The bulk CrI2 crystallizes in the P63mc space group and is consisting of two CrI2 monolayers in AB stacking. The crystal structure of bulk CrI2 is shown in Fig. 1(a), the chromium and iodine atoms are displayed with blue and purple spheres, respectively. The spin-polarized band structures of bulk CrI2 is shown in Fig. 1(b) (antiferromagnetic) and Fig. 1(c) (ferromagnetic), to compare the total energy difference between ferromagnetic and antiferromagnetic orderings, a 2 × 1 × 1 supercell is used, and the band dispersions of spin majority and spin minority is indicated by red and green lines. The corresponding spin spatial distribution is illustrated in inserts of Figs. 1(b) and 1(c)) with the same color-coding. Since the total energy difference between ferromagnetic and antiferromagentic states is 20 meV/unit cell, one can find out that, bulk CrI2 take a ferromagnetic ground state.
CrI2 monolayer is cleaved from a fully relaxed bulk crystal. Each chromium atom is bonded to six iodine atoms in the monolayer, and all the atoms are arranged in the 1T phase. Noticing the similarity of CrI2 monolayer to the famous transitional metal dichalcogenide monolayers, it is necessary to consider the 2H phase. The 1T and 2H phases of CrI2 monolayers are illustrated in Fig. 2.
In Fig. 3, the spin-resolved band structures, the total spin density of states (DOS) and spin spatial distributions of 1T and 2H CrI2 monolayers are shown. 2 × 1 × 1 supercells are also employed, to determine the magnetic ground states, by performing constrained spin-polarized first-principles calculations. The numerical results for 1T-FM, 1T-AFM, 2H-FM, 2H-AFM are displayed in panels Figs. 3(a)–3(d) accordingly, and the total energies for each configuration are listed in Table 1. One can find from Table 1 the most energy-favored configuration is 1T-AFM, which implies the ground state of monolayer CrI2 is antiferromagnetic.
Table 1 shows the total energies of the FM state and the AFM state of the 1T phase, where the energy differences between the FM and the AFM states are obtained by performing DFT+U calculations within Dudarev’s approach. The Ueff (U–J) varies from 1 to 4 eV, and the corresponding total energy differences are of 30 meV, which indicates the AFM state is more energetic favorable.
To investigate the magnetic effect of the interlayer interaction, we construct a CrI2 bilayer from 1T CrI2 monolayers, and to clarify the influence of stacking patterns, both AB stacking and AA stacking models are constructed. As shown in Fig. 4, we denote these models, for convenience, as AA-FM, AA-AFM-a, AA-AFM-f, AB-FM, AB-AFM-a and AB-AFM-f, where the appendix a (f) indicates that the intra-layer initial magnetic moment is set antiferromagnetic (ferromagnetic). The interlayer distance between the adjacent chromium layers in equilibrium is obtained by relaxation and reads XX for the AA stacking and XX for the AB stacking, respectively.
The spin-resolved band structures, total spin density of states and spin spatial distributions of each CrI2 bilayers are shown in Fig. 5. The total energies for each configuration are listed in Table 2. From Table 3, one can find the ground states of CrI2 bilayers are always antiferromagnetic independent of the stacking patterns, which implies the interlayer interaction is still antiferromagnetic in CrI2 up to few layers.