Abstract
1. Introduction
Two-dimensional (2D) magnets have become the subject of intensive research activities in condensed matter physics and material science thanks to their exciting and advanced properties, and potential applications in low dimensional spintronics devices. However, most intrinsic 2D materials are nonmagnetic and unfavorable for practical applications. At present, researchers have been devoted to exploring 2D van der Waals ferromagnetic (FM) materials, such as CrI3[
Starting from the perspective of applications, precise and flexible control of the magnetic and electronic properties of 2D materials is a target that is always pursued[
Here, we investigate a new 2D intrinsic FM Ir2TeI2 monolayer via first principles, which is magnetized out-of-plane and possesses large spin polarization, large MAE, and high Tc. Its magnetic control is relatively easy to be achieved by carrier injection, which can switch the magnetization axis between in-plane and out-of-plane directions. We find that biaxial strain can be used as a switch to achieve a stable switching between FM and antiferromagnetic (AFM) states. This behavior can be understood in terms of the competition between the direct exchange interaction and the super exchange interaction. In addition, the MAE increased under biaxial compression strain. This work provides a multifunctional 2D material and broadens its range.
2. Computational method
First-principles calculations are primarily carried out using the Vienna Ab initio Simulation Package (VASP)[
2.1. Geometric structures and stabilities
The Ir2TeI2 monolayer is homogeneous to one of the layers of the M2ZX2-type van der Waals(vdW) layered telluride Ln2TeI2 (Ln = La, Gd)[
Figure 1.(Color online) (a) Lattice structure of Ir2TeI2 monolayer. (b) Diagram of the first Brillouin zone of 2D hexagonal structure. (c) The phonon dispersion of Ir2TeI2. (d) The energy change when Ir2TeI2 monolayer is stripped.
To verify the dynamic stability, we calculated the phonon spectrum of the Ir2TeI2 and no appreciable imaginary phonon modes are observed, indicating that this lattice is dynamical stable, as shown in Fig. 1(c). Experimentally, the synthesis and mechanical peeling of 2D vdW materials are an ideal technology to realize a single-layer structure[
We have also investigated the mechanical properties of Ir2TeI2 and calculated the elastic constants: c11= 200.7 N/m, c22 = 197.2 N/m, c12= 55.6 N/m, c66 = 17.98 N/m, which meet the Bonn criterion:
where
2.2. Electronic band structures
After determining the stability, we investigate its electronic and magnetic properties. Figs. 2(a) and 2(b) show the electronic energy band structures of Ir2TeI2 and the partial density of states (PDOS) for the distinguished spin channel of Ir atoms, respectively. It has an insulating state in the spin-down channel and a metallic state in the spin-up channel, thus possessing intrinsic half-metallic properties. The band gap of the spin-down channel is up to 1.29 eV (As shown in Fig. S1, the HSE is 1.62 eV that more than PBE 0.3 eV), which is sufficient to prevent hot spin flipping. Due to the strong spinpolarization at the fermi level, 100% spin filter efficiency can be maintained over a wide range of positive or negative bias of about 0.5 V. This makes Ir2TeI2 an attractive candidate for spin injection.
Figure 2.(Color online) (a) Electron band structure of Ir2TeI2 monolayer, the red represents spin up, blue represents spin down. (b) The PDOS of Ir atom in different spin channels.
2.3. Magnetic properties
The FM state of Ir2TeI2 exhibits an integer magnetic moment of 2 μB per unit cell, mainly contributed by two equivalent Ir atoms in the unit cell. the magnetization of Ir ions can be well understood by the electron local function and spin charge density (given in Figs. S2(a) and S2(b)), only a few spin-polarized electrons are located around the Ir ion, thus resulting in a magnetic moment of 1.0 µB/Ir. The FM coupling of Ir2TeI2 monolayers can be well understood by the competition between direct exchange and superexchange of Ir atoms mediated by Te and I atoms. To verify the magnetic ground state, we build the supercell to evaluate the relative stability of FM and AFM states, so we construct FM and three possible AFM configurations; as illustrated in Fig. 3(a). The total energy calculation proves that FM coupling is more energy stable than AFM coupling. According to Goodstoy-Kanamori-Anderson (GKA) rule[
Figure 3.(Color online) (a) FM and three types of AFM magnetic order diagrams of magnetic atoms, purple and blue represent different spin orientations, respectively. Δ
According to Mermin-Wagner's theorem[
Due to the strong MA and the magnetic axis along the out-of-plane, based on the Ising model, the Tc of the 2D ferromagnet is calculated by using Monte Carlo (MC) simulation. Here, the Hamiltonian equation is given as:
In Eq. (3), J1 and J2 are the nearest neighbor and second neighbor exchange coupling parameters, respectively, which is extracted from the energy difference between FM state and AFM state.mi is the spin vector of Ir atom. We use the equations above to fit the nearest-neighbor exchange interaction, we have J1 = 17.8 meV and the second-nearest-neighbor exchange interaction J2 = 3 meV are both positive, which also prove that the Ir2TeI2 prefers the FM state. Average magnetic moment (m) and specific heat (Cv) results are plotted in Fig. 3(b), the Tc is extracted from the phase transition point from FM to the paramagnetic state at about 293 K, which may be beyond the room temperature magnetic applications.
Based on the symmetry of a uniaxial quadrilateral of a 2D system, the angle dependence of MAE[
In Eq. (5), K1 and K2 are the anisotropic constants associated with the system and θ is the azimuth angle of rotation. The positive values of both K1 and K2 indicate that the structure has a strong Ising ferromagnetism with the magnetization direction parallel to the z-axis, while K1 < 0 indicates an in-plane magnetization axis. As shown in Table 1, K1 and K2 of Ir2TeI2 are both positive, belonging to the 2D Ising family. MAE reaches the maximum value of 0.5 meV/Ir at θxz = θyz = π/2. Figs. 4(a) and 4(b) give the variation of MAE in the xz and xy planes as the rotation axis rotates, respectively. The MAE is strongly correlated with the azimuthal angle (θ), while the dependence on the polarity angle (φ) is extremely small, which again confirms the strong MA of the Ir2TeI2 monolayer. Therefore, it can be inferred that a large MAE is sufficient to stabilize the ferromagnetism and thus resist thermal fluctuations at a specific temperature.
Figure 4.(Color online) Angle dependence of MAE of Ir2TeI2 in (a)
2.4. Magnetic controlling
Low-dimensional materials generally exhibit a sensitive response to external stimuli, which allows their electronic or magnetic properties to be adjusted. For example, through the orbital occupation caused by charge doping in the Fe/graphene complex system, the MAE value and the orientation of the easy axis of magnetization have been successfully adjusted[
Here, we observe that the MAE of Ir2TeI2 can be significantly tuned via charge doping, meanwhile the orientation of the easily magnetized axis can be switched. The calculated results are plotted in Fig. 5(a). It can be seen that under different magnetization directions, the total energy changes with the change of the carrier concentration (n). Under electronic doping (n < 0), the energy difference between out-of-plane and in-plane magnetization decreases with the increase of electronic doping. When n < –0.44 × 10 18 m–2, Ir2TeI2 transforms into in-plane magnetization. In contrast, hole doping (n > 0) maintains the out-of-plane magnetization within a certain range and increases the doping concentration, which could transform it into in-plane magnetization. The critical concentration of hole doping is higher than 2.56 × 10 18 m–2. Experimentally, it is effective to make the carrier concentration of 1017–1018 m–2 in a 2D system, Therefore, carrier doping can be an effective way to regulate ferromagnetism.
Figure 5.(Color online) (a) Carrier injection regulates the magnetization direction in ferromagnetic state. (b) A schematic diagram of a 2D magnetoelectric device controlled by electrostatic doping to achieve the giant magnetoresistance effect, the 2D FM monomolecular layer is bi-gated, while the two by like SiO2 dielectric layers act to avoid direct tunneling.
Strain modulation is a flexible method for tuning the electronic properties of 2D layered structures. It can change the bond angles and distance between atoms to affect the interaction between atoms, resulting in the change of electronic properties. Lv et al.[
Figure 6.(Color online) (a) The variation of bond lengths of the closest neighbors Ir1-Ir2 and Ir-Te between layers and bond angle
The behavior transformation of intrinsic FM half-metal Ir2TeI2 monolayer under stress can be understood by the competition between two different exchange interactions. For a general 2D magnetic structure, the direct exchange interaction between magnetic atoms (represented by JD) will result in the AFM state, while the superexchange interaction between magnetic atoms (represented by JS) will contribute to the FM state with the same spin orientation. The magnetic state of Ir2TeI2 monolayer is jointly determined by JD + JS, where JD and JS are negative and positive, respectively. For Ir2TeI2 monolayer in ground state without strain, |JD| is less than JS; therefore, the system exhibits FM properties. As mentioned above, when compressive strain is applied, as shown in Fig. 6(a), the distance between Ir1-Ir2 increases, so the direct exchange effect weakens; that is, |JD| decreases. Correspondingly, the Ir1-Te-Ir2 distance decreases, so the superexchange interaction increases; that is, JS increases, so there is still JD + JS > 0 and increase, which means that the FM state is enhanced.
In the same way, for the next neighbor atoms in the same layer with weaker exchange effect, as shown in Fig. 6(b), its JS increases and JD decreases, so JS + JD is a small negative value, which will result in a weak AFM state. Since the influence of the exchange interaction between the nearest neighbor magnetic atoms is much greater than that of the next neighbor atoms, on the whole, the compressive stress will lead to a stronger FM state. When the strain approaches 2%, the bond angle is close to 90˚ and reaches the critical point of magnetic order transition. At this time, JS is equal to |JD| and JD + JS = 0. Similarly, when the strain is greater than 2%, the nearest neighbor |JD| between layers increases and JS decreases, so the magnetic order orientation of the structure is an AFM state. Conversely, changes in the same layer lead to FM state but interlayer JD prioritize the determination of magnetism, with JD+JS < 0, so the Ir 2TeI2 monolayer transforms to the AFM state. These results demonstrate that strain is an effective method to regulate the magnetic and electrical properties of monolayers and also provides a potential candidate material for future nanoelectronic applications, which is worthy of further study in the experiment.
3. Conclusions
In summary, we computationally predicted a stable half-metal Ir2TeI2 monolayer, where the ground state exhibits intrinsic FM properties and strong MAE. The Tc is estimated to be 293 K, which is higher than that reported for 2D CrI3 and Cr2Ge2Te6 crystals, the bands are spin-polarized with a spin-down band gap of 2.9 eV, sufficient to prevent thermal inversion. The analysis of the MAE demonstrated that the structure is easy to be magnetized outside the plane and the MAE is up to 0.5 meV/Ir. The doping of holes and electrons can switch the magnetization axis between the in-plane and out-plane directions, which can effectively control the spin injection/detection in the 2D structure. In addition, we find that biaxial strain can induce the conversion of the states of FM and AFM. Under tensile strain, the AFM order tends to be stable. However, under compressive strain, the FM order is further stable, the half-metal properties are maintained and the MAE is increased. Our results provide potential candidates for future applications of functional nanoelectrons and are worthy of further study.
Acknowledgements
This work is supported by the Taishan Scholar Program of Shandong Province (No. ts20190939), National Natural Science Foundation of China (Grant No. 62071200, 12004137, 11804116, 52173283), the Natural Science Foundation of Shandong Province (Grant No. ZR2018MA035, ZR2020QA052, ZR2019MA041), Independent Cultivation Program of Innovation Team of Jinan City (Grant No. 2021GXRC043).
Appendix A. Supplementary materials
Supplementary materials to this article can be found online at https://doi.org/10.1088/1674-4926/43/5/052001.
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