Excitonic magnetism involving superpositions of singlet and triplet states is expected to arise for two holes in strongly correlated and spin-orbit-coupled t2g orbitals. However, uncontested material examples for its realization are rare. We apply the variational cluster approach to the square lattice to investigate excitonic antiferromagnetism and the impact of a crystal field. We give a phase diagram depending on spin-orbit coupling and crystal field and find excitonic magnetism to survive in the presence of substantial crystal-field-induced orbital order. We address the specific example of Ca2RuO4 using ab initio modeling and conclude it to realize such excitonic magnetism despite its pronounced orbital polarization. We also reproduce magnetic excitations and show the maximum at momentum (0,0) to be related to the excitonic character of the magnetic order.
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