Quantum versus classical nature of the low-temperature magnetic phase transition in TbAl3(BO3)(4)

DOI: https://dx.doi.org/10.1103/PhysRevB.105.094418

Specific heat $C_B$ of a ${\mathrm{TbAl}}_3{\left({\mathrm{BO}}_3\right)}_4$ 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, nonphonon ($C_m$), and lattice contributions to $C_B$ were separated. Lowering of $T_c$ with an increase in magnetic field parallel to the easy magnetization axis $\left(B_{\parallel }\right)$ was found. It was established that $C_m$ and a Grüneisen ratio depend on $B_{\parallel }$ and $T$ in a way characteristic of systems in which a classical transition is driven by quantum fluctuations (QFs) to a quantum critical point at $T=0$ by tuning a control parameter ($B_{\parallel }$). The $B_{\parallel }-T$ 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 ${\mathrm{Tb}}^{3+}$ magnetic moments, however, lowering of $T_c$ with increase in $B_{\parallel }$ is opposite to the classical behavior. Hence, a dominant role of QFs was supposed.