Kavli Affiliate: Bo Gu
| First 5 Authors: Jia-Wen Li, Zhen Zhang, Jing-Yang You, Bo Gu, Gang Su
| Summary:
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.
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