Spin-Orbital Excitations in Ca2RuO4 Revealed by Resonant Inelastic X-Ray Scattering

Abstract

The strongly correlated insulator Ca2RuO4 is considered as a paradigmatic realization of both spin-orbital physics and a band-Mott insulating phase, characterized by orbitally selective coexistence of a band and a Mott gap. We present a high-resolution oxygen K-edge resonant inelastic X-ray scattering study of the antiferromagnetic Mott insulating state of Ca2RuO4. A set of lowenergy (∼80 and 400 meV) and high-energy (∼ 1.3 and 2.2 eV) excitations are reported that show strong incident light polarization dependence. Our results strongly support a spin-orbit coupled band-Mott scenario and explore in detail the nature of its exotic excitations. Guided by theoretical modelling, we interpret the low-energy excitations as a result of composite spin-orbital excitations. Their nature unveil the intricate interplay of crystal-field splitting and spin-orbit coupling in the band-Mott scenario. The high-energy excitations correspond to intra-atomic singlet-triplet transitions at an energy scale set by the Hund's coupling. Our findings give a unifying picture of the spin and orbital excitations in the band-Mott insulator Ca2RuO4.Introduction. Spin-orbit coupling (SOC) is a central thread in the search for novel quantum material physics [1]. A particularly promising avenue is the combination of SOC and strong electron correlations in multiorbital systems. This scenario is realized in heavy transition metal oxides composed of 4d and 5d elements. Iridium-oxides (iridates) such as Sr 2 IrO 4 are prime examples of systems where SOC plays a defining role in shaping the Mott insulating ground state [2]. In fact, spin-orbit entanglement essentially outplays the effectiveness of the usually influential crystal field δ. Of equal interest is the complex regime where SOC and crystal field energy scales are comparable. Here Ca 2 RuO 4 is a topical material that displays a wealth of physical properties. A record high non-superconducting diamagnetic response has, for example, been reported recently [3]. Superconductivity emerges in strained films [4] or upon application of hydrostatic pressure to bulk crystals [5]. Neutron and Raman scattering experiments have demonstrated both phase and amplitude spin-excitation modes consistent with the existence of a spin-orbit exciton [6][7][8]. Moreover, measurements of the paramagnetic insulating band structure [9] were interpreted in favor of an orbitally differentiated band-Mott insulating ground state [10,11]. This rich phenomenology of Ca 2 RuO 4 is a manifestation of the interplay between multiple energy scales, specifically, the Coulomb interaction U , the Hund's coupling J H , the crystal field splitting δ and SOC λ. In particular, a tendency towards an orbital selective Mott state is expected to be driven by the Hund's coupling [12]. Furthermore, the band-Mott scenario is triggered by a

Persistence of antiferromagnetic order upon La substitution in the 4d4 Mott insulator Ca2RuO4

“…The ground-state wave function of the Ru 4+ ion was described in terms of an admixture of xy, yz, and zx orbitals, whose respective contribution depends on the relative strength of the tetragonal crystal field δ and SOC λ [20,[48][49][50][51][52][53]. Within this picture, the tuning of the crystal field caused by the elongation of the RuO 6 octahedra [ Fig.…”

Photoemission spectrum of Ca2RuO4 : Spin polaron physics in an S=1 antiferromagnet with anisotropies

“…Using Eqs. (29) and (30) we obtain the self-consistent equation for the self energy (28) in the SCBA approximation…”

“…24, 26, and 27 the spin model is highly anisotropic, with the suggested values of thê z (x) axis anisotropy being equal to = 5.6J (γ = 0.25J), respectively, with J = 5.6 meV reproducing the spin wave dispersion observed in the inelastic neutron scattering experiment 24,26,27 . We note that such a large spin anisotropy originates in the large spin-orbit coupling on the ruthenium ions which, however, is quite widely considered as not strong enough to stabilise the S = 0 ground state 21,24,26,30,32 . Although the latter result can naively be understood as a consequence of the crystal field splitting (between the xz, yz and the xy orbitals) being about twice larger than the spin-orbit coupling 30 and therefore the spin S = 0 states having considerably higher energy than the spin S = 1 states, see Fig.…”

“…We note that such a large spin anisotropy originates in the large spin-orbit coupling on the ruthenium ions which, however, is quite widely considered as not strong enough to stabilise the S = 0 ground state 21,24,26,30,32 . Although the latter result can naively be understood as a consequence of the crystal field splitting (between the xz, yz and the xy orbitals) being about twice larger than the spin-orbit coupling 30 and therefore the spin S = 0 states having considerably higher energy than the spin S = 1 states, see Fig. S1 of 27 , it has been postulated 27,33,35,36 that nevertheless the 'excitonic magnetism' can be at play here.…”

“…To investigate this rather general problem, we take a closer look at one of the intensively investigated transition metal oxides-Ca 2 RuO 4 19-33 which is a spin S = 1 antiferromagnetically ordered 21,24,26,30,32 and Mott insulating analogue of the unconventional superconductor Sr 2 RuO 4 34 . The other reason for choosing this system is that recently its detailed photoemission spectrum was not only studied experimentally but also successfully modelled using a multiband Hubbard model 28 .…”