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

TL;DR

This paper investigates how Coulomb interactions in spin-orbit coupled systems break pseudo-spin rotation symmetry, revealing implications for magnetic anisotropy and ordering in materials like Sr2IrO4.

Contribution

It provides a systematic analysis of symmetry-breaking Coulomb terms in the pseudo-spin basis, highlighting their physical effects on magnetic properties.

Findings

Hubbard and density interactions are symmetry-invariant.

Hund's coupling and pair-hopping break pseudo-spin symmetry.

Accounts for magnetic anisotropy and magnon gaps in iridates.

Abstract

By transforming from the pure-spin-orbital ($t_{\rm 2g}$) 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 ($\rm Sr_2 Ir O_4$) and other $d^5$ pseudo-spin compounds.