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Magnetic resonance in the quasi-2D square lattice easy-plane antiferromagnet Ba$_2$MnGe$_2$O$_7$

We report results of a multi-frequency (0.8-60 GHz) electron spin resonance study of the spin dynamics in the quasi-2D square lattice antiferromagnet Ba$_2$MnGe$_2$O$_7$ both in antiferromagnetically ordered and paramagnetic phases. We directly observe two zero-field gaps in the excitation spectrum of the ordered phase, the larger one being due to easy-plane anisotropy, and the smaller one indicates the presence of fourth-order in-plane anisotropy probably related to the multiferroic properties of this compound. We observe effects of hyperfine interaction on the electron spin resonance spectra in the antiferromagnetically ordered state, which turns out to be comparable with in-plane anisotropy. The hyperfine field strength is found from the observed low-temperature electron spin resonance data. The spin dynamics of the paramagnetic phase is characterized by strong broadening of the ESR absorption line, which can be ascribed to the vortex dynamics of a 2D magnet.