Pseudo-spin rotation symmetry breaking by Coulomb interaction terms in spin-orbit coupled systems

Abstract

By transforming from the pure-spin-orbital ($t_{2g}$) basis to the spin-orbital entangled pseudo-spin-orbital basis, the pseudo-spin rotation symmetry of the different Coulomb interaction terms is investigated under SU(2) transformation in pseudo-spin space. While the Hubbard and density interaction terms are invariant, the Hund's coupling and pair-hopping interaction terms explicitly break pseudo-spin rotation symmetry systematically. The form of the symmetry-breaking terms obtained from the transformation of the Coulomb interaction terms accounts for the easy $x$-$y$ plane anisotropy and magnon gap for the out-of-plane mode, highlighting the importance of mixing with the nominally non-magnetic $J$=3/2 sector, and providing a physically transparent approach for investigating magnetic ordering and anisotropy effects in perovskite ($\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$) and other $d^5$ pseudo-spin compounds.

22 pages and 4 figure

References in corpus (10)

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Cited by in corpus (2)

• Coupled spin-orbital fluctuations in a three orbital model for $4d$ and $5d$ oxides with electron fillings $n=3,4,5$ -- Application to $\mathrm{NaOs}{\mathrm{O}}_3$, $\mathrm{C}{\mathrm{a}}_2\mathrm{Ru}{\mathrm{O}}_4$, and $\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$
• Microscopic model realization of $\mathbf{d}$-wave pseudospin current order in Sr${}_2$IrO${}_4$