Quantum magnets with large single-ion easy-plane anisotropy in magnetic field

We propose a theory describing low-temperature properties of magnets with integer spin and large single-ion easy-plane anisotropy $D$ in magnetic field $H$ directed parallel to the hard axis. Considering the exchange interaction between spins as a perturbation and using the bosonic spin representation proposed in our recent paper [1] we find thermal corrections to the elementary excitation spectrum, magnetization and specific heat in the vicinity of the quantum critical point (QCP) $H=H_{c1}(0)\sim D$ in the first nonvanishing orders of the perturbation theory. An expression is found for the boundary of the paramagnetic phase $H_{c1}(T)$ in the $H$–$T$-plane. The effective interaction between bosons is derived near the QCP. The proposed theory describes well experimental data obtained in NiCl$_2$–4SC(NH$_2$)$_2$ (DTN).