  We studied electron spin resonance in a quantum magnet NiCl2-4SC(NH2)2,
demonstrating a field-induced quantum phase transition from a
quantum-disordered phase to an antiferromagnet. We observe two branches of the
antiferromagnetic resonance of the ordered phase, one of them has a gap and the
other is a Goldstone mode with zero frequency at a magnetic field along the
four-fold axis. This zero frequency mode acquires a gap at a small tilting of
the magnetic field with respect to this direction. The upper gap was found to
be reduced in the doped compound Ni(Cl(1-x)Br(x))2-4SC(NH2)2 with $x=0.21$.
This reduction is unexpected because of the previously reported rise of the
main exchange constant in a doped compound. Further, a nonresonant diamagnetic
susceptibility $\chi^{\prime}$ was found for the ordered phase in a wide
frequency range above the quasi-Goldstone mode. This dynamic diamagnetism is as
large as the dynamic susceptibility of the paramagnetic resonance. We speculate
that it originates from a two-magnon absorption band of low-frequency
dispersive magnon branch.
