Dependence of electronic properties on Coulomb repulsion and electric field in single layer FeI2

The Coulomb repulsion was applied in the framework of LDA+U approach and electric field to find out the electronic properties of a single layer 1T-FeI2. This calculation relies on the density functional theory of non-collinear magnetic structure. From the curve of energy dispersion, increasing the Coulomb parameter and electric field yields an electronic transition from a metallic state to an insulating state. This only holds in case the spin-orbit coupling is incorporated. While the magnetism still holds as the Coulomb parameter is tuned, the magnetism vanishes as the electric field is included. However, as the magnetism disappears, the spin splitting appears when increasing the electric field. This indicates that the Coulomb repulsion and electric field give a prominent impact on the electronic properties in the single layer FeI2 as the spin-orbit coupling is included.


Introduction
Iron diiodide (FeI2) is a family of metal dihalides having a 3 ̅ 1 space group (CdI2 structure) [1].In a primitive unit cell, this single layer crystal consists of an Fe atom and two I atoms.Similar to the FeCl2, the collinear calculation adopting the density functional theory (DFT) predicted that this material is a half metal, namely, the band energy of one spin shows the semiconducting state while the other displays the metallic state [2].
The interesting case of a single layer FeI2 is related to the multiferroic material.Even though the noncollinear DFT calculation predicted the ferromagnetic ground state, the spiral ground state may appear if the hole-electron doping is incorporated [3].This spiral structure will generate a stable multiferroic state, which is important for future spintronics [4,5].
Our purpose is to find out the electronic properties in a single layer FeI2 by employing the Coulomb repulsion based on the LDA+U approach and external electric field.The electronic properties are then analyzed via the band energies.Also, we can predict if the magnetism in a single layer FeI2 still preserves or not by observing the magnetic moment of Fe atom.
We organize the paper as follows.We describe the primitive unit cell of a single layer FeI2 and the basis sets in section 2. In section 3, we provide the band energies with and without the Coulomb parameter and electric field.We then state our concluding remarks based on the results.

Method
We used the primitive cell of a single layer FeI2, as shown in Fig. 1.To enable two-dimensional material, we adjusted the vacuum area larger than 16 Å in the z direction to avoid the interaction between the periodic cells.Here, we set an out of plane ferromagnetic state in the Fe atom.After that, we applied the Coulomb parameter U and electric field E (along z axis) to discuss the electronic properties via the band energy.We include the basis sets of s, p, d, and f for the Fe atom (cutoff radius of 6.0 Bohr) and s, p, and d for the I atom (cutoff radius of 7.0 Bohr) as implemented in the OpenMX package [6].At the same time, the self-consistent noncollinear calculations with the spin-orbit coupling were performed with the functional of generalized gradient approximation [7], the cutoff energy of 250 Ryd, and k-point mesh of 20 × 20 × 1.

Results and Discussions
Calculated band energy of a single layer FeI2 without U and E is shown in Fig. 2. Similar to the FeCl2 case, the metallic state is observed, in excellent agreement with Ref. [8].Notice that the half-metallic state will be observed if the collinear calculation is performed.As the U increases the band gap increases, thus appearing the transition from a metallic state to a semiconducting/insulating state, as shown in Fig. 3.Note that this transition only happens as the spinorbit coupling is included.It is also obtained that the magnetic moment of Fe atom remains unchanged which is about 3   , thus the magnetism holds as the U increases.The latter case also holds for the other single layer metal dihalides if the U is not so large [9,10].For the insulating magnetic materials, increasing U also increases the band gap and maintains the magnetic moment of the magnetic atom [11].Here, the experimental lattice parameter of 4.04 Å is used [12].
The calculations also show the additional properties as the E is included.First, as the E increases, the transition from metallic state to the semiconducting/insulating state also occurs, as displayed in Fig. 4.However, the spin splitting appears both in the conduction band and in the valence band.So, the E may generate the spin splitting which is very worthwhile for the spintronic application.Contrary to the U case, the magnetic of moment of Fe atom vanishes, thus the magnetism in FeI2 disappears.Notice that these properties also occur as the spin-orbit coupling is included.
Regarding the inclusion of E in the low-dimensional materials, some authors also reported that the half-metallicity [13,14] and spin spiral ground state [15,16] can be induced in the zigzag graphene nanoribbons without including the spin-orbit coupling.This means that the inclusion of E may generate the new electronic properties with or without the spin-orbit coupling.Based on the achievements, it is concluded that the inclusion of spin-orbit coupling gives significant electronic properties in the metal dihalides.This vital role also holds in the other two-dimensional materials such as the metal dichalcogenides to generate the spin splitting [17].

Conclusions
We have examined the effect of the Coulomb repulsion and electric field on the electronic properties via the band energy by including the spin-orbit coupling based on the DFT.The inclusion of Coulomb repulsion changes the metallic state to the semiconducting/insulating state.However, there is no spin splitting available.
As the electric field is incorporated, not only the transition state happens but also the spin splitting appears.However, the magnetism in FeI2, consequently, disappears.This indicates that the spin splitting only holds if the magnetism vanishes.This phenomenon is supported by the existence of spin splitting in the two-dimensional non-magnetic metal dichalcogenides.

Figure 1 .
Figure 1.Primitive cell of single layer FeI2 from top view.

Figure 2 .
Figure 2. Band energies of single layer FeI2 without the Coulomb repulsion  and electric field E.