Extension of the Bloch T3/2 Law to Magnetic Nanostructures: Bose-Einstein Condensation
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.
- Publication:
-
Physical Review Letters
- Pub Date:
- April 2005
- DOI:
- 10.1103/PhysRevLett.94.147210
- Bibcode:
- 2005PhRvL..94n7210D
- Keywords:
-
- 75.75.+a;
- 71.35.Lk;
- 75.60.Ej;
- Magnetic properties of nanostructures;
- Collective effects;
- Magnetization curves hysteresis Barkhausen and related effects