Electrical current driven by a coherent spin wave in a bulk ferromagnetic semiconductor

Abstract

We theoretically investigate the effect of electrical current generation by a coherent spin wave propagated in a bulk ferromagnetic semiconductor. This is one of the effects in conductive magnetic materials that are based on spin-transfer torque concept first proposed by J. C. Slonszewski [J. Magn. Magn. Mater. 159, L1 (1996)] and L. Berger [Phys. Rev. B 54, 9353 (1996)]. Due to the relatively simple description of interaction between conduction electrons and a coherent spin wave (in the framework of s-d exchange), the spin-transfer torque effect is considered here ab initio. A systematic analysis of current generation effect is done by quantum kinetics methods; relaxation processes are considered within the τ approximation. We derive an analytical expression for the stationary current density and make estimations for a ferromagnetic semiconductor of the CdCr 2 Se 4 type.Conductive magnetic materials with a strong s-d exchange interaction have the mutual influence of electronic and magnetic properties, resulting in rather "significant" effects. Thus the effects, which we call direct effects (DEs), have been a focus of attention from the midnineties until the present (Refs. 1-7 and references therein). DEs consist in manipulation of conductive magnetic material magnetization by electrical current. Also of great interest are inverse effects (IEs), consisting in current (voltage) generation in conductive magnetic materials as a result of temporal inhomogeneous magnetization variation. [8][9][10][11][12][13][14][15][16] The interpretation of both effects is based on the "spin-transfer torque" (STT) concept proposed by Slonszewski 3 and Berger. 1 The corresponding theoretical models have various approximations and constraints due to certain "scenarios"of experiments where DEs, as well as IEs, are observed. The main problem here is to find an exact solution of the time-dependent Schrodinger equation describing electron behavior in an s-d exchange field.However, in some particular cases, the exact solution of the corresponding Schrodinger equation can be obtained and STT can be considered ab initio. A solution to the time-dependent Schrodinger equation describing an electron in an s-d exchange field of a coherent spin wave (CSW) propagated in a bulk magnetic material can be easily found. The present work, taking advantage of the possibility of finding such an exact solution, is dedicated to one of the IE variants corresponding to this case: this is the current generation effect in a bulk ferromagnetic material by a CSW. Let us note here that the work (Ref. 6; see also Ref. 2) studies DEs as an STT effect specifically for bulk systems. This effect consists in planar spin spiral (SS) rotation around its axis driven by electrical current. The analysis carried out in Ref. 6 also applies to conical SS. Rotation of conical SS around its axis is described mathematically similarly to the description of a CSW propagated in a spontaneous magnetization direction. Therefore, the effect studied in the present work is considered the ...