Octupolar order and Ising quantum criticality tuned by strain and dimensionality: Application to $d$-orbital Mott insulators

Abstract

Recent experiments have discovered multipolar orders in a variety of $d$-orbital Mott insulators. Motivated by uncovering the exchange interactions which underlie octupolar order proposed in the osmate double perovskites, we study a two-site model using exact diagonalization on a five-orbital Hamiltonian, incorporating spin-orbit coupling (SOC) and interactions, and including both intra-orbital and inter-orbital hopping. Using an exact Schrieffer-Wolff transformation, we then extract an effective pseudospin Hamiltonian for the non-Kramers doublets, uncovering dominant ferrooctupolar coupling driven by the interplay of two distinct intra-orbital hopping terms. Using classical Monte Carlo simulations on the face-centered cubic lattice, we obtain a ferrooctupolar transition temperature which is in good agreement with experiments on the osmate double perovskites. We also explore the impact of uniaxial strain and dimensional tuning via ultrathin films, which are shown to induce a transverse field on the Ising octupolar order. This suppresses $T_c$ and potentially allows one to access octupolar Ising quantum critical points. We discuss possible implications of our results for a broader class of materials which may host such non-Kramers doublet ions.

11 pages, 8 figures

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Cited by in corpus (19)

• Theory of electric, magnetic, and toroidal polarizations in crystalline solids with applications to hexagonal lonsdaleite and cubic diamond
• Competing multipolar orders in a face-centered cubic lattice: Application to the osmium double perovskites
• Modelling Magnetic Multipolar Phases in Density Functional Theory
• Probing octupolar hidden order via Janus impurities
• Hidden orders in spin-orbit entangled correlated insulators
• Field-induced Kitaev multipolar liquid in spin-orbit coupled $d^2$ honeycomb Mott insulators
• Effects of charge doping on Mott insulator with strong spin-orbit coupling, Ba${}_2$NaOsO${}_6$
• Multipolar magnetism in $5d^2$ vacancy-ordered halide double perovskites
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• Fate of multipolar physics in $5d^2$ double perovskites
• Multipolar spin liquid in an exactly solvable model for $j_{\mathrm{eff}}=\frac{3}{2}$ moments
• Multipolar multiferroics in $4d^2$/$5d^2$ Mott insulators
• Impact of gapped spin-orbit excitons on low energy pseudospin exchange interactions
• Emergence of quadrupolar order under magnetic field in $5d^2$ double perovskites
• Pseudo-chiral phonon splitting from octupolar magnetic order
• The toric code under antiferromagnetic isotropic Heisenberg interactions
• Polaron-driven switching of octupolar order in doped 5d${}^2$ double perovskite