Quantum versus classical nature of a low-temperature magnetic phase transition in TbAl$_3$(BO$_3$)$_4$

TL;DR

This study investigates a low-temperature magnetic phase transition in TbAl$_3$(BO$_3$)$_4$, revealing quantum fluctuations influence the transition, with evidence suggesting a quantum critical point driven by magnetic field tuning.

Contribution

It provides experimental evidence of a quantum fluctuation-driven phase transition in a magnetic material, including phase diagram construction and critical exponent estimation.

Findings

Phase transition at $T_c=0.68$ K was identified.

Lowering of $T_c$ with increasing magnetic field indicates quantum fluctuation influence.

Constructed the $B_{||}-T$ phase diagram and estimated the dynamical critical exponent.

Abstract

Specific heat, $C_B$, of a TbAl$_3$(BO$_3$)$_4$ crystal was studied for 50 mK $<T<$ 300 K, with emphasis on $T<1$ K, where a phase transition was found at $T_c =0.68$ K. Nuclear, non-phonon ($C_m$), and lattice contributions to $C_B$ were separated. Lowering of $T_c$ with ncrease of magnetic field parallel to the easy magnetization axis, $B_{||}$, was found. It was established that $C_m$ and a Gr\"uneisen ratio depend on $B_{||}$ and $T$ in a way characteristic of systems, in which a classical transition is driven by quantum fluctuations, QF, to a quantum critical point at $T=0$, by tuning a control parameter ($B_{||}$). The $B_{||} - T$ phase diagram was constructed and the dynamical critical exponent $0.82 \le z \le 0.96$ was assessed. Nature of the transition was not established explicitly. Magnetization studies point at the ferromagnetic ordering of Tb$^{3+}$ magnetic moments, however, lowering of $T_c$ with increase in $B_{||}$ is opposite to the classical behavior. Hence, a dominant role of QF was supposed.