Direct observation of the crystal electric-field splitting under magnetic field and uncovering field-induced magnetic phase transition in triangular rare-earth magnet CsErSe$_2$

Abstract: An indispensable step toward understanding magnetic interaction in rare-earth magnets is the determination of spatially anisotropic single-ion properties resulting from the crystal electric field (CEF) physics. The CEF Hamiltonian exhibits a discrete energy spectrum governed by a set of independent parameters that reflect the site symmetry of the magnetic ion. However, experimentally determining these parameters for magnetic ions at low-symmetry sites has been proven highly challenging. In this study, we directly measured the CEF level splitting under magnetic fields (B) using optical spectroscopy and extracted both CEF parameters and the exchange energies of a triangular insulating magnet CsErSe$_2$ as a model system. With increasing field, we find many CEF levels undergo level-crossing, which accompanies switching of the eigenstate. Particularly, such a crossing occurring at the ground state results in a step-like increase in magnetization that we captured with the low-temperature AC magnetic susceptibility measurements. Our work demonstrates that the accurately determined CEF Hamiltonian parameters enable uncovering the rich physics of field-induced collective magnetic phenomena, and potentially lead to a new route to magnetic frustration.