Spin-orbit torques in strained PtMnSb from first principles

Abstract

We compute spin-orbit torques (SOTs) in strained PtMnSb from first\nprinciples. We consider both tetragonal strain and shear strain. We find a\nstrong linear dependence of the field-like SOTs on these strains, while the\nantidamping SOT is only moderately sensitive to shear strain and even\ninsensitive to tetragonal strain. We also study the dependence of the SOT on\nthe magnetization direction. In order to obtain analytical expressions suitable\nfor fitting our numerical \\textit{ab-initio} results we derive a general\nexpansion of the SOT in terms of all response tensors that are allowed by\ncrystal symmetry. Our expansion includes also higher-order terms beyond the\nusually considered lowest order. We find that the dependence on the strain is\nmuch smaller for the higher-order terms than for the lowest order terms. In\norder to judge the sensitivity of the SOT on the exchange correlation potential\nwe compute the SOT in both GGA and LDA. We find that the higher-order terms\ndepend significantly on the exchange-correlation potential, while the lowest\norder terms are insensitive to it. Since the higher-order terms are small in\ncomparison to the lowest order terms the total SOT is insensitive to the\nexchange correlation potential in strained PtMnSb.\n