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

Specific heat C-B of a TbAl3(BO3)(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 (B-parallel to) was found. It was established that C-m and a Gruneisen ratio depend on B-parallel to 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 to). The B-parallel to - T phase diagram was constructed, and the dynamical critical exponent 0.82 <= z <= 0.96 was assessed. Nature of the transition was not established explicitly. Magnetization studies point at the ferromagnetic ordering of Tb3+ magnetic moments, however, lowering of T-c with increase in B-parallel to is opposite to the classical behavior. Hence, a dominant role of QFs was supposed.