By quantum Monte Carlo simulation of a realistic multiorbital Anderson impurity model, we study the spin-orbit interaction (SOI) of an Fe impurity in Au host metal. We show, for the first time, that the SOI is strongly renormalized by the quantum spin fluctuation. Based on this mechanism, we can explain why the gigantic spin Hall effect in Au with Fe impurities was observed in recent experiment, while it is not visible in the anomalous Hall effect. In addition, we show that the SOI is strongly renormalized by the Coulomb correlation U. Based on this picture, we can explain past discrepancies in the calculated orbital angular momenta for an Fe impurity in an Au host.
Effective masses, Burstein-Moss shift, and bandgap renormalization in degenerate Al-doped ZnO from broadband ellipsometry and Hall measurements
Pontificia Universidad Católica del Perú（秘鲁天主教宗座大学）；Helmholtz-Zentrum Berlin für Materialien und Energie GmbH（柏林亥姆霍兹材料与能源中心有限公司）；Eindhoven University of Technology（埃因霍温理工大学）
The spin-orbit interaction in a solid couples the spin of an electron to its momentum. This coupling gives rise to mutual conversion between spin and charge currents: the direct and inverse spin Hall effects. The spin Hall effects have been observed in metals and semiconductors. However, the spin/charge conversion has not been realized in one of the most fundamental semiconductors, silicon, where accessing the spin Hall effects has been believed to be difficult because of its very weak spin-orbit interaction. Here we report observation of the inverse spin Hall effect in silicon at room tempera…
A reply to the Comment arXiv:1401.6407 on Phys. Rev. Lett. 111, 217204 (2013), "Detection of Microwave Spin Pumping Using the Inverse Spin Hall Effect"
In this study, the temperature dependence of the spin Hall angle of palladium (Pd) was experimentally investigated by spin pumping. A Ni80Fe20/Pd bilayer thin film was prepared, and a pure spin current was dynamically injected into the Pd layer. This caused the conversion of the spin current to a charge current owing to the inverse spin Hall effect. It was found that the spin Hall angle varies as a function of temperature, whereby the value of the spin Hall angle increases to ca. 0.02 at 123 K.
Using Y3Fe5O12 (YIG) thin films grown by our sputtering technique, we study dynamic spin transport in nonmagnetic (NM), ferromagnetic (FM) and antiferromagnetic (AF) materials by ferromagnetic resonance (FMR) spin pumping. From both inverse spin Hall effect (ISHE) and damping enhancement, we determine the spin mixing conductance and spin Hall angle in many metals. Surprisingly, we observe robust spin conduction in AF insulators excited by an adjacent YIG at resonance. This demonstrates that YIG spin pumping is a powerful and versatile tool for understanding spin Hall physics, spin-orbit coupli…
A generalized definition of intrinsic and extrinsic transport coefficients is introduced. We show that transport coefficients from the intrinsic origin are solely determined by local electronic structure, and thus the intrinsic spin Hall effect is not a transport phenomenon. The intrinsic spin Hall current is always accompanied by an equal but opposite intrinsic orbital-angular-momentum Hall current. We prove that the intrinsic spin Hall effect does not induce a spin accumulation at the edge of the sample or near the interface.
A new kind of charge-Hall effect is shown. Unlike in the usual Hall effect, the driving force in the longitudinal direction is a spin force, which may originate from the gradient of a Zeeman field or a spin-dependent chemical potential. The transverse force is provided by a Berry curvature in a mixed position-momentum space. We can establish an Onsager relation between this effect and the spin-Hall effect provided the spin current in the latter is modified by a torque dipole contribution. This remarkable relation leads to new ways for experimental detection of spin accumulation predicted by th…
We investigate the spin Hall effect of W-Hf thin films, which exhibit a phase transition from a segregated phase mixture to an amorphous alloy below 70% W. The spin Hall angle was determined with a planar harmonic Hall voltage technique. Due to the accompanying jump in resistivity, the spin Hall angle shows a pronounced maximum at the composition of the phase transition. The spin Hall conductivity does, however, reduce from W to Hf with a weak discontinouity across the phase transition. The maximum spin Hall angle of $θ_\mathrm{SH} = -0.25$ is obtained for amorphous W$_{0.7}$Hf$_{0.3}$. A deta…
Reversible spin Hall effect comprising the "direct" and "inverse" spin Hall effects was successfully detected at room temperature. This experimental demonstration proves the fundamental relations called Onsager reciprocal relations between spin and charge currents. A platinum wire with a strong spin-orbit interaction is used not only as a spin current absorber but also as a spin current source in the present lateral structure specially designed for clear detection of both charge and spin accumulations via the spin-orbit interaction. The obtained spin Hall conductivity is much larger than the r…
In this study, by engineering the molecular structure, we optimize the spin Hall conductivity and the spin Hall angle in organics by more than five and three orders of magnitude, respectively. We identify two important characteristics of organic molecules, namely substitution of heavy elements and the torsion angles between constituent units of the polymer, which have significant effects on the spin Hall signal. These characteristics are directly related to the spin-orbit coupling and the energetic disorder, both of which offer a wide scope of chemical tunability in high-mobility polymers. We …
The spin Hall effect does not generally result in a charge Hall voltage. We predict that in systems with inhomogeneous electron density in the direction perpendicular to main current flow, the spin Hall effect is instead accompanied by a Hall voltage. Unlike the ordinary Hall effect, we find that this Hall voltage is quadratic in the longitudinal electric field for a wide range of parameters accessible experimentally. We also predict spin accumulation in the bulk and sharp peaks of spin-Hall induced charge accumulation near the edges. Our results can be readily tested experimentally, and would…
Large charge-to-spin conversion (spin Hall angle) and spin Hall conductivity are prerequisites for development of next generation power efficient spintronic devices. In this context, heavy metals (e.g. Pt, W etc.), topological insulators, antiferromagnets are usually considered because they exhibit high spin-orbit coupling (SOC). In addition to the above materials, 5d transition metal oxide e.g. Iridium Oxide (IrO 2 ) is a potential candidate which exhibits high SOC strength. Here we report a study of spin pumping and inverse spin Hall effect (ISHE), via ferromagnetic resonance (FMR), in IrO 2…
Antiferromagnetic (AFM) materials recently have shown interest in the research in spintronics due to its zero stray magnetic field, high anisotropy, and spin orbit coupling. In this context, the bi-metallic AFM Mn2Au has drawn attention because it exhibits unique properties and its Neel temperature is very high. Here, we report spin pumping and inverse spin Hall effect investigations in Mn2Au and CoFeB bilayer system using ferromagnetic resonance. We found large spin Hall angle θ_SH = 0.22
Harmonic Hall voltage measurements are a wide-spread quantitative technique for the measurement of spin-orbit induced effective fields in heavy-metal / ferromagnet heterostructures. In the vicinity of the voltage pickup lines in the Hall bar, the current is inhomogeneous, which leads to a hitherto not quantified reduction of the effective fields and derived quantities, such as the spin Hall angle or the spin Hall conductivity. Here we present a thorough analysis of the influence of the aspect ratio of the voltage pickup lines to current channel widths on the apparent spin Hall angle. Experimen…
Spin Hall effect in a nonlocal spin-injection device is theoretically studied. Using a nonlocal spin-injection technique, a pure spin current is created in a nonmagnetic metal (N). The spin current flowing in N is deflected by spin-orbit scattering to induce the Hall current in the transverse direction and accumulate charge at the edges of N, yielding the spin-current induced Hall effect. We propose a method for extracting information for spin-orbit scattering in nonmagnetic metals.
It is proposed that the new generation of spintronics should be ideally massless and dissipationless for the realization of ultra-fast and ultra-low-power spintronic devices. We demonstrate that the spin-gapless materials with linear energy dispersion are unique materials that can realize these massless and dissipationless states. Furthermore, we propose four new types of spin Hall effects which consist of spin accumulation of equal numbers of electrons and holes having the same or opposite spin polarization at the sample edge in Hall effect measurements, but with vanishing Hall voltage. These…
The intrinsic spin Hall effect (SHE) originates from the topology of the Bloch bands in momentum space. The duality between real space and momentum space calls for a spin Hall effect induced from a real space topology in analogy to the topological Hall effect (THE) of skyrmions. We theoretically demonstrate the topological spin Hall effect (TSHE) in which a pure transverse spin current is generated from a skyrmion spin texture.
The spin Hall angle (SHA) is a measure of the efficiency with which a transverse spin current is generated from a charge current by the spin-orbit coupling and disorder in the spin Hall effect (SHE). In a study of the SHE for a Pt$|$Py (Py=Ni$_{80}$Fe$_{20}$) bilayer using a first-principles scattering approach, we find a SHA that increases monotonically with temperature and is proportional to the resistivity for bulk Pt. By decomposing the room temperature SHE and inverse SHE currents into bulk and interface terms, we discover a giant interface SHA that dominates the total inverse SHE current…
We propose a mechanism of intrinsic spin Hall effect (SHE). In this mechanism, local orbital angular momentum (OAM) induces electron position shift and couples with the bias electric field to generate orbital Hall effect (OHE). SHE then emerges as a concomitant effect of OHE through the atomic spin-orbit coupling. Spin Hall conductivity due to this mechanism is estimated to be comparable to experimental values for heavy metals. This mechanism predicts the sign change of the spin Hall conductivity as the spin-orbit polarization changes its sign, and also correlation between the spin Hall conduc…
Conceptual framework behind the intrinsic spin Hall effect in three-dimensional conductors is discussed. Theory suggests how the spin Hall current should depend on symmetry and orientation of the crystal.
Relativistic band theoretical calculations reveal that intrinsic spin Hall conductivity in hole-doped archetypical semiconductors Ge, GaAs and AlAs is large $[\sim 100 (\hbar/e)(Ωcm)^{-1}]$, showing the possibility of spin Hall effect beyond the four band Luttinger Hamiltonian. The calculated orbital-angular-momentum (orbital) Hall conductivity is one order of magnitude smaller, indicating no cancellation between the spin and orbital Hall effects in bulk semiconductors. Furthermore, it is found that the spin Hall effect can be strongly manipulated by strains, and that the $ac$ spin Hall conduc…
Spin pumping in ferromagnets provides a source of pure spin currents. Via the inverse spin Hall effect a spin current is converted into a charge current and a corresponding detectable DC-voltage. The ratio of injected spin current to resulting charge current is given by the spin Hall angle. However, the number of experiments more or less equals the number of different values for spin Hall angles, even for the most studied normal metal platinum. This publication provides a full study of inverse spin Hall effect and anisotropic magnetoresistance for different NiFe(Py) / normal metal bilayers usi…
In this review, we describe in detail two important spin-transport phenomena: the extrinsic spin-Hall effect (coming from spin-orbit interactions between electrons and impurities) and the spin-Coulomb drag. The interplay of these two phenomena is analyzed. In particular, we discuss the influence of scattering between electrons with opposite spins on the spin current and the spin accumulation produced by the spin-Hall effect. Future challenges and open questions are briefly discussed.
We show that the spin Hall conductivity in insulators is related with a magnetic susceptibility representing the strength of the spin-orbit coupling. We use this relationship as a guiding principle to search real materials showing quantum spin Hall effect. As a result, we theoretically predict that bismuth will show the quantum spin Hall effect, both by calculating the helical edge states, and by showing the non-triviality of the Z_2 topological number, and propose possible experiments.
We analyze the Landau level (LL) structure and spin Hall effect in a MoS2 trilayer. Due to orbital asymmetry, the low-energy Dirac fermions become heavily massive and the LL energies grow linearly with $B$, rather than with $\sqrt{B}$. Spin-orbital couplings break spin and valley degenerate LL's into two time reversal invariant groups, with LL crossing effects present in the valence bands. We find a field-dependent unconventional Hall plateau sequence $ν=...$ $-2M-6$, $-2M-4$, $-2M-2$, $-2M-1$, ..., -5, -3, -1, 0, 2, 4 .... In a p-n junction, spin-resolved fractionally quantized conductance ap…
We consider spin Hall effect in a system of massless Dirac fermions in a graphene lattice. Two types of spin-orbit interaction, pertinent to the graphene lattice, are taken into account - the intrinsic and Rashba terms. Assuming perfect crystal lattice, we calculate the topological contribution to spin Hall conductivity. When both interactions are present, their interplay is shown to lead to some peculiarities in the dependence of spin Hall conductivity on the Fermi level.
While the helical character of the edge channels responsible for charge transport in the quantum spin Hall regime of a two-dimensional topological insulator is by now well established, an experimental confirmation that the transport in the edge channels is spin-polarized is still outstanding. We report experiments on nanostructures fabricated from HgTe quantum wells with an inverted band structure, in which a split gate technique allows us to combine both quantum spin Hall and metallic spin Hall transport in a single device. In these devices, the quantum spin Hall effect can be used as a spin …
Spin Hall effects intermix spin and charge currents even in nonmagnetic materials and, therefore, ultimately may allow the use of spin transport without the need for ferromagnets. We show how spin Hall effects can be quantified by integrating permalloy/normal metal (N) bilayers into a coplanar waveguide. A dc spin current in N can be generated by spin pumping in a controllable way by ferromagnetic resonance. The transverse dc voltage detected along the permalloy/N has contributions from both the anisotropic magnetoresistance (AMR) and the spin Hall effect, which can be distinguished by their s…
The spin Hall effect and its inverse play key roles in spintronic devices since they allow conversion of charge currents to and from spin currents. The conversion efficiency strongly depends on material details, such as the electronic band structure and the nature of impurities. Here we show an anomaly in the inverse spin Hall effect in weak ferromagnetic NiPd alloys near their Curie temperatures with a shape independent of material details, such as Ni concentrations. By extending Kondo's model for the anomalous Hall effect, we explain the observed anomaly as originating from the second-order …
We predict spin Hall angles up to 80% for ultrathin noble metal films with substitutional Bi impurities. The colossal spin Hall effect is caused by enhancement of the spin Hall conductivity in reduced sample dimension and a strong reduction of the charge conductivity by resonant impurity scattering. These findings can be exploited to create materials with high efficiency of charge to spin current conversion by strain engineering.
We report the observation of negative nonlocal resistances in multiterminal mesoscopic gold Hall bar structures whose characteristic dimensions are larger than the electron mean-free path. Our results can only be partially explained by a classical diffusive model of the nonlocal transport, and are not consistent with a recently proposed model based on spin Hall effects. Instead, our analysis suggests that a quasiballistic transport mechanism is responsible for the observed negative nonlocal resistance. Based on the sensitivity of our measurements and the spin Hall effect model, we find an uppe…
We show that the bulk Dresselhauss ($k^3$) spin-orbit coupling term leads to an intrinsic spin-Hall effect in n-doped bulk GaAs, but without the appearance of uniform magnetization. The spin-Hall effect in strained and unstrained bulk GaAs has been recently observed experimentally by Kato {\emph{et. al.}} \cite{kato2004A}. We show that the experimental result is quantitatively consistent with the intrinsic spin-Hall effect due to the Dresselhauss term, when lifetime broadening is taken into account. On the other hand, extrinsic contribution to the spin-Hall effect is several orders of magnitud…
Through combined ferromagnetic resonance, spin-pumping and inverse spin Hall effect experiments in Co|Pt bilayers and Co|Cu|Pt trilayers, we demonstrate consistent values of spin diffusion length $\ell_{\rm sf}^{\rm Pt}=3.4\pm0.4$ nm and of spin Hall angle $θ_{\rm SHE}^{\rm Pt}=0.051\pm0.004$ for Pt. Our data and model emphasize on the partial depolarization of the spin current at each interface due to spin-memory loss. Our model reconciles the previously published spin Hall angle values and explains the different scaling lengths for the ferromagnetic damping and the spin Hall effect induced v…
We measured the spin rectify effect and the inverse spin Hall effect in Nb-doped SrTiO$_3$ by injecting the spins from ferromagnetic thin films to SrTiO$_3$ using spin pumping. It was shown that the spin injection is increased when the doping level is increased. However, the spin Hall angle decreases when Nb occupies more than $\sim$2\% of the Ti sites, which is due to that beyond this concentration, the electron contributed the spin Hall effect is from the $d-$orbitals of Nb instead those from the Ti. Our work points to the importance of orbital occupations in the (inverse) spin Hall effect. …
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.
Spin torque oscillators placed onto a nonmagnetic heavy metal show synchronized auto-oscillations due to the coupling originating from spin Hall magnetoresistance effect. Here, we study a system having two spin torque oscillators under the effect of the spin Hall torque, and show that switching the external current direction enables us to control the phase difference of the synchronization between in-phase and antiphase.
In ferromagnet/normal metal heterostructures, spin pumping and spin-transfer torques are two reciprocal processes that occur concomitantly. Their interplay introduces a dynamic feedback effect interconnecting energy dissipation channels of both magnetization and current. By solving the spin diffusion process in the presence of the spin Hall effect in the normal metal, we show that the dynamic feedback gives rise to: (i) a nonlinear magnetic damping that is crucial to sustain uniform steady-state oscillations of a spin Hall oscillator at large angles. (ii) a frequency dependent spin Hall magnet…
A theoretical formulation of magnetoresistance effect in a metallic ferromagnetic/nonmagnetic bilayer originated from the charge-spin conversion by the anomalous Hall effect is presented. Analytical expressions of the longitudinal and transverse resistivities in both nonmagnet and ferromagnet are obtained by solving the spin diffusion equation. The magnetoresistance generated from charge-spin conversion purely caused by the anomalous Hall effect in the ferromagnet is found to be proportional to the square of the spin polarizations in the ferromagnet and has fixed sign. We also find additional …
Spin Hall effect, an electric generation of spin current, allows for efficient control of magnetization. Recent theory revealed that orbital Hall effect creates orbital current, which can be much larger than spin Hall-induced spin current. However, orbital current cannot directly exert a torque on a ferromagnet, requiring a conversion process from orbital current to spin current. Here, we report two effective methods of the conversion through spin-orbit coupling engineering, which allows us to unambiguously demonstrate orbital-current-induced spin torque, or orbital Hall torque. We find that o…
