Bose Glass-BEC Transition of Magnons in Tl${}_{1-x}$K${}_x$CuCl${}_3$

Abstract

We report the magnetic-field induced Bose glass$-$BEC transition of magnons in Tl${}_{1-x}$K${}_x$CuCl${}_3$ and its critical behavior investigated through specific heat and ESR measurements. The field dependence of the BEC transition temperature $T_{\mathrm{N}}$ can be described by the power law $\left[H-H_{\mathrm{c}}\right]\propto T_{\mathrm{N}}^{\varphi }$ near the quantum critical point $H_{\mathrm{c}}\sim 3.5$ T. The critical exponent $\varphi$ tends to reach a value smaller than 1/2 with decreasing fitting window in contrast with $\varphi \to 3/2$ for the standard BEC in pure system. At sufficiently low temperatures, the ESR line shape for $H\simeq H_{\mathrm{c}}$ is intermediate between Gaussian and Lorentzian. This indicates the localization of magnons for $H<H_{\mathrm{c}}$ at T=0.

5 pages, 3 figures