⇦Chinese Physics Letters, 2024, Vol. 41, No. 5, Article code 057501 Hole-Doped Nonvolatile and Electrically Controllable Magnetism in van der Waals Ferroelectric Heterostructures Xinxin Jiang (姜新新)1, Zhikuan Wang (王智宽)1, Chong Li (李冲)2, Xuelian Sun (孙雪莲)1, Lei Yang (杨磊)1, Dongmei Li (李冬梅)1*, Bin Cui (崔彬)1*, and Desheng Liu (刘德胜)1* Affiliations 1School of Physics, National Demonstration Center for Experimental Physics Education, Shandong University, Jinan 250100, China 2School of Physics and Microelectronics, Zhengzhou University, Zhengzhou 450001, China Received 14 February 2024; accepted manuscript online 19 April 2024; published online 28 May 2024 *Corresponding authors. Email: li_dm@sdu.edu.cn; cuibin@sdu.edu.cn; liuds@sdu.edu.cn Citation Text: Jiang X X, Wang Z K, Li C et al. 2024 Chin. Phys. Lett. 41 057501    Abstract Electrical control of magnetism in van der Waals semiconductors is a promising step towards development of two-dimensional spintronic devices with ultralow power consumption for processing and storing information. Here, we propose a design for two-dimensional van der Waals heterostructures (vdWHs) that can host ferroelectricity and ferromagnetism simultaneously under hole doping. By contacting an InSe monolayer and forming an InSe/In$_{2}$Se$_{3}$ vdWH, the switchable built-in electric field from the reversible out-of-plane polarization enables robust control of the band alignment. Furthermore, switching between the two ferroelectric states ($P_\uparrow$ and $P_\downarrow$) of hole-doped In$_{2}$Se$_{3}$ with an external electric field can interchange the ON and OFF states of the nonvolatile magnetism. More interestingly, doping concentration and strain can effectively tune the magnetic moment and polarization energy. Therefore, this provides a platform for realizing multiferroics in ferroelectric heterostructures, showing great potential for use in nonvolatile memories and ferroelectric field-effect transistors.
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 DOI:10.1088/0256-307X/41/5/057501 © 2024 Chinese Physics Society Article Text Since the experimental preparation of intrinsic two-dimensional (2D) magnetic materials, such as Cr$_{2}$Ge$_{2}$Te$_{6}$,[1] CrI$_{3}$,[2] Fe$_{3}$GeTe$_{2}$,[3] and VSe$_{2}$,[4] tuning ferromagnetism (FM) in 2D systems by an electric field has been an intriguing long-term goal in materials research[5-8] that still faces enormous challenges. For example, electric modulation of magnetic properties usually requires an ultra-strong electric field which is hardly met by the usual gate electrodes. One promising method is dielectric gating, which could achieve such a field but may affect the structure.[9,10] With this method, carrier densities of 10$^{15}$cm$^{-2}$ can be achieved in 2D materials.[11,12] Another issue is that electrically tuned magnetism is volatile (maintaining the magnetic state requires continuous power, resulting in high energy costs) and/or irreversible (non-tunable). Therefore, it would be desirable to obtain nonvolatile electric-field-dependent magnetism in nonmagnetic (NM) materials. On the other hand, ferroelectric (FE) materials with tunable broken inversion symmetry always exhibit a strong size effect, and the depolarization field provided by the surface charges is opposite to the internal polarization and will try to compensate the internal polarization.[13-15] In particular, the polarization may disappear when the film thickness is very small, such as in BaTiO$_{3}$ and PbTiO$_{3}$. Therefore, as the dimensionality decreases to the nanoscale, the depolarization field becomes extremely strong and may cancel the polarization.[16] Surprisingly, a series of atomically thin 2D FE materials, such as SnTe,[17] CuInP$_{2}$S$_{6}$,[18] Sc$_{2}$CO$_{2}$,[19] and In$_{2}$Se$_{3}$,[20] have recently been discovered through calculations and experiments.[21,22] Due to their nanoscale size, 2D FE materials with switchable electrical polarization are suitable for next-generation data storage. In particular, FE In$_{2}$Se$_{3}$ exhibits out-of-plane and in-plane polarizations, conducive to practical device applications in high-density integration.[23] Compared with other storage devices (e.g., FM memories), the nonvolatility of FE memory is advantageous for realizing long-term data preservation. Furthermore, to simultaneously enhance the data reliability and reduce disturbance of the reading operation, we would expect to separate the operations of writing and reading using multiferroic materials, for example, writing with an electric field and reading with a magnetic probe in an FE–FM material. Besides some chance discoveries,[24-27] single-phase 2D multiferroic materials with both FE and FM orders promise the control of disparate properties. However, they remain rarely reported because multiferroic materials are challenged by the contradictory preferences of different kinds of ferroic materials for metal ion $d$-orbitals, i.e., FE requires empty $d$-orbitals but FM usually comes from partially filled $d$-orbitals.[28] Fortunately, different 2D flakes can stack into van der Waals heterostructures (vdWHs) because 2D materials have no surface dangling bonds and can be precisely stacked without leading to lattice mismatch. Therefore, using 2D FE materials in a vdWH provides an additional degree of freedom to control magnetism by flipping the polarization direction,[29] i.e., one can electrically control the magnetism in an FE–FM coupled heterostructure, which is promising for extending applications in data storage devices. Recently, several studies have revealed that hole doping can cause magnetism in some 2D systems due to their inherent Mexican-hat-like band dispersion.[30-34] The Mexican-hat-like dispersion provides a sharp van Hove singularity (VHS) near the Fermi level ($E_{\scriptscriptstyle{\rm F}})$ on the density of states (DOS), leading to significant exchange splitting of the electronic states of the two spin channels under proper hole doping and resulting in a net magnetic moment and spontaneous polarization.[35] Therefore, modulating FE states to control FM states in 2D vdWHs is promising for designs of nonvolatile memory devices. In this Letter, we propose a design for realizing 2D multiferroics (coexistence of FE and FM) in FE heterostructures comprising only d$^{0}$ semiconductors. We choose 2D InSe and FE In$_{2}$Se$_{3}$ monolayers to describe the principles, forming an InSe/In$_{2}$Se$_{3}$ vdWH in which both monolayers can almost hold the same band structures as those of the isolated individuals, respectively, and the band edge alignment couples directly to the polarization state. As the polarization is towards the InSe layer, the Mexican-hat-like band dispersion of the In$_{2}$Se$_{3}$ aligns on the top of the valence band (VB). Hence, under proper hole doping it evokes considerable magnetic polarization energy. In contrast, the reversed polarization pushes the VB maximum (VBM) of the InSe over the In$_{2}$Se$_{3}$ VB as the global edge of VBs. Therefore, much heavier doping is needed to evoke spin polarization with a rather tiny magnetic polarization energy. Therefore, with the FE reversion, the magnetic state bears an ON and OFF switch, which is promising for data storage devices. Computational Methods. All calculations were performed by the spin-polarized density functional theory (DFT) method as implemented in the Vienna ab initio simulation package (VASP),[36] and the Perdew–Burke–Ernzerhof (PBE) functional was used in the generalized gradient approximation (GGA)[37] scheme. The $k$-point samples and energy cutoff for structural optimization were set to be $15\times 15\times 1$ and 500 eV, respectively. The vdW interaction between layers was described by the DFT-D$_{3}$ method.[38] Dipole correction was employed due to the asymmetric layer arrangement.[39] Phonon dispersions were calculated with density functional perturbation theory using the PHONOPY code.[40] Hole doping was simulated by removing electrons in a system with a compensated uniform negative background. Results and Discussion. To realize memory devices with high speed and low energy consumption we propose a design of nonvolatile and switchable magnetic states based on 2D multiferroic vdWHs. These vdWHs should meet the following stringent conditions: (i) one of the materials is an FE material; (ii) the band alignment is tuned during polarization flipping; and (iii) one of the materials has a rather sharp DOS, for example, a VHS that can be easily realized by a Mexican-hat-like band dispersion, near the $E_{\scriptscriptstyle{\rm F}}$. Guided by these strategies, we propose an InSe/In$_{2}$Se$_{3}$ FE vdWH as an example to demonstrate the feasibility of this design. Notably, $d$ or $f$ electrons are not necessary for this proposal.
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Fig. 1. Top (upper) and side (lower) views of (a) InSe and (b) In$_{2}$Se$_{3}$ monolayers. The magenta and green beads represent In and Se atoms, respectively. The orange dashed rhombi mark the unit cells. The two polarization states of InSe/In$_{2}$Se$_{3}$ vdWHs are shown in (c) and (d), respectively. The red double-headed arrows mark the interlayer distances, $d$.
We chose the experimentally accessible In$_{2}$Se$_{3}$ and InSe monolayers,[41,42] as shown in Figs. 1(a) and 1(b), as the FE and auxiliary layers, respectively, forming a vdWH as shown in Fig. S1 and Table S1 in the Supplementary Material.[43] The 2D FE In$_{2}$Se$_{3}$ contains five atomic sublayers in the Se–In–Se–In–Se order. The central Se atomic sublayer deviates from the middle position between the top and bottom Se atomic layers, resulting in out-of-plane polarization. Besides the FE property of In$_{2}$Se$_{3}$, it possesses a narrow VB with Mexican-hat-like band dispersion. InSe is chosen because of its semiconductor property and proper hexagonal lattice (i.e., its lattice parameters are similar to those of In$_{2}$Se$_{3})$. Although the lattice mismatch plays a trivial role in the vdWH, matched lattices can save on calculation expenses. InSe and In$_{2}$Se$_{3}$ are indirect bandgap semiconductors with bandgaps of 1.53 and 0.81 eV, respectively, as shown in Figs. 2(a) and 2(b), consistent with the previous results.[21,44] The polarization state is marked as $P_\uparrow$ and $P_\downarrow$ when the central Se atom shifts close to the bottom and top layers, respectively. The polarization plays the role of a ‘handle’ that can modulate the electronic characteristics of the vdWH. Compared with the symmetrical InSe monolayer, the electrostatic potentials on both sides of FE In$_{2}$Se$_{3}$ are noticeably different, as shown in Fig. 2(c), leading to an electrostatic potential difference of 1.179 eV. In the vdWH, the InSe layer interacts with the $P_\uparrow$ or $P_\downarrow$ states of the In$_{2}$Se$_{3}$ layer, as depicted in Figs. 1(c) and 1(d), resulting in different band alignments. Given their relative positions, the two different polarization states ($P_\uparrow$ or $P_\downarrow$) are equal to the two cases in which the InSe layer contacts the In$_{2}$Se$_{3}$ layer from different sides. In addition, no imaginary mode occurs on the phonon spectra of the vdWH, illustrating good structural stability as shown in Fig. S2.[43] The band structures are shown in Figs. 3(a) and 3(b). The VBM and conduction band minimum (CBM) vary slightly compared with the isolated InSe and In$_{2}$Se$_{3}$ monolayers, as shown in Fig. 2(d), due to the weak interlayer interaction.
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Fig. 2. Band structures of (a) InSe and (b) In$_{2}$Se$_{3}$ monolayers (PDOS, partial density of states). (c) Average electrostatic potential of an In$_{2}$Se$_{3}$ monolayer. (d) Band alignment of InSe/In$_{2}$Se$_{3}$ ($P_\uparrow$) and InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) with respect to the vacuum level.
To further analyze the change in electronic properties, we plot the projected band structures of the InSe/In$_{2}$Se$_{3}$ vdWHs, as shown in Figs. 3(a) and 3(b). Although the bandgaps of InSe/In$_{2}$Se$_{3}$ vdWHs are slightly different in the two polarization directions, i.e., the bandgaps for InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) and InSe/In$_{2}$Se$_{3}$ ($P_\uparrow$) are 0.48 and 0.45 eV, respectively, the band alignments are distinctly different. For the InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) vdWH, the CBM and VBM are contributed by the InSe and In$_{2}$Se$_{3}$ layers, respectively. Conversely, by reversing the polarization of In$_{2}$Se$_{3}$ (to $P_\uparrow$), the band edge of the In$_{2}$Se$_{3}$ layer shifts downward, resulting in the VBM of the InSe layer being closer to $E_{\scriptscriptstyle{\rm F}}$. Therefore, according to the design principles, flipping the polarization of the FE layer can switch band alignment. Because the VBMs of both monolayers possess Mexican-hat-like dispersion, there is a one-dimensional-like VHS at the VB edge on the DOS spectrum. Therefore, as proper hole doping shifts $E_{\scriptscriptstyle{\rm F}}$ to the VHS, spin degeneracy will be lifted due to electronic interaction, similar to the previous report on GaSe.[35] Therefore, we calculated the two FE polarization cases for the vdWH. The relevant results for InSe and In$_{2}$Se$_{3}$ monolayers are shown in Fig. S3.[43] This displays the dependence of magnetic moment and magnetization energy on the number of doped holes, where one hole per unit cell corresponds to a doping concentration of approximately $7\times 10^{14}$ cm$^{-2}$. For the InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) case, the In$_{2}$Se$_{3}$ layer dominates the VBM. Quite light doping could drive the system to spin polarization with tremendous magnetic polarization energy ($E_{\rm p})$, defined as the energy difference between the FM and NM states, as depicted in Fig. 3(c), as in our previous report on a In$_{2}$Se$_{3}$ monolayer.[45] Figure 3(c) shows that the magnetic moment suddenly emerges at a concentration of about $4.53\times 10^{14}$ cm$^{-2}$ and increases continuously as the hole doping level enhances gradually then rapidly saturates at about 0.5 $\mu_{\scriptscriptstyle{\rm B}}$/hole, indicating magnetization of the vdWH. As shown in the inset of Fig. 3(c), the spin density is rather delocalized and is mainly distributed around all top layer Se atoms of In$_{2}$Se$_{3}$, so the magnetic moment comes from itinerant holes due to the homogeneous distribution in the top Se sublayer of In$_{2}$Se$_{3}$. The large DOS at Fermi energy level indicates FM instability according to the Stoner criterion, and this itinerant magnetism can persist over a sizable range of doping concentrations. $E_{\rm p}$ becomes more negative as doping increases, indicating more robust spin polarization and magnetic stability. Noticeably, $E_{\rm p}$ remains more negative than $-26$ meV from the doping concentration of $9.75\times 10^{14}$ to $1.39\times 10^{15}$ cm$^{-2}$, implying big spin polarization of the InSe/In$_{2}$Se$_{3}$ vdWH. However, the InSe layer makes a major contribution to the VBM for the InSe/In$_{2}$Se$_{3}$ ($P_\uparrow$) case. Under hole doping, the system can be spin-polarized but with trivial $E_{\rm p}$, indicating an NM nature, as shown in Fig. 3(d), similarly with doping in GaSe. Consequently, as the FE polarization determines the manner of band alignment dominating the electronic structure and then determines the spin polarization, we can tune the FE polarization with an external electric field to modulate the electricity and magnetism in the vdWH.
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Fig. 3. Projected band structures for neutral (a) InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) and (b) InSe/In$_{2}$Se$_{3}$ ($P_\uparrow$). Doping concentration dependence of the magnetic moment for (c) InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) and (d) InSe/In$_{2}$Se$_{3}$ ($P_\uparrow$). The light blue region indicates large spin polarization energies. The inset of (c) is the spin density distribution in the FM state of InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) at a hole density of $9.75\times 10^{14}$ cm$^{-2}$. (e) Spin-polarized band structure and (f) spin-polarized partial density of states (PDOS) of InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) vdWH for a hole density of $9.75\times 10^{14}$ cm$^{-2}$. Blue (red) and cyan (orange) lines represent the contributions of the InSe (In$_{2}$Se$_{3})$ layer with the spin-up and spin-down bands, respectively. The inset of (e) is the differential charge density before and after the hole doping of InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$). The $E_{\scriptscriptstyle{\rm F}}$ is set to be zero and marked with a black dashed line.
Moreover, we project the spin-polarized energy bands to the two layers, in the $P_\downarrow$ case at a hole density of $9.75\times 10^{14}$ cm$^{-2}$, as shown in Fig. 3(e). The spin degeneracy of the energy band from the In$_{2}$Se$_{3}$ layer is lifted with a large exchange splitting of about 0.28 eV. As a result, the spin-up band (red line) is fully occupied and lies about 0.2 eV below $E_{\scriptscriptstyle{\rm F}}$, while the spin-down band (orange line) intersected by $E_{\scriptscriptstyle{\rm F}}$ lies much higher. In contrast, the bands originating from the InSe layer are still degenerate. Since the VBs (blue and cyan lines) of the InSe layer are very dispersive, there is no exchange splitting of the holes residing on the InSe layer. As shown in the inset of Fig. 3(e), the holes are mainly doped on Se$_{1}$ and Se$_{5}$ atoms. Therefore, half of the holes gather in the InSe layer and the other half reside in the In$_{2}$Se$_{3}$ layer. Thus, the total magnetic moment saturates at about 0.5 $\mu_{\scriptscriptstyle{\rm B}}$/hole. According to our test calculations for the noncollinear magnetic moments, the magnetically easy axis is in the out-of-plane direction with a magnetic anisotropic energy of 0.2 meV. By considering the unit cell magnetic moment as an integral (this is a coarse approximation), we could examine the parallel and antiparallel magnetic configurations in a $2\times 2$ supercell and find that the parallel configuration is about 99.6 meV more favorable than the antiparallel one. Based on the Heisenberg model, we could make a rough estimation of the nearest-neighbor exchange integral to be $J=24.91$ meV and the Curie temperature to be $T_{\rm C} \sim 84$ K, by means of classic Monte Carlo simulations, as stated in Note III and Fig. S4 in the Supplementary Material.[43]
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Fig. 4. (a) The minimum energy pathway of an InSe/In$_{2}$Se$_{3}$ vdWH from the $P_\uparrow$ to the $P_\downarrow$ phase. (b) The energy barrier as a function of hole doping levels.
We have also plotted the band structure and DOS for InSe/In$_{2}$Se$_{3}$ ($P_\uparrow$) at the same hole density for comparison between $P_\uparrow$ and $P_\downarrow$. As shown in Fig. S5,[43] there is no spin splitting in InSe/In$_{2}$Se$_{3}$ ($P_\uparrow$). The semiconductor InSe auxiliary layer in this tunable multiferroic vdWH contributes to the global VBM on the $P_\uparrow$ state of the In$_{2}$Se$_{3}$ layer, making the system NM (OFF) under light hole doping. Although it becomes spin polarized under heavier doping, $E_{\rm p}$ is too small to hold the magnetism. Therefore, the InSe/In$_{2}$Se$_{3}$ ($P_\uparrow$) case is NM over the entire doping range. Hence, with the semiconductor InSe, nonvolatile and switchable magnetism under hole doping can be coded by setting the FE state of the In$_{2}$Se$_{3}$ layer. Emphatically, the magnetic state switches from ON to OFF when the polarization direction of In$_{2}$Se$_{3}$ alters from $P_\downarrow$ to $P_\uparrow$. Both states are robust even if the external electric field is removed, which benefits information nonvolatility and a reduction in energy consumption. Experimentally, the switchable behavior has been successfully realized in the 2D polar material WTe$_{2}$.[46] Moreover, as shown in Fig. 4, based on the nudged elastic band calculation of migration paths, the energy barriers between $P_\uparrow$ and $P_\downarrow$ states could be decreased upon hole doping, which benefits FE phase transition. As the doping concentration reaches 1.4 holes/u.c., the magnetic moment of the system reaches saturation. At this point, the value of the energy barrier is 0.064 eV, which ensures that the higher-energy electrically polarized state is stable compared with the lower-energy electrically polarized state. Additionally, we have computed the polar atomic displacements in the InSe/In$_{2}$Se$_{3}$ vdWH ($P_\downarrow$) as a function of charge-carrier concentration obtained via the background charge method. Figure S6 suggests that the polar phase can support a substantial number of charged defects while maintaining the polar structure. Therefore, we believe that the external electric field can accurately control the spin states by flipping the FE polarization of In$_{2}$Se$_{3}$ in the vdWH. The above analyses show that the magnetism-switching behavior of InSe/In$_{2}$Se$_{3}$ vdWH comes from two aspects: (i) the coupling at the InSe/In$_{2}$Se$_{3}$ vdWH interface renders different band alignments under different polarization states, and (ii) the Mexican-hat-like band edge dispersion can realize magnetism under hole doping. These two aspects are not exclusive to the InSe/In$_{2}$Se$_{3}$ vdWH. Therefore, modulating ON–OFF switchable and nonvolatile magnetism under hole doping by interface engineering may also be extended to other heterostructures. Additionally, implementing nonvolatile magnetic switching via an FE switch relies on two common features of FE materials, namely the FE bistable state and broken spatial-inversion symmetry, which shows that engineering semiconductor-aided multiferroic heterostructures is a general strategy for realizing nonvolatile magnetic switching. Usually, magnetic properties are strain sensitive. So, we examine the effect of biaxial strain on the doping-induced magnetization of the InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) vdWH. We simulate the biaxial strain by changing the lattice constant, and the strain is defined as $\varepsilon =(a-a_{0})/a_{0}$, where $a$ ($a_{0})$ is the lattice constant of the strained (unstrained) InSe/In$_{2}$Se$_{3}$ (P$\downarrow)$ vdWH. We calculate the magnetic moment and $E_{\rm p}$ for various strains. The magnetic moment and $E_{\rm p}$ are strongly strain-dependent in magnetic transition, as shown in Figs. 5(a) and 5(b). The magnetism can be turned on at a lower doping concentration under tensile strain, i.e., the tensile strain can lose the constraint of the doping concentration to achieve magnetism. We calculate the biaxial-strain-dependent magnetic moment at three doping levels, $4.9\times 10^{14}$ cm$^{-2}$ (red), $7.0\times 10^{14}$ cm$^{-2}$ (blue) and $9.8\times 10^{14}$ cm$^{-2}$ (green), respectively, as presented in Fig. 5(c). The doping-induced magnetization is suppressed under compressive strain when the doping level is relatively low ($4.9\times 10^{14}$ cm$^{-2}$). Conversely, its magnetic moment rapidly increases to saturation under tensile strain. At a doping concentration of $9.8\times 10^{14}$ cm$^{-2}$, the magnetic moment retains saturation under stronger strains. To reveal the underlying mechanisms of the strain-induced variation in magnetism, we plot the band structures of InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) vdWH under different strains, as shown in Fig. 5(d). Compared with the pristine one (cyan line) in Fig. 5(d), the radius of the Mexican-hat band edge ($k_{\rm r})$ becomes larger under tensile strain (blue line). The band edge circle will extend in the Brillouin zone, enhancing and sharpening the DOS peak and increasing hole accommodation near $E_{\scriptscriptstyle{\rm F}}$. As a result, a sharper DOS peak means that the Stoner criterion is more easily fulfilled under hole doping. In contrast, $k_{\rm r}$ becomes smaller when a compressive strain is applied (red line), thus weakening the magnetism. Because the orbital overlaps less (more) after the extension (compression), the VB becomes flatter (more dispersive) and easily (hardly) fulfills the Stoner criterion. In addition, the tensile strain also raises the energy band near the $K$ point, which leads to a sharper and higher DOS peak close to the Fermi level. This explains why the onset of magnetism occurs at a lower hole doping concentration under tensile strain, as shown in Fig. 5(a). Conversely, under compressive strain, the appearance of magnetism requires a higher hole doping concentration. Therefore, mechanical modulation can strongly affect magnetism in the InSe/In$_{2}$Se$_{3}$ vdWH. Furthermore, we propose a data storage device, as illustrated in Fig. 6, for nonvolatile magnetic switching applications based on this InSe/In$_{2}$Se$_{3}$ FE vdWH, with a 2D insulator such as hexagonal boron nitride (h-BN) as the substrate. Since the vdWH is made of atomically thin layered materials, the doping levels of our device could be electrostatically tuned by a gate. The properties of the InSe/In$_{2}$Se$_{3}$ vdWH, in either the FM or NM state under hole doping, are controlled by the polarization state ($P_\downarrow$ or $P_\uparrow$) of the In$_{2}$Se$_{3}$. As mentioned above, the data writing operation is performed by coding the FE polarization, similar to the case in an In$_{2}$Se$_{3}$-only device. In addition, to illustrate the influence of the substrate on the properties of the system, we also calculated the partial density of states of the InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) vdWH on a single-layer h-BN substrate, as shown in the inset in Fig. 6. Remarkably, the effect of the h-BN substrate on the inherent characteristics of the InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) vdWH is negligible. The In$_{2}$Se$_{3}$ layer accounts for the dominant proportion (red) in the VB peaks compared with those of the InSe (blue) and BN (magenta) layers, so the magnetic switching character can also be achieved with the BN substrate, and the magnetic moment does not substantially change. Therefore, an InSe/In$_{2}$Se$_{3}$-based data storage device can be prepared on an h-BN substrate with proper hole doping. The data reading process can be performed by checking the magnetoelectric signal differences from the damage-free current.[47] Such a strategy is ideal for nano-spintronic devices with nonvolatility and low energy consumption.
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Fig. 5. (a) Magnetic moment and (b) polarization energy under different strains. (c) Strain dependence of the hole doping magnetic moment at different concentrations. (d) Band structures of InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) vdWH under 4% tensile strain, no strain and 2% compressive strain, respectively. The radius of the Mexican-hat band edge ($k_{\rm r})$ is indicated by black double-headed arrows.
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Fig. 6. Dependence of the magnetic moment of the h-BN/InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) vdWH on doping concentration. Bottom inset: concept and sketch diagram of the data storage device based on the h-BN/InSe/In$_{2}$Se$_{3}$ vdWH. Upper right inset: partial density of states (PDOS) of the h-BN/InSe/In$_{2}$Se$_{3}$ ($P_\downarrow$) vdWH. The light blue regions indicate large spin polarization energies.
In summary, an intriguing strategy is proposed to introduce a semiconductor auxiliary to an FE layer to control the magnetic state. Interestingly, hole-doped InSe/In$_{2}$Se$_{3}$ transits from NM to FM when the polarization direction is flipped. Therefore, this approach is general for securing and engineering new material systems for nonvolatile data storage applications. Acknowledgments. The authors are grateful to Professor Xiaohui Liu in Shandong University for constructive discussion. This work was supported by the Natural Science Foundation of Shandong Province (Grant Nos. ZR2020MA068, ZR2022MA083, and ZR2023MA018), and the Major Basic Research Project of Shandong Province (Grant No. ZR2020ZD28). The authors acknowledge technical support from the Micro-modular Data Platform of the School of Physics at Shandong University. References Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystalsLayer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limitGate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2Chemically Exfoliated VSe2 Monolayers with Room‐Temperature FerromagnetismSpintronics: A Spin-Based Electronics Vision for the FutureDesign of a noble-metal-free direct Z-scheme photocatalyst for overall water splitting based on a SnC/SnSSe van der Waals heterostructureDesign of atomically localized magnetic moment by adatoms chemisorbed on grapheneLocalized magnetic moment induced by boron adatoms chemisorbed on grapheneRecent progress in voltage control of magnetism: Materials, mechanisms, and performanceElectrical control of Co/Ni magnetism adjacent to gate oxides with low oxygen ion mobilityControlling many-body states by the electric-field effect in a two-dimensional materialGate Tuning of Electronic Phase Transitions in Two-Dimensional NbSe 2 Ferroelectricity in 2D Elemental MaterialsFerroelectricity and Large Rashba Splitting in Two-Dimensional TelluriumFerroelectricity in Pulsed Laser Deposited Ba(Fe1/2 Nb1/2 )O3 Thin FilmsDepolarization-Field-Induced Instability in Thin Ferroelectric Films—Experiment and TheoryDiscovery of robust in-plane ferroelectricity in atomic-thick SnTeRoom-temperature ferroelectricity in CuInP2S6 ultrathin flakesFerroelectricity, Antiferroelectricity, and Ultrathin 2D Electron/Hole Gas in Multifunctional Monolayer MXeneOut-of-Plane Piezoelectricity and Ferroelectricity in Layered α-In2 Se3 NanoflakesPrediction of intrinsic two-dimensional ferroelectrics in In2Se3 and other III2-VI3 van der Waals materialsIntrinsic Two-Dimensional Ferroelectricity with Dipole LockingRoom‐Temperature Ferroelectricity in Hexagonally Layered α‐In2 Se3 Nanoflakes down to the Monolayer LimitElectrical Control of Magnetic Phase Transition in a Type-I Multiferroic Double-Metal Trihalide MonolayerSingle-phase multiferroics: new materials, phenomena, and physicsγ-GeSe: A two-dimensional ferroelectric material with doping-induced ferromagnetismStrong Coupled Magnetic and Electric Ordering in Monolayer of Metal Thio(seleno)phosphatesWhy Are There so Few Magnetic Ferroelectrics?Kinetic control of tunable multi-state switching in ferroelectric thin filmsMultiferroic Two-Dimensional MaterialsOrigin and Enhancement of Hole-Induced Ferromagnetism in First-Row d 0 SemiconductorsRoom-temperature half-metallicity in monolayer honeycomb structures of group-V binary compounds with carrier dopingTunable Magnetism and Extraordinary Sunlight Absorbance in Indium Triphosphide MonolayerSpin-polarized current in wide bandgap hexagonal boron nitrides containing 4|8 line defectsTunable Magnetism and Half-Metallicity in Hole-Doped Monolayer GaSeEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setGeneralized Gradient Approximation Made SimpleSemiempirical GGA-type density functional constructed with a long-range dispersion correctionDipole correction for surface supercell calculationsFirst principles phonon calculations in materials scienceControlled Synthesis of High-Quality Monolayered α-In2 Se3 via Physical Vapor DepositionMagnetotransport and lateral confinement in an InSe van der Waals HeterostructureAb initio study of carrier mobility of few-layer InSeExotic magnetism in As-doped α/β-In2 Se3 monolayers with tunable anisotropic carrier mobilityFerroelectric switching of a two-dimensional metalNonvolatile Electrical Control and Heterointerface‐Induced Half‐Metallicity of 2D Ferromagnets
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