  Spin dynamics of the square lattice Heisenberg antiferromagnet, \BaMnGeO, is
studied by a combination of bulk measurements, neutron diffraction, and
inelastic neutron scattering techniques. Easy plane type antiferromagnetic
order is identified at $T \le 4.0$ K. The exchange interactions are estimated
as $J_1$ = 27.8(3)${\mu}$eV and $J_2$ = 1.0(1) ${\mu}$eV, and the saturation
field $H_{\rm C}$ is 9.75 T. Magnetic excitation measurements with high
experimental resolution setup by triple axis neutron spectrometer reveals the
instability of one magnon excitation in the field range of $0.7H_{\rm C}
\lesssim H \lesssim 0.85H_{\rm C}$.
