Crystal-Field Symmetry Constraints in Layered Honeycomb ErBr$_3$
Crystal-field symmetry restricts the ground-state Kramers doublet of ErBr$_3$ to one of two classes. We show that the compressed octahedral environment selects the class with $\langle ψ_\pm | J^{\pm} | ψ_\mp \rangle = 0$, suppressing the lowest-order $J^{\pm}$-mediated exchange. Thermodynamic measurements reveal two zero-field anomalies at 0.375 and 0.200~K. Under an in-plane magnetic field, the thermodynamic response separates into a phase boundary and a broader crossover line. Inelastic neutron scattering measurements at 2 K reveal no well-defined low-energy dispersive magnetic modes. These results connect the ground-state symmetry with the field-dependent thermodynamic response of ErBr$_3$, providing a microscopic starting point for understanding its low-energy magnetic behavior.