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

2005; American Physical Society; Volume: 94; Issue: 14 Linguagem: Inglês

10.1103/physrevlett.94.147210

1092-0145

E. Della Torre, L. H. Bennett, R. E. Watson,

Magnetic properties of thin films

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).