Anderson Localization Triggered by Spin Disorder—With an Application to Eu x Ca1−x B6

Abstract

The phenomenon of Anderson localization is studied for a class of one-particle Schr\"odinger operators with random Zeeman interactions. These operators arise as follows: Static spins are placed randomly on the sites of a simple cubic lattice according to a site percolation process with density x and coupled to one another ferromagnetically. Scattering of an electron in a conduction band at these spins is described by a random Zeeman interaction term that originates from indirect exchange. It is shown rigorously that, for positive values of x below the percolation threshold, the spectrum of the one-electron Schr\"odinger operator near the band edges is dense pure-point, and the corresponding eigenfunctions are exponentially localized. Localization near the band edges persists in a weak external magnetic field, H, but disappears gradually, as H is increased. Our results lead us to predict the phenomenon of colossal (negative) magnetoresistance and the existence of a Mott transition, as H and/or x are increased. Our analysis is motivated directly by experimental results concerning the magnetic alloy Eu_x Ca_1-x B_6.