Possibility of Potts Spin-Ice in Rare Earth Twisted-Kagome Layers: an Example of DyAgGe

Three-dimensional (3D) spin-ice compounds, predominantly based on the pyrochlore or spinel structure, have been attracting considerable interest in the last two decades. A two-dimensional (2D) analogue is the spin-ice consisting of kagome planes. So far, only Ising spin ice has been discovered in any material, and only one 2D material, the kagome compound HoAgGe, has been identified as a spin ice. In this Letter, we show that another rare-earth twisted Kagome magnetic compound, DyAgGe, is in fact a Potts spin ice (or color ice), where at each site not two but four spin directions are allowed. We argue that an 8-state spin ice may also exist in this class of systems. We present a first-principles calculation of magnetic interactions in DyAgGe, and confirm the 4-state Potts structure of this material by matching our model predictions with the available experimental data.