Intrinsic spin Hall effect in platinum: first-principles calculations

Giant Room Temperature Interface Spin Hall and Inverse Spin Hall Effects

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 with potentially major consequences for applications.

Asymmetric magnetic proximity effect in a Pd/Co/Pd trilayer system

In spintronic devices consisting of ferromagnetic/nonmagnetic systems, the ferromagnet-induced magnetic moment in the adjacent nonmagnetic material significantly influences the spin transport properties. In this study, such magnetic proximity effect in a Pd/Co/Pd trilayer system is investigated by x-ray magnetic circular dichroism and x-ray resonant magnetic reflectivity, which enables magnetic characterizations with element and depth resolution. We observe that the total Pd magnetic moments induced at the top Co/Pd interface are significantly larger than the Pd moments at the bottom Pd/Co interface, whereas transmission electron microscopy and reflectivity analysis indicate the two interfaces are nearly identical structurally. Such asymmetry in magnetic proximity effects could be important for understanding spin transport characteristics in ferromagnetic/nonmagnetic systems and its potential application to spin devices.

Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn3Ge

It is well established that the anomalous Hall effect displayed by a ferromagnet scales with its magnetization. Therefore, an antiferromagnet that has no net magnetization should exhibit no anomalous Hall effect. We show that the noncolinear triangular antiferromagnet Mn3Ge exhibits a large anomalous Hall effect comparable to that of ferromagnetic metals; the magnitude of the anomalous conductivity is ~500 (ohm·cm)(-1) at 2 K and ~50 (ohm·cm)(-1) at room temperature. The angular dependence of the anomalous Hall effect measurements confirms that the small residual in-plane magnetic moment has no role in the observed effect except to control the chirality of the spin triangular structure. Our theoretical calculations demonstrate that the large anomalous Hall effect in Mn3Ge originates from a nonvanishing Berry curvature that arises from the chiral spin structure, and that also results in a large spin Hall effect of 1100 (ħ/e) (ohm·cm)(-1), comparable to that of platinum. The present results pave the way toward the realization of room temperature antiferromagnetic spintronics and spin Hall effect-based data storage devices.

Spin Hall Magnetoresistance in Metallic Bilayers

Spin Hall magnetoresistance (SMR) is studied in metallic bilayers that consist of a heavy metal (HM) layer and a ferromagnetic metal (FM) layer. We find a nearly tenfold increase of SMR in W/CoFeB compared to previously studied HM/ferromagnetic insulator systems. The SMR increases with decreasing temperature despite the negligible change in the W layer resistivity. A model is developed to account for the absorption of the longitudinal spin current to the FM layer, one of the key characteristics of a metallic ferromagnet. We find that the model not only quantitatively describes the HM layer thickness dependence of SMR, allowing accurate estimation of the spin Hall angle and the spin diffusion length of the HM layer, but also can account for the temperature dependence of SMR by assuming a temperature dependent spin polarization of the FM layer. These results illustrate the unique role a metallic ferromagnetic layer plays in defining spin transmission across the HM/FM interface.

Reciprocal spin Hall effects in conductors with strong spin-orbit coupling: a review

Spin Hall effect and its inverse provide essential means to convert charge to spin currents and vice versa, which serve as a primary function for spintronic phenomena such as the spin-torque ferromagnetic resonance and the spin Seebeck effect. These effects can oscillate magnetization or detect a thermally generated spin splitting in the chemical potential. Importantly this conversion process occurs via the spin-orbit interaction, and requires neither magnetic materials nor external magnetic fields. However, the spin Hall angle, i.e. the conversion yield between the charge and spin currents, depends severely on the experimental methods. Here we discuss the spin Hall angle and the spin diffusion length for a variety of materials including pure metals such as Pt and Ta, alloys and oxides determined by the spin absorption method in a lateral spin valve structure.

Tunable giant spin hall conductivities in a strong spin-orbit semimetal: Bi(1-x) Sb(x)

Intrinsic spin Hall conductivities are calculated for strong spin-orbit Bi(1-x)Sb(x) semimetals, from the Kubo formula and using Berry curvatures evaluated throughout the Brillouin zone from a tight-binding Hamiltonian. Nearly crossing bands with strong spin-orbit interaction generate giant spin Hall conductivities in these materials, ranging from 474 (ℏ/e)(Ω  cm)^{-1} for bismuth to 96 (ℏ/e)(Ω  cm)^{-1} for antimony; the value for bismuth is more than twice that of platinum. The large spin Hall conductivities persist for alloy compositions corresponding to a three-dimensional topological insulator state, such as Bi(0.83)Sb(0.17). The spin Hall conductivity could be changed by a factor of 5 for doped Bi, or for Bi(0.83)Sb(0.17), by changing the chemical potential by 0.5 eV, suggesting the potential for doping or voltage tuned spin Hall current.

Phase-sensitive detection of spin pumping via the ac inverse spin Hall effect

We use a phase-sensitive, quantitative technique to separate inductive and ac inverse spin Hall effect (ISHE) voltages observed in Ni(81)Fe(19)/normal metal multilayers under the condition of ferromagnetic resonance. For Ni(81)Fe(19)/Pt thin film bilayers and at microwave frequencies from 7 to 20 GHz, we observe an ac ISHE magnitude that is much larger than that expected from the dc spin Hall angle Θ(SH)(Pt) = 0.1. Furthermore, at these frequencies, we find an unexpected, ≈ 110° phase of the ac ISHE signal relative to the in-plane component of the resonant magnetization precession. We attribute our findings to a dominant intrinsic ac ISHE in Pt.

Electrically tunable anomalous Hall effect in Pt thin films

Pt is often considered to be an exchange-enhanced paramagnetic material, in which the Stoner criterion for ferromagnetism is nearly satisfied and, thus, external stimuli may induce unconventional magnetic characteristics. We report that a nonmagnetic perturbation in the form of a gate voltage applied via an ionic liquid induces an anomalous Hall effect (AHE) in Pt thin films, which resembles the AHE induced by the contact to Bi-doped yttrium iron garnet. Analysis of detailed temperature and magnetic field experiments indicates that the evolution of the AHE with temperature can be explained in terms of large local moments; the applied electric field induces magnetic moments as large as ~10 μ(B) that follow the Langevin function.

Anisotropy of spin relaxation and transverse transport in metals

Using first-principles methods we explore the anisotropy of the spin relaxation and transverse transport properties in bulk metals with respect to the real-space direction of the spin-quantization axis in paramagnets or of the spontaneous magnetization in ferromagnets. Owing to the presence of the spin-orbit coupling the orbital and spin character of the Bloch states depends sensitively on the orientation of the spins relative to the crystal axes. This leads to drastic changes in quantities which rely on interband mixing induced by the spin-orbit interaction. The anisotropy is particularly striking for quantities which exhibit spiky and irregular distributions in the Brillouin zone, such as the spin-mixing parameter or the Berry curvature of the electronic states. We demonstrate this for three cases: (i) the Elliott-Yafet spin-relaxation mechanism in paramagnets with structural inversion symmetry; (ii) the intrinsic anomalous Hall effect in ferromagnets; and (iii) the spin Hall effect in paramagnets. We discuss the consequences of the pronounced anisotropic behavior displayed by these properties for spin-polarized transport applications.

Maximum intrinsic spin-Hall conductivity in two-dimensional systems with k-linear spin-orbit interaction

We analytically calculate the intrinsic spin-Hall conductivities (ISHCs) (σ(z)(xy) and σ(z)(yx)) in a clean, two-dimensional system with generic k-linear spin-orbit interaction. The coefficients of the product of the momentum and spin components form a spin-orbit matrix β̃. We find that the determinant of the spin-orbit matrix detβ̃ describes the effective coupling of the spin sz and orbital motion Lz. The decoupling of spin and orbital motion results in a sign change of the ISHC and the band-overlapping phenomenon. Furthermore, we show that the ISHC is in general unsymmetrical (σ(z)(xy) ≠ -σ(z)(yx)), and it is governed by the asymmetric response function Δβ̃, which is the difference in band-splitting along two directions: those of the applied electric field and the spin-Hall current. The obtained non-vanishing asymmetric response function also implies that the ISHC can be larger than e/8π, but has an upper bound value of e/4π. We will show that the unsymmetrical properties of the ISHC can also be deduced from the manifestation of the Berry curvature in the nearly degenerate area. On the other hand, by investigating the equilibrium spin current, we find that detβ̃ determines the field strength of the SU(2) non-Abelian gauge field.

First-principle calculations of the Berry curvature of Bloch states for charge and spin transport of electrons

Recent progress in wave packet dynamics based on the insight of Berry pertaining to adiabatic evolution of quantum systems has led to the need for a new property of a Bloch state, the Berry curvature, to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principle calculations of the Berry curvature. Finally, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties such as the anomalous and spin Hall conductivity as well as the anomalous Nernst conductivity and discuss the influence of the Berry curvature on the de Haas-van Alphen oscillation.

Extrinsic and intrinsic contributions to the spin Hall effect of alloys

A fully relativistic description of the spin-orbit induced spin Hall effect is presented that is based on Kubo's linear response formalism. Using an appropriate operator for the spin-current density a Kubo-Středa-like equation for the spin Hall conductivity (SHC) is obtained. An implementation using the Korringa-Kohn-Rostoker band structure method in combination with the coherent potential approximation allow detailed investigations on various alloy systems. A decomposition of the SHC into intrinsic and extrinsic contributions is suggested. Accompanying calculations for the skew-scattering contribution of the SHC using the Boltzmann equation demonstrate the equivalence to the Kubo formalism in the dilute alloy regime and support the suggested decomposition scheme.

Anisotropic spin Hall effect from first principles

We report on first principles calculations of the anisotropy of the intrinsic spin Hall conductivity (SHC) in nonmagnetic hcp metals and in antiferromagnetic Cr. For most of the metals of this study we find large anisotropies. We derive the general relation between the SHC vector and the direction of spin polarization and discuss its consequences for hcp metals. Especially, it is predicted that for systems where the SHC changes sign due to the anisotropy the spin Hall effect may be tuned such that the spin polarization is parallel either to the electric field or to the spin current.

Extrinsic spin Hall effect from first principles

We present an ab initio description of the spin Hall effect in metals. Our approach is based on density functional theory in the framework of a fully relativistic Korringa-Kohn-Rostoker method and the solution of a linearized Boltzmann equation including the scattering-in term (vertex corrections). The skew scattering mechanism at substitutional impurities is considered. Spin-orbit coupling in the host as well as at the impurity atom and the influence of spin-flip processes are fully taken into account. A sign change of the spin Hall effect in Cu and Au hosts is obtained as a function of the impurity atom, and even light elements like Li can cause a strong effect. It is shown that the gigantic spin Hall effect in Au can be caused by skew scattering at C and N impurities which are typical contaminations in a vacuum chamber.

Spin-Hall effect and spin-Coulomb drag in doped semiconductors

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.

Intrinsic spin Hall Effect in the s-wave superconducting state: analysis of the Rashba model

A general expression for spin Hall conductivity (SHC) in the s-wave superconducting state at finite temperatures is derived. Based on the expression, we study SHC in a two-dimensional electron gas model in the presence of Rashba spin-orbit interaction (SOI). SHC is zero in the normal state, whereas it takes a large negative value as soon as the superconductivity occurs, due to the change in the quasiparticle contributions. Since this remarkable behavior is independent of the strength of the SOI, it will be widely observed in thin films of superconductors with surface-induced Rashba SOI, or in various noncentrosymmetric superconductors.

Enhanced spin Hall effect by resonant skew scattering in the orbital-dependent Kondo effect

The enhanced spin Hall effect in Au metal due to the resonant skew scattering is studied with first-principles band structure calculations. Especially the gigantic spin Hall angle gammaS congruent with 0.1 observed recently [T. Seki, Nature Mater. 7, 125 (2008)] is attributed to the orbital-dependent Kondo effect of Fe in the Au host metal, where the t2g orbitals are in the mixed-valence region while eg orbitals are in the Kondo limit. The enhanced spin-orbit interaction by the electron correlation in the t2g orbitals leads to the gigantic spin Hall effect. Impurities with 5d orbitals are also discussed.

Giant orbital Hall effect in transition metals: origin of large spin and anomalous Hall effects

In transition metals and their compounds, the orbital degrees of freedom gives rise to an orbital current, in addition to the ordinary spin and charge currents. We reveal that considerably large spin and anomalous Hall effects observed in transition metals originate from an orbital Hall effect (OHE). To elucidate the origin of these novel Hall effects, a simple periodic s-d hybridization model is proposed as a generic model. The giant positive OHE originates from the orbital Aharonov-Bohm phase factor, and induces spin Hall conductivity that is proportional to the spin-orbit polarization at the Fermi level, which is positive (negative) in metals with more than (less than) half filling.