Simulating the interplay of dipolar and quadrupolar interactions in NMR by spin dynamic mean-field theory

The simulation of nuclear magnetic resonance (NMR) experiments is a notoriously difficult task, if many spins participate in the dynamics. The recently established dynamic mean-field theory for high-temperature spin systems (spinDMFT) represents an efficient yet accurate method to deal with this scenario. SpinDMFT reduces a complex lattice system to a time-dependent single-site problem, which can be solved numerically with small computational effort. Since the approach retains local quantum degrees of freedom, a quadrupolar term can be exactly incorporated. This allows us to study the interplay of dipolar and quadrupolar interactions for any parameter range, i.e., without the need for a perturbative treatment. We obtain a remarkable agreement with experimental data for an aluminium nitride monocrystal, which strongly suggests the use of spinDMFT as a prediction tool. Furthermore, we draw a comparison between a quantum-mechanical and a classical version of spinDMFT showing that local quantum effects are of great importance for the studied type of system.