Surrogate Models and Statistical Mechanics of Hexagonal Orderings in Delafossites

Artificial ordered materials can be synthesized in laboratory settings. Of great interest is to identify layered materials where the in layer order appears spontaneously. One class of materials are PdCrO₂ based delafossites where doping on the Pd plane could potentially change triangular ordering in the layer to a Kagome or honeycomb structure. We will explore the effect of chemical doping to control the change of this in plane ordering between honeycomb and Kagome patterns in delafossites of the form Pd_1-x A_x CrO₂ by generating surrogate models based on first principles calculations. The first principles calculations consider unbiased disorder realizations to capture the interactions inside the planes based on the chemical environment. These models form the basis for our Monte-Carlo simulations where we identify the transitions between the differently ordered states as a function of chemical composition as well as the transition temperatures for these hexagonal orders.