order by YIG/Pt100−X(Cu0.5Ru0.5)X, and YIG/Pt100−XRuX, although both of Cu and Ru have equally small spin Hall angle in the single state. The X-ray diffraction analysis showed that Cu doping most widely decreased the unit cell size of alloy, and consequently increased the resistivity. It is considered as a reason of improvement of the extrinsic spin Hall angle and the spin Seebeck voltage.

Efficient spin current generation in low-damping Mg(Al, Fe)2O4 thin films

Low-damping magnetic insulators are essential for pure spin current-based electronics as they can generate and transfer spin currents without associated charge currents. Nanometer-thick epitaxial thin films of low-damping magnetic insulators are particularly important in order to control and switch the magnetization via spin transfer torques. We have recently developed films of the ferromagnetic insulator MgAl0.5Fe1.5O4 (MAFO) with a low Gilbert damping parameter (∼0.001). In contrast to Y3Fe5O12 (YIG), MAFO films can be grown on a variety of substrates and have significant in-plane magnetic anisotropy, leading to higher spin-wave frequencies. Here, we demonstrate efficient spin current injection from MAFO into adjacent Pt and β-W layers by ferromagnetic resonance (FMR) broadening and inverse spin Hall effect measurements. Angular dependent magnetoresistance (ADMR) measurements indicate that the proximity effect magnetoresistance is small compared to the spin Hall magnetoresistance associated with spin pumping. FMR and ADMR measurements indicate that MAFO/Pt interfaces have a spin-mixing conductance of ∼2 × 1014 Ω−1 m−2, comparable to that of YIG/Pt. These measurements also show that the spin transport can be described by Dyakonov-Perel spin relaxation combined with an extrinsic spin Hall effect (from skew scattering). These results demonstrate the promise of spinel ferrites for spin current-based spintronics.

Extrinsic-intrinsic crossover of the spin Hall effect induced by alloying

We report the observation of the crossover between the extrinsic and intrinsic spin Hall effect induced by alloying. We found that the spin Hall angle, the ratio of the spin Hall conductivity to the electric conductivity, changes drastically by tuning the composition of Au-Cu alloy. The spin Hall angle changes the sign only in a limited range of the Cu concentration due to the extrinsic skew scattering, while the intrinsic contribution becomes dominant with increasing the Cu concentration. This observation provides essential information for fundamental understanding of spin-orbit physics.

Anomalous Hall Effect in 2D Dirac Materials.

We present a unified theory of charge carrier transport in 2D Dirac systems with broken mirror inversion and time-reversal symmetries (e.g., as realized in ferromagnetic graphene). We find that the entanglement between spin and pseudospin SU(2) degrees of freedom stemming from spin-orbit effects leads to a distinctive gate voltage dependence (change of sign) of the anomalous Hall conductivity approaching the topological gap, which remains robust against impurity scattering and thus is a smoking gun for magnetized 2D Dirac fermions. Furthermore, we unveil a robust skew scattering mechanism, modulated by the spin texture of the energy bands, which causes a net spin accumulation at the sample boundaries even for spin-transparent disorder. The newly unveiled extrinsic spin Hall effect is readily tunable by a gate voltage and opens novel opportunities for the control of spin currents in 2D ferromagnetic materials.

Determination of the spin Hall effect and the spin diffusion length of Pt from self-consistent fitting of damping enhancement and inverse spin-orbit torque measurements

Understanding the evolution of spin-orbit torque (SOT) with increasing heavy-metal thickness in ferromagnet/normal metal (FM/NM) bilayers is critical for the development of magnetic memory based on SOT. However, several experiments have revealed an apparent discrepancy between damping enhancement and damping-like SOT regarding their dependence on NM thickness. Here, using linewidth and phase-resolved amplitude analysis of vector network analyzer ferromagnetic resonance (VNA-FMR) measurements, we simultaneously extract damping enhancement and both field-like and damping-like inverse SOT in Ni$_{80}$Fe$_{20}$/Pt bilayers as a function of Pt thickness. By enforcing an interpretation of the data which satisfies Onsager reciprocity, we find that both the damping enhancement and damping-like inverse SOT can be described by a single spin diffusion length ($\approx$ 4 nm), and that we can separate the spin pumping and spin memory loss (SML) contributions to the total damping. This analysis indicates that less than 40% of the angular momentum pumped by FMR through the Ni$_{80}$Fe$_{20}$/Pt interface is transported as spin current into the Pt. On account of the SML and corresponding reduction in total spin current available for spin-charge transduction in the Pt, we determine the Pt spin Hall conductivity ($\sigma_\mathrm{SH} = (2.36 \pm 0.04)\times10^6 \Omega^{-1} \mathrm{m}^{-1}$) and bulk spin Hall angle ($\theta_\mathrm{SH}=0.387 \pm0.008$) to be larger than commonly-cited values. These results suggest that Pt can be an extremely useful source of SOT if the FM/NM interface can be engineered to minimize SML. Lastly, we find that self-consistent fitting of the damping and SOT data is best achieved by a model with Elliott-Yafet spin relaxation and extrinsic inverse spin Hall effect, such that both the spin diffusion length and spin Hall conductivity are proportional to the Pt charge conductivity.

Large enhancement of spin-orbit torques in Pd/CoFeB: The role of boron

The conversion of charge current into pure spin current based on the spin Hall effect provides a new way of spin injection and manipulation in novel spintronic architectures. The realization of a large conversion efficiency between the charge and spin currents is a crucial issue for its applications. Here we report a giant enhancement of spin Hall angle (SHA) in palladium through boron engineering. We measure a large SHA of 0.16 in palladium, with perpendicular magnetic anisotropy in the Pd/CoFeB-based structure compared to the Pd/CoFe-based structure ($\mathrm{SHA}=0.02$). Combined with theoretical calculations, it is found that both intrinsic and extrinsic spin Hall effects have been significantly enhanced through the introduction of boron. Taking into account the incorporation of boron in the thin films, the enhanced SHA is attributed to significant microscopic and electronic changes in the Pd host metal. This finding illustrates a crucial role of boron in manipulating spin-orbit torques. Together with high conductivity and long spin diffusion length, this work makes Pd a promising candidate for spintronic devices with magnetization switching by current pulse injection.

Intrinsic and Extrinsic Spin Hall Effects of Dirac Electrons

We investigate the spin Hall effect (SHE) of electrons described by the Dirac equation, which is used as an effective model near the $L$-points in bismuth. By considering short-range nonmagnetic impurities, we calculate the extrinsic as well as intrinsic contributions on an equal footing. The vertex corrections are taken into account within the ladder type and the so-called skew-scattering type. The intrinsic SHE which we obtain is consistent with that of Fuseya et al. [J. Phys. Soc. Jpn. 81, 93704 (2012)]. It is found that the extrinsic contribution dominates the intrinsic one when the system is (semi)metallic. The extrinsic SHE due to the skew scattering is proportional to $\Delta / n_{\rm i} u$, where $2\Delta$ is the band gap, $n_{\rm i}$ is the impurity concentration, and $u$ is the strength of the impurity potential.