NMR quadruopole spectra of PZT from first-principles

High performance piezoelectric materials are disordered alloys, so it can be difficult to determine the local atomic geometry. Recently, high field NMR measurements have shown great promise as a microscopic probe of $\mathrm{ABO_{3}}$ perovskite-based alloys \footnote{G. L. Hoatson, D. H. Zhou, F. Fayon, D. Massiot, and R. L. Vold, Phys. Rev. B, {\bf 66}, 224103 (2002).} by their ability to resolve line-splittings due to nuclear quadrupolar coupling with the electric field gradient (EFG) at the nucleus. We report first-principles LDA calculations of the EFG's in monoclinic and tetragonal Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ systems using the linear augmented planewave (LAPW) method, and we compute NMR static powder spectra for $^{91}$Zr, $^{47}$Ti, and $^{17}$O atoms as a function of applied strain. With decreasing $c/a$ ratio PZT converts from tetragonal to monoclinic symmetry. We observe that the calculated NMR spectra show dramatic deviations with decreasing $c/a$ from that in tetragonal $P4mm$ well before the electric polarization begins to rotate away from the [001] direction. This indicates that NMR measurements can be a very accurate probe of local structural changes in perovskite piezoelectrics.