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The phenomenon of Anderson localization is studied for a class ofone-particle Schr\"odinger operators with random Zeeman interactions. Theseoperators arise as follows: Static spins are placed randomly on the sites of asimple cubic lattice according to a site percolation process with density x andcoupled to one another ferromagnetically. Scattering of an electron in aconduction band at these spins is described by a random Zeeman interaction termthat originates from indirect exchange. It is shown rigorously that, forpositive values of x below the percolation threshold, the spectrum of theone-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 predictthe phenomenon of colossal (negative) magnetoresistance and the existence of aMott transition, as H and/or x are increased.  Our analysis is motivated directly by experimental results concerning themagnetic alloy Eu_x Ca_1-x B_6.

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