Three-Dimensional XY Universality and Nonlinear Magnetic Susceptibility in a Kagome Ice Compound

Kagome spin ice is an intriguing class of spin systems constituted by in-plane Ising spins with ferromagnetic interaction residing on the kagome lattice, theoretically predicted to host a plethora of magnetic transitions and excitations. In particular, different variants of kagome spin ice models can exhibit different sequences of symmetry breaking upon cooling from the paramagnetic to the fully ordered ground state. Recently, it has been demonstrated that the frustrated intermetallic HoAgGe stands as a faithful solid-state realization of kagome spin ice. However, whether any of the established symmetry-breaking pathways apply to this material remains unaddressed. Here, we use single-crystal neutron diffuse scattering to map the spin ordering of HoAgGe at various temperatures more accurately; surprisingly, we find that the ordering sequence appears to be different from previously known scenarios: From the paramagnetic state, the system first enters a partially ordered state with fluctuating magnetic charges, in contrast to a charge-ordered paramagnetic phase, before reaching the fully ordered state. Through Monte Carlo simulations and scaling analyses using an extended three-dimensional (3D) spin model for the distorted kagome spin ice in HoAgGe, we elucidate a single 3D XY phase transition into the ground state with broken time-reversal symmetry (TRS). However, the 3D XY transition has a long crossover tail before the fluctuating magnetic charges fully order. More interestingly, we find, both experimentally and theoretically, that the TRS-breaking phase of HoAgGe features an unusual, hysteretic response: Despite their vanishing magnetization, the two time-reversal partners are distinguished and selected by a nonlinear magnetic susceptibility tied to the kagome ice rule. Our discovery not only unveils a new symmetry-breaking hierarchy of kagome spin ice but also demonstrates the potential of TRS-breaking frustrated spin systems for information technology applications.