Hidden order and its quantum excitations in the triangular-lattice magnet TmMgGaO₄

Certain magnetic materials exhibit exotic hidden-order phases, which are not directly accessible to conventional magnetic measurements due to the lack of internal field. Thus, experimental identification and theoretical understanding of a hidden order are difficult. Here we combine neutron scattering and thermodynamic probes to study the newly discovered rare-earth triangular-lattice magnet TmMgGaO₄. Magnetic Bragg peaks at K points are observed in the elastic neutron diffraction measurements. More interesting, however, is the observation of sharp and highly dispersive spin excitations that cannot be explained by a magnetic dipolar order, but instead is the direct consequence of the preformed multipolar order that arises from a rather weak crystal field splitting and is “hidden” in the conventional magnetic measurements. We demonstrate that the observed unusual spin correlations and thermodynamics can be accurately described by a transverse field Ising model on the triangular lattice with an intertwined dipolar and ferro-multipolar order.