  It is found that single-cycle THz electromagnetic fields efficiently excite a
GHz spin resonance mode in ferrimagnetic Tm$_3$Fe$_5$O$_{12}$, despite the near
absence of GHz spectral components in the exciting THz pulse. By analyzing how
the efficiency of excitation depends on the orientation and strength of the THz
electric field, we show that it can be explained in terms of the nonlinear THz
inverse Cotton-Mouton effect. Here, the THz electric field gets effectively
rectified and acts on the ferrimagnetic spins as a uni-polar effective magnetic
field pulse. This interpretation is confirmed by a theoretical model based on
the phenomenological analysis of the effective magnetic field, combined with
the equations of motion derived from the effective Lagrangian for a
ferrimagnet. Moreover, by using the outcome of two-dimensional THz
spectroscopy, we conjecture a quantum-mechanical interpretation of the observed
effect in terms of stimulated Raman scattering of THz photons by the
crystal-field split f-f electronic transitions of Tm$^{3+}$.
