THz magneto-optic study of a clean and a bond-disordered $S=1$ quantum magnet DTN

We report THz absorption spectroscopy results from 3 to 40\,cm$^{-1}$ (0.09 to 1.2\,THz) for a spin-1 quantum magnet NiCl$_2\cdot$4SC(NH$_2$)$_2$ (DTN) and its magnetic bond-disordered derivate Ni(Cl$_{0.87}$Br$_{0.13}$)$_2\cdot$4SC(NH$_2$)$_2$ (DTNX) at temperatures down to 0.3\,K in magnetic fields from 0 to 12\,T. In DTN the single optically active mode at 9 cm\,$^{-1}$ in zero field corresponds to the top of the magnon band excitation. In DTNX, an additional broad feature is observed at about 1.5\,cm$^{-1}$ above the 9\,cm$^{-1}$ mode in agreement with the recent inelastic neutron scattering data [PRB92, 024429, (2015)]. Both modes undergo Zeeman splitting in magnetic field with similar g-factors, but the weak mode loses intensity as the systems order antiferromagnetically in 2\,T at 0.3\,K. We are able to resolve several modes around 15\,cm$^{-1}$ in the ordered phase, which above ordering temperature merge into the broad mode reported earlier by ESR. As DTNX approaches the second critical field 11.5\,T of the induced ferromagnetic transition at 0.3K, an additional mode, not present in DTN, emerges at 14 cm$^{-1}$. These new data assist in constructing a detailed microscopic Hamiltonian for DTN and will be discussed in the context of Bose glass physics reported for DTNX.