Two-dimensional Heisenberg models with materials-dependent superexchange interactions

TL;DR

This paper introduces a method combining DFT and Wannier functions to accurately determine 2D Heisenberg models based on material-specific superexchange paths, leading to predictions of magnetic properties in various 2D materials.

Contribution

The authors develop a general approach to derive 2D Heisenberg models from first principles, accounting for material-dependent superexchange interactions, improving upon fixed, experience-based models.

Findings

Calculated Curie temperature for Cr3Te6 matches experimental data (328 K vs. 344 K).

Predicted stable 2D ferromagnetic semiconductors Cr3O6 and Mn3O6 with Tc of 218 K and 208 K.

Derived detailed Heisenberg models with multiple exchange couplings for these materials.

Abstract

The two-dimensional (2D) van der Waals ferromagnetic semiconductors, such as CrI$_3$ and Cr$_2$Ge$_2$Te$_6$, and the 2D ferromagnetic metals, such as Fe$_3$GeTe$_2$ and MnSe$_2$, have been obtained in recent experiments and attracted a lot of attentions. The superexchange interaction has been suggested to dominate the magnetic interactions in these 2D magnetic systems. In the usual theoretical studies, the expression of the 2D Heisenberg models were fixed by hand due to experiences. Here, we propose a method to determine the expression of the 2D Heisenberg models by counting the possible superexchange paths with the density functional theory (DFT) and Wannier function calculations. With this method, we obtain a 2D Heisenberg model with six different nearest-neighbor exchange coupling constants for the 2D ferromagnetic metal Cr$_3$Te$_6$, which is very different for the crystal structure of Cr atoms in Cr$_3$Te$_6$. The calculated Curie temperature Tc = 328 K is close to the Tc = 344 K of 2D Cr$_3$Te$_6$ reported in recent experiment. In addition, we predict two stable 2D ferromagnetic semiconductors Cr$_3$O$_6$ and Mn$_3$O$_6$ sharing the same crystal structure of Cr$_3$Te$_6$. The similar Heisenberg models are obtained for 2D Cr$_3$O$_6$ and Mn$_3$O$_6$, where the calculated Tc is 218 K and 208 K, respectively. Our method offers a general approach to determine the expression of Heisenberg models for these 2D magnetic semiconductors and metals, and builds up a solid basis for further studies.