A nearly single cycle intense terahertz (THz) pulse with peak electric and magnetic fields of 0.5 MV=cm and 0.16 T, respectively, excites both modes of spin resonances in the weak antiferromagnet FeBO 3 . The high frequency quasiantiferromagnetic mode is excited resonantly and its amplitude scales linearly with the strength of the THz magnetic field, whereas the low frequency quasiferromagnetic mode is excited via a nonlinear mechanism that scales quadratically with the strength of the THz electric field and can be regarded as a THz inverse Cotton-Mouton effect. THz optomagnetism is shown to be more energy efficient than similar effects reported previously for the near-infrared spectral range.