Excitonic magnetism at the intersection of spin-orbit coupling and crystal-field splitting

Abstract

Excitonic magnetism involving superpositions of singlet and triplet states is expected to arise for two holes in strongly correlated and spin-orbit-coupled t 2g 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 Ca 2 RuO 4 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.

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

“…As expected [26], stripy magnetism is found when both SOC and CF are weak, and checkerboard order (as seen in Ca 2 RuO 4 ) takes over when either becomes strong enough to sufficiently lift orbital degeneracy. For negative CF, i.e., disfavoring doubly occupied xy orbitals, we find an additional intermediate phase with rather complex magnetic order.…”

“…In the present paper, we study the competition of CF ∆ and SOC λ in t 4 2g systems in more depth and for a wider parameter space. We investigate an effective spin-orbit model obtained in second-order perturbation theory, as also used for Ca 2 RuO 4 [26]. This extends the comparison of CF and SOC acting on the itinerant regime (without magnetic ordering) [10] to magnetic Mott insulators.…”

“…In a previous publication, some of us have used the variational cluster approach (VCA) based on ab initio parameters to show that excitonic antiferromagnetism can coexist with substantial CF's and that Ca 2 RuO 4 falls into this regime [26,27] of orbitally polarized excitonic antiferromagnetism. In the present paper, we study the competition of CF ∆ and SOC λ in t 4 2g systems in more depth and for a wider parameter space.…”

Van Vleck excitons in Ca2RuO4

“…By exclusively considering the an-tiferromagnetically ordered Ru 4+ moments contained in the first two coordination shells within the (a, b) basal plane that are coupled with isotropic magnetic exchange constants J 1 and J 2 , Eq. 10 yields two unique expressions for the Fourier transform of the exchange constants: (18) and…”

“…Neutron scattering measurements nevertheless observe long-range ordered antiferromagnetism, albeit with a reduced ordered moment ∼ 1 µ B . The result is an unusual manifestation of a spin-orbit induced mixing of higher energy crystal field levels 18 that stabilizes a static magnetic moment in a naively j eff = 0 singlet ground state-a higher order state mixing leading to analogies with Van Vleck susceptibility. 19 The ground state in Ca 2 RuO 4 is different from the weakly magnetic ground states observed in compounds based on Kramers ions (e.g.…”