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