Giant tunneling magnetoresistance in two-dimensional magnetic tunnel junctions based on double transition metal MXene ScCr₂C₂F₂

Abstract

Two-dimensional (2D) transition metal carbides (MXenes) with intrinsic magnetism and half-metallic features show great promising applications for spintronic and magnetic devices, for instance, achieving perfect spin-filtering in van der Waals (vdW) magnetic tunnel junctions (MTJs). Herein, combining density functional theory calculations and nonequilibrium Green's function simulations, we systematically investigated the spin-dependent transport properties of 2D double transition metal MXene ScCr₂C₂F₂-based vdW MTJs, where ScCr₂C₂F₂ acts as the spin-filter tunnel barriers, 1T-MoS₂ acts as the electrode and 2H-MoS₂ as the tunnel barrier. We found that the spin-up electrons in the parallel configuration state play a decisive role in the transmission behavior. We found that all the constructed MTJs could hold large tunnel magnetoresistance (TMR) ratios over 9 × 10⁵%. Especially, the maximum giant TMR ratio of 6.95 × 10⁶% can be found in the vdW MTJ with trilayer 2H-MoS₂ as the tunnel barrier. These results indicate the potential for spintronic applications of vdW MTJs based on 2D double transition metal MXene ScCr₂C₂F₂.

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Introduction

A magnetic tunnel junction (MTJ) is an important spintronic device, which consists of two ferromagnets divided by a thin insulating barrier.^1,2 MTJs are widely utilized in magnetic random-access memory, hard disks, and magnetic sensors, etc.^3–6 Furthermore, much efforts have been put into the relevant research for MTJs since the tunneling magnetoresistance (TMR) effect was firstly discovered in Fe/Ge/Co multilayer films.^7–9 Herein, the TMR ratio is regarded as one of the most important factors for estimating the performance of MTJs. To enhance the TMR ratio, an effective method involves employing intrinsic magnetic materials with high spin polarizabilities as the electrode material.^10,11 In early years, three-dimensional (3D) magnetic metals such as Fe, Ni, and Co are employed as the ferromagnetic electrodes in MTJs.¹² Unfortunately, the limited spin polarizations lower than 50% result in low TMR ratios for these 3D magnetic metals.^13–15 It is interesting to note that the TMR ratios of MTJs could be improved to a higher level by employing half-metallic (HM) materials as electrodes.^16–18 This is because HM materials possess 100% spin polarization theoretically.¹⁹ However, controlling the quality of the interface between the electrode materials and barrier layers is one of the thorny challenges in 3D HM material-based MTJs.²⁰ When constructing the MTJs by cleaving 3D materials, the surface dangling bonds will inevitably cause atomic distortion, disorder, and point defects, which could strengthen the interfacial scattering, and lead to the reduction of the TMR ratio.²¹

Recently, the successful synthesis of intrinsic magnetic two-dimensional (2D) materials, such as CrI₃,²² Cr₂Ge₂Te₆,²³ and Fe₃GeTe₂,²⁴ has opened a new horizon for spintronic devices. Constructing van der Waals (vdW) MTJs via perpendicularly stacking magnetic and dielectric 2D materials together through vdW interactions offers impressive performance with high TMR ratios.²⁵ For example, a TMR ratio of 160% has been experimentally obtained in Fe₃GeTe₂|h-BN|Fe₃GeTe₂ vdW MTJs at low temperatures.²⁶ Moreover, the TMR ratio of graphene/CrI₃/graphene vdW MTJ up to 19 000% has been experimentally realized by increasing the CrI₃ layer thickness.²⁷ It is theoretically predicted that a giant zero-bias TMR ratio of up to 48 000% can be achieved using CrOCl/CrOX bilayer as the spin-filter tunnel barriers.²⁸ On the other hand, the vdW MTJs based on 1T-VSe₂ possess a high TMR ratio of 5600%, and the TMR ratio is sharply increased to 1.7 × 10⁵% by inserting 2H-MoSe₂.²⁹ Two kinds of 6,6,12-graphyne-based molecular magnetic tunnel junctions have novel transport behaviors, and the maximum order of magnitude of tunneling magnetoresistance values reaches 10⁶%.³⁰ Wang et al. reported the spin-dependent transport properties of a molecular junction made of two manganese phthalocyanine molecules linked by single-walled carbon nanotubes and predicted a high spin-filter efficiency and magnetoresistance ratio.³¹ However, it is still challenging to develop 2D materials with intrinsic magnetism to achieve giant TMR ratios in MTJs.

Among various 2D materials, 2D transition metal carbides/nitrides (MXene) materials have attracted much attention due to their fascinating tunable physical and chemical properties from the remarkable variety of chemical diversity.^32–34 MXenes have a general formula of M_n+1X_nT_x, where M, X, and T represent early transition metals, carbon/nitrogen, and the functional groups (such as O, OH, and F), respectively.³⁵ It is worth noting that MXene Cr₂C without the surface functional groups is predicted to have intrinsic half-metallicity, and ferromagnetic to antiferromagnetic transitions accompanied by metal-to-insulator transitions can be observed after adsorbing different surface functional groups.³⁶ Moreover, some intrinsic magnetic MXenes, such as Cr₂NX₂ (X = O, F, OH),³⁷ Mn₂CT₂ (T = F, Cl, OH, O, and H)³⁸ are found to possess HM polarization nature and are proposed as potential candidates for vdW MTJs or spin filters.^39,40 Apart from that, double transition metal (DTM) MXenes, including two different transition metals with the general formula of ^41,42 offer more possibilities for fantastic magnetic properties.^43–45 Recently, impressive intrinsic magnetic properties have been found in HM DTM MXenes, such as ScCr₂C₂F₂, ZrCr₂C₂H₂ and YCr₂C₂H₂.⁴⁶ Herein, ScCr₂C₂F₂ presents a high Curie temperature of 230 K based on the Metropolis Monte Carlo (MC) simulations. Although T_C could be theoretically overestimated, recently good agreement between theoretical results and experimental values have been achieved, for instance, in the case of CrI₃ and Fe₃GeTe₂.^46,47 The MC predicted T_C of 230 K indicates that ScCr₂C₂F₂ is anticipated to achieve distinguished MTJ performance as the ferromagnetic electrodes. Therefore, a systematical understanding and optimization of ScCr₂C₂F₂-based vdW MTJs are of great interest and importance.

In this work, by employing ScCr₂C₂F₂ as the spin-filter tunnel barriers, 1T-MoS₂ and 2H-MoS₂ respectively, as the electrode and tunnel barrier, we have designed and optimized the 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJs with different stacking configurations and tunnel barrier layer numbers. The interlayer charge transfers, spin-dependent transmission coefficients, spectra projected local density of states, and TMR ratios in the equilibrium state of the constructed vdW MTJs were investigated. The negative binding and formation energies of ScCr₂C₂F₂/1T-MoS₂ and ScCr₂C₂F₂/2H-MoS₂ heterostructures demonstrate that different layers could stack spontaneously in experiments. Besides, the energetically favorable stacking-II of the ScCr₂C₂F₂/1T-MoS₂ interface and stacking-I configurations for the ScCr₂C₂F₂/1T-MoS₂ interface are selected to construct the vdW MTJs, which will increase the experimental feasibility. Furthermore, it reveals that the monolayer ScCr₂C₂F₂ can maintain half-metallicity with perfect polarization after application in the vdW MTJs. Large TMR ratios of over 9 × 10⁵% are found in all the constructed vdW MTJs, and the maximum TMR ratio of 6.95 × 10⁶% was detected in such vdW MTJ with a trilayer 2H-MoS₂ tunnel barrier. Our findings demonstrate that such DTM MXene-based vdW MTJs have application potential in spintronics.

Computational methods

In order to obtain the interlayer structures before modeling the vdW MTJs, the different stacking configurations for ScCr₂C₂F₂/1T-MoS₂ and ScCr₂C₂F₂/2H-MoS₂ heterostructures were built using the ALKEMIE platform,^48,49 and investigated based on the density functional theory (DFT) calculations using the Vienna Ab initio Simulation Package (VASP).⁵⁰ The generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE)⁵¹ was used for the exchange and correlation potentials. To better describe the correlation effect of localized 3d electrons in Cr atoms, the GGA + U method with the on-site effective interaction parameter U = 3.0 eV was used.⁵² The plane-wave cut-off energy of 500 eV and 12 × 12 × 1 K-points were utilized for the optimization and self-consistent calculations. The DFT-D3 method^53,54 was adopted to describe the interlayer van der Waals force. To avoid the interlayer interaction, a 20 Å vacuum was added on top of the 2D materials. The heterostructures were relaxed with the convergence energy for electrons and convergence forces for atoms to 1 × 10⁻⁵ eV and 0.01 eV Å⁻¹, respectively.

The optimizations and spin-dependent transport calculations of vdW MTJs were implemented using the QuantumWise Atomistix Toolkit (QuantumATK) Q-2021.06 package,⁵⁵ based on DFT combined with the nonequilibrium Green's function (NEGF).⁵⁶ The generalized gradient approximation (GGA) of the Perdew–Burke–Ernzerhof (PBE)⁵¹ functional with a linear combination of atomic orbitals (LCAO) norm-conserving PseudoDojo pseudopotential⁵⁷ were included to deal with the electron exchange and correctional interactions. The double-zeta basis set used to expand wave functions was employed for the calculations.⁵⁸ The plane-wave cut-off of 105 Hartree was employed, 10 × 10 × 1 Monkhorst k-point meshes were used for the optimization of the MTJs before performing the spin-dependent transport calculations, and the convergence criterion of the force was set to 0.01 eV Å⁻¹. The electron temperature was set at 300 K, which was determined by the Fermi–Dirac distribution via the occupation number of each state. When performing the self-consistent calculation, 10 × 10 × 1 Monkhorst k-point meshes were utilized for the central scattering regions. Besides, inspired by the set of electrodes of the recently proposed NiI₂/In₂Se₃ multiferroic devices,⁵⁹ the dense enough k-points set was required for the electrodes along the transport direction since they are regarded as the periodic bulk structures for the transport calculations. The Monkhorst k-point meshes for the electrodes were set to 10 × 10 × 150, which is dense enough to ensure the accuracy of the results, and 151 × 151 Monkhorst–Pack grids were used for the spin-dependent transport calculations.

Results and discussion

In 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJs, the origin of TMR effects arise from the different densities of states for spin-up and spin-down channels of the ScCr₂C₂F₂ layers, which act as the spin-filter tunnel barriers. The corresponding transportation mechanism is illustrated in Fig. 1. When the external magnetic fields are applied in vdW MTJs, the magnetic configurations of the two ScCr₂C₂F₂ layers are manipulated to parallel configuration (PC) and antiparallel configuration (APC) states, individually. The tunneling resistances in vdW MTJs vary widely varied in PC and APC. Herein, the TMR ratio is the most important factor in estimating the performance of the magnetic tunnel junctions, which is defined as⁶⁰where R_APC and R_PC are the tunneling resistances in PC and APC, respectively. P₁ and P₂ represent the spin polarization of the left and right ferromagnetic materials, respectively. When the device is in the PC state, the spin-up electrons from the left 1T-MoS₂ electrode can hop to the spin-up states around the Fermi level in the left ScCr₂C₂F₂ layer, which can further go through the 2H-MoS₂ barrier layer due to the quantum tunneling effect. Subsequently, the spin-up electrons around the Fermi level can hop to the spin-up states of the right ScCr₂C₂F₂ layer, and finally hop to the spin-up states of the right 1T-MoS₂ electrode. However, owing to the semiconducting feature of the left ScCr₂C₂F₂ in the spin-down channel, a rare state is observed around the Fermi level. Hence, the spin-down electrons from the left 1T-MoS₂ electrode cannot hop to the spin-down states of the left ScCr₂C₂F₂ layer. As a result, the vdW MTJ is in a high conductivity state with the contribution of the conductive spin-up electron channel. When the device is in the APC state, both the spin-up and spin-down electrons can hardly pass through the vdW MTJ since the spin-up and spin-down electrons are prevented from hopping to the left and right ScCr₂C₂F₂ layers, respectively. As a result, the vdW MTJ is in a high resistance state. Therefore, a considerable difference in the tunneling resistances is obtained from the 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJ with different spin configurations, where the high conductivity PC state and high resistance APC state are regarded as “1” and “0” states for data storage.^61,62

Fig. 1 The electron tunneling mechanism of the 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ MTJ in (a) PC and (b) APC states.

The crystal structures of ScCr₂C₂F₂, 1T-MoS₂ and 2H-MoS₂ monolayers are shown in Fig. 2a–c. Herein, ScCr₂C₂F₂ and 1T-MoS₂ have hexagonal crystal structures with the space group of P3̄m1, and 2H-MoS₂ has the space group of P6̄m2. The optimized lattice constant of ScCr₂C₂F₂ is 3.12 Å. The optimized lattice constants of both 1T-MoS₂ and 2H-MoS₂ are 3.18 Å, which not only agrees well with the experimental values,^63–66 but also exhibits a perfect lattice match with ScCr₂C₂F₂. Fig. 2d and f illustrates the calculated band structures for ScCr₂C₂F₂, 1T-MoS₂, and 2H-MoS₂ monolayers. From Fig. 2d, ScCr₂C₂F₂ shows the metallic properties in the spin-up channel and semiconducting properties in the spin-down channel, revealing its half-metallic magnetic features. On the other hand, from Fig. 2e and f, 1T-MoS₂ and 2H-MoS₂ are demonstrated to be metallic conducting and semiconducting, respectively. Therefore, 1T-MoS₂ and 2H-MoS₂ could be employed as the electrodes and tunnel barrier for the vdW MTJs.

Fig. 2 The crystal structures and band structures for monolayers of (a) and (d) ScCr₂C₂F₂, (b) and (e) 1T-MoS₂, (c) and (f) 2H-MoS₂.

In 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJs, there are two important vdW interfaces: the ScCr₂C₂F₂/1T-MoS₂ interface and the ScCr₂C₂F₂/2H-MoS₂ interface. To find the stable interfacial connections in the vdW MTJs, we investigated the different stacking configurations of ScCr₂C₂F₂/1T-MoS₂ and ScCr₂C₂F₂/2H-MoS₂ heterostructures. As depicted in Fig. 3, each of them owns six different possible stacking configurations. For stacking-I of ScCr₂C₂F₂/1T-MoS₂ heterostructure, the Mo atoms of the 1T-MoS₂ layer lie on top of the upper F atoms of the ScCr₂C₂F₂ layer, and the upper Cr and C atoms sit right across the upper and bottom S atoms, respectively. Stacking-II and stacking-III are obtained from stacking-I by shifting the 1T-MoS₂ layer along the [110] direction of 1/3 and 2/3a, respectively. For stacking-IV, the Mo atoms of the 1T-MoS₂ layer lie on top of the Sc atoms and upper F atoms of the ScCr₂C₂F₂ layer, and the upper Cr and C atoms sit right from the bottom and upper S atoms, respectively. Similarly, stacking-V and stacking-VI are obtained from stacking-IV by shifting the 1T-MoS₂ layer along the [110] direction of 1/3 and 2/3a, respectively. For stacking-I of ScCr₂C₂F₂/2H-MoS₂ heterostructure, the Mo atoms of the 2H-MoS₂ layer lie on top of the upper C atoms, and the S atoms sit right across the upper Cr atoms. For stacking-IV of ScCr₂C₂F₂/2H-MoS₂ heterostructures, the Mo atoms of the 2H-MoS₂ layer lie on top of the upper Cr atoms, and the S atoms sit right across the upper C atoms. The transition of ScCr₂C₂F₂/2H-MoS₂ heterostructures from stacking-I to stacking-II/stacking-III and from stacking-IV to stacking-V/stacking-VI is the same as that in the ScCr₂C₂F₂/1T-MoS₂ heterostructure.

Fig. 3 The structure schematic diagrams of (a) ScCr₂C₂F₂/1T-MoS₂ heterostructure and (b) ScCr₂C₂F₂/2H-MoS₂ heterostructure with different stacking configurations.

To estimate the stabilities of the different stacking configurations, the binding energies (E_bind) and formation energies (E_form) were calculated using the following equations^67,68

E_form = E_{ScCr2C2F2/MoS2} − E_ScCr2C2F2 − E_MoS2 (3)

where E_{ScCr2C2F2/MoS2}is the total energy of the ScCr₂C₂F₂/1T-MoS₂ (or ScCr₂C₂F₂/2H-MoS₂) heterostructures, stand for the total energies of ScCr₂C₂F₂ and 1T-MoS₂ (or 2H-MoS₂) monolayers constrained in the corresponding heterostructure lattice, respectively. S is the interface area. E_ScCr2C2F2 and E_MoS2 represent the free-standing total energies of ScCr₂C₂F₂ and 1T-MoS₂ (or 2H-MoS₂) monolayers. The calculated E_bind and E_form are summarized in Table 1. The negative E_bind and E_form demonstrate that all the stacking configurations of ScCr₂C₂F₂/1T-MoS₂ and ScCr₂C₂F₂/2H-MoS₂ heterostructures can form spontaneously. It is worth noting that the stacking-II of ScCr₂C₂F₂/1T-MoS₂ heterostructure and stacking-I of ScCr₂C₂F₂/1T-MoS₂ heterostructure are more favorable to exist in experiments due to their lowest E_bind and E_form among various stacking configurations in Table 1. Based on the E_bind and E_form results, energetically-favorable stacking-II for the ScCr₂C₂F₂/1T-MoS₂ interface and stacking-I configurations for the ScCr₂C₂F₂/1T-MoS₂ interface were selected to construct the vdW MTJs.

Table 1 Formation energies E_form (meV) and binding energies E_bind (meV Å⁻²) of different stacking configurations of ScCr₂C₂F₂/1T-MoS₂ and ScCr₂C₂F₂/1T-MoS₂ heterostructures

Stacking	ScCr2C2F2/1T-MoS2		ScCr2C2F2/2H-MoS2
	E form	E bind	E form	E bind
I	−247.46	−29.88	−208.23	−25.15
II	−255.79	−30.91	−152.59	−18.69
III	−193.68	−23.43	−152.39	−18.65
IV	−250.63	−30.24	−201.82	−24.47
V	−251.70	−30.48	−204.12	−24.64
VI	−193.92	−23.44	−199.54	−24.15

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The work function (W_G) and charge transfer between different materials in the MTJ could strongly influence the interfacial effects and the devices' performance.^69,70 To further understand the interfacial effects in the 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJ, we calculated the electrostatic potential for the 1T-MoS₂, 2H-MoS₂ and ScCr₂C₂F₂ monolayers, as shown in Fig. 4a–c, respectively. The work function is defined as the difference between the vacuum energy level and the Fermi level of a 2D material. As depicted in Fig. 4a–c, the values of W_G for 1T-MoS₂, 2H-MoS₂, and ScCr₂C₂F₂ monolayers are 5.06, 5.84, and 6.78 eV, respectively. When two different 2D materials are in contact, the electrons of the lower work function side will flow to the higher work function side until their Fermi levels are equal.⁷¹ Therefore, the interlayer charge transfers from 1T-MoS₂/2H-MoS₂ to ScCr₂C₂F₂ layers are inferred due to the difference in work functions. To verify the corollary, the charge redistributions in the corresponding 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ heterostructure are represented from the differential charge density plots in Fig. 4d and e. As seen in the interfacial regions marked with magenta dashed boxes, charge accumulations occur at the F terminations in the ScCr₂C₂F₂ layers, and charge depletions are found at the S terminations in the 1T-MoS₂ and 2H-MoS₂ layers.

Fig. 4 The electrostatic potential E_p for (a) 1T-MoS₂, (b) monolayer ScCr₂C₂F₂ and (c) 2H-MoS₂. The differential charge density of 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ heterostructure in (d) PC and (e) APC states. The isosurface value is set to 0.0002 e bohr⁻¹,³ and the yellow and cyan regions represent the accumulation and depletion of electrons, respectively. The magenta dashed box represents the interfacial region.

To investigate whether the half-metallicity of ScCr₂C₂F₂ can be retained in vdW MTJs, we calculated the spin-dependent projected band structures of the 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ heterostructure when the ScCr₂C₂F₂ layers are in PC and APC states. Compared with the band structures of corresponding monolayers in Fig. 2, the projected band structures of the 1T-MoS₂ and 2H-MoS₂ layers move up with respect to the Fermi level, as shown in Fig. 5a, c and e. On the other hand, a conversely downward shift is found for the projected band structures of the ScCr₂C₂F₂ layers, as shown in Fig. 5b and d. The energy-level shift agrees well with the charge transfers of electrons in the process of forming the heterostructure we have shown previously. Furthermore, the half-metallic electronic structures of the left and right ScCr₂C₂F₂ layers are well maintained, and only the spin-up channel of the PC state is conductive, while the other three channels are insulating. The difference in transmission mainly comes from the spin-up channel of ScCr₂C₂F₂ that allows the electrons to pass through, while its spin-down channel prevents electrons from passing through. Therefore, the spin filter effect is mainly contributed by the spin-resolved band structures of ScCr₂C₂F₂, rather than the interface between ScCr₂C₂F₂ and 2H-MoS₂. Tis phenomenon reveals a large conductivity difference between PC and APC states, which indicates a distinguished performance of the ScCr₂C₂F₂-based vdW MTJs.

Fig. 5 The spin-dependent projected band structures of (a) left-1T-MoS₂ (b) left-ScCr₂C₂F₂ (c) 2H-MoS₂ (d) right-ScCr₂C₂F₂ and (e) right-1T-MoS₂ in the 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ heterostructure.

Furthermore, to understand the thickness effects of the tunnel barrier, odd layer number 2H-MoS₂ with different layer n (n = 1, 3, 5) was taken into account, following the principle of control variables. In the following discussion, 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJs with one, three and five 2H-MoS₂ layers are abbreviated as MTJ-HM, MTJ-3HM and MTJ-5HM, respectively. The corresponding atomically structured schematics of the vdW MTJs are illustrated in Fig. 6. Herein, after the full-structure optimizations of the vdW MTJs, the relaxed interface distances between different materials are summarized in Table 2. For all the vdW MTJs, the distances between 2H-MoS₂ and ScCr₂C₂F₂ (d_LC and d_RC) are around 2.7–3 Å, and the distances between 1T-MoS₂ and ScCr₂C₂F₂ (d_L and d_R) hold smaller values around 2.4–2.5 Å, revealing weak vdW connections in the MTJs.

Fig. 6 The schematic illustrations of 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJs with (a) one (MTJ-HM) (b) three (MTJ-3HM) and (c) five (MTJ-5HM) 2H-MoS₂ tunnel barrier layers.

Table 2 The interface distances d_L, d_LC, d_RC and d_R (Å) of left-1T-MoS₂/left-ScCr₂C₂F₂, left-ScCr₂C₂F₂/2H-MoS₂, 2H-MoS₂/right-ScCr₂C₂F₂ and right-ScCr₂C₂F₂/right-1T-MoS₂ interfaces in different vdW MTJs

MTJs	d L	d LC	d RC	d R
MTJ-HM	2.44	3.01	2.93	2.49
MTJ-3HM	2.48	2.76	2.76	2.48
MTJ-5HM	2.48	2.72	2.78	2.44

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To investigate the spin-dependent transport properties, we calculated the transmission coefficients at the equilibrium state for the 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJs. Fig. 7 shows the zero-bias transmission coefficient curves from −1.2 eV to 1.2 eV for MTJ-HM, MTJ-3HM, and MTJ-5HM in PC and APC states. For all the vdW MTJs in the PC state, the maximum spin-up and spin-down transmission coefficients appear around −1 eV below the Fermi level, and the spin-down transmission coefficients suffer more reduction than spin-up transmission coefficients with the energy region approaching the Fermi level. Therefore, the spin-up transmission coefficients at the Fermi level are several orders of magnitude larger than the spin-down transmission coefficients. Herein, the spin-up channel plays a decisive role in the transmission process. When the vdW MTJs are in an APC state, the spin-up transmission coefficients are almost equivalent to the spin-down transmission coefficients of the entire energy region, and the minimum values occur around the Fermi level. Hence, the transmission capacity of both spin channels is tiny in the APC state.

Fig. 7 The transmission coefficients for (a) MTJ-HM, (b) MTJ-3HM, and (c) MTJ-5HM in PC and APC states.

To quantitatively analyse the device performance of the 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJs, the TMR ratios can be calculated using the following equation^14,72

TMR = (G_PC − G_APC)/G_APC × 100% (4)

where G_PC and G_APC are the total spin-dependent conductance of the PC and APC states, which are defined as

G_PC = T^↑_PC(E_f) + T^↓_PC(E_f) (5)

G_APC = T^↑_APC(E_f) + T^↓_APC(E_f) (6)

where T^↑_PC(E_f) and T^↓_PC(E_f) represent the spin-up and spin-down transmission coefficients at the Fermi level when the vdW MTJs are in the PC state, and T^↑_APC(E_f) and T^↓_APC(E_f) represent the spin-up and spin-down transmission coefficients, respectively, at the Fermi level when the vdW MTJs are in the APC state. Table 3 lists the calculated spin-dependent transmission coefficients at the Fermi level, total spin-dependent conductances, and TMR ratios. It was observed that the total spin-dependent conductances decrease exponentially with the increase in the 2H-MoS₂ barrier layers. It was noted that G_PC of MTJ-HM is five orders of magnitude larger than G_APC, which results in the giant TMR ratios of 2.95 × 10⁶%. Interestingly, although, G_PC and G_APC was reduced by several orders of magnitude, when the tunnel-barrier 2H-MoS₂ increases to three layers, the TMR ratio of MTJ-3HM increases to 6.95 × 10⁶% since the corresponding G_PC is six orders of magnitude larger than G_APC. Besides, when the number of tunnel-barrier 2H-MoS₂ increases to five layers, the TMR ratios of MTJ-5HM decrease to 9.24 × 10⁵%, which is still a considerable giant value. Furthermore, the transmission calculations by including the spin–orbit coupling (SOC) are shown in Table S1.† It is noted that the SOC should contribute to the spin-flip scattering, enhancing the transmission probability in antiparallel configuration and reducing the TMR. Nevertheless, the proposed vdW MTJ devices showed considerable TMR values at a 10⁴% level.

Table 3 The calculated transmission coefficients (e²/h) of the spin-up channel in the PC state T^↑_PC(E_f), spin-down channel in the PC state T^↓_PC(E_f), spin-up channel in the APC state T^↑_APC(E_f), and spin-down channel in the APC state T^↓_APC(E_f), total spin-dependent conductances (e²/h) in the PC state G_PC and the APC state G_APC, and TMR ratios for MTJ-HM, MTJ-3HM, and MTJ-5HM devices

MTJs	T PC ^↑(Ef)	T PC ^↓(Ef)	T APC ^↑(Ef)	T APC ^↓(Ef)	G PC	G APC	TMR (%)
MTJ-HM	1.19 × 10^−5	1.76 × 10^−12	2.03 × 10^−10	2.02 × 10^−10	1.19 × 10^−5	4.05 × 10^−10	2.95 × 10^6
MTJ-3HM	1.30 × 10^−8	3.43 × 10^−15	9.36 × 10^−14	9.27 × 10^−14	1.30 × 10^−8	1.86 × 10^−13	6.95 × 10^6
MTJ-5HM	5.51 × 10^−11	1.96 × 10^−15	2.32 × 10^−15	3.64 × 10^−15	5.51 × 10^−11	5.96 × 10^−15	9.24 × 10^5

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Moreover, we calculated the spin-dependent k_‖-resolved transmission spectrums at the Fermi level to better represent the physical origin of the giant TMR effects in the 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJs. Herein, Fig. 8 illustrates the transmission spectrum of MTJ-3HM as an example since it shows the highest TMR ratio. For reference, the transmission spectra of MTJ-HM and MTJ-5HM are presented in Fig. S3 and S4,† respectively. Fig. 8a shows that there are six crescent-shaped high transmission regions in the spin-up transmission spectrum for MTJ-3HM in the PC state. However, there is no distinguishable high transmission region in the whole k_‖-resolved regions for the spin-down transmission spectrum in Fig. 8b. On the other hand, the transmission regions of both spin-up and spin-down channels are similar for MTJ-3HM in the APC state. Herein, it is noted that the transmission capacity of the APC state is several orders of magnitude smaller than that of the PC state, which leads to the apparent TMR effect. In addition, the spin-dependent projected local density of states of MTJ-HM, MTJ-3HM, and MTJ-5HM along the transport direction are shown in Fig. S5, 9 and S6,† respectively. The corresponding vdW MTJ model is illustrated in the bottom panel for reference. Regardless of the PC or APC states, it was observed that the 1T-MoS₂ electrodes and 2H-MoS₂ barriers still exhibit their metallic and semiconducting properties, respectively. However, the ScCr₂C₂F₂ monolayer shows metallic properties in the spin-up channel but presents a semiconducting feature in the spin-down channel in the PC state and vice versa in the APC state. As a result, in the PC state, for the electron transport process from the left to right in the 1T-MoS₂ electrodes, the spin-up electrons only need to go through the potential barrier of the 2H-MoS₂ layer. However, the spin-down electrons have to overcome a much higher potential barrier, which is from the left and right ScCr₂C₂F₂ layers as well as the 2H-MoS₂ layers. On the other hand, in the APC state, the spin-up (spin-down) electrons have to overcome the potential barriers of the right (left) ScCr₂C₂F₂ layer and the 2H-MoS₂ layers for the electron transport process from the left to right 1T-MoS₂ electrodes. Therefore, the spin-up electrons in the PC state are proved to play a decisive role in the transmission behavior, which agrees well with our previously electronic structure analysis.

Fig. 8 The spin-dependent k_‖-resolved transmission spectrums of MTJ-3HM at the Fermi level for (a) spin-up and (b) spin-down channels in the PC state and (c) spin-up and (d) spin-down channels in the APC state.

Fig. 9 The spin-dependent projected local density of states of MTJ-3HM for (a) spin-up and (b) spin-down channels in the PC state, (c) spin-up, and (d) spin-down channels in the APC state.

Conclusion

In summary, by combining density functional theory and nonequilibrium Green's function calculations, we investigated the transport properties of 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ vdW MTJs with different thicknesses of the 2H-MoS₂ tunnel barrier. The different stacking configurations of ScCr₂C₂F₂ relative to 1T-MoS₂ and 2H-MoS₂ were firstly studied to determine the stable interface configurations. The calculated formation energies and binding energies indicated that all the interface configurations can form spontaneously. Besides, the interlayer charge transfers from the 1T-MoS₂/2H-MoS₂ to ScCr₂C₂F₂ layers can be inferred due to the work function differences. The projected band structures of the corresponding 1T-MoS₂/ScCr₂C₂F₂/2H-MoS₂/ScCr₂C₂F₂/1T-MoS₂ heterostructure revealed that the ScCr₂C₂F₂ monolayer can still maintain half-metallicity with perfect polarization in vdW MTJs. Subsequently, the thickness of the 2H-MoS₂ tunnel barrier was considered for further performance optimizations. It is remarkable to note that all the vdW MTJs hold giant TMR ratios over 9 × 10⁵%, and the maximum TMR ratio of 6.95 × 10⁶% was obtained in vdW MTJ with a trilayer 2H-MoS₂ tunnel barrier, demonstrating the potential of such vdW MTJs for applications.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 52201022, 21973012, 51872017, and 51871009), the Natural Science Foundation of Fujian Province (Grant No. 2021J06011, 2020J01351, 2020J01474, and 2021J01590), and the “Qishan Scholar” Scientific Research Project of Fuzhou University.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2na00623e

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