Journal of Statistical Physics

, Volume 143, Issue 5, pp 970–989 | Cite as

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



The phenomenon of Anderson localization is studied for a class of one-particle Schrödinger 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 Schrödinger 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 Ca1−x B6.


Anderson localization Spin disorder Magnetoresistance 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsETH ZürichZürichSwitzerland
  2. 2.Laboratory for Solid State PhysicsETH ZürichZürichSwitzerland

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