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We investigate two holes in the the $t_{2g}$ levels of a square-lattice Mottinsulator with strong spin-orbit coupling. Exact diagonalization of aspin-orbital model valid at strong onsite interactions, but arbitraryspin-orbit coupling and crystal field is complemented by an effective triplonmodel (valid for strong spin-orbit coupling) and by a semiclassical variant ofthe model. We provide the magnetic phase diagram depending on crystal field andspin-orbit coupling, which largely agrees for the semiclassical and quantummodels, as well as excitation spectra characterizing the various phases.

Magnetic phases for two $t_{2g}$ holes with spin-orbit coupling and crystal field