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Nonlinear manipulation of nuclear and electron spins is the basis for alladvanced methods in magnetic resonance including multidimensional nuclearmagnetic and electron spin resonance spectroscopies, magnetic resonanceimaging, and in recent years, quantum control over individual spins. Themethodology is facilitated by the ease with which the regime of strong couplingcan be reached between radiofrequency or microwave magnetic fields and nuclearor electron spins respectively, typified by sequences of magnetic pulses thatcontrol the magnetic moment directions. The capabilities meet a bottleneck,however, for far-infrared magnetic resonances characteristic of correlatedelectron materials, molecular magnets, and proteins that contain high-spintransition metal ions. Here we report the development of two-dimensionalterahertz magnetic resonance spectroscopy and its use for direct observation ofthe nonlinear responses of collective spin waves (magnons). The spectra showmagnon spin echoes and 2-quantum signals that reveal pairwise correlationsbetween magnons at the Brillouin zone center. They also show resonance-enhancedsecond-harmonic and difference-frequency signals. Our methods are readilygeneralizable to multidimensional magnetic resonance spectroscopy and nonlinearcoherent control of terahertz-frequency spin systems in molecular complexes,biomolecules, and materials.

Two-dimensional terahertz magnetic resonance spectroscopy of collective spin waves