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arXiv · 1101.4852

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

Daniel Egli·Jürg Fröhlich·Hans-Rudolf Ott
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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 Ca_1-x B_6.

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Daniel Egli, Jürg Fröhlich, Hans-Rudolf Ott. 2011-01-25. Anderson Localization Triggered by Spin Disorder---with an Application to Eu_x Ca_1-x B_6. https://doi.org/10.1007/s10955-011-0216-9

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