Abstract
The rare-earth magnet TmMgGaO$_{4}$ is proposed to be an intrinsic quantum Ising magnet described by the antiferromagnetic transverse field Ising model (TFIM) on a triangular lattice, where the relevant degrees of freedom are the non-degenerate dipole-multipole doublets of the Tm$^{3+}$ ions and the transverse field has an intrinsic origin from the weak splitting of the doublet. We compare this special doublet of Tm$^{3+}$ with the dipole-octupole Kramers doublet. We study the proposed effective model for the Tm-based triangular lattice and consider the effects of external magnetic fields and finite temperatures. From the "orthogonal operator approach", we show that the TFIM with the three-sublattice intertwined ordered state agrees with the experiments and further clarify the discrepancy in the nubmers of the magnetic sublattices and the measured magnon branches. We make specific predictions for the evolution of the magnetic properties with the external magnetic field. Furthermore, we demonstrate that an emergent U(1) symmetry emerges in thermal melting of the underlying orders and at the criticality, and summarize the previously known signatures related to the finite-temperature Berezinskii-Kosterlitz-Thouless (BKT) physics. We discuss the broad relevance of intrinsic quantum Ising magnets to many other systems, especially the Tm-based materials.
Highlights
Frustrated magnetism is an exciting field in modern condensed-matter physics and has been under active investigation for the past few decades
VI, we explore the effect of the external magnetic fields in various physical quantities
With zero external magnetic field, the ψ corresponding to the ground states are located at a circle in the complex plane with Arg ψ = (2n + 1)π /6 (n = 0, 1, ..., 5) that are protected by the translation and time-reversal symmetry [see Fig. 5(a)]
Summary
Frustrated magnetism is an exciting field in modern condensed-matter physics and has been under active investigation for the past few decades. The usual non-Kramers doublet that occurs in, for example, the Pr3+ ion [31,32] of Pr2Zr2O7 and Pr2Ir2O7 or other rare-earth triangular lattice magnets [30], is composed of two degenerate crystal-field states, and their degeneracy is not protected by time reversal but protected by the point-group symmetry. These states comprise the 2D irreducible representation. Nondegenerate DM doublet DO doublet original moment time reversal time reversal degeneracy threefold rotation integer Sz → −Sz Sx,y → Sx,y two separate singlets eigenvalue +1 half-odd integer Sz → −Sz
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