Quantum Criticality of an Ising-like Spin-1/2 Antiferromagnetic Chain in a Transverse Magnetic Field

We report on magnetization, sound velocity, and magnetocaloric-effect measurements of the Ising-like spin-1/2 quantum antiferromagnetic chain BaCo$_2$V$_2$O$_8$ as a function of temperature down to 1.3~K and applied transverse magnetic field up to 60~T. While across the Ne\'{e}l temperature of $T_N\sim5$~K anomalies in magnetization and sound velocity confirm the antiferromagnetic ordering transition, at the lowest temperature in the field-dependent measurements we find a sharp softening of sound velocity and a clear temperature minimum at $B^{c,3D}_\perp=21.4$~T, indicating suppression of the antiferromagnetic order. At higher fields, magnetocaloric-effect measurements reveal a broad temperature minimum at $B^c_\perp = 40$~T, accompanied by a broad minimum of sound velocity and a saturation-like level-off in magnetization. These features signal a quantum phase transition that is further quantified by the divergent behavior of Gr\"{u}neisen parameter $\Gamma_B \propto (B-B^{c}_\perp)^{-1}$. By contrast, at the critical field the Gr\"{u}neisen parameter converges to a constant as temperature decreases towards zero, which is a distinct characteristics of the one-dimensional transverse-field Ising quantum critical point.