Discrete degeneracies distinguished by the anomalous Hall effect in a metallic kagome ice compound

In magnetic crystals, despite the explicit breaking of time-reversal symmetry, two equilibrium states related by time reversal are always energetically degenerate. In ferromagnets, this time-reversal degeneracy is reflected in the hysteresis of the magnetic field dependence of the magnetization and, if metallic, in that of the anomalous Hall effect (AHE). Under time-reversal, both these quantities change signs but not their magnitude. Here we show that a time-reversal-like degeneracy appears in the metallic kagome spin ice HoAgGe when magnetic fields are applied parallel to the kagome plane. We find vanishing hysteresis in the field dependence of the magnetization at low temperature, but finite hysteresis in the field-dependent AHE. This suggests the emergence of states with nearly the same energy and net magnetization but different sizes of the AHE and of the longitudinal magnetoresistance. By analysing the experimental data and a minimal tight-binding model, we identify a time-reversal-like operation connecting these near-degenerate states, which is related to the non-trivial distortion of the kagome lattice in HoAgGe. Our work demonstrates the diagnostic power of transport phenomena for identifying hidden symmetries in frustrated spin systems.