Magnetic-Field Induced Bose-Einstein Condensation of Magnons and Critical Behavior in Interacting Spin Dimer System TlCuCl${}_3$

Magnetization measurements were performed to investigate the critical behavior of the field-induced magnetic ordering in gapped spin system TlCuCl${}_3$. The critical density of the magnons was obtained as a function of temperature and the magnon-magnon interaction constant was evaluated. The experimental phase boundary for $T<5$ K agrees almost perfectly with the magnon BEC theory based on the Hartree-Fock approximation with realistic dispersion relations. The phase boundary can be described by the power law $[H_N(T)-H_c]propto{T}^{phi}$. With decreasing fitting temperature range, the critical exponent $phi$ decreases and converges at $ph{i}_{BEC}=3\mathrm{/}2$ predicted by the magnon BEC theory.