Unusual Magnetic Response of an S = 1 Antiferromagetic Linear-Chain Material.

An $S = 1$ antiferromagnetic polymeric chain, [Ni(HF$_2$)(3-Clpy)$_4$]BF$_4$ (py = pyridine), has been identified to have nearest-neighbor antiferromagnetic interaction $J/k_B = 4.86$~K and single-ion anisotropy $D/k_B = 4.3$~K, while avoiding long-range order down to 25~mK.\footnote{J.L.~Manson \emph{et al.}, Inorg.~Chem.~{\bf 51} (2012) 7520.} With $D/J = 0.88$, this system is close to the $D/J \approx 1$ gapless quantum critical point between the topologically distinct Haldane and Large-$D$ phases. The magnetization was studied over a range of temperatures, 50~mK $\leq T \leq 1$~K, and magnetic fields, $B \leq 10$~T. The results allow an upper bound of the critical field, $B_c$, which closes the Haldane gap, to be estimated. Specifically, $B_c \leq (35 \pm 10)$~mT, which is close to the predicted 46~mT,\footnote{S.~Hu \emph{et al.}, Phys.~Rev.~B {\bf 84} (2011) 220402.} when using the reported$^2$ values of $J$, $D$, and $g$. In low fields, the magnetic signal increases with decreasing $T$ for 400~mK $< T < 800$~mK but is independent of $T$ for 50~mK $\leq T \leq 400$~mK. This observation is consistent with a significant increase in the specific heat arising from the accumulation of entropy in the vicinity of the quantum critical point.