Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO4

Abstract

The rare-earth magnet TmMgGaO4 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 nondegenerate dipole-multipole doublets of the Tm3+ ions and the transverse field has an intrinsic origin from the weak splitting of the doublet. We compare this special doublet of Tm3+ 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 numbers 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 physics. We discuss the broad relevance of intrinsic quantum Ising magnets to many other systems, especially Tm-based materials.