Bose–Einstein Condensation of Magnons in TlCuCl3: Phase Diagram and Specific Heat from a Self-consistent Hartree–Fock Calculation with a Realistic Dispersion Relation

Abstract

We extend the self-consistent Hartree–Fock–Popov calculations by Nikuni et al. [Phys. Rev. Lett. 84 (2000) 5868] concerning the Bose–Eistein condensation of magnons in TlCuCl 3 to include a realistic dispersion of the excitations. The result for the critical field as a function of temperature behaves as H c ( T )- H c (0)∼ T 3/2 below 2 K but deviates from this simple power-law at higher temperature and is in very good agreement with the experimental results. The specific heat is computed as a function of temperature for different values of the magnetic field. It shows a λ-like shape at the transition and is in good qualitative agreement with the results of Oosawa et al. [Phys. Rev. B 63 (2001) 134416].