$^{105}$Pd NMR and NQR study of the cubic heavy fermion system Ce$_3$Pd$_{20}$Si$_6$

We report $^{105}$Pd NMR and NQR measurements on a single crystal of Ce$_3$Pd$_{20}$Si$_6$, where antiferroquadrupolar and antiferromagnetic orders develop at low temperature. From the analysis of NQR and NMR spectra, we have determined the electric field gradient (EFG) tensors and the anisotropic Knight shift components for both inequivalent Pd sites - Pd(32f) and Pd(48h). The observed EFG values are in excellent agreement with our state-of-the-art DFT calculations.