Statistical Mechanics of Chemical Disorder and Magnetic Order in MnSb₂Te₄ and MnBi₂Te₄

The magnetic ordering in the layered topological insulator materials MnSb₂Te₄ and MnBi₂Te₄ has been observed to depend strongly on the disorder and defects on the Mn and Sb/Bi sublattices. Here we will explore the effect of this chemical disorder on the magnetic interactions and we will present models of the magnetic interactions in these materials that have been extracted from large scale first principles density functional theory calculations. The first principles calculations consider unbiased disorder realizations to capture the magnetic interactions both inside the planes as well as between planes based on the chemical environment. These models form the basis for our Monte-Carlo simulations where we identify the magnetic transitions between the ferromagnetic and antiferromagetic states as a function of disorder as well as the transition temperatures for these magnetic orders.