Multipolar magnetism in d-orbital systems: Crystal field levels, octupolar order, and orbital loop currents

Abstract

Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. We carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions, finding that either explicitly including the $e_g$ orbitals, or going beyond the rotationally invariant Coulomb interaction within the $t_{2g}$ sector, causes a degeneracy breaking of the $J=2$ level degeneracy. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar moments and an excited triplet which supports magnetic dipole moments, bolstering our previous phenomenological proposal for the stabilization of ferro-octupolar order in heavy transition metal oxides. We show that the spontaneous time-reversal symmetry breaking due to ferro-octupolar ordering within the non-Kramers doublet leads to electronic orbital loop currents. The resulting internal magnetic fields can potentially explain the small fields inferred from muon-spin relaxation ($\mu$SR) experiments on cubic $5d^2$ osmate double perovskites Ba${}_2$ZnOsO${}_6$, Ba${}_2$CaOsO${}_6$, and Ba${}_2$MgOsO${}_6$, which were previously attributed to weak dipolar magnetism. We make further predictions for oxygen NMR experiments on these materials. We also study the reversed level scheme, where the $J=2$ multiplet splits into a low-lying magnetic triplet and excited non-Kramers doublet, presenting single-ion results for the magnetic susceptibility in this case, and pointing out its possible relevance for the rhenate Ba${}_2$YReO${}_6$. Our work highlights the intimate connection between the physics of heavy transition metal oxides and that of $f$-electron based heavy fermion compounds.

arXiv comment9 pages, 8 figures, published version

References in corpus (29)

• Strong electronic correlations from Hund's coupling
• Exotic phases induced by strong spin-orbit coupling in ordered double perovskites
• Kondo Effects and Multipolar Order in the cubic PrTr2Al20 (Tr=Ti, V)
• Arrested Kondo effect and hidden order in URu_2Si_2
• Hidden Orbital Order in $UR{u}_{2}S{i}_2$
• Detection and Implications of a Time-reversal breaking state in underdoped Cuprates
• Heavy Fermion Superconductivity in the Quadrupole Ordered State of PrV2Al20
• Triple-q octupolar ordering in NpO_2
• Spin-orbit coupling in $d^2$ ordered double perovskites
• Parity-breaking phases of spin-orbit-coupled metals with gyrotropic, ferroelectric and multipolar orders
• A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd${}_2$Re${}_2$O${}_7$
• Ferro-quadrupolar ordering in PrTi${}_2$Al${}_{20}$
• The frustrated FCC antiferromagnet Ba2YOsO6: structural characterization, magnetic properties and neutron scattering studies
• Mixing of $t_{2g}$-$e_g$ orbitals in 4d and 5d transition metal oxides
• Octupolar vs Néel Order in Cubic 5$d^2$ double perovskites
• Determination of Hund's coupling in 5d Oxides using Resonant Inelastic X-ray Scattering
• An anisotropic local modification of crystal field levels in Pr-based pyrochlores: a muon-induced effect modelled using density functional theory
• Octupolar order in d-orbital Mott insulators
• Long-Range Magnetic Order in the 5d^2 Double Perovskite Ba2CaOsO6: Comparison with Spin-Disordered Ba2YReO6
• Unveiling Hidden Orders: Magnetostriction as a Probe of Multipolar-Ordered States
• Effective magnetic interactions in spin-orbit coupled $d^4$ Mott insulators
• Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: implication to 5$d$ transition metal oxides $A$OsO${}_4$ ($A=$ K, Rb, and Cs)
• Landau theory of multipolar orders in Pr(TM)${}_2$X${}_{20}$ Kondo materials
• Octupolar ordering of Gamma8 ions in magnetic field
• Spin-orbit coupled systems in the "atomic" limit: rhenates, osmates, iridates
• Two-stage multipolar ordering in Pr(TM)${}_2$Al${}_{20}$ Kondo materials
• Classical Monte Carlo study for antiferro quadrupole orders in a diamond lattice
• Cubic interaction parameters for t2g Wannier orbitals
• Emergent non-Fermi-liquid phenomena in multipolar quantum impurity systems

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• Noncollinear Magnetic Multipoles in Collinear Altermagnets
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• Elastic Quantum Criticality in Nematics and Altermagnets via the Elasto-Caloric Effect
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• Resonant inelastic X-ray scattering investigation of Hund's and spin-orbit coupling in $5d^2$ double perovskites
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• Possibility of ferro-octupolar order in Ba${}_2$CaOsO${}_6$ assessed by X-ray magnetic dichroism measurements
• Dipolar and quadrupolar correlations in the $5d^2$ Re-based double perovskites Ba${}_2$YReO${}_6$ and Ba${}_2$ScReO${}_6$
• Multipolar ferroelectricity in the Mott regime
• Polaron-driven switching of octupolar order in doped 5d${}^2$ double perovskite