Nonlinear NMR signals and nuclear relaxation in coupled electron-nuclear spin systems

We present a new theoretical description of the coupled electron-nuclear spin systems which takes into account an indirect relaxation of nuclear spins via the electron subsystem. In our theory the magnitude of the nuclear magnetization is conserved for arbitrary large excitation powers, similar to the Landau-Lifshitz-Gilbert model of relaxation. This is drastically different from the conventional heating scenario based on the phenomenological Bloch equations. The predictions of our theory are compared with the experimental nonlinear NMR signals obtained in a weakly anisotropic antiferromagnetic MnCO$_3$ sample at temperatures below $1\,$K and good quantitative agreement is observed. The proposed theory brings together the properties of magnetic nuclear resonance in, on the one hand, the magnetic systems considered here and, on the other hand, the superfluid ${^3}$He where the magnitude of the nuclear magnetization vector is also conserved.