Hidden multipolar orders of dipole-octupole doublets on a triangular lattice

Abstract

Motivated by the recent development in strong spin-orbit-coupled materials, we consider the dipole-octupole doublets on the triangular lattice. We propose the most general interaction between these unusual local moments. Due to the spin-orbit entanglement and the special form of its wavefunction, the dipole-octupole doublet has a rather peculiar property under the lattice symmetry operation. As a result, the interaction is highly anisotropic in the pseudospin space, but remarkably, is uniform spatially. We analyze the ground state properties of this generic model and emphasize the hidden multipolar orders that emerge from the dipolar and octupolar interactions. We clarify the quantum mutual modulations between the dipolar and octupolar orders. We predict the experimental consequences of the multipolar orders and propose the rare-earth triangular materials as candidate systems for these unusual properties.

5+3 pages, 3+2 figures

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• Anisotropic exchange Hamiltonian, magnetic phase diagram and domain inversion of Nd${}_2$Zr${}_2$O${}_7$
• Magnetic properties and signatures of moment ordering in triangular lattice antiferromagnet KCeO${}_2$
• Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules
• Energy scales in 4f1 delafossite magnets: crystal-field splittings larger than the strength of spin-orbit coupling in KCeO2
• Homogenous reduced moment in a gapful scalar chiral kagome antiferromagnet