  Low-energy magnon excitations in magnetoelectric LiFePO$_4$ have been
investigated by high-frequency high-field electron spin resonance spectroscopy
in magnetic fields up to B = 58 T and frequencies up to f = 745 GHz. For
magnetic fields applied along the easy magnetic axis, the excitation gap
softens and vanishes at the spin-flop field of BSF = 32 T before hardening
again at higher fields. In addition, for B smaller than BSF we observe a
resonance mode assigned to excitations due to Dzyaloshinskii-Moriya
(DM)-interactions, thereby evidencing sizable DM interaction of approx 150
micro eV in LiFePO4. Both the magnetisation and the excitations up to high
magnetic fields are described in terms of a mean-field theory model which
extends recent zero field inelastic neutron scattering results. Our results
imply that magnetic interactions as well as magnetic anisotropy have a sizable
quadratic field dependence which we attribute to significant magnetostriction.
