Eur. Phys. J. B 78, 429-437 (2010)
https://doi.org/10.1140/epjb/e2010-10596-7

Bose-Einstein condensation at finite momentum and magnon condensation in thin film ferromagnets

Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt, Germany

Corresponding author: ^a kreisel@itp.uni-frankfurt.de

Received: 2 August 2010
Revised: 22 October 2010
Published online: 15 December 2010

Abstract

We use the Gross-Pitaevskii equation to determine the spatial structure of the condensate density of interacting bosons whose energy dispersion ϵ_k has two degenerate minima at finite wave-vectors ± q. We show that in general the Fourier transform of the condensate density has finite amplitudes for all integer multiples of q. If the interaction is such that many Fourier components contribute, the Bose condensate is localized at the sites of a one-dimensional lattice with spacing 2 π/|q|; in this case Bose-Einstein condensation resembles the transition from a liquid to a crystalline solid. We use our results to investigate the spatial structure of the Bose condensate formed by magnons in thin films of ferromagnets with dipole-dipole interactions.