Current patterns in magnetically inhomogeneous conductors

Abstract

We determine the current distributions in conducting strips whose resistivity and Hall angle vary with longitudinal position along the wire. We consider isolated, finite rectangular Hall bars between semi-infinite leads, as well as periodic structures. The approaches used avoid standard approximations such as perfectly-conducting leads, well-separated interfaces, or small resistivity changes. We find that as an isolated Hall bar is shortened, one enters a regime of closed current loops in the classical Hall effect. Related behavior is found for periodic Hall patterns.