Bose Einstein condensation of magnons in mesoscopic ferromagnets.

Bulk magnetic materials are comprised of magnetic domains. As the size of the sample is reduced, it forms a single domain state. Further reduction of particle size yields a superparamagnetic state. There is an apparent phase transition\footnote{J.J. Becker, ``Precipitation and magnetic annealing in a Cu-Co alloy,'' \textit{Trans Met SocAIME,} \textbf{212} 138-144 (1958).} between the single domain state and the superparamagnetic state at some critical size in the single-domain mesoscopic region. We had found\footnote{E. Della Torre, L.H. Bennett, and R.E. Watson, ``Extension of the Bloch T$^{3/2}$ law to magnetic nanostructures: Bose-Einstein condensation'', \textit{Phys. Rev. Lett. }\textbf{94, }147210 (2005).}$^{,}$\footnote{S. Rao, E. Della Torre, L. H. Bennett, H. M. Seyoum, and R.E. Watson, ``Temperature variation of the fluctuation field in Co/Pt'', \textit{J. Appl. Phys.} \textbf{97}, 10N113 (2005).} a Bose-Einstein condensation in a number of mesoscopic ferromagnets (30 - 60 nm diam). We hypothesize that the superparamagnetic-to-single domain ferromagnetic transition involves the same type of Bose-Einstein condensation.