Nonlinear couplings between magnetic excitations revealed by coherent two-dimensional terahertz magnetic resonance polarimetry

Excitation and control of spin orders in terahertz (THz) frequencies is a thriving field and holds promise for ultrafast spintronics. The magnetic components of intense THz pulses can resonantly drive spin excitations without involving other degrees of freedom. However, the Zeeman interaction is generally assumed to be a weak effect and the nonlinear couplings between individual magnetic excitations have remained unexplored. Here, we develop a state-of-the-art two-dimensional THz magnetic resonance spectroscopy with polarization selectivity and demonstrate that inherent couplings exist between the ferromagnetic (F) and antiferromagnetic (AF) magnon modes in two canted antiferromagnets YFeO₃ and ErFeO₃. In both systems, we find that simultaneous excitations of these two modes can induce second-order nonlinear responses at their sum and difference frequencies, revealing radiative two-quantum coherences between the two magnons. In addition, by driving the F mode to large spin deflections in ErFeO₃, a coherent THz emission at the AF mode frequency emerges, indicative of nonperturbative spin dynamics. The present work provides a comprehensive view of how THz magnetic fields can interact with magnetic excitations nonlinearly and provides a new way to achieve ultrafast manipulation and coherent control of spin waves.