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

TL;DR

This study investigates the quantum phase transition from Bose glass to Bose-Einstein condensate of magnons in a doped quantum magnet, revealing critical behavior and magnon localization near the transition point through specific heat and ESR measurements.

Contribution

It provides the first detailed analysis of the Bose glass-BEC transition in Tl$_{1-x}$K$_x$CuCl$_3$, highlighting the critical exponent behavior and magnon localization effects.

Findings

Critical exponent $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, ightarrow$ less than 1/2 near the quantum critical point.

Magnon localization at $H < H_c$ indicated by ESR line shape.

Power law behavior of $T_N$ near critical field with a non-standard exponent.

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 $T_{\rm N}$ can be described by the power law $\left[H\,{-}\,H_{\rm c}\right]\,{\propto}\,T_{\rm N}^{\phi}$ near the quantum critical point $H_{\rm c}\,{\sim}\,3.5$ T. The critical exponent ${\phi}$ tends to reach a value smaller than 1/2 with decreasing fitting window in contrast with ${\phi}\rightarrow 3/2$ for the standard BEC in pure system. At sufficiently low temperatures, the ESR line shape for $H\,{\simeq}\,H_{\rm c}$ is intermediate between Gaussian and Lorentzian. This indicates the localization of magnons for $H\,{<}H_{\rm c}$ at T=0.