Pseudo-Spin Rotation Symmetry Breaking By Coulomb Interaction Terms In Spin-Orbit Coupled Systems

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 (Sr2IrO4) and other d(5) pseudo-spin compounds.