Anisotropic magnetoresistance of spin-orbit coupled carriers scattered from polarized magnetic impurities

Abstract

Anisotropic magnetoresistance ͑AMR͒ is a relativistic magnetotransport phenomenon arising from combined effects of spin-orbit coupling and broken symmetry of a ferromagnetically ordered state of the system. In this work we focus on one realization of the AMR in which spin-orbit coupling enters via specific spin-textures on the carrier Fermi surfaces and ferromagnetism via elastic scattering of carriers from polarized magnetic impurities. We report detailed heuristic examination, using model spin-orbit coupled systems, of the emergence of positive AMR ͑maximum resistivity for magnetization along current͒, negative AMR ͑minimum resistivity for magnetization along current͒, and of the crystalline AMR ͑resistivity depends on the absolute orientation of the magnetization and current vectors with respect to the crystal axes͒ components. We emphasize potential qualitative differences between pure magnetic and combined electromagnetic impurity potentials, between short-range and long-range impurities, and between spin-1/2 and higher spin-state carriers. Conclusions based on our heuristic analysis are supported by exact solutions to the integral form of the Boltzmann transport equation in archetypical two-dimensional electron systems with Rashba and Dresselhaus spin-orbit interactions and in the three-dimensional spherical Kohn-Littinger model. We include comments on the relation of our microscopic calculations to standard phenomenology of the full angular dependence of the AMR, and on the relevance of our study to realistic, two-dimensional conduction-band carrier systems and to anisotropic transport in the valence band of diluted magnetic semiconductors.

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

“…͑18͒ can also be understood using the basic properties of spin-3/2 states. 11 The idea is that ͉z kn ͘ is an eigenstate ͑with nonzero eigenvalue͒ to ê M · s for k oriented along ê M thereby allowing scattering to a state with −k that contributes strongly to the transport relaxation rate of Eq. ͑3͒.…”

“…Our approach 21 is based on the relaxation-time approximation ͑RTA͒ and it would be desirable to put the present results into more precise terms by exactly solving the Boltzmann equation in its full integral form as the authors did for the simpler Rashba system recently. 11,22 Although this solution is presently not available, we explain in a short discussion at the end of Sec. IV that the RTA reproduces at least the basic features of the AMR as presented in this work.…”

“…Consequently, very large AMR can arise if this mechanism is important. 11 We show in this paper that metallic ͑Ga,Mn͒As is a favorable system for the purposes of studying AMR. Not only because of its relatively simple ͑effective͒ Hamiltonian ͑de-scribed in Sec.…”

Interfacial contribution to thickness dependent in-plane anisotropic magnetoresistance

“…ρ ∥ > ρ ⊥ , and symmetry, i.e., cos 2 θ dependence, as 'conventional' AMR. 18 Unconventional AMR in an adjacent layer with strong SOI may also arise due to Rashba SOI, but has a different angular symmetry to conventional AMR. 19 Enhanced AMR due to structurally symmetric adjacent layers with strong SOI has also been suggested by Liu et al 3 Overall, such results suggest that the in-plane AMR in a single ultra-thin FM metal film may have a previously unconsidered interfacial contribution, as a result of anisotropic interface scattering and/or interfacial spin-orbit interactions.…”

Giant Negative Magnetoresistance Driven by Spin-Orbit Coupling at theLaAlO3/SrTiO3Interface

“…An explanation has been proposed [13,14] in terms of the Kondo effect: Variation of the electron density or magnetic field drives a quantum phase transition between a highresistance correlated electronic phase with screened magnetic impurities and a low-resistance phase of polarized impurity moments. The relevance of spin-orbit coupling for magnetotransport is widely appreciated [10,[14][15][16][17][18][19], but it was generally believed to be too weak an effect to provide a single-particle explanation of the giant magnetoresistance.In this work we provide experimental data (combining magnetic field, gate voltage, and temperature profiles for the resistance of the LAO=STO interface) and theoretical calculations that support an explanation fully within the single-particle context of Boltzmann transport. The key ingredients are the combination of spin-orbit coupling, band anisotropy, and finite-range electrostatic impurity scattering.…”