Crystal-Field Symmetry Constraints in Layered Honeycomb ErBr${}_3$

We show that the local crystal-field symmetry of ErBr${}_3$ enforces $⟨{\psi }_{\pm }\mathrm{\mid }{J}^{\pm }\mathrm{\mid }{\psi }_{\mp }⟩=0$ within the ground-state Kramers doublet, thereby removing the lowest-order transverse channel from the low-energy sector. Thermodynamic measurements reveal two zero-field anomalies. Under an in-plane magnetic field, the thermodynamic response separates into a phase boundary and a broader crossover line. Consistently, inelastic neutron scattering measurements above the ordering temperature reveal no well-defined low-energy dispersive magnetic modes. These results show that the crystal-field ground-state symmetry strongly constrains the low-energy dynamics and provides a natural framework for understanding the field-dependent thermodynamic response of ErBr${}_3$.