Interplay of superexchange and vibronic effects in the hidden order of Ba${}_2$MgReO${}_6$ from first principles

Abstract

The origin of the "hidden" quadrupolar and unconventional magnetic low-temperature orders observed in the spin-orbit double perovskite Ba${}_2$MgReO${}_6$ defies explanation through standard experimental and theoretical techniques. Here we address this problem by deriving and solving an ab initio low-temperature effective Hamiltonian including inter-site electronic exchange and vibronic (electron-lattice) couplings between $J_{eff}=3/2$ Jahn-Teller-active Rhenium states. Our findings disclose the nature of these elusive states, attributing it to intertwined exchange and electron-lattice couplings, thus diverging from the conventional dichotomy of purely electronic or lattice driving mechanisms. Our results indicate the resilience of the quadrupolar hidden order under pressure, yet its rapid suppression under uniaxial strain suggests that external or lattice-induced distortions play a pivotal role in determining the relative stability of competing phases in Ba${}_2$MgReO${}_6$ and similar $d^1$ double perovskites.

arXiv comment6 pages + 18 pages of Supplementary, 4 Figures

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• Dipolar and quadrupolar correlations in the $5d^2$ Re-based double perovskites Ba${}_2$YReO${}_6$ and Ba${}_2$ScReO${}_6$
• Coupled-cluster approach to vibronic effects in resonant inelastic x-ray scattering of quantum materials: Application to a $5d^1$ rhenium oxide
• Pseudo-chiral phonon splitting from octupolar magnetic order
• Polaron-driven switching of octupolar order in doped 5d${}^2$ double perovskite