Abstract
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.
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Egli, D., Fröhlich, J. & Ott, HR. Anderson Localization Triggered by Spin Disorder—With an Application to Eu x Ca1−x B6 . J Stat Phys 143, 970–989 (2011). https://doi.org/10.1007/s10955-011-0216-9
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DOI: https://doi.org/10.1007/s10955-011-0216-9