Magnetic Excitations in the Spin-1 Anisotropic Heisenberg Antiferromagnetic Chain System NiCl$_2$-4SC(NH$_2$)$_2$

Electron spin resonance studies of magnetic excitations in NiCl$_2$-4SC(NH$_2$)$_2$ (DTN, a quantum $S=1$ chain system with strong easy-pane anisotropy and a new candidate for the Bose-Einstein condensation of the spin degrees of freedom) in fields up to 25 T are presented. Based on analysis of the frequency-field dependence of single-magnon mode in the high- field spin-polarized phase and previous experimental results [Phys. Rev. Lett. 96, 07724 (2006)], a revised set of spin- Hamiltonian parameters is obtained. Our results yield $D=8.9$ K, $J_c=2.2$ K, and $J_{a,b}=0.18$ K for the anisotropy, intra- and inter-chain exchange interactions, respectively. These values are used to calculate the AFM-phase boundary, low- temperature magnetization and the frequency-field dependence of two-magnon bound-state excitations predicted by theory and observed in DTN for the first time. Excellent quantitative agreement with experimental data is obtained.