Modelling of 2D Ising and Potts Hamiltonians on a twisted Kagome lattice

HoAgGe and its cousin compound, DyAgGe are two uniquely frustrated 2D spin-ice materials with a twisted Kagome lattice which exhibit magnetic properties yet to be fully explained. In magnetic field, they exhibit step-like magnetization plateaus at simple fractions of the saturation magnetization. It is believed that this phenomenon results from strong single-site anisotropy, which in HoAgGe was found to be in-plane, forming a site-dependent Ising Hamiltonian and resulting in a two-dimensional spin-ice. Existing Monte Carlo simulations with empirical exchange parameters (Js) to some extent agree with the experiment supporting the model. In DyAgGe, preliminary experimental results indicate that the easy axis in is tilted away for the plane, this generating a site-dependent Potts model. In this work we (a) present first principle calculations of J and easy axes (which reproduce the experimental anisotropy well) in both materials and (b) direct energy minimization as well as Monte-Carlo simulations of the field-dependent phase diagram. We find that in case of HoAgGe the calculated J are very different from the earlier suggested empirical ones, yet describe the phase diagram as accurately. The case of DyAgGe is much more complicated; we will present some preliminary results for that material as well.