Universality of magnetic-field-induced Bose-Einstein condensation of magnons

CsFeBr₃ is an S0.16em0ex=0.16em0ex1 hexagonal antiferromagnet that has a singlet ground state owing to its large easy-plane single-ion anisotropy. The critical behavior of the magnetic-field-induced phase transition for a magnetic field parallel to the c axis, which can be described by the Bose-Einstein condensation (BEC) of magnons under the $U(1)$ symmetry, was investigated via magnetization and specific heat measurements down to 0.1 K. For the specific heat measurement, we have developed a method of effectively suppressing the torque acting on a sample with strong anisotropy that uses the spin dimer compound Ba₂CoSi₂O₆Cl₂ with large and anisotropic Van Vleck paramagnetism. The temperature dependence of the transition field Hc(T) was found to follow the power-law ${H}c(T){{0.16em}{0ex}}{-}{{0.16em}{0ex}}{H}c{{0.16em}{0ex}}{∝}{{0.16em}{0ex}}{T}^{{φ}}$ with a critical exponent of ${φ}{{0.16em}{0ex}}={{0.16em}{0ex}}1.50{{0.16em}{0ex}}±{}{{0.16em}{0ex}}0.02$ and critical field of ${H}c{{0.16em}{0ex}}={{0.16em}{0ex}}2.60{{0.16em}{0ex}}T$. This result verifies the universality of the three-dimensional BEC of magnons described by ${{φ}}BEC{{0.16em}{0ex}}={{0.16em}{0ex}}3/2$.