  Nonlinear manipulation of nuclear and electron spins is the basis for all
advanced methods in magnetic resonance including multidimensional nuclear
magnetic and electron spin resonance spectroscopies, magnetic resonance
imaging, and in recent years, quantum control over individual spins. The
methodology is facilitated by the ease with which the regime of strong coupling
can be reached between radiofrequency or microwave magnetic fields and nuclear
or electron spins respectively, typified by sequences of magnetic pulses that
control the magnetic moment directions. The capabilities meet a bottleneck,
however, for far-infrared magnetic resonances characteristic of correlated
electron materials, molecular magnets, and proteins that contain high-spin
transition metal ions. Here we report the development of two-dimensional
terahertz magnetic resonance spectroscopy and its use for direct observation of
the nonlinear responses of collective spin waves (magnons). The spectra show
magnon spin echoes and 2-quantum signals that reveal pairwise correlations
between magnons at the Brillouin zone center. They also show resonance-enhanced
second-harmonic and difference-frequency signals. Our methods are readily
generalizable to multidimensional magnetic resonance spectroscopy and nonlinear
coherent control of terahertz-frequency spin systems in molecular complexes,
biomolecules, and materials.
