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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 $phi_{BEC} =3/2$ predicted by the magnon BEC theory.