Symmetry of Longitudinal Magneto-resistance in the Presence of Multiple Domain Walls in Ferromagnetic Thin Films with Perpendicular Magnetic Anisotropy

摘要

@@ Contemporary developments in spintronics provide a strong motivation for understanding the interplay between electrical transport and magnetic domain walls (DWs) in both ferromagnetic metals and in ferromagnetic semiconductors. Although the mechanisms of various magnetoresistance (MR) effects are different, most of the intrinsic MR effects, such as the ordinary MR in nonmagnetic metals, the anistropic magnetoresistance in ferromagnetic metals, the giant magnetoresistance in metallic multilayers'81, and spin valve effect in ferromagnetic semiconductor multilayers'91, share the common symmetry obeying Onsager reciprocity, i.e., field dependence of longitudinal MR should be symmetric with respect to the sign of the magnetic field H, i.e.,△ Rxx(H) =△RXX(-H). However, the presence of a single domain wall, both in metallic metals and ferromagnetic semiconductors, changes this symmetry . The physical origin of the antisymmetric term in the ferromagnets with perpendicular magnetic anisotropy (PMA) can be understood as follows. When a DW is formed, creating a spatially inhomogeneous magnetization, the current density is perturbed by circulating current that flows in the vicinity of DWs. This current is accompanied by an electric field essentially parallel to it, resulting in an antisymmetric Hall resistivity contribution to the longitudinal MR. However, the study on the interplay of DW and electrical transport have been focused on the effect of a single domain wall , while the effect of multiple domain walls on the longitudinal MR is rarely reported.