Bose-Einstein condensation of magnons in polycrystalline gadolinium with nano-size grains

We report the observation of Bose-Einstein condensation (BEC) of magnons in nanocrystalline Gd. Employing a self-consistent approach, the variations with magnetic field (H) of the BEC transition temperature, Tc(H), and the volume, V (H), over which the condensate wavefunction retains its phase coherence, the temperature and magnetic field variations of the chemical potential, μ(T, H), and the average occupation number for the ground state, (n0(T, H)), are accurately determined from the magnetization, M(T, H), and specific heat, C(T, H), data. The variation of Tc with magnetic field has the functional form Tc(H) = Tc(H = 0) + aH2/3 that is characteristic of BEC. In conformity with the predictions of BEC theory (i) for T ≤ Tc, the condensate fraction (n0(T, H))/(n0(T = 1.8 K, H)) at constant H scales with the reduced temperature as [T/Tc(H)]3/2, (ii) in the limit H → 0, μ(T,H) ≅ 0 for T ≤ Tc and abruptly falls to large negative values as the temperature exceeds Tc, and (iii) the magnetic-field-induced change in magnon entropy, deduced from both M(T, H) and C(T, H), follows the T3/2 power law at low temperatures T << Tp* and goes through a peak at Tp*.