Novel approach to description of quantum magnets with large singe-ion easy-plane anisotropy

We introduce a new representation of an integer spin $S$ via bosonic operators which is useful in describing the paramagnetic phase and transitions to magnetically ordered phases in magnetic systems with large single-ion easy-plane anisotropy $D$. Considering the exchange interaction between spins as a perturbation and using the diagram technique we derive the elementary excitation spectrum and the ground state energy in the third order of the perturbation theory. In the special case of S=1 we obtain these expressions also using simpler spin representations some of which were introduced before. Comparison with results of previous numerical studies of 2D systems with S=1 demonstrates that our approach works better than other analytical methods applied before for such systems. We apply our results for the elementary excitation spectrum analysis obtained experimentally in $\rm NiCl_2$-$\rm 4SC(NH_2)_2$ (DTN). It is demonstrated that a set of model parameters (exchange constants and $D$) which has been used for DTN so far describes badly the experimentally obtained spectrum. A new set of parameters is proposed using which we fit the spectrum and values of two critical fields of DTN.