Extension of the Bloch T3/2 Law to Magnetic Nanostructures: Bose-Einstein Condensation

E. Della Torre, L. H. Bennett, and R. E. Watson
Phys. Rev. Lett. 94, 147210 – Published 15 April 2005

Abstract

We report a newly observed phenomenon, namely, the observation of a visible anomaly in the Bloch T3/2 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 TBE 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 TBE.

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  • Received 16 November 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.147210

©2005 American Physical Society

Authors & Affiliations

E. Della Torre1,2, L. H. Bennett1,2, and R. E. Watson3

  • 1Electrical and Computer Engineering Department, George Washington University, Washington, D.C. 20052, USA
  • 2National Institute of Standards Technology, Gaithersburg, Maryland 20899-8552, USA
  • 3Department of Physics, Brookhaven National Laboratory, Upton, New York 11973, USA

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Issue

Vol. 94, Iss. 14 — 15 April 2005

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