  Transition metal compounds with the $(t_{2g})^4$ electronic configuration are
expected to be nonmagnetic atomic singlets both in the weakly interacting
regime due to spin-orbit coupling, as well as in the Coulomb dominated regime
with oppositely aligned $L=1$ and $S=1$ angular momenta. However, starting with
the full multi-orbital electronic Hamiltonian, we show the low energy effective
magnetic Hamiltonian contains isotropic superexchange spin interactions but
anisotropic orbital interactions. By tuning the ratio of superexchange to
spin-orbit coupling $J_\mathrm{SE}/\lambda$, we obtain a phase transition from
nonmagnetic atomic singlets to novel magnetic phases depending on the strength
of Hund's coupling, the crystal structure and the number of active orbitals.
Spin-orbit coupling plays a non-trivial role in generating a triplon condensate
of weakly interacting excitations at antiferromagnetic ordering vector $\vec
k=\vec \pi$, regardless of whether the local spin interactions are
ferromagnetic or antiferromagnetic. In the large $J_\mathrm{SE} / \lambda$
regime, the localized spin and orbital moments produce anisotropic orbital
interactions that are frustrated or constrained even in the absence of
geometric frustration. Orbital frustration leads to frustration in the spin
channel opening up the possibility of spin-orbital liquids with both spin and
orbital entanglement.
