Unidirectional magnetoresistance and spin-orbit torque in NiMnSb

J Železný,K Olejník,T Jungwirth,C Gould,L W Molenkamp,J Patchett,T Tichý,J Zemen,C Gomez-Olivella,C Ciccarelli,F Gerhard,Z Fang

doi:10.1103/physrevb.104.054429

Abstract

Spin-dependent transport phenomena due to relativistic spin-orbit coupling and broken space-inversion symmetry are often difficult to interpret microscopically, in particular when occurring at surfaces or interfaces. Here we present a theoretical and experimental study of spin-orbit torque and unidirectional magnetoresistance in a model room-temperature ferromagnet NiMnSb with inversion asymmetry in the bulk of this half-heusler crystal. Besides the angular dependence on magnetization, the competition of Rashba and Dresselhaus-like spin-orbit couplings results in the dependence of these effects on the crystal direction of the applied electric field. The phenomenology that we observe highlights potential inapplicability of commonly considered approaches for interpreting experiments. We point out that, in general, there is no direct link between the current-induced non-equilibrium spin polarization inferred from the measured spin-orbit torque and the unidirectional magnetiresistance. We also emphasize that the unidirectional magnetoresistance has not only longitudinal but also transverse components in the electric field -- current indices which complicates its separation from the thermoelectric contributions to the detected signals in common experimental techniques. We use the theoretical results to analyze our measurements of the on-resonance and off-resonance mixing signals in microbar devices fabricated from an epitaxial NiMnSb film along different crystal directions. Based on the analysis we extract an experimental estimate of the unidirectional magnetoresistance in NiMnSb.

Highlights

Anisotropic magnetoresistance (AMR) is an example of a relativistic transport phenomenon in ferromagnets with a long history
We emphasize that the unidirectional magnetoresistance has longitudinal and transverse components in the electric field: current indices which complicate its separation from the thermoelectric contributions to the detected signals in common experimental techniques
When an electrical current is passed in the plane perpendicular to the growth direction, carriers acquire a nonequilibrium spin polarization δsSO, which in general can be decomposed into a component that is parallel to the in-plane magnetization of the

Summary

INTRODUCTION

Anisotropic magnetoresistance (AMR) is an example of a relativistic transport phenomenon in ferromagnets with a long history. The model was based on a general argument that the magnetization-dependent conductivity tensor σi j (m), like any other observable [2], reflects the symmetry of the ferromagnetic crystal. The accumulated spin can introduce a proportional change in the exchange splitting of the bands, further affecting the conductivity by influencing spin transmission of minority and majority spins Another UMR mechanism considers that the magnons’ population of the ferromagnet is increased or decreased depending on the orientation of δsSO relative to the magnetization. This leads to a change in the average magnetization, which results in a net change of the magnetoresistance.

Current-induced spin polarization and spin-orbit torque

Unidirectional magnetoresistance

MEASURED DATA AND DISCUSSION

SUMMARY