Large tunneling magnetoresistance and its high bias stability in Weyl half-semimetal based lateral magnetic tunnel junctions

Magnetic tunnel junctions (MTJs) based on novel states of two-dimensional (2D) magnetic materials will significantly improve the value of the tunneling magnetoresistance (TMR) ratio. However, most 2D magnetic materials exhibit low critical temperatures, limiting their functionality to lower temperatures rather than room temperature. Moreover, most MTJs experience the decay of TMR ratio at large bias voltages within a low spin injection efficiency (SIE). Here, we construct a series of MTJs with Weyl half-semimetal (WHSM, e.g. MnSiS3, MnSiSe3, and MnGeSe3 monolayers) as the electrodes and investigate the spin-dependent transport properties in these kind of lateral heterojunctions by employing density functional theory combined with non-equilibrium Green’s function method. We find that an ultrahigh TMR (∼109%) can be obtained firmly at a small bias voltage and maintains a high SIE even at a large bias voltage, and MnSiSe3 monolayer is predicted to exhibit a high critical temperature. Additionally, we reveal that the same structure allows for the generation of fully spin-polarized photocurrent, irrespective of the polarization angle. These findings underscore the potential of WHSMs as candidate materials for high-performance spintronic devices.

The MAX 3 family (M = V, Cr, Mn, Fe, Co, Ni; A = Si, Ge, Sn; X = S, Se, Te), known as transition-metal trichalcogenides, not only share a similar structure with the MPX 3 family but also exhibit different magnetic states [26][27][28][29][30].In this case, the bipyramids at the center of the honeycomb lattice, constructed by transition-metal ions M, consist of (A 2 X 6 ) 6− rather than (P 2 X 6 ) 4− .These two families offer a robust platform for device design due to their analogous crystal structures and diverse fundamental properties [28,29].
In this work, we find a new state in MnSiS 3 , MnSiSe 3 , and MnGeSe 3 monolayers, i.e. the Weyl half-semimetal (WHSM) state.We aim to construct a high-performance multifunctional device based on this state.It is well-known that ferromagnetic (FM) MTJs consist of two FM regions separated by an insulating section.As for the insulating area, ZnPS 3 , ZnPSe 3 , and ZnAsSe 3 monolayers are selected due to a lower lattice mismatch ratio with the electrode materials aforementioned.A series of lateral MTJs are constructed, resulting in an ultrahigh TMR ratio of 10 9 % at low bias voltage.Moreover, a fully spin-polarized photocurrent and a nearly pure spin photocurrent were observed within the same MnSiSe 3 /ZnPSe 3 /MnSiSe 3 structure.The results of MnSiSe 3 /ZnPSe 3 /MnSiSe 3 MTJs are exhibited in the main text, whereas the results of MnSiS 3 /ZnPS 3 /MnSiS 3 and MnGeSe 3 /ZnAsSe 3 /MnGeSe 3 MTJs are indicated in supporting information for simplicity.

Methodology
In our study, first-principles calculations are performed using the Vienna ab initio simulation package employing the projector augmented wave method [31][32][33].The exchange-correlation energy is estimated using the Perdew-Burke-Ernzerhof (PBE) parameterization of the generalized gradient approximation [34].Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) is adopted to ensure band alignment [35].Energy and force convergence criteria are defined as 10 −6 eV and 0.001 eV Å −1 , respectively, utilizing a plane wave energy cutoff of 500 eV, and a vacuum of 20 Å along the z-direction is chosen.The DFT-D3 method with zero-damping is selected to treat the vdW interaction [36].The Brillouin zone is sampled using a Γ-centered k-mesh with a 12 × 12 × 1 grid for self-consistent calculations, and the total energy of four magnetic states is compared to ascertain the ground state of monolayers MnSiX 3 .The on-site effective interaction parameter U eff is set to 4.0 eV for the Mn atom, consistent with previous works [29,30].The Berry curvature is calculated with WANNIER90 and WANNIERTOOLS packages [37,38].
The critical temperature is determined through Monte Carlo simulations using a 24 × 24 × 1 supercell and employing the Metropolis algorithm, which is based on the classical spin Hamiltonian [39,40]: where the J 1 , J 2 , and J 3 are defined as the nearest neighbor (NN), the second-nearest neighbor (SNN), and the third-nearest neighbor (TNN) exchange interaction parameters, respectively.The choice of the unit cell depends on the magnetic ground state of the MnSiX 3 monolayer, and the number of steps for each temperature is set to 10 6 .Phonon dispersion (0 K) spectra are calculated using the finite displacement method with a 3 × 3 × 1 supercell implemented in the Phonopy code [41,42].An ab initio molecular dynamics (AIMD) simulation at 300 K is conducted for a duration of 10 ps to account for the effects of finite temperature.The resulting phonon dispersion (300 K) is plotted and renormalized using the DynaPhoPy code [43].
The spin transport properties and photocurrent of MnSiSe 3 /ZnPSe 3 /MnSiSe 3 lateral heterojunction are calculated using the non-equilibrium Green's function (NEGF) method, which is implemented in package NANODCAL [44,45].The exchange-correlation functional takes the PBE with the double-zeta plus polarization atomic orbital basis sets, and the on-site Coulomb interaction is also considered.The electronic self-consistent calculations are performed separately for the electrodes and the center region.For the Brillouin zone sampling, a grid of 100 × 6 × 1 k points is used for the electrodes, while a grid of 3 × 6 × 1 k points is used for the center region.An energy cutoff of 80 Hartree is applied in these calculations.The transport calculation uses a grid of 1 × 100 × 1 k points for the Brillouin zone sampling.
In our case, we investigate the magnetization configurations of parallel (P) and anti-parallel (AP) orientations.In the P configuration, the spin orientations of Mn atoms in the left and right electrodes are the same, while in the AP configuration, they are inverse.Applying the proper external magnetic field will cause the spin to reverse.The TMR ratio is defined as TMR = IP−IAP IAP × 100%, where I P(AP) is the total current in the parallel (anti-parallel) state, and the spin-resolved current is calculated using the following equation: where T ↑(↓) (E, V) is the transmission coefficient at energy E with spin ↑ (↓) under the applied bias voltage V, f (E−µ L(R) ) denotes the Fermi distribution function of electrons in the left (right) electrode, while µ L(R) signifies the chemical potential of the left (right) electrode.
A system considered the electron-photon interaction could be described by the Hamiltonian Ĥ = Ĥ0 + Ĥe×ph , where the electron-photon interaction, Ĥe×ph = e m0 A • P, is taken into account as a perturbation to analyze the photocurrent, where P is the momentum of the electron and A is the polarization vector of the light.A is usually given by: where μr , εr , and ε are the relative susceptibility, relative dielectric constant, and absolute dielectric constant, respectively.e = cosθe 1 + sinθe 2 represents polarization of the field, I ω is the photon flux, b and b † are the bosonic annihilation and creation operators (In our calculations, the incidence direction of the light, e 1 × e 2 , is always perpendicular to the transport plane).Subsequently, the electron-photon interaction can be written in matrix form as: where l and m are atomic orbital labels, a and a † are electron annihilation and creation operators.The self-energy ∑ >,< lm (E), linewidth function of the electrodes Γ, and greater or lesser Green's function G >/<(ph) (E) could be calculated.Finally, the photocurrent injected into the electrode L can be written as [46][47][48]: )]} dE. (5)

Results and discussion
Figure 1 displays the unit cell of both ZnPSe 3 and MnSiSe 3 monolayers, which belong to a triangular lattice exhibiting the symmetry of point group D 3d .The structural parameters for all ZnPX 3 and MnSiX 3 monolayers are listed in table S1 (see supplemental material for more details).These optimized cells align with previous calculations and are highly conducive to constructing a heterojunction due to a minute contraction (1%) observed in all three partners [28,29].
The magnetic ground state of ZnPX 3 and MnSiX 3 monolayers requires identification.It is easy to predict that ZnPX 3 is non-magnetic due to the full-filled 3d shell of Zn.As for MnSiX 3 , the magnetic ground state is determined using the state mapping method: the FM state for MnSiSe 3 and MnSiTe 3 monolayer, which agrees with previous works [28][29][30].The exchange interaction parameters can be extracted from DFT calculations where E FM , E NAFM , E SAFM , and E ZAFM represent the total energy of the FM state, Néel antiFM state, stripy antiFM state, and zigzag antiFM state, respectively; The J 1 , J 2 , and J 3 are defined as the NN, the SNN), and the TNN exchange interaction parameters, respectively (see supplemental material for more details).
Remarkably, the situation of MnSiSe 3 monolayer closely resembles that of the hole-doped MnPSe 3 monolayer, which was thoroughly investigated in our prior study [49].The critical temperatures we simulated are 314 K, 442 K, and 271 K for the MnSiS 3 , MnSiSe 3, and MnSiTe 3 monolayers, respectively (figure S3 in supplemental material).The energy differences between the antiFM and FM states in MnSiS 3 , MnSiSe 3 , and MnSiTe 3 monolayers are 0.33 eV, 0.35 eV, and 0.26 eV, respectively.Consequently, MnSiSe 3 monolayer exhibits the highest resistance to spin flipping, followed by MnSiS 3 and MnSiTe 3 .As a result, the phase transition temperature is highest for MnSiSe 3 , followed by MnSiS 3 , and lowest for MnSiTe 3 .
Figure 2 illustrates that ZnPX 3 monolayer exhibits semiconductor properties, while MnSiSe 3 monolayer in the FM state is Weyl half semi-metallic and the half-metallic gap is 0.33 eV.Notably, based on the higher critical temperature, more significant half-metallic gap, and appropriate lattice constants, ZnPSe 3 and MnSiSe 3 are deliberately selected to construct the lateral heterojunction, as depicted in figures 1(c) and (d).
The AIMD and phonon dispersion under finite temperature are considered to ascertain the stability of the MnSiSe 3 monolayer (refer to the supplemental material for further details).In AIMD simulation, the total   energy oscillates at equilibrium, and the tiny imaginary frequencies in the zero-temperature phonon spectrum are eliminated at room temperature.
In contrast to the semiconducting nature of MnPSe 3 or CrGeTe 3 , MnSiSe 3 monolayer exhibits half-metallic properties.Detailed projected band structures of the MnSiSe 3 monolayer are plotted, focusing on the bands near the Fermi level, which primarily originate from the 4p orbitals of the Se atom (figure S7 in the supplemental material for additional information).Consequently, the magnetic moment of Mn remains local, indicating the presence of a Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling responsible for the remarkably large TNN FM interaction, similar to that observed in the MnSiTe 3 monolayer [30].
Figure 3(a) presents the spin-resolved currents, which vary with bias voltage along the zigzag directions.In this context, the spin-up and spin-down currents are denoted as I ↑ and I ↓ , respectively.The results show that I ↑ in the P magnetization configuration is more extensive and remains stable when a bias voltage is applied, even though the I ↑ under the AP magnetization configuration is increasing rapidly.This characteristic indicates a significant TMR and remarkably high SIE, which are highly beneficial for spintronic applications of MTJs. Figure 3(b) illustrates the TMR as a function of the applied bias voltage, following equation ( 2).The calculated TMR exhibits a remarkable value exceeding 10 9 % and remains stable within a bias voltage range of 0-200 mV.Even though the larger bias voltages reduce the magnetoresistance due to continuously increasing I ↑ under the AP magnetization configuration, the TMR remains above 10 3 % at a bias voltage of 900 mV.SIE is defined as SIE = (I ↑ +I ↓ ) (I ↑ −I ↓ ) × 100%, and our calculation demonstrates a consistent SIE of nearly 100% across the entire 0-900 mV bias voltage range.There is no transport anisotropy here.The only distinction between the zigzag and armchair directions lies in the smaller current observed in the armchair direction, which is attributed to the more extended barrier width (figure S9 in supplemental material for more details]. The k-resolved transmission coefficients for the spin-up state in the P magnetization configuration are represented in figure 3(c), where the contributions are divided into two parts: the k y component falls within (k y -Weyl) or outside (k y -other) the projected range of the two Weyl points, as shown in the inset of figure 3(c).In our calculations, the applied potential on the left electrode is higher than that on the right electrode, meaning that electrons move from the right to the left electrode.As the increment of bias voltage (from the bottom to the top in figure 3(c)), the contribution of k y -Weyl near the chemical potential of the right electrode (the dashed-dot gray rectangle in figure 3(c)) to the transport becomes more significant.The same situation also occurred in MnGeSe 3 /ZnAsSe 3 /MnGeSe 3 MTJs (figure S16 in supplemental material for more details).
The spin-resolved local density of states (LDOS) of MnSiSe 3 /ZnPSe 3 /MnSiSe 3 MTJ is depicted in figure 4, and a typical MTJ image is shown.The LDOS analysis reveals that, under the P magnetization configuration, two channels are present in the left and right electrodes for electrons with spin-up (figure 4(a)).Consequently, I ↑ exhibit a maximum value in this configuration (refer to figure 3(a)).In contrast, the P magnetization configuration lacks any electron channel for electrons with spin-down (figure 4(b)), indicating the absence of states in the electrode regions that connect the entire device.As a result, I ↓ attain a minimum value under the parallel magnetization configuration.In the AP magnetization configuration, only one electron channel exists for the spin-up or spin-down state (figures 4(c) and (d)), causing the current to assume a median value.
The results obtained from the LDOS demonstrate that the electron channel exclusively relies on the spin direction.Specifically, only spin-up electrons can go through the barrier, blocking the passage of spin-down electrons.This behavior can be primarily attributed to the half-metallic nature of the MnSiSe 3 monolayer in the electrode part.In contrast, the electrons capable of passing through the barrier layer depend on the symmetry selection within the barrier region rather than the electrode in the case of traditional MTJ (e.g.CoFeB/MgO/CoFeB MTJs).It is worth noting that during the computation of NEGFs, we assume that the left and right electrodes are semi-infinite, disregarding any spin polarization direction alteration due to lattice thermal motion, defects, or impurities.
As an illustration of the benefits of our selection, we conducted spin-dependent transport property tests on MnSiTe 3 /ZnPTe 3 /MnSiTe 3 lateral MTJ.In simple terms, the performance of MnSiTe 3 /ZnPTe 3 /MnSiTe 3 MTJ is significantly inferior to that of MnSiSe 3 /ZnPSe 3 /MnSiSe 3 MTJ due to its complete lack of a half-metallic gap.As the bias increases from 0 to 500 meV, the TMR value is always below 10 3 %.We also attempted to keep the electrodes fixed while altering the barrier layer and found that the barrier layer did not significantly affect the device's performance.Note that the related results are shown in table 1, including the  phase transition temperature of electrode materials, the bandgap value of barrier materials, and the maximum TMR achieved after forming an MTJ (refer to the supplemental material for additional information).
In optoelectronics, the generation and manipulation of spins offer promising prospects for spin-optoelectronics, facilitating the investigation of novel spin photovoltaic effects and spin photocurrents.Due to the unique Weyl half-metallic properties exhibited by monolayer MnSiSe 3 , MnSiSe 3 /ZnPSe 3 /MnSiSe 3 structure is expected to demonstrate remarkable characteristics in its optoelectronic response.These characteristics include a fully spin-polarized photocurrent, an impeccable spin-filtering effect, an excellent spin-valve effect, and a pure spin photocurrent.
Figure 5 illustrates that all photocurrent exhibits a cosine relationship with the polarization angle, which aligns with previous findings [50][51][52].Within the energy range of 1.6-2.4eV, the P magnetization configuration shows a significantly higher spin-up photocurrent than the spin-down photocurrent (figures 5(a) and (b)).This observation indicates the presence of a fully spin-polarized photocurrent, and this holds for all polarization angles.Compared to the previous investigation, where the spin-polarized photocurrent could only be obtained at some specific polarization angles, this result undeniably broadens the applicability of this structural configuration.[32] Within the entire range of visible light, this structure exhibits a distinct difference in the sign of the photocurrent for spin-up and spin-down under the AP magnetization configuration (figures 5(c) and (d)), indicating opposing flow directions.Consequently, it potentially functions as an efficient generator of pure spin current.
Notably, the current's relative magnitude differs under illumination compared to when bias is applied.In the P magnetization configuration, two channels exist for spin-up electrons (refer to figure 4(a)).When incident on the insulating layer, the photo-generated electrons with spin-up can move toward both the left and right electrodes, resulting in a reduced net value (figure 5(a)).Due to the absence of a channel for spin-down electrons (refer to figure 4(b)), the P magnetization configuration results in an almost negligible current value (figure 5(b)).In the AP magnetization configuration, the channels for spin-up and spin-down electrons are positioned on the left and right, respectively (refer to figures 4(c) and (d)).Therefore, photo-generated electrons with differing spins can exclusively move towards their respective sides, resulting in a peak photocurrent value (figures 5(c) and (d)), where a new path to generate and manipulate spin-polarized currents has been unveiled.

Conclusions
In summary, we employed a NEGF method to investigate the properties of spin transport and optoelectronic response in MnSiSe 3 /ZnPSe 3 /MnSiSe 3 lateral heterojunction.Our results show that MnSiS 3 , MnSiSe 3 , and MnGeSe 3 monolayers are predicted to be WHSM.A series of lateral heterojunctions are constructed based on the novel property first.Additionally, the atomic and electronic structures support the rationality of the MnSiSe 3 /ZnPSe 3 /MnSiSe 3 heterojunction, characterized by high critical temperature, a tiny lattice mismatch ratio, and structural stability of components.We found an ultrahigh TMR ratio within a high SIE and a fully spin-polarized photocurrent in the same lateral heterojunction.Furthermore, our study elucidates that these outstanding properties depend highly on the Weyl half-metallic nature of electrode materials.Thus, our study not only indicates that the lateral heterojunction of MnAX 3 /ZnBX 3 /MnAX 3 holds excellent promise as a multifunctional device but also provides insights for the design of high-performance spintronic devices based on WHSM and related structures.

Figure 1 .
Figure 1.Unit cell of monolayer (a) ZnPSe3 (b) MnSiSe3, where bipyramids are also exhibited.Top and side views of the device model based on MnSiSe3/ZnPSe3/MnSiSe3 lateral heterojunction along (c) zigzag and (d) armchair directions.The polarization angle, θ, is also plotted in (c) for the zigzag direction under normal incidence.

Figure 3 .
Figure 3. Calculated (a) spin-resolved current, (b) TMR, and (c) k-resolved transmission coefficients for the spin-up state of MnSiSe3/ZnPSe3/MnSiSe3 MTJ along the zigzag direction.The solid black regular hexagon and dashed light-blue rectangle in subfigure (c) illustrate the first Brillouin zone of the reciprocal lattice for the primitive and rectangular cells in MnSiSe3 monolayers, respectively.In subfigure (c), the red and black lines represent whether the ky component falls within or outside the projected range (the red lines along the M-M ′ path in the inset) of the two Weyl points (the red points located at the Γ-M path in the inset).The dashed-dot gray rectangle represents the energy range for Weyl points under different bias voltages.

Figure 4 .
Figure 4. Spin-resolved logarithmic LDOS of (a) spin-up and (b) spin-down electrons under the parallel configuration.Spin-resolved logarithmic LDOS of (c) spin-up and (d) spin-down electrons under the anti-parallel configuration.

Figure 5 .
Figure 5. (a) Spin-up and (b) spin-down photocurrents vary with polarization angle for different photon energies under parallel configuration.(c) Spin-up and (d) spin-down photocurrents vary with polarization angle for different photon energies under anti-parallel configuration.

Table 1 .
Phase transition temperature for MnSiX3 monolayer, bandgap for ZnPX3 monolayer, and the maximum TMR achieved after forming a magnetic tunnel junction.