Interfacial atomic orbital controlled spin-hybridization proximity effects in vdW heterostructures

Abstract

Interfacial effects have emerged as a promising tool in engineering localized and global magnetic properties of van der Waals heterostructures. Understanding the underlying mechanism of such interfacial effects is crucial for precise control over the interface induced properties and phenomena. Herein, this paper proposes a hypothesis on the deterministic role of atomic sub-orbitals of interfacial atoms in interfacial spin hybridization, which controls the magnetic proximity effect between a magnetic conductor and a non-magnetic material with a band gap. This work demonstrates that the mere presence of electronic bands of adjacent materials in the same energy window in a heterostructure does not ensure interfacial hybridization. Instead, atomic sub-orbitals of interfacial atoms – particularly the p_z orbital – are the principal hybridizing agents. We propose that the asymmetric contribution of p_z-up and p_z-down orbitals to the Fermi level of magnetic conductors is the principal parameter that governs induced magnetism via hybridization proximity in non-magnets.

---

1 Introduction

The study of interfacial magnetic effects has garnered considerable attention in recent years within the realm of two-dimensional (2D) materials. These effects in hybrid systems have emerged as a powerful tool for engineering novel quantum states, which lead to electronic and magnetic properties at the interface that are absent in the adjacent constituent materials.^1–19 Understanding the impact of interface coupling, such as interfacial hybridization, is crucial in engineering heterostructures, where hybridization can be precisely controlled by external perturbations. Interfacial hybridization significantly influences van der Waals (vdW) heterostructures, especially in heterobilayers where the valence bands and conduction bands of pristine monolayers are present in different energy ranges. For instance, in heterostructures of ferromagnetic insulators and metallic non-magnets, valence bands of one spin channel shift and align with the Fermi level of the metallic non-magnets. In such a situation, only that spin channel hybridizes with the conducting bands and generates a new electronic and magnetic state in the heterostructures.²⁰ However, in heterostructures of a non-magnetic material with a band gap and a ferromagnetic metal, the scenario will be different. In this case, the non-spin polarized bands of the non-magnetic system will be shifted and aligned with the Fermi level of the ferromagnetic metal. As both spin channels of the ferromagnetic metal are present around the Fermi level, they will be coupled with the bands of the non-magnet. The magnetic properties of such heterostructures will depend on how these spin channels couple at the interface. A thorough understanding of this interfacial coupling and how interfacial atoms and their atomic orbitals affect interlayer hybridization and magnetism is essential for engineering materials with tailored properties.

Janus materials, a unique class of 2D materials, with asymmetric compositional elements on each side,^21–34 present an ideal platform for such interfacial studies, offering the opportunity to explore different interfaces while maintaining consistent electronic and magnetic properties in the adjacent materials. These materials facilitate the formation of stacking-dependent heterostructures. Since all other parameters are similar in such heterostructures with different interfaces, exploration of interfacial magnetic effects, such as spin splitting in these types of heterostructures, paves the way for detailed understanding of the effects of interfacial atoms on interlayer magnetic coupling in vdW heterostructures. CrSTe is one such material that has different compositional elements on the two sides, which can be synthesized following the procedures for the synthesis of Janus monolayers.^{21,22,32,33,35,36} Moreover, despite having a broken mirror symmetry, CrSTe shows very weak Dzyaloshinki–Moriya interaction and has long range ferromagnetic order with perpendicular magnetic anisotropy.^37–39 These properties make the material suitable for studying the magnetic proximity effects. For exclusive understanding of the interfacial effect on non-magnetic materials with a band gap, a material with a single atomic layer is a suitable candidate. This is because in such single atomic layer materials, that single layer, which is supposed to be the interfacial layer, controls the global properties of the system. Therefore, any interfacial change is reflected in the global change of properties in the system. Keeping this advantage of single layered materials in view, we consider a SnC monolayer to design a heterostructure with CrSTe due to the minimal lattice mismatch of 1.1% between SnC (lattice constant = 3.49 Å)⁴⁰ and CrSTe (lattice constant = 3.45 Å)³⁷ and the high band gap of SnC.⁴⁰

In this article, we report the deterministic role of interfacial atomic orbitals in interfacial magnetic coupling. We demonstrate that spin-dependent interfacial atomic orbital hybridization is controlled by the p_z interfacial orbitals and it induces reverse spin splitting in the non-magnet. Our findings reveal that spin-dependent charge transfer between the systems as a consequence of selective hybridization significantly influences their electronic and magnetic properties. Our results show that all the atomic sub-orbitals do not contribute equally to interfacial hybridization. We also discuss the influence of the interface, interfacial atoms, and their orbitals on this hybridization process. Based on the observations, we propose that the asymmetric presence of p_z orbitals of interfacial atoms at the Fermi level is essential for inducing magnetism in a non-magnetic system. This proposed orbital selective hybridization explains the cause of the presence or absence of proximity induced magnetism in vdW heterostructures. Our proposed mechanism provides new insights into the prevailing electronic band structure-based understanding of the hybridization-induced magnetic proximity effect.

2 Computational details

Our first principles calculations were performed based on density functional theory (DFT) using a generalized gradient approximation (GGA) exchange–correlation functional of the Perdew–Burke–Ernzerhof form^41,42 as implemented in Quantum ESPRESSO.^43,44 Projector-augmented wave (PAW) pseudopotentials⁴⁵ were used in the calculation and it includes semi-core electrons (except for C) and treats the d-electron explicitly, particularly the 3d electrons of Cr. We used a plane wave basis set with a 90 Ry cut-off energy and a 24 × 24 × 2 k-mesh for Brillouin zone integration. Grimme's DFT-D2 method was used for vdW correction.⁴⁶ Moreover, DFT-D3 methods were also tested for geometric optimization and it was found that the interlayer separation of the optimized magnetic heterostructures calculated using DFT-D2 and DFT-D3 corrections differs by less than 0.1 Å and the binding energy differs by less than 4 meV per atom. Furthermore, the orbital resolved band structure of the stable heterostructure calculated using DFT-D2 and DFT-D3 correction yields the same results as shown in the SI, Fig. S2. Since orbital resolved band structures are the prime results that establish the main finding of the study and matching band structures were obtained using DFT-D2 and DFT-D3 corrections, DFT-D2 corrections were employed in this study. A force convergence criterion of 10⁻⁶ Ry per Bohr was used for ionic relaxation with an energy convergence criterion of 10⁻¹⁰ Ry for all the calculations. A 15 Å vacuum was included along the z-axis to prevent periodic interaction along the vertical direction. For the visualization of the crystal structure and charge density profile, VESTA⁴⁷ was used. The VAMPIRE⁴⁸ atomistic simulation package was used for estimation of the Curie temperature.

3 Results and discussion

The CrSTe monolayer is a metallic ferromagnet with perpendicular magnetic anisotropy,^37–39 while the SnC monolayer is a non-magnetic semiconductor.^40,49,50 SnC features a graphene-like honeycomb structure, and the Janus CrSTe monolayer has S and Te atoms on opposite surfaces (Fig. 1(a and b)). This allows for the formation of two distinct heterostructures depending on the interface. In one heterostructure, the interface is formed between the S surface and the SnC layer, denoted as CrTeS/SnC, while in the other, the interface is formed between the Te surface and the SnC layer, denoted as CrSTe/SnC, as illustrated in Fig. 1(c) and (d). We explored five possible stacking dependent configurations for each heterostructure, which are shown in the SI (Fig. S1), to determine the most stable configuration using the energy difference method. Geometric optimization identified CrTeS/SnC with C lying in the same vertical position as Te in the hollow region above the S interfacial layer and Sn lying on top of S (Te–C(h)–S–Sn(t)) (Fig. 1(c)) and CrSTe/SnC with C lying in the same vertical position as Cr in the hollow region and Sn lying in the same vertical position as S in the hollow region above the Te interfacial layer(Cr–C(h)–S–Sn(h)) (Fig. 1(d)) as the most stable configurations, with interlayer separations of 2.84 Å and 3.37 Å, respectively. Furthermore, the stability of these two stacking configurations over other configurations is confirmed by calculating the formation energies and binding energies of all the heterostructures. The formation energy is calculated using eqn 1:⁵¹

E_formation = E^total_{heterostructure} − E^total_CrSTe − E^total_SnC (1)

where E^total_{heterostructure}, E^total_CrSTe, and E^total_SnC represent the total energy of the heterostructure and corresponding pristine monolayers respectively. From the calculation, it is found that the formation energy for all the stacking is negative, which confirms the possibility of formation of a heterostructure between CrSTe and SnC. Calculated results for formation energy show that the Te–C(h)S–Sn(t) heterostructure is the most stable configuration for the CrTeS/SnC system and Cr–C(h)–S–Sn(h) is the most stable configuration for the CrSTe/SnC interface. Formation energies of all the stacking dependent heterostructures are listed in the SI (Table SI).

Fig. 1 Optimized structures of the most stable heterostructures. Top and side view of 2 × 2 monolayers of (a) CrSTe and (b) SnC with periodic atoms. Labels for different atoms are shown in the figure. Side view of a 2 × 2 heterostructure of (c) CrTeS/SnC and (d) CrSTe/SnC with periodic atoms. (c) The Te–C(h)S–Sn(t) heterostructure and (d) the Cr–C(h)–S–Sn(h) heterostructure. The black lines represent the edge of the 2 × 2 supercell and the red circles connected by a red line represent the pair of atoms that are vertically aligned at the same vertical coordinate. In CrTeS/SnC (c) Sn is aligned with S and C is aligned with Te. In CrSTe/SnC (d), C is aligned with Cr and Sn is aligned with S. 2.84 Å and 3.37 Å, representing the interlayer separation of the corresponding heterostructures.

Moreover, the binding energies of the heterostructures are evaluated using eqn 2: ^51,52

E_binding = E^total_{heterostructure} − E^total_CrSTe+SnC (2)

where E^total_CrSTe+SnCis the sum of energies of the two independent monolayers in the heterostructure environment. From the binding energy calculation, it is found that binding energies of all the heterostructures are negative, which confirms the stability of the vdW heterostructures. From the calculation, it is found that the two abovementioned stackings give the most stable configuration for the respective interface. The binding energy details of all the heterostructures are listed in the SI (Table SI).

In the two heterostructures, the proximity of magnetic CrSTe to non-magnetic SnC suggests a potential magnetic proximity effect. Our initial investigations revealed a strong induced magnetic moment (−0.1225μ_B) in the C atom of the SnC layer of the CrTeS/SnC heterostructure, which is opposite to the magnetic orientation of CrSTe. This induced magnetic moment has a similar value to earlier reported values of proximity induced magnetic moment in heterostructures and within the experimentally detectable range.^53–57 Moreover, since this induced magnetism is subjected to a substrate ferromagnet CrSTe, whose Curie temperature in the heterostructure is estimated to be 285 K (SI Fig. S2), the induced magnetic state will be operable at high temperatures under the influence of the CrSTe's magnetic effect. On the other hand, no magnetism was induced in the SnC layer of the CrSTe/SnC heterostructure. This asymmetric finding is particularly intriguing, as one would expect a similar, albeit not quantitatively identical, magnetic effect of CrSTe on SnC in both heterostructures, due to the similar magnetic environment provided by CrSTe. However, these results demonstrate a completely asymmetric magnetic effect of CrSTe on SnC, driven by variations in the interface and interlayer separation.

To investigate the role of interlayer separation on the induced magnetism, we analyzed two additional heterostructures with adjusted interlayer separations with clamped ion approximation. Specifically, we set the interlayer separation of CrTeS/SnC as equal to that of the optimized CrSTe/SnC and vice versa, as shown in the SI (Fig. S3). While the induced magnetism was slightly reduced in the modified CrTeS/SnC, no magnetism was induced in SnC in the modified CrSTe/SnC. This indicates that interlayer separation is not the primary factor behind the asymmetric magnetic effect. Instead, the asymmetry must stem from an alternative interfacial mechanism. Given the correlation between magnetic and electronic properties, we next examined the electronic properties of the two heterostructures to understand the asymmetric magnetic effect.

Fig. 2 shows the spin-polarized band structures of the two heterostructures compared to the monolayer CrSTe and SnC. CrSTe exhibits spin polarization (Fig. 2(a)), while SnC does not (Fig. 2(b)). In Fig. 2(c) and (d), both heterostructures have bands crossing the Fermi level near the K-high-symmetry point, a feature absent in the pristine monolayers. Notably, the band structures differ significantly between the two heterostructures. In CrSTe/SnC, bands of both spins cross the Fermi level at the K-high-symmetry point without spin splitting, whereas in CrTeS/SnC, bands of only one spin cross the Fermi level, resulting in a strong spin splitting of 447 meV between the majority and minority spin channels at the K-high-symmetry point. This spin splitting between spin up and spin down bands is shown in the SI, Fig. S4. These observations are particularly intriguing because the presence or absence of spin splitting at the K-high-symmetry point correlates with the observed induced magnetism in the SnC layer. This spin splitting at the K-high-symmetry point correlates with induced magnetism in the SnC layer, while the absence of splitting corresponds to an absence of induced magnetism. This suggests that electronic states at the K-high-symmetry point are associated with SnC in the heterostructure, and the interfacial electronic coupling of spin up and spin down bands is asymmetric in CrTeS/SnC. To gain further insights into this asymmetric behavior, we analyzed the projected atomic band structures of the two heterostructures. The projected atomic band structures as shown in Fig. 3(a–d) confirm that the new electronic states above the Fermi level at the K-high-symmetry point are primarily contributed by C-p orbitals. Comparison of the band structures between the heterostructures and the pristine monolayers reveals that the valence band of SnC shifts toward the Fermi level as a result of heterostructure formation, allowing these shifted bands to participate in hybridization and cause the spin splitting of 447 meV in the SnC layer. However, in CrTeS/SnC, only the spin-up electrons from C strongly hybridize with CrSTe as shown in Fig. 3(a), while spin-down hybridization is very weak as shown in Fig. 3(b), as the spin down bands contributed by the SnC in the heterostructure retain the exclusive signature of the SnC bands shown in Fig. 2(b). This result is again very significant because, according to the hybridization proximity theory,²⁰ when both spin-up and spin-down bands of CrSTe are present at the Fermi level, both spin channels of SnC should participate in hybridization with CrSTe. In CrSTe/SnC, both spin channels hybridize weakly, as indicated by the retained SnC band features shown in Fig. 3(c) and (d). These inferences lead to the conclusion that electrons with opposite spins hybridize differently in the CrTeS/SnC heterostructure and hybridization strength depends on the interface. This asymmetric hybridization of spin up and spin down electrons at the interface induces a half-metallic character in the SnC layer in the CrTeS/SnC heterostructure. The PDOS for SnC exhibiting a half-metallic character in CrTeS/SnC is shown in the SI (Fig. S5). SnC in the CrTeS/SnC system has a band gap of zero for the spin-up channel, whereas it has a band gap of 0.73 eV for spin-down channel, which demonstrates the half-metallic characteristics of SnC in the magnetic heterostructure.

Fig. 2 Electronic band structures of (a) CrSTe monolayer, (b) SnC monolayer, (c) CrTeS/SnC heterostructure and (d) CrSTe/SnC heterostructure.

Fig. 3 Projected band structures of Cr-d, S-p, Te-p, Sn-p and C-p for up (a and c) and down (b and d) bands of CrTeS/SnC (a and b) and the CrSTe/SnC heterostructure (c and d). The larger the circle (thickness of bands), the larger is the contribution of the corresponding atoms to the band. Only the band line without any circle signifies the absence of contribution of the corresponding atoms to the band.

To understand the strong spin-dependent hybridization of C atoms with CrSTe in specific interfaces, we examined the projected orbital density of states (PDOS) for pristine CrSTe and the orbital-resolved atomic band structure of CrSTe and SnC. The orbital resolved projected band structures for the surface atoms of pristine CrSTe and SnC are shown in the SI, Fig. S6 and S7. The orbital-resolved PDOS of interfacial atoms shown in Fig. 4(a and b) reveals that the p_z orbitals of S significantly contribute to the spin-up bands at the Fermi level, while the p_z orbitals of Te contribute minimally and neither of the two p_z orbitals contributes to the spin-down band at the Fermi level. These variations of p_z orbital contribution align with the observed strength of hybridization in the S-side and Te-side interfaces. Additionally, the valence band maximum in SnC is dominated by C-p_z orbitals, allowing p_z-up hybridization between C and S at the S-side interface. However, negligible p_z-up orbital presence in Te leads to weak hybridization at the Te-side interface. The absence of p_z-down orbital contributions prevents spin-down hybridization in both interfaces. The lack of hybridization between Sn and CrSTe is due to the absence of Sn-p_z orbitals in the maxima of the SnC valence band as shown in the SI, Fig. S8 and hence, no magnetism is induced in Sn. However, no such correlation between hybridization and the contribution of p_x and p_y orbitals is observed in the two heterostructures. The Te atom shows a significant contribution of p_x and p_y orbitals around the Fermi level, but no hybridization in the Te interface heterostructure is observed. Although both spins of electrons contribute to the bands at the Fermi level in both heterostructures, it is the interfacial atom and its p_z orbital contribution that dominate in determining the strength and possibility of interlayer hybridization during the formation of a heterostructure. Based on these results, we propose that the contribution of p_z orbitals at the Fermi level of spin-polarized interfacial atoms governs interfacial hybridization. Furthermore, asymmetric p_z-up and p_z-down orbital contributions at the Fermi level are crucial for introducing spin polarization and magnetism in non-magnetic materials through interfacial hybridization.

Fig. 4 (a) PDOS for p_x, p_y, p_z orbitals of (a) S atom and (b) Te atom in the CrSTe monolayer. (c–e) Schematic representation of atomic orbital dependency on interfacial hybridization. It schematically shows that the orbital contribution of system B is shifted towards the Fermi level on the formation of a heterostructure and hybridizes when the p_z sub-orbital is present in the band of system A (c), and no hybridization takes place when the p_z sub-orbital is absent in the band of A (d). (e) Schematic representation showing that the asymmetric contribution of p_z-up and p_z-down orbitals in system A induced new spin polarized features in non-magnetic system B upon formation of a heterostructure.

This proposed mechanism of p_z orbital mediated interfacial hybridization is schematically illustrated in Fig. 4(c–e). Fig. 4(c) schematically shows that when the magnetic system (A) contributes p_z orbitals to the electronic band around the Fermi level, then these p_z orbitals undergo interfacial hybridization with the electronic state of another material (B) when a heterostructure is formed between the two materials (A and B). In the figure, A and B schematically represent the electronic profile of two materials A and B, whereas A/B schematically represents the electronic profile of the heterostructure of A and B. In Fig. 4(c), the red line in A/B represents a new electronic state, which is not present in A or B and originates due to the interfacial hybridization between the p_z orbitals of A and B. In contrast, there is no p_z orbital around the Fermi level of A in Fig. 4(d). Therefore, there is no new electronic state in the heterostructure between A and B, which implies an absence of interfacial hybridization. Fig. 4(d) schematically demonstrates that the presence of p_z orbitals is essential for interfacial hybridization, which is hypothesized from the results of the study. Fig. 4(e) shows that material A makes a p_z-up electronic contribution around the Fermi level, while there is no p_z-down contribution. Consequently the p_z-up orbital hybridizes with the electronic state of B and a new state is generated for the up band. However, due to the absence of a p_z-down orbital, no hybridization occurs and hence no new electronic state is generated for the down bands, which results in a spin polarized band for the material B in the heterostructure A/B. Fig. 4(e) schematically demonstrates the induced spin splitting in the non-spin polarized B system due to the presence of p_z-up and the absence of p_z-down orbitals around the Fermi level in system A. This explains the asymmetric magnetic effect of CrSTe on SnC in which the contribution of p_z-up and p_z-down sub-orbitals is asymmetric around the Fermi level in different interfaces.

To validate the proposed interfacial orbital-dependent spin-asymmetric behavior in the heterostructures, the charge redistribution profiles of both heterostructures were analyzed. Since interfacial hybridization is linked to charge transfer, higher charge transfer is expected for electrons with strong hybridization. The total, spin-up, and spin-down charge density differences for CrTeS/SnC and CrSTe/SnC are shown in Fig. 5(a–c) and (d–f). From the figures, it is evident that the charge transfer from SnC to the interfacial region is asymmetric for spin-up and spin-down charges in CrTeS/SnC. In CrTeS/SnC, spin-up charge transfer occurs from SnC (particularly C) to CrSTe due to strong spin-up hybridization at the Fermi level, while spin-down charge transfer is negligible due to the absence of hybridization. In contrast, CrSTe/SnC shows symmetric but minimal charge transfer for both spin channels, as confirmed by Bader charge analysis^58–61 in Table 1. This minimal transfer is due to the lack of hybridization in both spins for CrSTe/SnC. The Bader analysis also shows significant spin-up charge transfer in CrTeS/SnC, which supports the proposed orbital hybridization mechanism. The change in charge density (Δρ) due to the formation of a heterostructure is calculated by subtracting the total Bader charge within the Bader volume of each atomic species in the pristine system from the Bader charges of the corresponding layers of the heterostructure. A positive value of (Δρ) represents the accumulation of charge in that layer, while a negative value represents a depletion of charge from that layer.

Fig. 5 (a) Total, (b) spin-up, and (c) spin-down charge density difference in the CrTeS/SnC heterostructure. (d) Total, (e) spin-up, and (f) spin-down charge density difference in the CrSTe/SnC heterostructure. Cyan color and yellow color represent depletion and accumulation of charges. The iso-surface value for panels (a)–(c) is 10 times the iso-surface value for panels (d)–(f). (g–l) PDOS for p_z orbitals of the S atom in the CrSTe monolayer under different strains as mentioned in the corresponding panel. The μ_B values in panels represent the induced magnetic moments in SnC under the corresponding strain in the CrTeS/SnC heterostructure.

Table 1 Bader charge analysis of the two heterostructure. Δρ represents the change in charge density due to formation of a heterostructure in terms of electrons. A positive value represents charges transferred to the layer and a negative value represents charges transferred from the layer

System	Δρ (total) (e)	Δρ (up) (e)	Δρ (down) (e)
CrTeS/SnC
CrSTe	0.1681	0.0979	0.0703
SnC	−0.1681	−0.1847	0.0165
CrSTe/SnC
CrSTe	0.0424	0.0250	0.0174
SnC	−0.0424	−0.0181	−0.0244

---

Furthermore, since there is small lattice mismatch between CrSTe and SnC, to assess the impact of lattice matching on induced magnetism, we applied in-plane compressive and tensile strains ranging from −3% to +3% by adjusting the in-plane lattice constant as shown in the SI, Fig. S9. Tensile strain gradually enhances induced magnetism and spin splitting, while compressive strain suppresses them as shown in Fig. 5(g–l). These variations of induced magnetism align with the variation of p_z orbital contributions at the Fermi level of CrSTe's interfacial atoms under strain. As p_z-up orbital contributions increase or decrease, induced magnetism in the SnC layer follows a similar trend. This supports our hypothesis of the p_z dependency in interfacial hybridization induced magnetic proximity effect.

Collectively, the figures and analyses reveal a magnetic proximity effect due to the spin-dependent interfacial hybridization controlled by atomic sub-orbitals of interfacial atoms. The observed interface-dependent asymmetric orbital hybridization in the two heterostructures arises from the asymmetric contribution of p_z orbitals by CrSTe's interfacial atoms to the electronic band at the Fermi level. These interface and spin selectivities reveal that the presence or absence of a contribution of p_z interfacial orbitals at the Fermi level determines the possibility of the presence or absence of hybridization in the heterostructure. When p_z interfacial orbitals contribute, strong hybridization generates a new conducting state; otherwise, no hybridization occurs. These observations lead us to the proposed mechanism of interfacial hybridization, which states that the asymmetric contribution of p_z-up and p_z-down atomic sub-orbitals of the interfacial atom in a heterostructure is the principal driving factor of the interfacial hybridization induced magnetic proximity effect. These insights enable interface engineering of heterostructures by selecting materials with desired interfacial orbital contributions for application purposes.

4 Conclusion

In conclusion, our study reveals interfacial atomic orbital controlled spin dependent hybridization proximity effect induced magnetism in vdW heterostructures of a ferromagnetic conducting monolayer and a non-magnetic material with a band gap. We propose that the mere presence of electronic bands at the Fermi level does not ensure a magnetic proximity effect governing hybridization between the interfacial atoms. Instead, the interfacial hybridization is controlled by the orbital contribution of the p_z-sub-orbital of the interfacial atoms. Hence, an asymmetric contribution of p_z-up and p_z-down orbitals to the electronic bands of the ferromagnetic conductor at the Fermi level is crucial to induce magnetism in the non-magnetic material. This intriguing observation of an interfacial atomic orbital controlled spin-hybridization proximity effect in vdW materials holds significant promise for providing a new understanding for engineering magnetism in materials for desired applications in spintronic devices. Moreover, the robust spin-splitting and induced half-metallic character in the non-magnetic system under the influence of magnetic proximity in the heterostructure positions this system as a formidable candidate for a spin filter and spin injector for spintronic device applications.

Author contributions

All authors contributed equally to the work.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5nr03862f.

The code of Quantum Espresso used in this work is open source code and publicly available.

Acknowledgements

The authors acknowledge the Indian Institute of Technology, Kharagpur, for providing supercomputing facilities under the National Supercomputing Mission (NSM), Government of India. LG sincerely thanks S. Mohanty and A. K. Singh for productive scientific discussions.

References

1. S. Mashhadi, Y. Kim, J. Kim, D. Weber, T. Taniguchi, K. Watanabe, N. Park, B. Lotsch, J. H. Smet and M. Burghard, et al. , Nano Lett., 2019, 19, 4659–4665.
2. A. J. Lee, A. S. Ahmed, B. A. McCullian, S. Guo, M. Zhu, S. Yu, P. M. Woodward, J. Hwang, P. C. Hammel and F. Yang, Phys. Rev. Lett., 2020, 124, 257202.
3. B. Scharf, G. Xu, A. Matos-Abiague and I. Žutić, Phys. Rev. Lett., 2017, 119, 127403.
4. L. Ciorciaro, M. Kroner, K. Watanabe, T. Taniguchi and A. Imamoglu, Phys. Rev. Lett., 2020, 124, 197401.
5. Q. Chen, J. Liang, B. Fang, Y. Zhu, J. Wang, W. Lv, W. Lv, J. Cai, Z. Huang and Y. Zhai, et al. , Nanoscale, 2021, 13, 14688–14693.
6. Z. Qiao, W. Ren, H. Chen, L. Bellaiche, Z. Zhang, A. H. MacDonald and Q. Niu, Phys. Rev. Lett., 2014, 112, 116404.
7. S. Mohanty, W. Gao and P. Deb, Phys. Rev. B, 2023, 108, 054433.
8. P. Högl, T. Frank, K. Zollner, D. Kochan, M. Gmitra and J. Fabian, Phys. Rev. Lett., 2020, 124, 136403.
9. A. K. Singh, W. Gao and P. Deb, ACS Appl. Mater. Interfaces, 2024, 16, 35438–35446.
10. M. Bora and P. Deb, J. Phys.: Mater., 2021, 4, 034014.
11. M. Bora, S. K. Behera, P. Samal and P. Deb, Phys. Rev. B, 2022, 105, 235422.
12. M. Bora, S. Mohanty, A. Singh, W. Gao and P. Deb, Appl. Surf. Sci., 2023, 623, 157019.
13. D. Rakhmilevitch, S. Sarkar, O. Bitton, L. Kronik and O. Tal, Nano Lett., 2016, 16, 1741–1745.
14. L. Gogoi, W. Gao, P. M. Ajayan and P. Deb, Phys. Chem. Chem. Phys., 2023, 25, 1430–1456.
15. S. K. Behera, M. Bora, S. S. P. Chowdhury and P. Deb, Phys. Chem. Chem. Phys., 2019, 21, 25788–25796.
16. Z. Bian, J. Miao, Y. Zhao and Y. Chai, Acc. Mater. Res., 2022, 3, 1220–1231.
17. W. Zhang, L. Zhang, P. K. J. Wong, J. Yuan, G. Vinai, P. Torelli, G. van der Laan, Y. P. Feng and A. T. Wee, ACS Nano, 2019, 13, 8997–9004.
18. Y.-H. Chan, M. H. Naik, J. B. Haber, J. B. Neaton, S. G. Louie, D. Y. Qiu and F. H. da Jornada, Nano Lett., 2024, 24, 7972–7978.
19. B. Zhou, Z. Li, J. Wang, X. Niu and C. Luan, Nanoscale, 2019, 11, 13567–13575.
20. C. Cardoso, A. T. Costa, A. H. MacDonald and J. Fernández-Rossier, Phys. Rev. B, 2023, 108, 184423.
21. J. Zhang, S. Jia, I. Kholmanov, L. Dong, D. Er, W. Chen, H. Guo, Z. Jin, V. B. Shenoy and L. Shi, et al. , ACS Nano, 2017, 11, 8192–8198.
22. A.-Y. Lu, H. Zhu, J. Xiao, C.-P. Chuu, Y. Han, M.-H. Chiu, C.-C. Cheng, C.-W. Yang, K.-H. Wei and Y. Yang, et al. , Nat. Nanotechnol., 2017, 12, 744–749.
23. X. Wan, E. Chen, J. Yao, M. Gao, X. Miao, S. Wang, Y. Gu, S. Xiao, R. Zhan and K. Chen, et al. , ACS Nano, 2021, 15, 20319–20331.
24. Y. Chen, Y. Liang, L. Wang, M. Guan, Y. Zhu, X. Yue, X. Huang and G. Lu, Nanoscale, 2021, 13, 15151–15176.
25. Q. Zhang, Y. Xiong, Y. Gao, J. Chen, W. Hu and J. Yang, Nano Lett., 2024, 24, 3710–3718.
26. J. Liu and S. T. Pantelides, Phys. Rev. Lett., 2018, 120, 207602.
27. P. L. Tran, N. V. Hieu, Q. N. Cuong and N. N. Hieu, et al. , Nanoscale Adv., 2023, 5, 3104–3113.
28. N. P. Anh, N. Poklonski, V. T. Vi, C. Q. Nguyen and N. N. Hieu, RSC Adv., 2024, 14, 4966–4974.
29. A. Kandemir and H. Sahin, Phys. Rev. B, 2018, 97, 155410.
30. P. Nandi, A. Rawat, R. Ahammed, N. Jena and A. De Sarkar, Nanoscale, 2021, 13, 5460–5478.
31. Y. Chen, Q. Fan, Y. Liu and G. Yao, Phys. Rev. B, 2022, 105, 195410.
32. S. B. Harris, Y.-C. Lin, A. A. Puretzky, L. Liang, O. Dyck, T. Berlijn, G. Eres, C. M. Rouleau, K. Xiao and D. B. Geohegan, ACS Nano, 2023, 17, 2472–2486.
33. Y. Qin, M. Sayyad, A. R.-P. Montblanch, M. S. Feuer, D. Dey, M. Blei, R. Sailus, D. M. Kara, Y. Shen and S. Yang, et al. , Adv. Mater., 2022, 34, 2106222.
34. D. Bezzerga, E.-A. Haidar, C. Stampfl, A. Mir and M. Sahnoun, Nanoscale Adv., 2023, 5, 1425–1432.
35. Z. Gan, I. Paradisanos, A. Estrada-Real, J. Picker, E. Najafidehaghani, F. Davies, C. Neumann, C. Robert, P. Wiecha and K. Watanabe, et al. , Adv. Mater., 2022, 34, 2205226.
36. T. Zhang, A. Krayev, T. H. Yang, N. Mao, L. Hoang, Z. Wang, H. Liu, Y.-R. Peng, Y. Zhu and X. Zheng, et al. , Small, 2025, 21, 2504742.
37. L. Gogoi and P. Deb, Phys. Rev. B, 2024, 109, 174439.
38. Q. Cui, J. Liang, Z. Shao, P. Cui and H. Yang, Phys. Rev. B, 2020, 102, 094425.
39. Q.-Q. Li, W.-W. Liu, Z.-K. Ding, H. Pan, X.-H. Cao, W.-H. Xiao, N.-N. Luo, J. Zeng, L.-M. Tang and B. Li, et al. , Appl. Phys. Lett., 2023, 122, 121902.
40. D. M. Hoat, M. Naseri, R. Ponce-Péreze, N. N. Hieu, J. F. Rivas-Silva, T. V. Vu, H. D. Tong and G. H. Cocoletzi, Mater. Res. Express, 2019, 7, 015013.
41. M. Ernzerhof and G. E. Scuseria, J. Chem. Phys., 1999, 110, 5029–5036.
42. Y. Wang and J. P. Perdew, Phys. Rev. B:Condens. Matter Mater. Phys., 1991, 44, 13298–13307.
43. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni and I. Dabo, et al. , J. Phys.: Condens. Matter, 2009, 21, 395502.
44. P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli and M. Cococcioni, et al. , J. Phys.: Condens. Matter, 2017, 29, 465901.
45. G. Kresse and D. Joubert, Phys. Rev. B:Condens. Matter Mater. Phys., 1999, 59, 1758–1775.
46. S. Grimme, J. Comput. Chem., 2006, 27, 1787–1799.
47. K. Momma and F. Izumi, Appl. Crystallogr., 2011, 44, 1272–1276.
48. R. F. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. Ellis and R. W. Chantrell, J. Phys.: Condens. Matter, 2014, 26, 103202.
49. H. Şahin, S. Cahangirov, M. Topsakal, E. Bekaroglu, E. Akturk, R. T. Senger and S. Ciraci, Phys. Rev. B:Condens. Matter Mater. Phys., 2009, 80, 155453.
50. T.-Y. Lü, X.-X. Liao, H.-Q. Wang and J.-C. Zheng, J. Mater. Chem., 2012, 22, 10062–10068.
51. J. Chen, X. He, B. Sa, J. Zhou, C. Xu, C. Wen and Z. Sun, Nanoscale, 2019, 11, 6431–6444.
52. Q. Alam, S. Sardar, H. Din, S. Khan, M. Idrees, B. Amin, F. Rehman, S. Muhammad and A. Laref, Nanoscale Adv., 2022, 4, 3557–3565.
53. R. O. Aboljadayel, C. J. Kinane, C. A. Vaz, D. M. Love, R. S. Weatherup, P. Braeuninger-Weimer, M.-B. Martin, A. Ionescu, A. J. Caruana and T. R. Charlton, et al. , ACS Appl. Mater. Interfaces, 2023, 15, 22367–22376.
54. T. Koyama, Y. Guan, Y. Hibino, M. Suzuki and D. Chiba, J. Appl. Phys., 2017, 121, 123903.
55. A. Obinata, Y. Hibino, D. Hayakawa, T. Koyama, K. Miwa, S. Ono and D. Chiba, Sci. Rep., 2015, 5, 14303.
56. C. Ederer, M. Komelj, M. Fähnle and G. Schütz, Phys. Rev. B:Condens. Matter Mater. Phys., 2002, 66, 094413.
57. T. Kikkawa, M. Suzuki, J. Okabayashi, K.-I. Uchida, D. Kikuchi, Z. Qiu and E. Saitoh, Phys. Rev. B, 2017, 95, 214416.
58. W. Tang, E. Sanville and G. Henkelman, J. Phys.: Condens. Matter, 2009, 21, 084204.
59. E. Sanville, S. D. Kenny, R. Smith and G. Henkelman, J. Comput. Chem., 2007, 28, 899–908.
60. G. Henkelman, A. Arnaldsson and H. Jónsson, Comput. Mater. Sci., 2006, 36, 354–360.
61. M. Yu and D. R. Trinkle, J. Chem. Phys., 2011, 134, 064111.

---