Interplay of frustration and magnetic field in the two-dimensional quantum antiferromagnet Cu(tn)Cl${}_2$

Specific heat and ac magnetic susceptibility measurements, spanning low temperatures ($T\ge 40$ mK) and high magnetic fields ($B\le 14$ T), have been performed on a two-dimensional (2D) antiferromagnet Cu(tn)Cl${}_2$ (tn = C${}_3$H${}_{10}$N${}_2$). The compound represents an $S=1\mathrm{/}2$ spatially anisotropic triangular magnet realized by a square lattice with nearest-neighbor ($J\mathrm{/}{k}_B=3$ K), frustrating next-nearest-neighbor ($0 < J^{\prime}/J < 0.6$),andinterlayer($|J^{\prime \prime}/J| \approx 10^{-3}$) interactions. The absence of long-range magnetic order down to $T=$ 60 mK in $B=0$ and the $T^2$ behavior of the specific heat for $T\le 0.4$ K and $B \geq 0$ are considered evidence of high degree of 2D magnetic order. In fields lower than the saturation field, $B_{\text{sat}}=6.6$ T, a specific heat anomaly, appearing near 0.8 K, is ascribed to bound vortex-antivortex pairs stabilized by the applied magnetic field. The resulting magnetic phase diagram is remarkably consistent with the one predicted for the ideal square lattice, except that $B_{\text{sat}}$ is shifted to values lower than expected. Potential explanations for this observation, as well as the possibility of a Berezinski-Kosterlitz-Thouless (BKT) phase transition in a spatially anisotropic triangular magnet with the N'{e}el ground state, are discussed.