Spin–orbit coupling, orbitally entangled antiferromagnetic order, and collective spin–orbital excitations in Sr2VO4

Abstract

With electron filling $n=1$ in the $\rm Sr_2VO_4$ compound, the octahedrally coordinated $t_{\rm 2g}$ orbitals are strongly active when the tetragonal distortion induced crystal field is tuned by external agent such as pressure. Considering the full range of crystal field induced tetragonal splitting in a realistic three-orbital model, collective spin-orbital excitations are investigated using the generalised self consistent plus fluctuation approach. At ambient pressure, an entangled orbital + antiferromagnetic order is found to be stabilised beyond a critical value ($\sim$ 30 meV) of spin-orbit coupling which is in the realistic range for 3d ions. The behaviour of the calculated energy scales of collective excitations with crystal field is consistent with that of the transition temperatures with pressure as obtained from susceptibility and resistivity anomalies in high-pressure studies.

Spin–orbit coupling and magnetism in Sr2CrO4

“…However, we will mainly focus on the range λ ≳ 30 meV. This is justified because Cr and V are neighboring elements in the periodic table, and the condition λ ≳ 30 meV was recently obtained for the Sr 2 VO 4 compound [35]. In this study, the range λ < 30 meV was ruled out since the FM order obtained contradicts the experimentally obtained AFM order in Sr 2 VO 4 .…”

“…The electron filling n = 2 in the t 2g for the chromate compound. The Hamiltonian terms and the methodology used have been discussed earlier [33][34][35] for other related compounds with n = 1, 3, 4, 5, and are briefly summarized below.…”

“…The above approach was recently applied to several 4d and 5d compounds (NaOsO 3 , Ca 2 RuO 4 , Sr 2 IrO 4 ) with electron fillings n = 3, 4, 5 in the t 2g sector [33,34]. Recent application to the 3d compound Sr 2 VO 4 with n = 1 reveals an SOC induced transition from staggered orbital + ferromagnetic (FM) order to entangled orbital + AFM order at critical SOC value λ * ≈ 30 meV [35]. Generally, coupling of orbital moments to orbital fields and interaction-induced SOC renormalization effects highlight the important role of SOC induced OM condensates in the emergent spin-orbital physics [39].…”

“…The generalized fluctuation propagator in the random phase approximation (RPA) was studied recently for several 4d and 5d compounds with electron fillings n = 3, 4, 5 in the t 2g sector [34], and for the 3d compound Sr 2 VO 4 with n = 1 [35]. Since the generalized spin and charge operators ψ † µ σ α ψ ν include spin (µ = ν, α = x, y, z), orbital (µ ̸ = ν, α = c), and spinorbital (µ ̸ = ν, α = x, y, z) cases, the spectral function of the fluctuation propagator:…”

“…For this purpose, we will employ the generalized self consistent + fluctuations approach in which all physical elements are treated on equal footing. This approach was recently used to investigate spin-orbital fluctuations in several 4d and 5d compounds (NaOsO 3 , Ca 2 RuO 4 , Sr 2 IrO 4 ) with n = 3, 4, 5 electrons [33,34], and most recently in the 3d compound Sr 2 VO 4 with n = 1 electron [35].…”