Anderson Localization Triggered by Spin Disorder---with an Application to Eu_x Ca_1-x B_6

TL;DR

This paper rigorously demonstrates Anderson localization caused by spin disorder in a model inspired by Eu_x Ca_1-x B_6, predicting colossal magnetoresistance and a Mott transition as magnetic field and spin density increase.

Contribution

It introduces a new mathematical model for Anderson localization induced by spin disorder and analyzes its spectral properties under varying magnetic fields and spin densities.

Findings

Localization occurs near band edges for low spin density x

Weak magnetic fields preserve localization, which diminishes as H increases

Predictions include colossal magnetoresistance and a Mott transition

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.