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, 94 (14), 147210

Extension of the BLOCH T(3/2) Law to Magnetic Nanostructures: Bose-Einstein Condensation

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Extension of the BLOCH T(3/2) Law to Magnetic Nanostructures: Bose-Einstein Condensation

E Della Torre et al. Phys Rev Lett.

Abstract

We report a newly observed phenomenon, namely, the observation of a visible anomaly in the Bloch T(3/2) law for the temperature dependence of magnetization of nanostructured ferromagnets, for which we give a thermodynamic explanation. Our interpretation extends the Bloch law by introducing the system's chemical potential and assumes a finite Bose-Einstein condensation temperature T(BE) of the magnons. Our extension involves accounting for the possibility of a magnon or magnetic entropy term, leading to a magnon chemical potential (hitherto omitted in the traditional derivation) which varies with temperature. The result is a subtle upturn of the magnetization curves of ferromagnetic nanoparticles in the 10 to 50 K temperature range. Here we show experimental data for nanomaterials and an outline of the extended theory which includes T(BE).

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