Magnetic exchange interaction in two-dimensional lattice under generalized Bloch condition

Two-dimensional magnetic material which has been rapidly developed in recent years, has potential applications in developing spintronic devices. In order to understand the magnetic properties of two-dimensional magnetic materials, it is necessary to comprehend the magnetic interaction which is estimated by the exchange parameters between the magnetic atoms. The calculation of the magnetic exchange parameters is based on the first-principle. The commonly used method of determining the values of exchange parameters is energy-mapping. However, this method has some disadvantages. In this paper, the spin-spiral dispersion relationship is derived under the Heisenberg interaction and the Dzyaloshinskii-Moriya (DM) interaction through the generalized Bloch condition of three common two-dimensional magnetic structures: a tetragonal structure, a hexagonal structure in which the cell contains one magnetic atom, a hexagonal structure in which the cell contains two magnetic atoms. The magnetic exchange parameters of some materials are calculated through the first principle. These materials are MnB, VSe2 MnSTe and Cr2I3Cl3. Among them, the MnSTe and Cr2I3Cl3 are two-dimensional Janus materials, which means that they have space-reversal symmetry broken, that is why there is DM interaction in the system.