Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules

Abstract

In many quantum magnets especially the rare-earth ones, the low-lying crystal field states are not well separated from the excited ones and thus are insufficient to describe the low-temperature magnetic properties. Inspired by this simple observation, we develop a microscopic theory to describe the magnetic physics due to the collapses of the weak crystal field states. We find two cases where the excited crystal field states should be seriously included into the theory. One case is when the bandwidth of the excited crystal field states is comparable to the crystal field gap. The other case is when the exchange energy gain between the low-lying and excited crystal field states overcomes the crystal field gap. Both cases could drive a phase transition and result in magnetic orders by involving the excited crystal field states. We dub the above physics as upper branch magnetism and phase transition. We discuss the multitude of magnetic phases and the emergent selection rules for the detection of the underlying excitations. We expect our results to help improve the understanding of many rare-earth magnets with weak crystal field gaps such as Tb${}_2$Ti${}_2$O${}_7$ and Tb${}_2$Sn${}_2$O${}_7$, and also provide a complementary perspective to the prevailing local "$J$" physics in $4d$/$5d$ magnets.

9 pages, 4 figures, 2 tables. First two authors contributed equally. Suggestion of experimental relevances is welcome

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Cited by in corpus (11)

• Thermal Hall effects in quantum magnets
• Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO${}_4$ and beyond
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Exchange renormalized crystal field excitation in a quantum Ising magnet KTmSe${}_2$
• Induced quantum magnetism in CEF singlet ground state models: Thermodynamics and excitations
• Low Energy Magneto-optics of Tb${}_2$Ti${}_2$O${}_7$ in [111] Magnetic Field
• Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln${}_2$InSbO${}_7$ family
• Universal excitonic superexchange in spin-orbit-coupled Mott insulators
• Emergent transverse-field Ising model in ${\mathbf{d}}^4$ spin-orbit Mott insulators
• Upper branch thermal Hall effect in quantum paramagnets
• Impact of gapped spin-orbit excitons on low energy pseudospin exchange interactions