Modeling of a twisted kagome HoAgGe spin ice using reduced configuration space search and density functional theory

The kagome lattice is a two-dimensional (2D) network of corner-sharing triangles found in several rare-earth materials resulting in a complicated and often frustrated magnetic system. In the past decades, modifications of the motif, such as breathing kagome, asymmetric kagome, and twisted kagome, were brought into the limelight. In particular, the latter has symmetry lower than that of the original kagome and thus allows implementations of an ``Ising-local'' Hamiltonian, leading to a 2D spin ice. One such material implementation, HoAgGe, was recently reported to have an exceptionally rich phase diagram and is a strongly frustrated 2D spin-ice material with a twisted kagome geometry. In the presence of an external magnetic field the compound exhibits steplike 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 and along a high-symmetry direction. Previous Monte Carlo simulations with empirical exchange parameters explain some, but not all, experimental observations. In this work, we present (a) first-principles calculations of the crucial model parameters and (b) direct energy minimization via a reduced configuration space search, as well as Monte Carlo simulations of the field-dependent phase diagram. We find that for HoAgGe the calculated exchange parameters are very different from the earlier suggested empirical ones, and we describe the phase diagram much more accurately. This is likely because the first-principles parameters are, in addition to geometrically, also parametrically frustrated.