Anisotropic Magnetoresistance Components in (Ga,Mn)As

Abstract

Our experimental and theoretical study of the non-crystalline and crystalline components of the anisotropic magnetoresistance (AMR) in (Ga,Mn)As is aimed at exploring basic physical aspects of this relativistic transport effect. The non-crystalline AMR reflects anisotropic lifetimes of the holes due to polarized Mn impurities while the crystalline AMR is associated with valence band warping. We find that the sign of the non-crystalline AMR is determined by the form of spin-orbit coupling in the host band and by the relative strengths of the non-magnetic and magnetic contributions to the impurity potential. We develop experimental methods directly yielding the non-crystalline and crystalline AMR components which are then independently analyzed. We report the observation of an AMR dominated by a large uniaxial crystalline component and show that AMR can be modified by local strain relaxation. We discuss generic implications of our experimental and theoretical findings including predictions for non-crystalline AMR sign reversals in dilute moment systems. Anisotropic magnetoresistance (AMR) is a response of carriers in magnetic materials to changes of the magnetization orientation. Despite its importance in magnetic recording technologies the understanding of the microscopic physics of this spin-orbit (SO) coupling induced effect is relatively poor. Phenomenologically, AMR has a non-crystalline component, arising from the lower symmetry for a specific current direction, and crystalline components arising from the crystal symmetries [1,2]. In ferromagnetic metals, values for these coefficients can be obtained by numerical ab initio transport calculations [3], but these have no clear connection to the standard physical model of transport arising from spin dependent scattering of current carrying low mass s-states into heavymass d-states [4]. Experimentally, the non-crystalline and, the typically much weaker, crystalline AMR components in metals have been indirectly extracted from fitting the total AMR angular dependences [2].Among the remarkable AMR features of (Ga,Mn)As ferromagnetic semiconductors are the opposite sign of the non-crystalline component (compared to most metal ferromagnets) and the crystalline terms reflecting the rich magnetocrystalline anisotropies [5,6,7,8,9,10,11]. Microscopic numerical simulations [6,12] consistently describe the sign and magnitudes of the non-crystalline AMR and capture the more subtle crystalline terms associated with e.g. growth-induced strain [8,12]. As in metals, however, the basic microscopic physics of the AMR still needs to be elucidated which is the aim of the work presented here.Theoretically, we separate the non-crystalline and crystalline components by turning off and on band warping and match numerical microscopic simulations with model analytical results. This provides the physical interpretation of the origin of AMR, and of the sign of the noncrystalline term in particular. Experimentally, we obtain direct and independent access to the non-crystalline and crystalli...

Microscopic mechanism of the noncrystalline anisotropic magnetoresistance in (Ga,Mn)As

“…IV͒. This analysis is our main result together with the detailed explanation of the AMR sign in ͑Ga,Mn͒As ͑resistance parallel to magnetization is smaller than perpendicular to magnetization͒ which is observed experimentally 8,9,[12][13][14][15][16][17][18] and is opposite to most magnetic metals. 19,20 The results in Sec.…”

“…3 Diluted magnetic semiconductors, and ͑Ga,Mn͒As in particular, offer a promising system in which these issues become simplified: 7 Fermi level lies close to the top of the valence band so that k · p approximation can be used, few bands are involved in transport, and in addition, their SOI is strong. Moreover, experiments done so far show that the noncrystalline component of the AMR, 8,9 arising from the breaking of the symmetry by choosing a specific current direction, outweighs the crystalline components in most of the metallic highly Mn-doped materials. In attempting to describe the AMR in such system, we can begin with a model isotropic but still spin-orbit coupled band structure and add the effect of magnetization in the three possible distinct ways, as sketched in Fig.…”

Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance

“…32,33 A relatively simple host band structure in the DMS ferromagnets provides a pos-sibility for performing detailed microscopic calculations based on simple physical models. 34 However, the relaxationtime approximation used in such calculations is not always reliable since it does not fully take into account the anisotropies of the system. 35 The Kubo formula approach has been applied to the AMR calculations in Rashba systems and it has revealed the cancellation of the nonvertex and vertex parts, 36 similar to the spin Hall effect ͑SHE͒ and the AHE.…”

“…Within the Boltzmann equation approach, such calculations are usually performed by using the relaxation-time approximation in which the transport relaxation time is calculated from the scattering amplitudes without fully taking into account the asymmetries. 30,34 This approach was improved in Ref. 53 by introducing the perpendicular relaxation time Ќ .…”

Anisotropic conductivity in magnetic topological insulators

“…The spin-momentum locking of the surface electrons makes their scattering from magnetic impurities anisotropic and the standard relaxation time approximation (RTA) is not applicable. Many attempts have been devoted to the development of a generalized RTA for anisotropic systems [11,12,13,14]. However, it is still felt the lack of a closed form for the relaxation times of topological insulators with anisotropic scatterings.…”