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, T(c)(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, [linear span]n(0)(T, H)[linear span], are accurately determined from the magnetization, M(T, H), and specific heat, C(T, H), data. The variation of T(c) with magnetic field has the functional form T(c)(H) = T(c)(H = 0) + aH(2/3) that is characteristic of BEC. In conformity with the predictions of BEC theory (i) for T ≤ T(c), the condensate fraction [linear span]n(0)(T, H)[linear span]/[linear span]n(0)(T = 1.8 K, H)[linear span] at constant H scales with the reduced temperature as [T/T(c)(H)](3/2), (ii) in the limit H−>0, μ(T, H) ͠= 0 for T ≤ T(c) and abruptly falls to large negative values as the temperature exceeds T(c), and (iii) the magnetic-field-induced change in magnon entropy, deduced from both M(T, H) and C(T, H), follows the T(3/2) power law at low temperatures T