Band shifting and magnetic anisotropy switching induced by electric field in CrI₃/1T'-MX₂ heterojunction

The surge of research is growing with the boost of advanced techniques to manufacture varieties of two-dimensional (2D) materials [1–4]. However, according to the Mermin–Wagner theorem [5], the magnetic anisotropy counteracted by strong thermal fluctuationsat finite temperature in 2D materials, long-range magnetic order is prohibited. Therefore few 2D materials have the perfect performance for applications at present. Besides, it is well accepted that magnetic anisotropy energy (MAE) is an indispensable prerequisite for ferromagnetic (FM) order in 2D materials. It is also a crucial index to predict the performance of spintronics devices [6–8].

Among several familiar 2D materials, monolayer (ML) chromium triiodide (CrI₃) [9–11] is a typical Ising magnetic insulator; it possesses an FM ground state with a Curie temperature of 45 K [12], and the magnetic moment of each Cr atom is 3.0 μ_B. It hosts a relatively large MAE of 685.5 μeV/Cr with an easy axis along the c-direction [13]. CrI₃ has been deemed as a promising material that provides a new platform for the application of low dimensional spintronics devices. Recent works have reported that the magnetic states of ML CrI₃ can be manipulated electrically [14–18], allowing spintronics applications that are highly compatible with electronics technologies [15, 19]. Considerable attempts have been made to control the electronic structure and magnetism to achieve novel features in CrI₃ by an applied electric field (EF). To be specific, Ghosh et al [14] observed that ML CrI₃ has such efficient electronic screening that it has an extremely small structural response to the EF. Xu et al [15] found that EF can induce an antiferromagnetic (AFM)-to-FM phase transition of interlayer coupling in bilayer CrI₃. Jiang et al [16] reported that the applied EF creates an interlayer potential difference in AFM bilayer CrI₃, which results in a large linear magnetoelectric effect, i.e. the induction of magnetization (polarization) by an electric (magnetic) field. Huang et al [17] demonstrated electrostatic gate control of magnetism in bilayer CrI₃. At fixed magnetic fields near the metamagnetic transition, they realized voltage-controlled switching between AFM and FM states. Behera et al [18] showed that EF can induce the formation of sub-10 nm skyrmions in ML CrI₃.

Usually, constructing a van der Waals (vdW) heterojunction by stacking the isolated 2D vdW materials tightly together is an effective way to seek novel properties. It can combine multiple excellent capacities into one material so as to get the most advantages in spintronics applications. At present, CrI₃-based vdW heterojunctions are being extensively studied, including graphene/CrI₃, whose bandgap and magnetism can be manipulated by strain [20], realizing a Chern insulating state at high temperatures of up to 45 K [21]. In addition, a large modulation of the MAE can be achieved in CrI₃/bilayer-graphene using multiple methods such as chemical adsorption, substitutional doping and electrical/optical charge transfer [6]. It has been proposed that stacking-dependent magnetic states exist in the CrI₃/CrGeTe₃ heterostructure, and the magnetic coupling can be effectively modulated by the biaxial strain [22]. Placing a heavy-element atomic layer on the top of ML CrI₃ to form CrI₃/X (X = Bi, Sb or As) [23] can open up a sizable bulk gap to harbor a quantum anomalous Hall effect. In addition, in the WSe₂/CrI₃ heterojunction, an external EF can modify the bands around the Fermi level, which severely hybridize with orbits of W atoms and Cr atoms, resulting in a large valley splitting [24].

Another noteworthy material is 1T' phase transition metal dichalcogenides [25], denoted as 1T'-MX₂ (M = Mo, W; X = S, Se, Te). The 1T' phase is an unusual topological phase. It is also referred to as a quantum spin Hall insulator, and is characterized by an insulating bulk state and a conductive helical edge state [26]. A recent study found that the topological properties remain stable in the h-BN/1T'-MX₂ heterojunction by applying up to 4% biaxial strain [27]. ML 1T'-MX₂ has become one of the widely studied topological insulators (TIs).

Although these studies of CrI₃-based vdW materials mentioned above have made great achievements, magnetic vdW heterostructures consisting of CrI₃ and 2D TIs that possess lattice anisotropy and the subsequent application of a vertical EF to switch the magnetic characteristics have rarely been reported. It is due to the lattice anisotropy of 1T'-MX₂ that the symmetry of the super-lattice is broken when the heterojunction is formed, causing a series of novel behaviors at interfaces.

In this work, we aim to study the fundamental physical properties of a 2D vdW heterostructure formed by ML CrI₃ and 1T'-MX₂. By applying an external EF, we find that charge transfer occurs at the interface of the heterojunction because of the interaction between CrI₃ and 1T'-WTe₂ layers, which is similar to the N-type doping in CrI₃ [28], increasing the magnetic moment. We also note that the formation of the heterojunction gives rise to a wider regulating range of MAE by applying an EF, which is about 11 times that of isolated CrI₃. Our calculations show that MAE has a reversal from positive value to negative, which implies a transition of easy axis of magnetization from out-of-plane to in-plane. In addition, the topological properties of 1T'-WTe₂ are still preserved by a nontrivial topological invariant $\mathbb{Z}$ ₂ = 1, whether an external EF is applied or not. Our findings can provide theoretical guidance for the application in spintronics of heterojunctions that are formed by a 2D strong spin–orbit coupling (SOC) FM semiconductor and TI.

To obtain the electronic structures and magnetism of the CrI₃/1T'-MX₂ heterojunction, we use the Vienna ab initio Simulation Package (VASP) [29] with the projector augmented wave method [30] based on the density functional theory (DFT). The cut-off energy for the plane-wave basis was set at 350 eV. A Perdew–Burke–Ernzerhof-type generalized gradient approximation (GGA) [31] was used to approximate the exchange–correlation interaction. To improve the description of the on-site Coulomb interaction of the localized 3d states of Cr, the GGA+U scheme [32] was implemented with an effective Hubbard-like term U set to 2.0 eV. A vacuum space of at least 15 Å was applied in the z-axis to neutralize the interaction between adjacent lattices. The Monkhorst–Pack k-point grid mesh of 5 × 5 × 1 was adopted and SOC was included in self-consistent calculations. The atomic position was completely relaxed and converged with a force criterion of 0.01 eV Å⁻¹. In the CrI₃/1T'-MX₂ heterojunction, two layers are bounded by weak vdW interactions, which is described by the DFT-D2 potential [33]. The phonon dispersion was obtained using the Phonopy package [34] based on density functional perturbation theory. A band unfolding calculation was deployed using the VASPKIT package [35]. The $\mathbb{Z}$ ₂ invariant was calculated with surface Green's function methods [36, 37] using the WANNIER90 [38] and WANNIERTOOLS packages [39], based on the tight-binding Hamiltonian model from maximally localized Wannier functions.

ML CrI₃ is a well-known FM semiconductor material with a bandgap of 1.24 eV [40, 41], while 1T'-MX₂ is a 2D TI with a nontrivial helical edge state [25]. Herein, we construct a heterojunction system with ML 1T'-MX₂ as a substrate and ML CrI₃ on the top; the atomic structure is shown in figures 1(a) and (b). We calculate the energy difference ΔE (ΔE= E_FM − E_AFM) between the FM and AFM order of various CrI₃/1T'-MX₂ systems in figure S1(a) (see supplementary material available online at stacks.iop.org/JPD/54/395302/mmedia). It can be observed that ΔE becomes smaller with the increasing anion mass and the ground state eventually turns to FM from AFM when the anion becomes Te from S.

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To further confirm the origin of the ground state transition caused by different substrate materials, we investigated the changes in the fundamental parameters of CrI₃ including Cr–I–Cr bond angles, Cr–Cr distance and interlayer distance between heterojunctions. The parameters of isolated CrI₃ are 97.69° and 4.05 Å. As presented in table S1, our calculational results show that the Cr–I–Cr bond angle and Cr–Cr distance dropped largely when the anion X was S and Se. The corresponding parameters are, respectively, 71.99° (3.01 Å), 76.66° (3.21 Å), 71.68° (2.99 Å) and 76.52° (3.20 Å) for the four different S-based and Se-based systems. These changes are derived from the four 1T'-MS₂ and 1T'-MSe₂ substrate materials, which bring at least 3.50% and 5.86% compressive strains along the a- and b-axes (see figure S1(b) in supplementary material), respectively. Meanwhile, the data of the other two 1T'-MTe₂ substrate materials barely changed, introducing only a tiny tensile strain of about 2.02% on the a-axis and 0.26% on the b-axis to 1T'-WTe₂.

As mentioned above, the magnetic ground states of CrI₃/1T'-MS₂ and CrI₃/1T'-MSe₂ are of AFM order, while CrI₃/1T'-MTe₂ is FM. Generally speaking, the origin of the magnetic ground state in CrI₃ is determined by the competition between intralayer super-exchange and direct exchange. According to the Goodenough–Kanamori–Anderson rule [42–44], which has been widely used to understand the strengths and signs of super-exchange interactions, a 180° super-exchange manifests AFM coupling while a 90° super-exchange interaction represents FM order. For an intermediate bond angle between 90° and 180°, FM and AFM will compete against each other. In isolated CrI₃, the Cr–I–Cr bond angle is close to 90°, and is expected to be FM state [13]. As for CrI₃/1T'-MS₂ and CrI₃/1T'-MSe₂, the four compressed materials, the FM coupling is weakened due to the decreased bond angle. Meanwhile, the Cr–Cr distance shrinks greatly, which greatly enhances AFM-preferred direct exchange coupling. Both aspects make it show an AFM ground state eventually. On the contrary, the bond angle in the other two CrI₃/1T'-MTe₂ is close to 90°, so their super-exchange undoubtedly presents an FM state. However, because of the biggish Cr–Cr distance (>4.05 Å), the AFM-preferred direct exchange coupling is much smaller than the FM-preferred super-exchange. Therefore, the intralayer FM state is dominant in CrI₃/1T'-WTe₂ and CrI₃/1T'-MoTe₂ heterojunctions. We also plot the variation tendency of the magnetic moment depending on the different substrates in figure 1(c). It reveals that the magnetic moments of the Cr atom in all six heterojunction systems are enhanced with the increasing of the radius of anions. The reason for this magnetic moment change will be discussed later.

To examine the stability of this system, we calculated the phonon dispersions for ML CrI₃, ML 1T'-WTe₂ and the CrI₃/1T'-WTe₂ heterojunction (see figure S2 in supplementary material). For the two isolated materials, the absence of imaginary frequency confirms its dynamic stability. As for the heterojunction, although a small amount of imaginary frequency exists, we believe this is because lattice mismatch and small strain are unavoidably introduced when we perform modeling to find the minimal periodic unit. It has been reported that biaxial strain does affect structural stability to some extent [45–47]. However, this problem can almost be avoided in the experiment when two stable vdW materials are used to construct a heterojunction. Since CrI₃ and 1T'-WTe₂ have the lowest mismatch (see figure S1(b) in supplementary material), which is most consistent with the experimental facts in 2D materials, we will only take CrI₃/1T'-WTe₂ as the example to analyze all the subsequent results below.

To find out what really happened and how the interlayer interacts with the other layer when the heterojunction is formed, we calculate the band structures of the two isolated materials and the CrI₃/1T'-MX₂ heterojunction. Here, we redefined the lattice direction to convert 1T'-WTe₂ from an orthogonal lattice (with a = 6.27 Å and b = 3.48 Å) to a rhombohedral lattice. Both compounds share the same rhombohedral lattice with different in-plane lattice parameters (a = b = 7.01 Å for CrI₃ and a = 7.15 Å, b = 7.03 Å for 1T'-WTe₂), which is consistent with recent works [26, 48]. In order to eliminate the possible impact caused by our lattice transformation, we calculated both types of lattices onto their corresponding Brillouin zone. Figure 2(a) presents the unfolded band structures of the CrI₃/1T'-WTe₂ heterojunction, (b) shows only the 1T'-WTe₂ bands extracted from figures 2(a), and (c) shows isolated 1T'-WTe₂. All of the upper panels used an orthogonal lattice, while the lower panels, i.e. figures 2(d)–(f), refer to a rhombohedral lattice to ensure CrI₃ is not affected, which is consistent with the usual Brillouin zone path selection of two isolated materials in the literature [23, 26, 27, 40]. As can be seen from figure 2, compared with the isolated materials (figures 2(c) and (f)), the shapes of band structure that are extracted from the heterojunction (figures 2(b) and (e)) are basically the same except for some Zeeman-like splitting [49]. The interface band structure can be approximately regarded as an overlap of two isolated materials. That is to say that our lattice transformation does not affect the global band structure of either of the materials. But the main difference lies in the energy value. For 1T'-WTe₂, we find that the valence band maximum is mainly composed of a W-d orbital, and its energy is about 0.1 eV below the Fermi level (E_f), while the conduction band minimum of CrI₃ consists of Cr-d and I-p orbitals, which are about 0.5 eV above the E_f. When the heterojunction is formed, charge transfer occurs at the interface, resulting in a change of energy values of the two materials. In the heterojunction, the energy of the W-d orbital slightly increases due to the loss of charge, reaching 0.1 eV above E_f. However, the energy of the Cr-d and I-p orbitals drops remarkably by 0.5 eV, almost to the Fermi level, leading to a growing amount of charge transfer, which is similar to the N-type doping of CrI₃ [28].

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Furthermore, due to the existence of the heavy Cr atom, which provides a strong SOC effect between adjacent layers in the heterojunction, a sizable Zeeman-like spin splitting in 1T'-WTe₂ can be observed at the valance bands. We also calculated the band structures without considering the SOC effect. As shown in figure S4 in the supplementary material, the SOC effect has a relatively obvious influence on the CrI₃ band (which is in the range of 0–0.5 eV above the Fermi level) and only has a small effect on 1T'-WTe₂. We can conclude that the SOC effect only makes a small contribution to the gap opening of the CrI₃/1T'-WTe₂ heterojunction. However, in consideration of the existence of heavy Cr and W atoms, in order to determine the geometry and the electronic properties more accurately, our calculation result in the following text is obtained by considering SOC.

By applying an out-of-plane EF, pointing from 1T'-WTe₂ towards CrI₃, which is defined as the positive EF direction, the magnetism of this system keeps the FM order as the ground state. The band structure of both materials varies with increasing the EF without a big distortion of profiles but with an obvious move as shown in figure S5 (see supplementary material). When a positive (negative) EF is applied, the global band of CrI₃ moves upward (downward) away from (closer to) the Fermi level, which weakens (enhances) the orbital hybridization and opens (closes) the bandgap. A similar phenomenon of band shifting in the WSe₂/CrI₃ heterojunction has been mentioned in another recent work [24].

Aiming at a better understanding of the band splitting and shifting as mentioned above, we only focus on a few energy bands near the Fermi level in the Γ-K direction to demonstrate it. We plot the projections of the W-d and I-p orbits around the Fermi level in figure 3(a). In the absence of EF, the bands near the Fermi level are composed of W-d_z ², I-p_z , W-d_yz and I-p_z orbits separately within the energy region of −0.2 to 0.2 eV. When an EF is applied to 0.4 V Å⁻¹, the partial I-p_z orbit descends below E_F whereas the W-d_yz orbit ascends to 0.12 eV from 0.06 eV as shown in the schematic in figure 3(b). We find that a band inversion of W-d_yz and I-p_z occurs near the Г point when the EF exists, which implies a possible topological nontrivial topological feature of the heterojunction, accompanied by nontrivial topological edge states in theory [50]. This phenomenon is similar to that observed in a recent work on a WSe₂/CrI₃ system [24]. Hence, we have calculated the topological index of $\mathbb{Z}$ ₂ invariant for the CrI₃/1T'-WTe₂ heterojunction. The Wannier charge center with closed momentum surface under different EFs is shown in figure S7 in the supplementary material, and there is clearly a single cross point with the reference line. The calculational results indicate that $\mathbb{Z}$ ₂ = 1 and remains unchanged, suggesting that the 1T'-MX₂ in the heterojunction is still a TI no matter whether CrI₃ or EF have been introduced.

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We also calculate the differential charge density (DCD) distribution of the CrI₃/1T'-MX₂ heterojunction under different EFs. The DCD exhibits charge distribution variation on CrI₃ from the interface layer assisted by the super-exchange interaction between the layers, indicating the orbital reconstruction of CrI₃, as presented in figure 4. The formula is as follows: $\rho \;{\text{ = }}{\rho _{{\text{(Cr}}{{\text{I}}_{\text{3}}}{\text{/1T}}^{\prime} {\text{ }} - {\text{ WT}}{{\text{e}}_{\text{2}}})}}{\text{ }} - {\text{ }}{\rho _{\left( {{\text{Cr}}{{\text{I}}_{\text{3}}}} \right)}} - {\text{ }}{\rho _{({\text{1T}}^{\prime} - {\text{WT}}{{\text{e}}_{\text{2}}}{\text{)}}}}$, where ${\rho _{{\text{(Cr}}{{\text{I}}_{\text{3}}}{\text{/1T}}^{\prime} - {\text{WT}}{{\text{e}}_{\text{2}}}{\text{)}}}}$, ${\rho _{\left( {{\text{Cr}}{{\text{I}}_{\text{3}}}} \right)}}$ and ${\rho _{({\text{1T}}^{\prime} - {\text{WT}}{{\text{e}}_{\text{2}}}{\text{)}}}}$ denote total charge densities of the CrI₃/1T'-WTe₂ heterojunction, CrI₃ and 1T'-WTe₂, respectively. We can confirm that regardless of the magnitude of the EF, the charge transfer always moves from 1T'-WTe₂ to CrI₃ due to the interlayer proximity exchange. It is noted that a mass of charge transfer occurs at the interface between the CrI₃ layer and the 1T'-WTe₂ layer after the formation of the CrI₃/1T'-WTe₂ heterojunction. This is because the electronegativity of the I atom is greater than that of the Te atom, which makes the charge shift to the I atom layer. At the same time, for the I atom, the demand for electrons on Cr is reduced, giving rise to charge transfer from the Te atom to the Cr atom and eventually enhancing the magnetic moment of Cr atoms. With the EF ranging from −0.3 to 0.3 V Å⁻¹, electrons with Te involved will increase while electrons with I decrease. Both charge depletion and accumulation increase, indicating a growing quantity of charge transfer from Te to I as shown in figure 4. Thus, we come to the conclusion that this type of manipulation plays a significant role in determining the amount of charge transfer in the CrI₃/1T'-WTe₂ heterojunction.

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After the analyses of band structure and DCD above, we next investigate and discuss the magnetic properties of the CrI₃/1T'-WTe₂ heterojunction under the influence of EF. As shown in figure 5, the isolated CrI₃ ML hosts a magnetic moment of 2.99 μB/Cr in the absence of an external EF. The magnetic moment slightly increased up to 3.04 μB/Cr after the heterojunction is shaped. We believe the slight increase results from a small amount of charge in the interlayer being diverted from Te-p to Cr-d. When the EF is applied, regardless of how large it is, the magnetic moment of isolated CrI₃ maintains stability, which is consistent with recent works [15, 51]. This phenomenon may be caused by an efficient EF screening effect brought by I atom layer in isolated CrI₃ [14], which makes the structure response extremely weak to the EF [14]. Nevertheless, the heterojunction system exposed to the growing EF unexpectedly exhibits a small increment in the magnetic moment, which results from a strengthened Te-p and Cr-d orbital hybridization. This can be confirmed by the density of states (DOS) near the Fermi level in figure S8. With the growing EF, the DOS peak around the Fermi level of Cr-d and I-p moves to the left, while W-d and Te-p shift their peaks to the right, which means CrI₃ gains electrons and 1T'-WTe₂ loses electrons, leading to the emergence of Cr-d and Te-p orbital hybridization. Due to the mixture of spin orientations by the SOC effect, the spin-up and spin-down channels become indistinguishable. We also plot the DOS without including SOC. From figure S4, one can see that SOC has extremely little influence around the Fermi level. The same energy shifting can be found in the DOS without including SOC.

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As the negative EF decreases from −0.5 V Å⁻¹ to 0 and progressively increases to 0.5 V Å⁻¹, charge transfer from the 1T'-WTe₂ to the CrI₃ layer is promoted, making the magnetic moment increase by ∼3.3%. The insert in figure 5(b) illustrates the super-exchange interaction between the Te-p, I-p, and Cr-e_g, t_2g states. According to Hund's rule, the d orbitals of each spin state are roughly split into triply degenerate t_2g states and doubly degenerate e_g states. In CrI₃, the Cr³⁺ has a d³ electronic configuration as t_2g ³ e_g ⁰. As shown by the red arrow in the insert figure, with the empty e_g orbits provided by Cr, electrons from Te-p hopping to I-p and finally to Cr-e_g are allowed. This super-exchange interaction makes Cr-e_g partially occupied, causing a slight enhancement of the magnetic moment.

Besides the promotion of the magnetic moment of CrI₃/1T'-WTe₂, the MAE is also dramatically affected by the introduction of the EF. The MAE is defined here as the total energy difference with SOC between the in-plane and out-of-plane magnetic moment configuration (MAE = E_[100]–E_[001]). Thus, a positive MAE corresponds to the out-of-plane magnetization direction. Figures 6(a) and (b) demonstrate the MAE as a function of the external perpendicular EF in isolated CrI₃ and the CrI₃/1T'-WTe₂ heterojunction, respectively. In the absence of EF, by comparison with isolated CrI₃, the MAE of the heterojunction reduces to 0.41 meV from 0.72 meV. When taking the EF into account, the MAE in isolated CrI₃ is inversely proportional to the absolute value of the EF. With the EF ranging from −0.5 to 0.5 V Å⁻¹, the MAE varied between 0.60 and 0.74 meV, and the rangeability was only 0.14 meV. However, for our CrI₃/1T'-WTe₂ heterojunction, when an external EF is applied, the vacant e_g states of CrI₃ are occupied, contributing to the stabilization of the in-plane anisotropy [6]. As the EF increases, the value of MAE almost performs a monotone decreasing trend, eventually arriving at the region of negative values, corresponding to the in-plane magnetization. When the EF continues to increase from −0.5 to 0.5 V Å⁻¹, the MAE decreases from 0.71 meV to about −0.82 meV. It is worthwhile mentioning that within the same EF region, the amplitude of the heterojunction reached 1.53 meV, which is about 11 times that of isolated CrI₃ alone. Thus, we can conclude that the manipulation of the EF plays a significant role in determining the spin polarization direction of the CrI₃/1T'-WTe₂ heterojunction. That is to say, the future looks bright for the use of spintronics devices formed by heterojunctions, whose MAE has a wider controlling range. Particularly, even under a small EF, which is about 0.15 V Å⁻¹ in our calculations, a transition in the easy axis of magnetization from out-of-plane to in-plane is observed. The same phenomenon would not happen in isolated CrI₃ within the same EF region.

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In summary, we used first-principles calculations to study the band structures and magnetic properties of the CrI₃/1T'-MX₂ heterojunction under EF. The results show that a sizable Zeeman-like band splitting and inversion occur around the Γ point, which represent a nontrivial TI with robust ferromagnetism. When increasing the EF, band shifting and splitting are promoted. Furthermore, we find that the EF can modulate the magnetic moment and the MAE simultaneously. The magnetic moment of the CrI₃/1T'-MX₂ heterojunction was enhanced almost linearly under an increasing EF, whereas it stabilized at 3.0 µ_B in isolated ML CrI₃. Intriguingly, an easy-axis switching effect from out-of-plane to in-plane MAE can be observed at 0.15 V Å⁻¹ EF. In addition, whether an external EF is applied or not, the topological properties of 1T'-WTe₂ in the heterojunction are still preserved by a nontrivial topological invariant $\mathbb{Z}$ ₂ = 1. Our work reveals interesting results for 2D CrI₃/1T'-MX₂ vdW materials, and may provide an excellent opportunity for extensive engineering of electronic and spintronic applications.

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11804301), the Natural Science Foundation of Zhejiang Province (Grant Nos. LY21A040008 and LQ18E020003), and the Open Foundation of the Key Laboratory of Optical Field Manipulation of Zhejiang Province (Grant No. ZJOFM-2019-006).

All data that support the findings of this study are included within the article (and any supplementary files).