Evidence of relativistic field-derivative torque in nonlinear THz response of magnetization dynamics

Understanding the complete light-spin interactions in magnetic systems is the key to manipulating the magnetization using optical means at ultrafast timescales. The selective addressing of spins by terahertz (THz) electromagnetic fields via Zeeman torque is one of the most successful ultrafast means of controlling magnetic excitations. Here we show that this traditional Zeeman torque on the spins is not sufficient, rather an additional relativistic field-derivative torque is essential to realize the observed magnetization dynamics. We accomplish this by exploring the ultrafast nonlinear magnetization dynamics of rare-earth, Bi-doped iron garnet when excited by two co-propagating THz pulses. First, by exciting the sample with an intense THz pulse and probing the magnetization dynamics using magneto-optical Faraday effect, we find the collective exchange resonance mode between rare-earth and transition metal sublattices at 0.48 THz. We further explore the magnetization dynamics via the THz time-domain spectroscopic means. We find that the observed nonlinear trace of the magnetic response cannot be mapped to the magnetization precession induced by the Zeeman torque, while the Zeeman torque supplemented by an additional field-derivative torque follows the experimental evidences. This breakthrough enhances our comprehension of ultra-relativistic effects and paves the way towards novel technologies harnessing light-induced control over magnetic systems.