Abstract
In recent years, two-dimensional magnetic materials have attracted a lot of attention due to their unique magnetic properties, which can be manipulated by various degrees of freedom in a van der Waals stacked heterostructure, where different interlayer stackings affect the properties in different ways by exploiting weak interlayer interactions. An interesting example is CrI3, where the interlayer magnetic coupling can be determined by the stacking sequence. Here we present a systematic study of the magnetic properties of monolayer, bilayer, and trilayer CrI3 by using density functional theory and Monte Carlo simulations. The effects of different stacking sequences and the number of layers on the magnetic interaction in multilayer CrI3 have been critically analyzed. We have found that the antiferromagnetic interlayer coupling occurs with specific interlayer shifting, while intralayer exchange interactions increase with the number of layers. It is noteworthy that interlayer interactions are independent of the number of layers, whereas the magnetic ordering temperature rises with the increasing number of layers. Moreover, we present the Curie temperatures obtained from Monte Carlo simulations and adiabatic magnon spectra for all the stacking sequences considered here.
Highlights
Two-dimensional (2D) magnetic materials should not exist at a finite temperature due to the celebrated Mermin-Wagner theorem,[1] which tells us that the long-range magnetic order at any finite temperature will be completely destroyed by thermal spin fluctuations
For structural models of bilayer CrI3, we built structures with AB and AB′ stacking sequences according to the lateral shift mentioned above
For structural models of trilayer CrI3, we built nine different structures based on three basic combinations that come from our structural models for bilayer CrI3
Summary
Two-dimensional (2D) magnetic materials should not exist at a finite temperature due to the celebrated Mermin-Wagner theorem,[1] which tells us that the long-range magnetic order at any finite temperature will be completely destroyed by thermal spin fluctuations. The third lowest energy state occurs for the AB′C′ stacking with up−down−up magnetic ordering, which is the high-temperature phase in experiment These results are expected according to the results from bilayer CrI3: whenever there is a [1/3, 0] lateral shift between neighboring layers, the AFM ordering is preferred. For the ground state bilayer CrI3 (AB stacking with FM interlayer magnetic ordering), the calculated interlayer coupling is FM; there is one nearest, nine next-nearest, and 12 third-nearest couplings Interlayer exchange parameters of trilayer CrI3 are shown in Figure S5 of the Supporting Information for ABC stacking. We have calculated the adiabatic magnon dispersion for monolayer, bilayer, and trilayer For structures which have lateral shift equals to [−1/3, 0], such as AB′, ABC′, and AB′C′ stacking in Figure 9b−d, there is softening of one magnon branch around the Γ point, which might indicate magnetic instability in these structures
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