Anisotropic nature of zero-field nuclear magnetic resonance in iron-based superconductors

We predict how zero-field nuclear magnetic resonance (ZFNMR), nuclear magnetic resonance done without an external magnetic field, could be used to study spin fluctuations in Fe-based superconductors (FeSCs). In FeSCs, ZFNMR is influenced by a strong hyperfine field (HF) at the atom above the Fe plane and the interaction of this atom's electrically quadrupolar nucleus with the electric field gradient (EFG). Unique to ZFNMR, neither effect is a perturbation on the other. The transition frequencies depend on both the electric and magnetic interaction and can be averaged out depending on the nature of the spin fluctuations. In particular, the HF is affected by fluctuations of the spin state, and the EFG is affected by fluctuations between stripe directions. We show how the dynamic nature of the system, as affected by spin fluctuations, which manifests as changes in the orientations of the HF and EFG, can be captured by the anisotropic response to radio-frequency excitations. For instance, when the excitation is applied along the hyperfine field, 4 of the 6 possible transitions vanish, whereas 2 vanish when applied perpendicularly. Even in the paramagnetic phase where no HF exists and there is only one frequency due to the degeneracy of the spin 3/2 quadrupole Hamiltonian, the EFG parameters can be determined via the asymmetric response in the Rabi frequency and intensity. Using these principles, we show how spin fluctuations can be quantified via the HF and EFG parameters.