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Quasi-one-dimensional magnet NiCl$_2\cdot$4SC(NH$_2$)$_2$, usuallyabbreviated as DTN, does not order at zero field down to $T=0$: due to thestrong single-ion anisotropy of the "easy plane" type acting on $S=1$ Ni$^{2+}$ions, the $S_z=0$ ground state is separated from $S_z=\pm 1$ excitations by anenergy gap. Once the magnetic field is applied along the main anisotropy axis,the gap closes at $B_{c1}=2.18$ T and the field-induced antiferromagnetic orderarises. The low-energy excitations spectrum of this field-induced ordered stateincludes two branches of excitations, one of them have to be a gaplessGoldstone mode. Recent studies of excitations spectrum in a field-inducedordered state of DTN (T.Soldatov et.al, Phys.Rev.B 101, 104410 (2020)) haverevealed that Goldstone mode became gapped as magnetic field deviates from themain symmetry axis. This paper proposes simple description of antiferromagneticresonance modes of quasi-one-dimensional quantum $S=1$ magnet with strongsingle-ion anisotropy. The approach used is based on a combination of thestrong coupling model for the anisotropic spin chain with the conventionalmean-field model of antiferromagnetic resonance. The resulting model fits tothe known experimental results without additional tuning parameters.

Antiferromagnetic resonance in a spin-gap magnet with strong single-ion anisotropy