Selective measurements of intertwined multipolar orders: non-Kramers doublets on a triangular lattice

Abstract

Motivated by the rapid experimental progress on the spin-orbit-coupled Mott insulators, we propose and study a generic spin model that describes the interaction between the non-Kramers doublets on a triangular lattice and is relevant for triangular lattice rare-earth magnets. We predict that the system supports both pure quadrupolar orders and intertwined multipolar orders in the phase diagram. Besides the multipolar orders, we explore the magnetic excitations to reveal the dynamic properties of the systems. Due to the peculiar properties of the non-Kramers doublets and the selective coupling to the magnetic field, we further study the magnetization process of the system in the magnetic field. We point out the selective measurements of the static and dynamic properties of the intertwined multipolarness in the neutron scattering, NMR and $\mu$SR probes and predict the experimental consequences. The relevance to the existing materials such as TmMgGaO${}_4$, Pr-based and Tb-based magnets, and many ternary chalcogenides is discussed. Our results illustrate the rich physics and the promising direction in the interplay between strong spin-orbit-entangled multipole moments and the geometrical frustration.

arXiv comment13 pages, 9 figures. First two authors contributed equally. Replace Fig. 1 and small corrections to Discussion section

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• Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO${}_4$ and beyond
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• Quantum Spin Dynamics Due to Strong Kitaev Interactions in the Triangular-Lattice Antiferromagnet CsCeSe${}_2$
• Rare-Earth Chalcogenides: An Inspiring Playground For Exploring Frustrated Magnetism
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• Hidden orders in spin-orbit entangled correlated insulators
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• Crystal-field excitations and vibronic modes in triangular-lattice spin-liquid candidate TbInO${}_3$
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• Unusual double-peak specific heat and spin freezing in a spin-2 triangular lattice antiferromagnet FeAl${}_2$Se${}_4$
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• Distinguishing thermodynamics and spectroscopy for octupolar U(1) spin liquid of Ce-pyrochlores
• Revealing Quadrupolar Excitations with Non-Linear Spectroscopy
• Multipolar Skyrmion Crystals in Non-Kramers Doublet Systems
• Projected entangled pair states study of anisotropic-exchange magnets on triangular lattice
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• Emergent Halperin-Saslow mode and Gauge Glass in quantum Ising magnet TmMgGaO${}_4$
• Canted antiferromagnetism in a spin-orbit coupled $S_{\text{eff}}=3/2$ triangular-lattice magnet DyAuGe
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• Gapless spinon excitations emerging from a multipolar transverse field in the triangular-lattice Ising antiferromagnet NaTmSe2
• Theory of magnetism for rare-earth magnets on the Shastry-Sutherland lattice with non-Kramers ions
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• Emergent Dispersive Multipolar Excitations in NaErSe${}_2$
• Field-induced multipolar character in the dipolar ground state of the honeycomb rare-earth chalcohalide NdOF