Higgs mode and stability of xy -orbital ordering in Ca2RuO4

Abstract

We investigate the stability of $xy$ orbital ordering and the nature of the magnetic longitudinal excitations in ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$. To this end, we employ the local-density approximation $+$ dynamical mean-field theory approach, in combination with many-body perturbation theory. We show that the crossover to a nonperturbative spin-orbit regime----in which $xy$-like orbital ordering is to a large extent quenched---only takes place when the crystal field is sizably reduced with respect to its actual value in ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$. In the small crystal-field splitting limit, the spin-orbit interaction favors the metal-to-insulator transition. We find that the effects of the spin-orbit interaction remain perturbative even for the less distorted ${\mathrm{Ca}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{RuO}}_{4}$ with $0lxl0.2$ ($S$-Pbca phase) and for the ${S}^{*}$ phase. We show that, nevertheless, a Higgs mode at $\ensuremath{\omega}\ensuremath{\sim}50\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ is compatible with $xy$-like orbital ordering in ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$.