Bose‐Einstein Condensation of Magnons in Magnetic Systems

We briefly summerize the recent advances in understanding Bose‐Einstein condensation (BEC) of magnons in a variety of magnetic systems and report the first observation of BEC of magnons in nanocrystalline Gd. A self‐consistent approach is followed to accurately determine the BEC transition temperature, Tc(H), the chemical potential, μ(T,H), the average occupation number for the ground state, 〈n0(T,H)〉, and the volume (length) over which the condensate wavefunction retains its phase coherence, V(H)(L(H) = V(H)1/3) from the magnetization, M(T,H), and specific heat, c(T,H), data. In conformity with the predictions of the BEC theory, (i) Tc varies with the magnetic field as Tc(H) = Tc(H = 0)+a H2/3, (ii) at constant H, 〈n0(T,H)〉/〈n0(T = 1.8K,H)〉 scales with [T/Tc(H)]3/2, and (iii) in the limit H→0, μ(T,H)≅0 for T≤Tc and abruptly falls to large negative values as the temperature exceeds Tc.We briefly summerize the recent advances in understanding Bose‐Einstein condensation (BEC) of magnons in a variety of magnetic systems and report the first observation of BEC of magnons in nanocrystalline Gd. A self‐consistent approach is followed to accurately determine the BEC transition temperature, Tc(H), the chemical potential, μ(T,H), the average occupation number for the ground state, 〈n0(T,H)〉, and the volume (length) over which the condensate wavefunction retains its phase coherence, V(H)(L(H) = V(H)1/3) from the magnetization, M(T,H), and specific heat, c(T,H), data. In conformity with the predictions of the BEC theory, (i) Tc varies with the magnetic field as Tc(H) = Tc(H = 0)+a H2/3, (ii) at constant H, 〈n0(T,H)〉/〈n0(T = 1.8K,H)〉 scales with [T/Tc(H)]3/2, and (iii) in the limit H→0, μ(T,H)≅0 for T≤Tc and abruptly falls to large negative values as the temperature exceeds Tc.