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We derive an effective Lagrangian in the quasi-antiferromagneticapproximation that allows to describe the magnetization dynamics for uniaxialf-d (rare-earth - transition metal) ferrimagnet near the magnetizationcompensation point in the presence of external magnetic field. We performcalculations for the parameters of GdFeCo, a metallic ferrimagnet withcompensation point that is one of the most promising materials in ultrafastmagnetism. Using the developed approach, we find the torque that acts on themagnetization due to ultrafast demagnetization pulse that can be caused eitherby ultrashort laser or electrical current pulse. We show that the torque isnon-zero only in the non-collinear magnetic phase that can be acquired byapplying external magnetic field to the material. The coherent response ofmagnetization dynamics amplitude and its timescale exhibits critical behaviornear certain values of the magnetic field corresponding to a spin-flop likephase transition. Understanding the underlying mechanisms for these effectsopens the way to efficient control of the amplitude and the timescales of thespin dynamics, which is one of the central problems in the field of ultrafastmagnetism.

Ultrafast magnetization dynamics in uniaxial ferrimagnets with compensation point. GdFeCo