Tuning of spin-transfer torque in VSe₂-based vdW magnetic tunnel junctions by electrode polytypes

Abstract

Inspired by the promising properties of monolayer 1T-VSe₂, known for its ferromagnetic ordering and room-temperature Curie point, we developed a 2D van der Waals heterostructure featuring 1T-VSe₂ as the ferromagnetic layer, non-magnetic semi-infinite 1T- and 2H-TaS₂ electrodes, and 2H-MoS₂ as the tunneling barrier. Employing ab initio quantum transport simulations within the nonequilibrium Green’s function framework, we explored the impact of TaS₂ electrode polytypes on the device’s quantum transport properties. Devices with 1T-TaS₂ electrodes exhibit higher spin-dependent transmission compared to 2H-TaS₂. Incorporating 2H-MoS₂ enhances anisotropic tunnel magnetoresistance, reaching 168% for the 1T-device and 1419% for the 2H-device, peaking when 1T-VSe₂ magnetizations are antiparallel. Spin-transfer torque magnitude is highest at 90° and decreases towards 180°. 1T-device shows superior performance with lower Gilbert damping, and reduced critical current density and voltage for magnetization switching, compared to the 2H-device, which requires significantly higher current and voltage. These findings underscore the potential of 1T-VSe₂-based heterostructures in spintronics.

Introduction

Magnetic tunnel junctions (MTJs)¹ are critical components in the development of nonvolatile magnetic random access memories (MRAMs), featuring prominently in both research and application contexts^2,3. These junctions consist of two ferromagnetic (FM) layers, traditionally metallic, separated by a thin insulating barrier. The operation of MTJ hinges on the tunnel magnetoresistance (TMR) effect⁴, where a significant change in tunneling resistance occurs depending on the magnetic alignment—parallel or antiparallel—of the FM layers. One of these layers acts as a free layer, which is capable of storing information through its spins. At the same time, the other serves as a reference layer that provides a stable magnetic orientation for reading data from the free layer⁵. Traditional MTJ technologies, such as toggle-MRAM, rely on external magnetic fields for magnetization switching, a method increasingly challenged by issues such as field nonlocality and the growing critical fields required as devices are miniaturized. Recent advancements have seen the introduction of electrically driven alternatives, such as spin-transfer torque (STT) and spin-orbit torque, improving device integration and control^6,7.

Moreover, the discovery of magnetism in van der Waals (vdW) materials has paved the way for transformative advances in MTJ technology, suggesting avenues for significantly enhanced performance and novel applications in spintronics^8,9. Notably, the emergence of intrinsic two-dimensional (2D) ferromagnetism in materials such as CrBr₃¹⁰, CrI₃^10,11, Fe₃GeTe₂^12,13,14, CrPS₄¹⁵, Cr₂Ge₂Te₆¹⁶, and VSe₂^17,18 provides an exceptional platform for developing spintronic applications. In a recent publication, we have demonstrated efficient spin-dependent transmission and a high TMR value of 487% at low bias in Fe₄GeTe₂/GaTe/Fe₄GeTe₂ vdW heterostructures sandwiched between PtTe₂ electrodes¹⁹. In another study, Fe₃GeTe₂/InSe/Fe₃GeTe₂ MTJs exhibited a TMR of 41% at 10 K²⁰, while Fe₃GeTe₂/hBN/Fe₃GeTe₂ MTJs reach even higher TMR values of up to 300% at 4.2 K²¹. However, the TMR declines rapidly as the temperature approaches the Curie temperature (T_C) of Fe₃GeTe₂, vanishing near T_C, which is ~220 K in bulk form and around 130 K in monolayers^21,22. A substantial TMR of 85% has also been observed at room temperature (300 K) in a vdW MTJ featuring a thin WSe₂ semiconductor spacer layer (<10 nm) sandwiched between two Fe₃GaTe₂ electrodes. This TMR increases significantly as the temperature decreases, reaching up to 164% at 10 K²³. Strain engineering has also proven effective for controlling spintronic properties, as demonstrated in CrI₃/MnGeX₃ (X = Se, Te) heterostructures. Applying a 6% compressive strain in CrI₃/MnGeSe₃ expands the half-metallic band gap by 25% and boosts the TMR by 220%, indicating improved spin-polarized transport²⁴. Additionally, theoretical studies on vdW MTJs based on VSe₂/MoS₂ heterojunctions highlight their potential for spintronic applications, with VSe₂ acting as a ferromagnet exhibiting room-temperature ferromagnetism. These systems demonstrate a remarkable TMR of 846% at 300 K, clearly differentiating between parallel and antiparallel magnetic states²⁵. Moreover, intrinsic room-temperature ferromagnetic half-metals like 1T-MnSe₂, which offer 100% spin-polarized carriers, have garnered significant attention. A proposed 1T-MnSe₂/h-BN/1T-MnSe₂ MTJ structure achieves magnetization reversal in the central MnSe₂ layer via electric-field control, while maintaining antiparallel alignment in the outer layers, with theoretical TMR ratios reaching up to 2.56 × 10³%²⁶. Recent advancements have also explored sliding magnetic ferroelectric tunnel junctions (MFTJs) such as Au/CrI₃/bilayer h-BN/CrI₃-MnBi₂Te₄/Au. These devices allow control of four nonvolatile resistance states through electrical voltage and current, arising from the interplay between polarization orientations in h-BN and magnetization alignments in CrI₃. The MFTJs exhibit a giant TMR of up to 10,000% (2,000% with spin-orbit coupling) and a tunnel electroresistance of around 70%, demonstrating their potential for multifunctional spintronics devices²⁷.

For the next iteration of STT MRAM, an optimal high-performance MTJ must encompass several essential attributes, including a high T_C, robust TMR, efficient STT transfer, and a minimal critical switching current^28,29. While various strategies like proximity coupling³⁰, atomic ratio control³¹, and interfacial exchange coupling³² have been employed to enhance the T_C of materials, these methods often struggle to sufficiently boost magnetism for applications at room temperature due to the inherently lower T_C of some materials. In contrast, monolayer VSe₂ distinguishes itself with robust intrinsic ferromagnetism effective at room temperatures, offering significant advantages for practical use³³. Demonstrated through magneto-optical measurements, monolayer VSe₂, when synthesized via molecular beam epitaxy, exhibits FM properties at room temperature, which markedly contrasts with the paramagnetic nature of its bulk form¹⁷. Additionally, monolayer VSe₂ can be produced on a large scale through chemical exfoliation from the bulk material. With a Curie temperature exceeding room temperature (around 330 K) and a scalable production method, monolayer VSe₂ emerges as an exceptionally promising candidate for spintronic devices, outperforming alternatives in terms of the viability of operational temperatures. Recent advances in exfoliation methods have further improved the consistency with which monolayer VSe₂ can be isolated from its bulk crystal³³.

Here, we investigate the spin-polarized transport properties of VSe₂-based vdW MTJs using ab initio quantum transport simulations. These simulations incorporate non-collinear spin configurations and leverage the nonequilibrium Green’s function (NEGF) approach providing a reliable way to study ballistic transmission through ultrathin magnetic films^{25,27,34,35,36,37,38,39,40,41,42}. The MTJ heterostructure examined includes a ferromagnetic VSe₂ layer as the scattering region, which is placed between bulk TaS₂ leads that serve as the non-magnetic electrodes. Specifically, we have studied the effects of different structural polytypes of the electrode on spin-dependent transport. For studying anisotropic TMR, a monolayer of MoS₂ is employed as the tunneling barrier within the MTJ setup.

Results and discussion

Characterization of TaS₂/1T-VSe₂/TaS₂ heterostructures

Transition metal dichalcogenides (TMDs), such as TaS₂, are noted for their unique structural and electronic properties across two primary phases: the trigonal prismatic (2H) and the octahedral (1T) phases. These phases are differentiated by the coordination environment of the transition metal atoms. In addition to production techniques, controlling the structural phases of layered materials such as TaS₂ is crucial for tailoring their electronic and magnetic properties. For example, phase transformations in transition-metal dichalcogenides can be achieved through thermal annealing. Previous studies have shown that annealing VSe₂ at ~650 K induces a transition to the 2H phase in ultrathin samples due to its lower free energy. Given the similarities between VSe₂ and TaS₂, similar approaches, such as precise temperature regulation and controlled annealing environments, can likely facilitate phase transitions between the 1T and 2H phases in TaS₂. Such phase control methods could open new possibilities for optimizing TaS₂ for specific functionalities in spintronic and electronic devices⁴³. Typically, TMDs in the 2H phase display semiconducting properties, whereas the 1T phase is generally metallic. However, TaS₂ is an exception, exhibiting metallic behavior in both the 2H and 1T phases. The atomic structures of TaS₂ are depicted in Fig. 1, showing both (a) 1T and (b) 2H phases which crystallize into the ${D}_{3d}^{3}$ (P3m1) and ${D}_{6h}^{4}$ (P6₃/mmc) space groups, respectively. In both phases, each Ta atom is surrounded by six Sulfur (S) atoms arranged in either 1T or 2H configuration. The lattice parameters for the 1T-TaS₂ phase are a = 3.38 Å, and c = 6.17 Å. These phases consist of triple layers (S-Ta-S), where a sheet of Ta is sandwiched between two layers of S atoms in an octahedral coordination. The AA stacking configuration, noted for its stability, is typically used as electrodes in experimental setups. Conversely, 2H-TaS₂ features a trigonal prismatic coordination of Ta by S atoms. This phase commonly exhibits AB stacking of two layers along the c-axis per unit cell in hexagonal symmetry, with lattice parameters a = 3.35 Å, and c = 12.55 Å.

Fig. 1: Atomic and electronic structures of bulk 1T-TaS₂, 2H-TaS₂, and 1T-VSe₂.

a Atomic structure of bulk 1T-TaS₂, depicting the octahedral coordination of tantalum (blue spheres) by sulfur (yellow spheres) atoms. b Atomic structure of bulk 2H-TaS₂, illustrating the prismatic coordination of tantalum atoms by sulfur atoms in the 2H polytype. c Atomic structure of bulk 1T-VSe₂, showing the octahedral coordination of vanadium (red spheres) by selenium (green spheres) atoms. d Electronic band structure and orbital-projected density of states (DOS) for bulk 1T-TaS₂, highlighting dominant contributions from tantalum d-orbitals (red line) and sulfur p-orbitals (cyan line) near the Fermi energy. e Electronic band structure and orbital-projected DOS for bulk 2H-TaS₂, showing similar contributions from tantalum d-orbitals (red line) and sulfur p-orbitals (cyan line). f Spin-resolved electronic band structure and orbital-projected DOS for bulk 1T-VSe₂, emphasizing contributions from vanadium d-orbitals and selenium p-orbitals. Spin-orbit coupling effects are excluded in these calculations.

The electronic band structures and density of states (DOS) for bulk TaS₂ in both the 1T and 2H phases, depicted in Fig. 1d and e, respectively, reveal significant contributions from p and d orbitals around the Fermi level, suggesting metallic behavior in both phases, but with different characteristics. The disparity in electronic behaviors between the 1T and 2H phases of TaS₂ is evident in the energy range between 1.2 eV and 2 eV. Figure 1d shows bands for 1T-TaS₂, whereas Fig. 1e shows no bands for 2H-TaS₂ in this energy range. Additionally, in the out-of-plane properties along the Γ − A direction, the 2H phase lacks bands around the Fermi level, while the 1T phase exhibits bands from both d and p orbitals near the Fermi level. These differences in electronic structure lead to distinct transport properties for the two phases. Supplementary Fig. 1 illustrates the varying transmission coefficients for bulk 1T-TaS₂ and 2H-TaS₂. Specifically, 2H-TaS₂ exhibits zero transmission at the energy level around 2 eV due to the absence of electronic states at this energy level, as shown in Fig. 1e.

In this work, the 1T-phase of VSe₂ is integrated as the scattering region, a central element for investigating spin-polarized transport phenomena. The structural arrangement of this phase is depicted in Fig. 1c. The lattice constants for bulk VSe₂ are determined to be a = 3.43 Å, for the in-plane axis and c = 6.35 Å, for the out-of-plane axis. When the material is thinned to a monolayer, there is a noticeable reduction in the lattice constants, with the in-plane axis decreasing to 3.37 Å. This reduction is primarily due to the weakening of interlayer interactions as the material transitions to a single layer, which leads to structural relaxation, rather than being caused by large externally applied strain. This behavior has been observed across various transition-metal dichalcogenides. For example, in MoS₂, the lattice parameter a decreases from 3.17 Å in the bulk to 3.15 Å in the monolayer⁴⁴, and similarly, our findings show that VSe₂ shifts from 3.43 Å in the bulk to 3.37 Å in the monolayer. This dimensional adjustment ensures that the monolayer lattice parameters align closely with those of the TaS₂ electrodes used in the system, enhancing structural coherence. In this configuration, the VSe₂ layer undergoes minimal tensile strains of 0.23% and 0.39% when incorporated into the 1T and 2H devices, respectively. In the 1T device configuration, the separation between the Se atoms on the VSe₂ surface and the outer layer of TaS₂ in the left electrode is ~3.57 Å, while the distance to the outer layer of TaS₂ in the right electrode is slightly shorter, at around 3.51 Å. In contrast, in the 2H device configuration, due to the inherent symmetry of the 2H structure, the distance between the Se atoms on the VSe₂ surface and the S atoms on the outer layer of TaS₂ is uniform across both the left and right electrodes, measuring 3.38 Å, as shown in Fig. 2. Such alignment is likely to benefit the interface quality and thus the spin-polarized transport within the heterostructure.

Fig. 2: Atomic structure and local density of states in TaS₂/1T-VSe₂/TaS₂ heterostructures.

a, b Atomic structures of the TaS₂/1T-VSe₂/TaS₂ heterostructure with (a) 1T-TaS₂ and (b) 2H-TaS₂ electrodes. In the 1T configuration, the interlayer distances between the VSe₂ layer and the TaS₂ electrodes are 3.57 Å on the 1T-TaS₂ side and 3.51 Å on the VSe₂ side, whereas in the 2H configuration, both interfaces have a uniform distance of 3.38 Å. c, d Depict the local density of states (LDOS) at the Fermi level for the TaS₂ and VSe₂ layers for the (c) 1T and (d) 2H configurations. The spin-resolved LDOS (blue for spin-up and red for spin-down) highlights the electronic contributions from each layer. The shaded region in (c, d) corresponds to the LDOS of the 1T-VSe₂ layer, emphasizing its contribution to the heterostructure’s electronic properties.

Figure 1f presents the spin-resolved electronic band structure and orbital projected density of states of VSe₂, elucidating its metallic characteristics. The band structure, plotted over in-plane high-symmetry points in the Brillouin zone (Γ − M − K − Γ), exhibits crossings of both spin-up and spin-down bands at the Fermi level, confirming the material’s metallic behavior in these directions. In contrast, the out-of-plane band structure along the Γ − A direction specifically showcases that only spin-up bands cut the Fermi level, indicating a pronounced metallic phase for spin-up channels along this axis. The complex band structures of bulk 1T-VSe₂ are illustrated in Supplementary Fig. 4, showcasing the (a) spin-up and (b) spin-down channels along the out-of-plane Γ − A direction of the first Brillouin zone. In Supplementary Fig. 4a, the spin-up channel displays bands crossing the Fermi level, indicating metallic behavior and active electron transport in the real part of the band structure, alongside observable evanescent or decaying states in the imaginary part. In contrast, Supplementary Fig. 4b shows that the spin-down channel lacks any bands crossing the Fermi level in the real part, suggesting non-metallic behavior and dependence on evanescent states for electron dynamics in this channel. The d − orbital projected band structure in Supplementary Fig. 2 reveals that the out-of-plane bands of the spin-up channel at the channel at ${{\mathcal{E}}}_{F}$ originate from the ${d}_{{z}^{2}}$ orbitals. As a result, only the majority of Bloch states, arising from the inter-layer hybridization of the ${d}_{{z}^{2}}$ orbitals, can conduct current in the perpendicular direction. This selective conduction mechanism leads to perfect spin polarization in the linear response regime, where the material’s response to external perturbations, such as electric fields, results in a purely spin-polarized current. This characteristic feature significantly enhances the spintronic properties of the material, making it highly suitable for applications where spin filtering and magnetic manipulation are crucial. Notably, the orbital-resolved DOS analysis in the right panel of Fig. 1f reveals that the states near the Fermi level are predominantly derived from the d − orbitals. This d − orbital contribution is crucial as it suggests strong electron correlation effects and significant contributions to the material’s magnetic and electronic properties. Furthermore, the DOS panel illustrates that the contribution of the d − orbital is greater in the spin-up channel compared to the spin-down channel, suggesting a higher degree of d-p hybridization states within the spin-up channel.

The atomic arrangements of the device configuration of TaS₂/VSe₂/TaS₂ heterostructures are shown in Fig. 2, where (a) 1T-TaS₂ and (b) 2H-TaS₂ layers sandwich a central monolayer VSe₂. To ensure physical accuracy while maintaining computational feasibility, we conducted convergence tests with varying numbers of TaS₂ layers on each side of the scattering region, incorporating semi-infinite leads in the transport direction. These tests showed that the transmission coefficient at the Fermi level converges with six layers of TaS₂, with no significant changes in key transport properties observed when additional layers are included. The local density of states (LDOS), which shows the number of available electronic states at a specific energy level within a certain volume of the material, is illustrated along the z-axis of the heterostructure (transport direction) within the energy range from -5 eV to 5 eV in Fig. 2c and d for the 1T- and 2H-phases, respectively. The periodic peaks in the LDOS signify that the electronic states are strongly influenced by the interfaces between different layers and reflect the layered composition of the heterostructure, where each peak corresponds to the position of an atomic layer, highlighting the modulation of electronic states by the periodic potential of the layers. In the 1T-device, Fig. 2c, the LDOS of the 1T-TaS₂ layers in the left electrode and the same position in the right electrode exhibit noticeable asymmetry. The observed asymmetry arises from the non-uniform distance between the Se atoms on the VSe₂ surface and the S atoms on the outer layer of TaS₂ in the left and right electrodes, as previously discussed. This variation in spacing directly influences the electronic properties at the interface, leading to differences in the LDOS between the two electrodes. The lack of symmetry in the LDOS indicates that the electronic properties of the 1T-TaS₂ layers are differently affected by their proximity to the VSe₂ layer on each side. This uneven interaction between the 1T-TaS₂ and VSe₂ layers could have significant implications for the overall electronic transport. In contrast, Fig. 2d for the 2H-device shows symmetry in the LDOS, with the central part of this symmetry being the VSe₂ layer. This indicates that the TaS₂ layers exhibit similar LDOS at corresponding positions on the left and right sides of the VSe₂. The symmetric LDOS profiles suggest a more uniform interaction between the 2H-TaS₂ layers and the VSe₂ layer, leading to consistent electronic properties across the heterostructure. Therefore, it is expected that changing the phase of the electrode can tune the transport properties of the scattering path as it affects its electronic properties. At the interface, the close proximity of Ta atoms in 2H-TaS₂ and Se atoms in VSe₂ creates strong orbital hybridization. This interaction redistributes the electronic states, reducing the spin polarization transferred to the first 2H-TaS₂ layer adjacent to VSe₂. However, the 2H-TaS₂ layers farther from the interface experience weaker hybridization effects, allowing the spin-polarized states originating from VSe₂ to propagate more effectively. Consequently, the LDOS of 2H-TaS₂ layers farther from VSe₂ exhibits stronger spin polarization, underscoring the localized nature of hybridization at the interface and the gradual attenuation of its influence with increasing distance. Furthermore, in Fig. 2c, the LDOS for the 1T-TaS₂ electrodes exhibits double sharp peaks. This characteristic is attributed to the inherent asymmetry in the crystal structure of the 1T phase. On the other hand, Fig. 2d shows the LDOS for the 2H-TaS₂ electrodes, where only a single sharp peak is observed due to the inherent symmetry of the 2H phase. The asymmetry in 1T-TaS₂ breaks inversion symmetry along the stacking direction, causing a splitting of electronic states into two closely spaced maxima within each LDOS peak. Conversely, the symmetric 2H-TaS₂ phase preserves state degeneracy, resulting in a single dominant LDOS peak. From a device perspective, the split peaks in 1T-TaS₂ broaden the tunneling energy range, increasing sensitivity to interface conditions and potentially enhancing tunneling probability. In comparison, the single-peak LDOS of 2H-TaS₂ provides more uniform electronic properties, leading to stable and consistent tunneling behavior. Although the VSe₂ layer consistently adopts the 1T crystal structure, the phase of the TaS₂ electrodes (1T or 2H) critically affects the electronic environment at the interfaces and the spin-dependent properties of VSe₂. Local symmetry and orbital hybridization at the interfaces directly influence spin-up and spin-down electron occupancy. Switching from 1T to 2H electrodes modifies the potential landscape, crystal field splittings, and degeneracy of the V d-orbitals, thereby controlling the dominant spin channel and whether the LDOS peak remains intact or splits. In the 1T-TaS₂ configuration in Fig. 2c, asymmetry arises due to unequal spacing between the Se atoms of VSe₂ and the S atoms of TaS₂ on opposite sides of the monolayer. This uneven interface effectively breaks inversion symmetry for VSe₂, modifying orbital hybridization and lifting certain degeneracies of the V d-states. Consequently, spin-up states are shifted closer to the Fermi level, resulting in a pronounced spin-up LDOS. This asymmetry also splits the primary LDOS peak of VSe₂ into two closely spaced maxima, reflecting subtle variations in local bonding environments on either side of the monolayer. In contrast, with 2H-TaS₂ electrodes in Fig. 2d, the interfacial spacing and bonding angles around VSe₂ are more uniform, preserving a higher degree of symmetry for the VSe₂ layer. As a result, the orbital hybridizations that favor spin-up in the 1T configuration are no longer dominant. Instead, spin-down states are lowered relative to spin-up states, leading to a higher spin-down LDOS at the Fermi level. The more balanced interface also maintains near-degeneracy of these electronic states, resulting in a single main LDOS peak for VSe₂ rather than a split peak.

Moreover, Fig. 3 displays the orbital-projected LDOS for the TaS₂/VSe₂/TaS₂ heterostructure, featuring configurations with electrodes in the (a) 1T and (b) 2H phases. The figure is structured in three panels for each configuration: the left panel illustrates the LDOS for the second TaS₂ layer interfacing with VSe₂; the middle panel focuses on the LDOS for the TaS₂ electrode layer directly interfacing with VSe₂; and the right panel presents the LDOS within the VSe₂ layer itself. The LDOS plots of the electrodes reveal a mirror-like density of states, with minor discrepancies in the total density of states for spin-up and spin-down channels in both the 1T and 2H phases. These differences indicate the presence of spin-polarized states when the 1T or 2H polytype of TaS₂ is interfaced with a monolayer of VSe₂. In both the 1T and 2H phases, changes are observed in the LDOS of the TaS₂ layers directly interfacing with VSe₂ and the second TaS₂ layers compared to the DOS of 1T- and 2H-TaS₂, shown in Fig. 1d and e, respectively. Especially, at an energy level far from the Fermi level indicating enhanced electronic interactions and hybridization effects due to the proximity to VSe₂. A comparative examination of the LDOS in VSe₂ placed in the 1T and 2H devices, shown in Fig. 3a and b, respectively, with the DOS of a freestanding monolayer VSe₂ in Supplementary Fig. 3, reveals that the behavior around the Fermi level is consistently similar in both devices. This indicates stable electronic characteristics across different phase states of the electrodes, variations are observable in regions far from the Fermi level. These differences highlight how the electronic states at the interface are subtly influenced by the crystalline phase of the electrodes but remain largely unperturbed at the Fermi level. This implies that while the interface effects are present, they do not significantly disrupt the intrinsic electronic properties of the VSe₂ layer.

Fig. 3: Orbital-projected local density of states (LDOS) in TaS₂/1T-VSe₂/TaS₂ heterostructures with semi-infinite 1T- and 2H-TaS₂ electrodes.

Orbital-projected LDOS of the TaS₂/1T-VSe₂/TaS₂ heterostructures with (a) 1T-TaS₂ and (b) 2H-TaS₂ electrodes. The LDOS contributions are resolved into s-, p-, and d-orbitals for spin-up (solid lines) and spin-down (dashed lines). In (a) the left subpanel shows the LDOS of the second 1T-TaS₂ layer within the electrode, the middle subpanel represents the LDOS of the 1T-TaS₂ layer directly interfacing with the 1T-VSe₂ layer, and the right subpanel corresponds to the LDOS of the 1T-VSe₂ layer. b Presents the same arrangement for the 2H-TaS₂ electrodes. The spin- and orbital-resolved LDOS highlights the distinct electronic contributions from the individual layers and their coupling within the heterostructure.

Table 1 provides a comparative analysis of the atom-projected spin magnetic moments in units of Bohr magnetons (μ_B) for both monolayer and bilayer configurations of freestanding VSe₂ and when integrated within device structures with TaS₂ layers. The table illustrates the effects of physical form (monolayer vs. bilayer) and integration into device settings with varying phase configurations of TaS₂ electrodes on the spin magnetic moments of VSe₂. In both configurations, freestanding VSe₂ exhibits higher values of the magnetic moment compared to when it is integrated into device configurations. This is consistent with the results showing that monolayer 1T-VSe₂ exhibits a higher magnetic moment compared to its bulk counterpart¹⁷. The magnetic moment of a V atom in a monolayer is obtained as 1.06 μ_B, which is in good agreement with previous studies^45,46,47. In its freestanding form, the total spin magnetic moment for the monolayer VSe₂ is 0.82 μ_B. This value decreases to 0.7 μ_B in a 1T-device configuration and further reduces to 0.6 μ_B in a 2H-device configuration, highlighting a significant reduction in the magnetic moment when VSe₂ is sandwiched between TaS₂ layers, particularly in the 2H configuration. Conversely, the freestanding bilayer VSe₂ exhibits a considerably higher total magnetic moment of 1.96 μ_B. When part of a 1T-device, this value drops to 1.59 μ_B and further to 1.32 μ_B in the 2H-device configuration, mirroring the trend observed in the monolayer setup. These changes underscore a substantial decrease in the total magnetic moment when transitioning from a freestanding state to a device configuration, with pronounced reductions in the 2H-device setup for both monolayer and bilayer forms. This trend suggests that the electronic environment, possibly influenced by strain or interactions with TaS₂, significantly affects the magnetic properties of VSe₂. Moreover, in all cases where VSe₂ is placed between the electrodes, the S and Ta atoms in the interfacing layers of the left and right electrodes exhibit slight polarization, with spin magnetic moments around 0.003 μ_B for these atoms. This indicates that interface effects and interactions with the TaS₂ layers have a subtle but measurable impact on the magnetic properties of the interfacing atoms. The observed polarization is primarily attributed to charge transfer and orbital hybridization at the VSe₂/TaS₂ interface. The orbital-projected LDOS in Fig. 3 reveals that Ta d-orbitals and V d-orbitals couple near the Fermi level, leading to a redistribution of electron density. Although the overall LDOS profile at the interfaces, as shown in Fig. 3, remains dominated by d-states and does not undergo significant changes, this localized charge transfer induces dipoles, explaining the observed polarization without requiring large-scale structural distortions or significant strain.

Table 1 Comparison of atom-projected spin magnetic moments in freestanding and sandwiched 1T-VSe₂ configurations

Magneto-crystalline anisotropy energy (MAE) quantifies the energy differential required to reorient the magnetization of a crystal from its optimal direction to other orientations, marking a fundamental characteristic of ferromagnetic materials. MAE reflects how magnetic energy varies with direction within a crystal, which is vital for determining the magnetization’s stability and orientation. This directional dependency originates from the interaction between the crystal’s lattice structure and the electron spins, mediated by spin-orbit coupling, which significantly affects the material’s magnetic properties for applications like data storage and spintronics. Unlike variations in magnetic moments, which stem from differences in electron counts across spin states, MAE is primarily influenced by SOC effects. These effects are tied to the orbital characteristics of electrons across both filled and unfilled states, establishing the preferred direction of magnetization linked to angular momentum dynamics. The energy difference associated with MAE, denoted as ${{\mathcal{E}}}_{MAE}$, is calculated using the force theorem, which facilitates the computation by considering the difference in total electronic energies for different magnetization directions without full self-consistent field recalculations. The formula to calculate MAE is given by^48,49,50: ${{\mathcal{E}}}_{MAE}={\mathcal{E}}({\theta }_{1},{\phi }_{1})-{\mathcal{E}}({\theta }_{0},{\phi }_{0})$. Here, ${\mathcal{E}}({\theta }_{1},{\phi }_{1})$ and ${\mathcal{E}}({\theta }_{0},{\phi }_{0})$ are the electronic energies when the magnetization is aligned along specific angles θ and ϕ. These angles, with θ as the polar and ϕ as the azimuthal angle, determine the spin’s orientation in relation to a typical reference, often the material’s easy axis. Positive values of ${{\mathcal{E}}}_{MAE}$ indicate uniaxial anisotropy, supporting a singular easy axis, whereas negative values suggest planar anisotropy, where the easy axis extends across a plane. For the ferromagnetic ground state of VSe₂, the ${{\mathcal{E}}}_{MAE}$ is found to be in-plane. In the monolayer structure, ${{\mathcal{E}}}_{MAE}$ values are -0.19 meV and -0.04 meV for V and Se atoms, respectively, aligning with recent research⁵¹.

Collinear spin scattering and filtering through VSe₂

Figure 4 presents the transmission spectra of (a, c) monolayer and (b, d) bilayer VSe₂ sandwiched between two TaS₂ electrodes, with the electrodes in (a, b) 1T and (c, d) 2H phases under zero bias voltage, respectively. The results indicate ballistic transport near the Fermi level, showcasing distinct spin polarization across all configurations. The pronounced difference in transmission characteristics between the two spin channels strongly underscores the presence of spin-polarized transport properties in these VSe₂-based device configurations, originating from the distinct phases of the spin-up and spin-down channels along the transport direction (Γ − A), as depicted in Fig. 1f. Specifically, the upper panels reveal that in devices with 1T phase electrodes, Fig. 4a the transmission coefficient for the spin-up channel in monolayer VSe₂ configurations is higher, whereas in the bilayer VSe₂ configuration in Fig. 4b, the spin-down channel exhibits a broad transmission peak surpassing that of the spin-up channel. Conversely, the lower panels demonstrate that in devices with 2H phase electrodes, the transmission coefficient for the spin-up channel consistently remains higher than that for the spin-down channel in both Fig. 4c monolayer and Fig. 4d bilayer VSe₂ configurations at this energy level. The observed differences in the transmission coefficients for the spin-up and spin-down channels in the bilayer VSe₂ setups at the Fermi level are further corroborated by the LDOS as depicted in Supplementary Fig. 5. Specifically, the electronic states of the spin-down channel in Supplementary Fig. 5b for the bilayer VSe₂ configuration, when sandwiched between two 1T-TaS₂ electrodes, exhibit higher LDOS at the Fermi level compared to the spin-up channel. This enhancement in LDOS likely contributes to the higher transmission coefficient observed for the spin-down channel. Conversely, in the bilayer VSe₂ configurations within 2H-phase devices [as shown in Supplementary Fig. 5c], the spin-up channel demonstrates a higher LDOS at the Fermi level compared to the spin-down channel, resulting in a lower transmission coefficient for the spin-down channel at this energy level. However, analysis of the data in Fig. 3 indicates that the LDOS for both devices with monolayer VSe₂ placed between semi-infinite TaS₂ electrodes, whether equipped with 1T- or 2H-phase electrodes, displays slightly higher values for the spin-up channel at the Fermi level compared to the spin-down channel.

Fig. 4: Spin-resolved zero-bias transmission in monolayer and bilayer 1T-VSe₂ devices with semi-infinite 1T- and 2H-TaS₂ electrodes.

Zero-bias transmission spectra for VSe₂ sandwiched between semi-infinite TaS₂ electrodes in (a, b) the 1T phase and (c, d) the 2H phase. a, c Depict the transmission for monolayer VSe₂, while (b, d) show the transmission for bilayer VSe₂. The transmission spectra are resolved for spin-up (T^↑, blue lines) and spin-down (T^↓, red lines) channels. The energy (${\mathcal{E}}$) is measured relative to the Fermi level (${{\mathcal{E}}}_{F}=0$), indicated by the dashed vertical line. The effects of spin-orbit coupling are excluded in these calculations to focus on the intrinsic electronic transmission properties.

Moreover, Fig. 5 demonstrates spin-dependent k_∥-resolved transmission coefficients for VSe₂ sandwiched between TaS₂ electrodes at the Fermi level. Figure 5a, b illustrate the transmission for a monolayer VSe₂ in a 1T-phase TaS₂ device, specifically for spin-up and spin-down electrons, respectively. Figure 5e and f display analogous data for the monolayer VSe₂ within a 2H-phase TaS₂ device. For bilayer VSe₂, Fig. 5c and d show the transmission in a 1T-phase TaS₂ device for spin-up and spin-down electrons, respectively, while Fig. 5g and h provide the corresponding data for a 2H-phase TaS₂ device. These transmission patterns align with those observed in the bulk 1T-phase and 2H-phase TaS₂, as shown in Supplementary Fig. 1b and Supplementary Fig. 1c, respectively. The high-transmission regions in the 1T-phase and 2H-devices indicate effective electron pathways. Bilayer VSe₂ configurations (Fig. 5c and d for 1T, Fig. 5g and h for 2H) show a notable reduction in transmission, with isolated peaks suggesting that bilayer structures impede electron mobility more than their monolayer counterparts (panels a and b for 1T, e and f for 2H). Additionally, the overall transmission is generally lower in the 2H-phase for both monolayer and bilayer configurations (panels e, f, g, and h), highlighting the phase-dependent influence on electron transport dynamics. The transmission for spin-up electrons (panels a, c, e, and g) generally shows different patterns compared to spin-down electrons (panels b, d, f, and h), highlighting the spin-dependent nature of the transmission. Notably, the bilayer configurations display transmission predominantly for one spin channel, underscoring the selective spin filtering effect of the bilayer structure. This selective transmission effect, combined with the overall reduced transmission in the 2H-phase, underscores the critical role of both phase and layering in tuning the electronic transport properties of VSe₂ when integrated into TaS₂ devices.

Fig. 5: Spin-dependent k_∥-resolved transmission for monolayer and bilayer 1T-VSe₂ in devices with semi-infinite 1T- and 2H-TaS₂ electrodes.

Spin-dependent k_∥-resolved transmission coefficients for VSe₂ sandwiched between TaS₂ electrodes at the Fermi level. a, b Show the transmission for a monolayer VSe₂ in a 1T-phase TaS₂ device for spin-up and spin-down electrons, respectively. c, d Depict the transmission for a bilayer VSe₂ in a 1T-phase TaS₂ device for spin-up and spin-down channels, respectively. e, f Present the corresponding transmission for a monolayer VSe₂ in a 2H-phase TaS₂ device, while (g, h) show the transmission for a bilayer VSe₂ in a 2H-phase TaS₂ device. The color scale indicates the transmission coefficient. Here, the effects of spin-orbit coupling are excluded.

Another factor contributing to the differing transmission coefficients between the 1T- and 2H-device configurations stems from the distinct values of the chemical potentials in the leads of these setups. At zero bias, the chemical potential directly sets the Fermi level, which is crucial for the transmission coefficient. In a quantum transport setup with no applied bias, the chemical potentials of the two leads must be equal, ensuring their Fermi levels align. The transmission coefficient is highly sensitive to the alignment of the Fermi level with the available electronic states in both the leads and the central region. The chemical potential sets the energy window within which electrons are available for transport. If this energy window aligns with high-density states in the scattering region or with resonant energy levels, the transmission probability increases as more states become available for electron conduction. In these devices, the chemical potential of the leads in the 1T-device is measured at -5.29 eV, while in the 2H-device, it is at -6.03 eV. Consequently, with the same scattering region, different transport properties are expected due to these variations in chemical potential. The 1T-setup, having a higher chemical potential of -5.29 eV, is positioned closer to the Fermi level. This proximity allows it to access a broader range of conduction states above it, increasing the availability of states for conduction. Such alignment might boost the transmission coefficient, especially if it coincides with resonant states or high-density states near the Fermi level. On the other hand, the 2H-setup, with its chemical potential further down at -6.03 eV, may find its access limited to the higher energy conduction states necessary for enhanced transport. Electrons in these leads have lower energy, potentially diminishing their interaction with conduction states in the scattering region, unless there are suitable states reachable below this energy level.

Tunneling magnetoresistance in non-collinear magnetic tunnel junctions

In the context of MTJs, we have introduced the 2H phase of molybdenum disulfide (MoS₂) as a tunneling barrier, sandwiched between two VSe₂ ferromagnets that are connected to TaS₂ leads. This configuration leverages MoS₂’s semiconducting properties to enhance tunneling efficiency and device performance. MoS₂ also belongs to the family of TMDCs, notable for their unique structural and electronic properties⁵². In its monolayer form, each molybdenum (Mo) atom is covalently bonded to six surrounding S atoms in a trigonal prismatic configuration, forming a two-dimensional hexagonal pattern akin to that of graphene. Both the top and side views of the atomic structure of freestanding monolayer 2H-MoS₂ are shown in Fig. 6a, highlighting its layered and hexagonal atomic arrangement. The unit cell of monolayer MoS₂ is comprised of three atoms (one Mo and two S atoms), arranged in a rhombic lattice that defines its two-dimensional character. Our calculated lattice parameter for a single layer of MoS₂ is ~3.19 Å, closely matching that of VSe₂ and TaS₂. When a monolayer of 2H-MoS₂ is integrated into the TaS₂/1T-VSe₂/2H-MoS₂/1T-VSe₂/TaS₂ heterostructure, it experiences tensile strains of 2% in the 1T-device and 1.6% in the 2H-device. Figure 6b–d present the orbital-projected density of states for MoS₂ in three configurations: panel (b) shows the DOS for a freestanding monolayer 2H-MoS₂, while panels (c) and (d) illustrate the DOS for 2H-MoS₂ incorporated into magnetic tunnel junctions with 1T-TaS₂ and 2H-TaS₂ electrodes, respectively. Notably, monolayer 2H-MoS₂ typically exhibits semiconductor behavior, with a band gap of 1.6 eV^53,54,55. However, incorporation of a monolayer of MoS₂ into the device heterostructure leads to the observation of non-zero states in the DOS of MoS₂ at the Fermi level in both 1T- and 2H-TaS₂ electrode configurations. These states are known as metal-induced gap states and are responsible for the tunneling process, as shown in Fig. 6c and d. Additionally, similar to VSe₂ and TaS₂, the DOS for monolayer MoS₂ indicates that the d-orbitals play a predominant role in both the valence and conduction bands. These d-orbitals have a significant presence around the Fermi level, underlining their substantial contribution to the electronic structure of MoS₂. In the 1T-device, the DOS near the Fermi level is more pronounced, reflecting stronger hybridization and electronic coupling between MoS₂ and the 1T-TaS₂ electrodes. Conversely, the 2H-device exhibits a slightly reduced DOS near the Fermi level, indicating weaker coupling with the 2H-TaS₂ electrodes. These observations highlight the phase-dependent nature of the electronic interactions between MoS₂ and TaS₂ layers, which significantly influence the overall electronic properties of the heterostructure.

Fig. 6: Atomic structure and density of states (DOS) of freestanding monolayer 2H-MoS₂ and its integration into MTJs consisting of a TaS₂/1T-VSe₂/2H-MoS₂/1T-VSe₂/TaS₂ heterostructure with semi-infinite 1T- and 2H-TaS₂ electrodes.

a Top and side views of the atomic structure of freestanding monolayer 2H-MoS₂, highlighting its trigonal prismatic coordination and two-dimensional hexagonal lattice. b Orbital-projected density of states for the freestanding monolayer 2H-MoS₂, showing contributions from s-orbitals (green), p-orbitals (blue), and d-orbitals (red). c, d Orbital-projected DOS for the monolayer 2H-MoS₂ integrated into (c) a 1T-phase TaS₂ device configuration and (d) a 2H-phase TaS₂ device configuration, respectively. The energy (${\mathcal{E}}$) is plotted relative to the Fermi level (${{\mathcal{E}}}_{F}=0$), indicated by the dashed vertical line. The changes in DOS between freestanding and integrated configurations highlight the effects of electronic coupling between the MoS₂ monolayer and the TaS₂ electrodes in different phases.

From this point forward, we will incorporate SOC into our calculations, which have been neglected until now. The effect of SOC on the electronic properties of VSe₂ is substantial, as demonstrated by the bulk band structure in Supplementary Fig. 6. The comparison of the band structures with and without SOC reveals significant differences, emphasizing the importance of including SOC to accurately model the electronic properties of VSe₂. In the transport calculations for the MTJs, we initially configure the magnetization direction of both electrodes along the z-axis (transport direction). The left magnetization of ferromagnetic layers remains static while the magnetization of the right electrode undergoes a systematic rotation from 0° to 180° towards the x-axis, confined within the xz plane. This alteration allows us to meticulously assess how the transport properties of the MTJs evolve with varying magnetization angles, particularly at the Fermi energy. These evaluations utilize a projection rule associated with the Pauli matrices to derive various spin projections from the fundamental components of the transmission function T_σ(θ), including T_sum, T_X, T_Y, and T_Z.

$$\begin{array}{rcl}{T}_{{\rm{sum}}}(\theta )&=&{T}^{\uparrow \uparrow }(\theta )+{T}^{\downarrow \downarrow }(\theta )\\ {T}_{{\rm{X}}}(\theta )&=&2\text{Re}\,({T}^{\uparrow \downarrow }(\theta ))\\ {T}_{{\rm{Y}}}(\theta )&=&2\text{Im}\,({T}^{\uparrow \downarrow }(\theta ))\\ {T}_{{\rm{Z}}}(\theta )&=&{T}^{\uparrow \uparrow }(\theta )-{T}^{\downarrow \downarrow }(\theta )\end{array}$$

(1)

Here, T_+Z electrons are those associated with T_↑↑, indicating their spins aligned with the positive direction of the z-axis, while T_-Z electrons correspond to T_↓↓, aligned oppositely along the z-axis. The conductance for cases where there is no net spin current, known as zero spin current conductance, is derived from an equal balance of T_+Z and T_-Z electrons, leading to no dominant spin direction in the electrical current. The specific conductance associated with the net spin current, denoted G_Z, is calculated using $\frac{{e}^{2}}{h}({T}_{\uparrow \uparrow }-{T}_{\downarrow \downarrow })$. This measure effectively represents the difference in conductance between the T_+Z and T_-Z electrons, capturing the essence of the electrical spin current in the junction. Additionally, the total conductance, expressed as G_sum, and defined by $\frac{{e}^{2}}{h}({T}_{\uparrow \uparrow }+{T}_{\downarrow \downarrow })$, encompasses the total conductance contributed by all electrons crossing the junction, regardless of their spin orientation. The two terms T_X and T_Y represent the real and imaginary parts of the spin-mixing conductance arising due to the spin accumulation at the interfaces.

The atomic structures of the MTJ devices in which a 1T-VSe₂/2H-MoS₂/1T-VSe₂ trilayer is sandwiched between 1T-phase and 2H-phase TaS₂ semi-infinite electrodes are shown in Fig. 7a and b, respectively. Notably, the positions of atoms in MoS₂ differ between the two devices, as clearly illustrated in these panels. These structural deviations result from allowing all parts of the scattering region to relax independently, enabling each configuration to achieve its energy minimum. The interlayer distances obtained after structural relaxation are also displayed in the figure, highlighting how local atomic rearrangements lead to slightly distinct final geometries, despite similar initial configurations. The variable σ represents the components X, Y, and Z. The illustration highlights the direction of the magnetization vector M in the left ferromagnetic electrode (VSe₂ layer), which is fixed along the transport direction. On the right side, the orientation of the magnetization vector M in the second electrode can rotate at an angle θ relative to the fixed magnetization of the left electrode. Figure 7c–h illustrates the θ-dependent noncollinear-spin-resolved conductance (c, d), spin polarization (e, f), and ATMR (g, h) at the Fermi energy for two MTJ setups: one with 1T-phase TaS₂ electrodes shown in the left panels and the other with 2H-phase TaS₂ electrodes depicted in the right panels. As shown in Fig. 7c and d, by increasing θ from 0°–180°, a general decrease in conductance is observed for both device types, albeit at different magnitudes. In the 1T-device (Fig. 7c), conductance values across all spin components, particularly the sum and Z components, start higher and taper less sharply compared to the 2H-device (Fig. 7d), where conductance drops off more steeply. This indicates a higher sensitivity of the 2H-device to changes in magnetization direction, possibly due to different electronic structure interactions between the two phases.

Fig. 7: θ-dependent noncollinear-spin-resolved conductance, spin polarization, and tunnel magnetoresistance in magnetic tunnel junctions with 1T- and 2H-TaS₂ electrodes.

a, b Show side views of the device geometries: (a) 1T-TaS₂/1T-VSe₂/2H-MoS₂/1T-VSe₂/1T-TaS₂ and (b) 2H-TaS₂/1T-VSe₂/2H-MoS₂/1T-VSe₂/2H-TaS₂ configurations, highlighting the interlayer distances that emerge after structural relaxation. The magnetization vector M in the left 1T-VSe₂ electrode is fixed, while the right 1T-VSe₂ electrode’s magnetization rotates at an angle θ relative to the fixed magnetization. c, d Show the spin-resolved conductance (G) as a function of θ for the 1T- and 2H-phase devices, respectively. e, f illustrate the spin polarization (P) as a function of θ, demonstrating the variation in spin polarization percentages across the different components for the two electrode phases. g, h Depict the angular-dependent tunnel magnetoresistance (ATMR) as a function of θ for the devices with semi-infinite 1T- and 2H-phase TaS₂ electrodes, respectively. The ATMR is defined as the percentage change in resistance between parallel (θ = 0°) and antiparallel (θ = 180°) magnetization configurations. The left (c, e, g) correspond to 1T-TaS₂ devices, while the right (d, f, h) correspond to 2H-TaS₂ devices. The effects of spin-orbit coupling are included in these calculations.

The angular dependence of noncollinear spin polarization, denoted as P_σ(θ), for the 1T-VSe₂/2H-MoS₂/1T-VSe₂ MTJ sandwiched between TaS₂ electrodes at the Fermi energy can be expressed by the relationship ${P}_{\sigma }(\theta )=\frac{{G}_{{\rm{sum}}}(\theta )}{{G}_{\sigma }(\theta )}$, as depicted in Fig. 7e and f, for 1T-and 2H-devices, respectively. This parameter quantifies the proportion of conductance attributed to each spin channel relative to the total conductance, thereby providing insight into the spin-specific conductance influence. The variation in P_σ(θ) directly mirrors the trends in G_σ(θ). For example, since G_Y remains approximately zero, P_Y(θ) is consistently minimal across all measured angles. Conversely, P_X(θ) demonstrates a rise and fall that corresponds closely with the non-monotonic behavior seen in G_X as θ adjusts. The observed behavior in P_Z(θ) combines the effects of a general reduction in total conductance G_sum and the fluctuating nature of G_Z. The data from both device setups reveal variations in P_X and P_Z, with the 1T-phase setup generally showing higher and more variable polarization across these components. Notably, P_Z(0°) values ~91% and 95% for the 1T- and 2H-phase TaS₂ configurations respectively, closely matching the MTJ device with Fe₄GeTe₂ electrodes at 97.8% and surpassing earlier reports of P_Z(0°) for MnSe₂ (74%), Fe₃GeTe₂ (22.8%), and Fe₅GeTe₂ (54%) electrode configurations, reflecting advanced polarization efficiency in these systems³⁶.

Apart from the conventional TMR effect, magnetic tunnel junctions exhibit anisotropic tunneling magnetoresistance (ATMR), where spin-orbit coupling causes the magnetoresistance to vary depending on the direction of the magnetization⁵⁶. The ATMR is mathematically defined by the formula:

$$\,\text{ATMR}\,(\theta )=\left(\frac{{G}_{{\rm{sum}}}({0}^{\circ })-{G}_{{\rm{sum}}}(\theta )}{{G}_{{\rm{sum}}}(\theta )}\right)\times 100 \%$$

(2)

This expression equates the ATMR measured in straight alignments (typically at θ = 180°) to that in noncollinear settings. As shown in Fig. 7g and h, ATMR(θ) for the MTJ with TaS₂ electrodes in both 1T- and 2H-phase configurations consistently rises with increasing θ. This upward trend in ATMR(θ) is mainly due to a steady reduction in G_sum(θ) over the angular range. The maximum ATMR is observed when θ = 180° equal to 168% for 1T-device and 1419% in 2H-device, indicating optimal magnetoresistive effectiveness when the magnetization of ferromagnetic layers are fully antiparallel. Notably, the 2H-phase device (Fig. 7g) demonstrates a more pronounced increase and higher ATMR values compared to the 1T-phase (Fig. 7h), suggesting that the 2H-phase electrodes significantly amplify the ATMR effect. These ATMR values exceed those reported for other MTJs based on 2D materials. For instance, an ATMR of ~160% at 4.2 K was observed in the FGT/BN/FGT junction²². Zhu et al. reported a maximum MR of 41% in a 2D FGT/InSe/FGT vertical spin-valve device with applied currents below 0.1 μA at 10 K²⁰. Zheng et al. observed an ATMR transition from positive (up to + 25.8%) to negative (− 4.3%) by varying the thickness of WSe₂ in FGT/WSe₂/FGT devices⁵⁷. Additionally, Fe₃GaTe₂ demonstrated a significant room-temperature magnetoresistance of up to 85% in Fe₃GaTe₂/WSe₂/Fe₃GaTe₂ MTJs²³. It should be noted that the real-world experimental setups often involve imperfections such as interface roughness, atomic defects, or non-ideal fabrication, which can significantly impact the TMR value^58,59,60,61. As this is a DFT study, we are limited in our ability to incorporate all potential imperfections into the atomic configuration of the junction due to computational constraints. Accordingly, we considered an idealized scenario to represent the upper limit of device performance.

Figure 8 displays the k_∥-resolved spin-sum transmission coefficients for the 1T-VSe₂/2H-MoS₂/1T-VSe₂ heterostructure interfaced with semi-infinite TaS₂ electrodes in both 1T-phase (upper row) and 2H-phase (lower row), evaluated at the Fermi energy. These transmission maps, incorporating spin-orbit coupling effects, reveal how transmission channels evolve with changes in θ. At θ = 0°, the transmission features numerous bright spots, indicative of robust electron passage. As θ progresses towards 180°, these spots diminish and shift, highlighting the system’s sensitivity to magnetic orientation. Across all angles, the distribution of transmission channels within the 2D Brillouin zone is consistent, though the intensity varies. The 1T-device configuration exhibits more distinct transmission features than the 2H-device, indicating phase-dependent differences in electron propagation or scattering mechanisms within these heterostructures.

Fig. 8: Angle-resolved transmission for 1T-VSe₂/2H-MoS₂/1T-VSe₂ with semi-infinite 1T- and 2H-TaS₂ electrodes.

Spin-sum transmission probabilities resolved by the parallel wave vector (k_∥) as a function of the magnetization angle (θ) for a 1T-VSe₂/2H-MoS₂/1T-VSe₂ heterostructure sandwiched between semi-infinite TaS₂ electrodes. The upper row corresponds to 1T-phase TaS₂ electrodes, while the lower row corresponds to 2H-phase TaS₂ electrodes. The magnetization vector M in the left 1T-VSe₂ electrode is fixed, while the right 1T-VSe₂ electrode’s magnetization rotates at an angle θ relative to the fixed magnetization. The panels illustrate the transmission for four different magnetization angles: θ = 0°, θ = 45°, θ = 90°, and θ = 180°. Calculations are performed at the Fermi level (${\mathcal{E}}={{\mathcal{E}}}_{F}$), and spin-orbit coupling effects are included. The color scale represents the transmission probability, ranging from 0 (low transmission) to 1 (high transmission). The results highlight the impact of angular variations in magnetization and electrode phase on the electronic transmission properties.

Characterizing magnetic dynamics and spin transfer torque in magnetic tunnel junctions

Spin-transfer torque has gained significant focus in recent research due to its pivotal role in magnetic applications. STT arises when a spin-polarized current is directed into a ferromagnetic material whose magnetization direction does not align with the current’s spin polarization. This misalignment enables the transfer of spin angular momentum to the magnetic moments of the ferromagnetic layer, effectively applying a torque that can alter the magnetization orientation. This phenomenon, first predicted theoretically by Slonczewski⁶² and Berger⁶³, has since been robustly validated through experimental studies^64,65,66. STT is particularly promising for technologies such as random access memory, where it facilitates an entirely electrical mechanism for both reading and writing data, enhancing the efficiency and scalability of memory devices. Figure 9 illustrates the atomic-scale distribution of the x and z components of the linear-response spin-transfer torkance, τ, within 1T-VSe₂/2H-MoS₂/1T-VSe₂ MTJs sandwiched between TaS₂ electrodes under zero bias conditions. Figure 9a and b feature electrodes in the 1T phase, while panels Fig. 9c and d feature electrodes in the 2H phase. The angle θ, representing the magnetization orientation in the right half (free magnetic layer) of the MTJ, is set at 45° for panels (a, c) and at 90° for panels (b, d). In all panels, the z-coordinate of the significant peaks near the midpoint suggests a strong interaction region, likely coinciding with the location of the VSe₂ layer, underscoring the dominant influence of each magnetization of ferromagnetic layers direction on the overall torque distribution within the device. When the rotation angle of the free layer is set to 45°, the distribution patterns and symmetry for the 1T (a) and 2H (c) phase electrodes are similar, suggesting that the phase of the electrodes does not significantly alter the fundamental symmetry of the torque distribution under these conditions. However, the peak values of τ_z vary depending on the electrode phase, a behavior attributed to the interference of multiple transmission channels with different parallel wave vectors (k_∥) at the Fermi level. In Fig. 9(b) and (d), for the MTJs with 1T and 2H phase electrodes at a magnetization angle of 90°, the spin-transfer torque components τ_x and τ_z exhibit symmetric distribution about the midpoint of the device. This centrosymmetric distribution indicates balanced contributions from both electrodes, despite their perpendicular magnetization orientations. The spin of the current is initially oriented along the z-axis when it enters the right part of the device and then shifts to align along the x-axis. As a result, the x-component of τ is non-zero only in the left-hand part of the device, while the z-component is non-zero only in the right-hand part. This distribution indicates that each electrode exerts a mirrored torque influence, thereby stabilizing the overall torque dynamics within the device.

Fig. 9: Atomic-scale distribution of spin-transfer torque in 1T-VSe₂/2H-MoS₂/1T-VSe₂ junctions with semi-infinite 1T- and 2H-TaS₂ electrodes.

a–d Depiction of the atomic-scale distribution of the x- and z-components of the linear-response spin-transfer torque (τ_x and τ_z) in 1T-VSe₂/2H-MoS₂/1T-VSe₂ magnetic tunnel junctions sandwiched between semi-infinite TaS₂ electrodes. (a, b) correspond to devices with 1T-TaS₂ electrodes, while (c, d) correspond to devices with 2H-TaS₂ electrodes. The torques are shown for two different magnetization angles between the 1T-VSe₂ ferromagnetic layers in the device configurations, θ = 45° in (a, c) and θ = 90° in (b, d). The z-axis represents the position along the device structure, with the spin-transfer torque values distributed across the atomic layers. The inset illustrates the corresponding device structure, showing the layered configuration of TaS₂, MoS₂, and VSe₂. Calculations are performed at zero bias.

Figure 10 illustrates the angle-dependent z-component of STT in an MTJ at zero bias, comparing two device configurations with 1T-phase and 2H-phase electrodes over a range of θ from 0°–180°. The variation in STT generally follows a sin(θ) pattern, consistent with theoretical models cited in ref. ⁶⁷. For both configurations, the STT magnitude dips to its lowest around 90° equal to −702 μeV/V for 1T-device and −1561 μeV/V 2H-device and subsequently rises towards 180°. This pattern might be related to a reduction in total conductance (G_sum) as the angle increases, affecting the number of electrons available to contribute to STT, thereby lowering its magnitude. The 1T-device consistently demonstrates higher STT values across all angles compared to the 2H-device, suggesting more efficient spin transfer in the 1T setup. The direction of STT—negative in these cases—indicates it opposes the existing magnetization alignment, potentially enabling magnetization reorientation or reversal. This negative STT may arise from adverse spin polarization or nonadiabatic interactions among the conduction electrons⁶⁸. As can be seen in Supplementary Fig. 5, analysis of the spin-dependent density of states in the VSe₂ layers of both 1T and 2H configurations shows a negative spin polarization at the Fermi level (−8% for 1T-device and −2% for 2H-device), supporting the observation of negative STT across these device setups.

Fig. 10: Angle-dependent z-component of spin-transfer torque in MTJ with semi-infinite 1T- and 2H-TaS₂ electrodes at zero bias.

The plot compares the z-component of the linear-response spin-transfer torque (τ_z) for a magnetic tunnel junction (MTJ) at zero bias with two different device configurations: 1T-phase TaS₂ electrodes (blue line) and 2H-phase TaS₂ electrodes (red line). The spin-transfer torque is evaluated as a function of the magnetization angle (θ), where the magnetization is fixed in one ferromagnetic 1T-VSe₂ layer and rotated in the other ferromagnetic 1T-VSe₂ layer from 0° to 180°. The results highlight the angular dependence of τ_z, with a stronger torque observed in the 1T-phase configuration compared to the 2H-phase configuration. Calculations are performed at zero bias, and spin-orbit coupling effects are included.

To deepen our understanding of the STT-based method, we have calculated the critical voltage V_c and current I_c necessary for the magnetization reversal. The Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation encapsulates the complex dynamics of magnetic moments under the influence of external fields and spin-polarized currents. The LLGS equation describes the spin dynamics as follows:

$$\frac{d{\bf{M}}}{dt}=-| \gamma | {\bf{M}}\times {{\bf{H}}}_{{\rm{eff}}}+\frac{\alpha }{{M}_{s}}\left({\bf{M}}\times \frac{d{\bf{M}}}{dt}\right)+{\tau }_{{\rm{STT}}}$$

(3)

The first term, −∣γ∣M × H_eff, describes the precessional motion of the magnetic moment M around the effective magnetic field H_eff. This precession is driven by the gyromagnetic ratio ∣γ∣, which quantifies the relationship between magnetic moment and angular momentum for a given particle. The damping term, $\frac{\alpha }{{M}_{s}}({\bf{M}}\times \frac{d{\bf{M}}}{dt})$, manages the energy dissipation within the magnetic system. It works to align the magnetic moment with the effective field, countering the precession induced by the gyromagnetic interaction. The efficiency of this alignment is critical as it determines how rapidly the system can stabilize after a disturbance, with a lower α generally enabling faster response times but requiring more precise control over the spin dynamics. Also, the third term refers to the spin transfer torque. We analyze conditions under which the STT can surpass the intrinsic damping to change the direction of magnetization. The critical voltage V_c and current I_c for magnetization reversal can then be written as

$${V}_{c}=\frac{\alpha \,{{\mathcal{E}}}_{{\rm{MAE}}}}{{\tau }_{z}^{{\rm{total}}}({\theta }_{m})},\quad {I}_{c}=G({\theta }_{m}){V}_{c}$$

(4)

which links the magnetic anisotropic energy ${{\mathcal{E}}}_{{\rm{MAE}}}$ and the total effective STT per unit voltage, τ_total, to the angle θ_m at which these effects are maximized. As illustrated in Fig. 10, the STT effects reach their maximum at an angle of 90°. Figure 9b and d show the centrosymmetric distribution of τ_x and τ_z around the midpoint of the device, which leads to ${\tau }_{x}^{{\rm{total}}}$ being nearly zero in the right half of the device. Also, since we are focusing on magnetization switching in the xz plane, ${\tau }_{y}^{{\rm{total}}}$ is neglected. Thus, by concentrating solely on ${\tau }_{z}^{{\rm{total}}}$ and focusing on the xz plane, we simplify our model to emphasize the primary dynamics of interest.

Table 2 shows the key magnetic properties for the TaS₂/1T-VSe₂/2H-MoS₂/1T-VSe₂/TaS₂ MTJs with semi-infinite 1T- and 2H-phase TaS2 electrodes at θ = 90° where the magnetization directions of the two 1T-VSe₂ ferromagnetic layers are perpendicular. The results of the in-plane magneto-crystalline anisotropy energy plots for 1T-VSe₂/2H-MoS₂/1T-VSe₂ MTJs sandwiched between TaS₂ electrodes, differentiated by 1T and 2H phase electrodes shown in Supplementary Fig. 8, reveals that the value of ${{\mathcal{E}}}_{{\rm{MAE}}}$ for 1T-device and 2H-device are equal to − 0.57 meV and − 0.35 meV, respectively. The 1T-device has a higher ${{\mathcal{E}}}_{{\rm{MAE}}}$, indicating it resists magnetization reorientation more strongly, and a lower Gilbert damping factor α (0.0033), leading to reduced energy dissipation during magnetic precession. It requires a lower critical current density (0.79 MA/cm²) and voltage (1.20 mV) for magnetization switching. Conversely, the 2H-device, with an ${{\mathcal{E}}}_{{\rm{MAE}}}$ of −0.35 meV and a significantly higher α of 0.16578, demands higher critical current density (14.44MA/cm²) and voltage (82.65 mV). A larger α means that more torque from STT is needed to achieve magnetization switching, which requires a larger spin-polarized current. Thus, materials with a smaller α generally result in lower power consumption due to less energy loss during switching. These differences suggest that the 1T-device, with its higher stability and energy efficiency, may exhibit slower switching dynamics because of its higher anisotropy energy and lower damping. In contrast, the 2H-device, with higher damping and lower anisotropy energy, can switch magnetization faster but at the cost of higher energy consumption, making it less efficient for low-power applications. Localized doping or the introduction of controlled defects can tune spin-orbit coupling and scattering rates, potentially lowering the high damping in 2H or increasing the low damping in 1T to find an optimal middle ground. Likewise, tailored interface engineering—for instance, adding an ultrathin interlayer or adjusting the interfacial composition—may shift energy levels near the Fermi level and modify spin relaxation. Finally, applying strain in selected regions can control orbital overlap at the interface, influencing the strength of spin-orbit coupling. The findings, especially for 1T-device, provide a better setup in terms of reducing power consumption compared to other studies that report large Gilbert damping in doped Ni₈₀Fe₂₀ films, where the addition of heavy rare earth atoms resulted in significant damping values ranging from 0.1 to 0.2⁶⁹. Similarly, a high Gilbert damping value of 0.58 was reported for Fe₃GeTe₂⁷⁰. Moreover, the calculated critical current densities of MTJs in our study are consistent with experimental reports, where values have shown a reduction from 7.05 MA/cm² in strongly coupled CoFeB/Ru/NiFe free layers to 2.65 MA/cm² in weakly coupled CoFeB/Ru/NiFe free layers⁷¹. Additionally, the minimum experimental critical current density for Co-Fe-B/MgO/Co-Fe-B MTJs was found to be 3.9 MA/cm²⁷². A Fe₃GeTe₂/WSe₂ heterostructure achieved a remarkably low switching current density of 3.90 MA/cm² at 150 K, which is comparable to or better than those of conventional thin films and systems⁸. Furthermore, a wafer-scale Fe₃GeTe₂/Bi₂Se₃ layered heterostructure demonstrated a notably low switching current density of 2.2 MA/cm² at room temperature, where the topological insulator Bi₂Se₃ played a crucial role in enhancing the Curie temperature of Fe₃GeTe₂ through exchange coupling⁹. Additionally, an FGT/Pt bilayer structure requires a switching current density of 13 MA/cm^{2 73}. Comparing the results in Table 2, it is clear that the 1T-device outperforms the 2H-device in several key aspects, including a lower Gilbert damping factor, reduced critical current density, and smaller voltage requirements for magnetization switching. These features make the 1T phase more energy-efficient and suitable for low-power spintronic applications. While the 2H phase demonstrates advantages in spin-polarized transport, such as stronger alignment and greater sensitivity to magnetization changes, these benefits are outweighed by the practical advantages of the 1T phase. The higher MAE of the 1T phase further enhances stability of the magnetization vector, improving reliability for long-term operation. This combination of lower energy dissipation, better efficiency, and stability positions the 1T phase as the more favorable choice for real-world applications, despite certain advantages exhibited by the 2H phase.

Table 2 Summary of key magnetic properties for the TaS₂/1T-VSe₂/2H-MoS₂/1T-VSe₂/TaS₂ MTJs with semi-infinite 1T- and 2H-phase TaS₂ electrodes at θ = 90°

Methods

Structural optimization

This study involved computational analyses focusing on geometry optimization and electronic structure, utilizing the linear combination of atomic orbitals (LCAO) approach. The calculations employed a basis set from PseudoDojo, featuring pseudopotentials tailored for the Perdew-Burke-Ernzerhof (PBE) form of the generalized gradient approximation (GGA). These procedures were executed using the QuantumATK software package⁷⁴. Integration within the Brillouin zone was achieved through a 14 × 14 × 1 Monkhorst-Pack k-point grid. A cutoff energy of 120 Hartree is chosen to balance the computational demands. The convergence criteria were rigorously defined to ensure the precision of the simulation outcomes. The total energy difference was maintained below 10⁻⁴ eV between consecutive self-consistent field (SCF) iterations to ensure solution stability. During the structural optimization phase, the process ceased when the residual forces on each atom dropped below 0.001 eV/Å. Furthermore, the vdW interactions, essential for capturing the physics of layered materials, were modeled using the vdW-D3 method with Becke-Jonson damping^75,76.

Spin-resolved transport simulations

Spin-resolved transport characteristics were simulated using density-functional theory (DFT) integrated with the NEGF formalism. For noncollinear calculations incorporating spin-orbit coupling (SOC), the exchange-correlation interactions were modeled using the noncollinear generalized gradient approximation (NCGGA), employing the PBE potential. Realistic device configurations, including the scattering region and attached leads, were constructed to analyze the transport properties. The same LCAO settings were applied across these quantum transport simulations. For simulations involving a gate-all-around (GAA) structure, the Poisson solver was implemented with specific boundary conditions to reflect the physical setup: periodic conditions along the x and y directions, and Dirichlet conditions along the z direction, which is the primary direction of transport. Simulations were conducted at a temperature of 300 K to represent typical operating conditions, using the Fermi-Dirac distribution to model the electron populations in the transport calculations. The k-point mesh utilized for the electrode regions was set to 9 × 9 × 150, providing high resolution along the transport axis, while the central region employed a denser 16 × 16 × 1 mesh to accurately capture state densities in the plane perpendicular to transport. To ensure efficiency in computation while retaining accuracy, the parallel conjugate gradient method was adopted for solving the system matrices.

The spin-dependent transmission coefficient, T_σ, is crucial for understanding the transport properties in spintronic devices and is determined using the NEGF formalism. This can be described by the following equation, which utilizes Green’s functions to evaluate the transmission for collinear magnetic configuration:

$${T}_{\sigma}({\mathcal{E}})\equiv \,\text{Tr}\,\left[{\Gamma }_{L}^{\sigma}({\mathcal{E}}){G}^{r,\sigma}({\mathcal{E}}){\Gamma }_{R}^{\sigma}({\mathcal{E}}){G}^{a,\sigma}({\mathcal{E}})\right],$$

(5)

In this equation, the subscript σ denotes the spin index (↑ or ↓). The term Γ_{{L, R}}, known as the linewidth function, is defined as $i[{\Sigma }_{\{L,R\}}-{\Sigma }_{\{L,R\}}^{\dagger }]$, where Σ_L(R) represents the retarded self-energy of the left (right) electrode. This self-energy term characterizes the coupling between the central scattering region and the semi-infinite leads, encapsulating the interaction and electron exchange dynamics at the interfaces. The symbols G^r and G^a denote the retarded and advanced Green’s function matrices, respectively. These matrices describe how electrons propagate through the device’s central region, considering both spin and orbital interactions. For a given energy ${\mathcal{E}}$, the transmission function ${T}_{\sigma }({\mathcal{E}})$ is computed by averaging the transmission coefficient ${T}_{\sigma }({\mathcal{E}})$ over all parallel wave vectors k_∥ within the irreducible Brillouin zone.

Spin transfer torque (STT) and Gilbert damping

The STT in magnetic heterostructures can be effectively analyzed using a linear-response method, accommodating small bias voltages δV_b to explore system dynamics^36,77,78. The STT is defined as:

$$STT=\,\text{Tr}\,(\delta {\rho }_{{\rm{neq}}}{\bf{\sigma }}\times {\bf B}_{{\rm{xc}}})$$

(6)

where (δρ_neq) denotes the non-equilibrium component of the density matrix, (σ) represents the vector of Pauli matrices, and (B_xc) is the exchange-correlation magnetic field. The non-equilibrium density matrix can be derived from the difference in density states under bias or estimated via linear response:

$$\delta {\rho }_{{\rm{neq}}}=\left({G}^{r}{\Gamma }_{L}{G}^{a}\right)q{V}_{b},$$

(7)

in which q denotes the electron charge. Spin-transfer torkance (STTk) defined as the coefficient of STT per unit bias on an atom site a, is calculated, given by ${\tau }^{a}=\frac{\delta {T}^{a}}{\delta {V}_{b}}$. Integrating this torque across all atomic sites provides the total linear-response STT:

$${\tau }^{{\rm{total}}}=\sum _{a}{\tau }^{a}$$

(8)

Here, we include SOC in our calculations to determine the STT at zero bias, where no net current is present. Despite the absence of applied voltage, non-trivial quantum mechanical phenomena, such as spin-orbit interactions and quantum fluctuations, can induce STT. By utilizing the linear-response STT framework, we are able to compute the STT in this context by examining the small perturbations introduced by SOC. The components of the torque operator STT_νij(k) by incorporating SOC effects, are expressed as:

$$ST{T}_{ij}^{\nu }(k)=\langle {\psi }_{ik}| [{{\boldsymbol{\sigma }}}_{\nu },{H}_{SO}]| {\psi }_{jk}\rangle$$

(9)

where σ_ν refers to the Pauli spin matrices that capture essential spin interactions, and H_SO is the spin-orbit term of the Hamiltonian, critical in materials with significant spin-orbit interactions such as heavy metals and topological insulators. The ψ_ik represents the Bloch eigenstates, depicting electron quantum states at each k-point in the Brillouin zone. The ψ_ik and ψ_jk are Bloch eigenstates, representing the quantum states of electrons at the k-points in the Brillouin zone.

Gilbert damping in magnetic systems plays a crucial role in describing how magnetization relaxes back to equilibrium and is effectively incorporated into the Landau-Lifschitz⁷⁹ equation to elucidate spin dynamics. This damping is recognized as a nonlinear spin relaxation phenomenon crucial for controlling the rate at which magnetization vectors stabilize. For a detailed understanding of these dynamics, the Gilbert damping tensor is computed using Kambersky’s torque-torque correlation model using the following formula^80,81,82:

$${\alpha }_{\mu \nu }=\frac{g}{\pi m}\sum _{k}{w}_{k}\sum _{ij}{W}_{ij}(k)ST{T}_{ij}^{\nu }(k){\left(ST{T}_{ij}^{\mu }(k)\right)}^{\dagger }$$

(10)

where g = 2.0023 denotes the electron spin g-factor, emphasizing the proportionality between magnetic dipole moment and angular momentum for electrons. μ and ν denote the spatial components of the magnetization dynamics. The magnetization m is quantified in Bohr magnetons, highlighting the quantum mechanical aspects of spin dynamics. The comprehensive summations over band indices i, j and the Brillouin zone (indexed by k with weights w_k) reflect the elaborate band structure interactions crucial for evaluating magnetic damping. Calculations utilize a dense Monkhorst-Pack k-point mesh of 40 × 40 × 1 to ensure precision in the linear-response STT calculation.

Integral to the damping calculation, the spectral overlap function W_ij(k) is defined by:

$${W}_{ij}(k)=\int\,\left(-\frac{\partial f({\mathcal{E}},{{\mathcal{E}}}_{F})}{\partial {\mathcal{E}}}\right){A}_{ik}({\mathcal{E}},\Lambda ){A}_{jk}({\mathcal{E}},\Lambda )d{\mathcal{E}}$$

(11)

$f({\mathcal{E}},{{\mathcal{E}}}_{F})$ is the Fermi-Dirac distribution, which dictates the occupancy of electronic states at energy ${\mathcal{E}}$ relative to the Fermi energy ${{\mathcal{E}}}_{F}$. ${A}_{ik}({\mathcal{E}},\Lambda )$ is a Lorentzian spectral function modeling the electron density of states around each band energy, with the broadening Λ due to interactions like electron-phonon coupling. When Λ exceeds the thermal energy scale k_BT_temp (T_temp refers to temperature), the derivative of the Fermi-Dirac function simplifies to a delta function:

$${W}_{ij}(k)\approx {A}_{ik}({{\mathcal{E}}}_{F},\Lambda ){A}_{jk}({{\mathcal{E}}}_{F},\Lambda )$$

(12)

This simplification aids computational models in efficiently determining the Gilbert damping tensor. In our studies of 2D VSe₂-based MTJs, we use a Monkhorst-Pack k-point mesh of 40 × 40 × 1, with a broadening parameter Λ = 0.01 eV, and focus on the diagonal components of the damping tensor: α_xx, α_yy, and α_zz.