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Despite the extensive studies on MTJs composed of vdW magnetic homojunction (denoted as homojunction MTJs), the ones composed of magnetic heterojunctions (denoted as heterojunction MTJs) have been rarely explored. Since the heterojunction geometry generally leads to additional symmetry breaking, much more distinguishable magnetoresistances are expected in a heterojunction MTJ than that in a homojunction one. Thus, unveiling the TMR properties of heterojunction MTJs is of great importance to the development of high-performance spintronic devices.
By using the first-principles calculations, here, we reveal distinguishable multi-state TMRs of vdW magnetic heterojunction composed of bilayer CrI3 and bilayer Cr2Ge2Te6. We find that the heterojunction can hold eight distinguishable magnetic states, which is more than two times larger than that of a four-layered magnetic homojunction. As a result, five sizable TMRs larger than 300% can be obtained, with the maximum TMR up to 620 000%. We also find that magnetic states of both bilayer CrI3 and bilayer Cr2Ge2Te6 can be efficiently tuned by an external electric field, showing that the magnetoresistances can be easily controlled via electric fields.
The calculation method is shown in the supplementary material. The calculated in-plane lattice constants of CrI3 and Cr2Ge2Te6 are 7.00 Å and 6.92 Å, respectively, which are in excellent agreement with previous studies.26–2826. R. Xu and X. Zou, J. Phys. Chem. Lett. 11, 3152 (2020). https://doi.org/10.1021/acs.jpclett.0c0056727. Y. F. Li, W. Wang, W. Guo, C. Y. Gu, H. Y. Sun, L. He, J. Zhou, Z. B. Gu, Y. F. Nie, and X. Q. Pan, Phys. Rev. B 98, 125127 (2018). https://doi.org/10.1103/PhysRevB.98.12512728. P. Li, X. Zhou, and Z. Guo, npj Comput. Mater. 8, 20 (2022). https://doi.org/10.1038/s41524-022-00706-w As shown in Figs. 1(b) and 1(d), in the AFM (FM) state, both bilayer Cr2Ge2Te6 and bilayer CrI3 are semiconductors with band gaps of 0.61 (0.40) and 1.14 (1.04) eV, respectively. Moreover, their conduction band minimum (CBM) is contributed by a pure spin-polarized state, indicating that they are ideal candidates for MTJ devices.The combination of bilayer Cr2Ge2Te6 and bilayer CrI3 forms a four-layered magnetic heterojunction. Here, we considered several typical stacking configurations (see Fig. S1) and found the configuration with para-position of I and Ge atoms at the interface is the most stable [Fig. S1(b)]. The Cr2Ge2Te6-CrI3 interlayer distance is 3.37 Å with the cohesive energy of about 17 meV/Å2, showing the nature of vdW interface coupling. We have also calculated the magnetocrystalline anisotropy energy (MAE) of heterojunction, which is defined as the energy difference with magnetization direction between [001] and [010] directions. The MAE of the heterojunction is −3.93 meV, showing the nature of perpendicular magnetization in the heterojunction. This result implies that the intrinsic spin-polarized electronic properties of CrI3 and Cr2Ge2Te6 can be preserved in the heterojunction.
According to the symmetry analysis, the four-layered magnetic heterojunction has eight distinguishable magnetic states, that is, ↑↑↑↑ (FM), ↑↓↑↓ (AFM-I), ↑↓↓↑(AFM-II), ↑↑↓↓ (AFM-III), ↑↑↑↓ (FIM-I), ↑↑↓↑ (FIM-II), ↓↑↑↑ (FIM-III), and ↑↓↑↑ (FIM-IV) [Fig. 1(e)]. The calculated total energies of the eight states are shown in Table S1, where the maximum energy difference is within 20 meV. Figure 2 additionally shows the projected energy bands of the eight possible states. A common characteristic is that the band structure morphologies of bilayer CrI3 and bilayer Cr2Ge2Te6 change little after stacking into a heterojunction, owing to the weak vdW interlayer coupling between Cr2Ge2Te6 and CrI3. As a result, the spin-projected band structures of the AFM-I state ↑↓↑↓ and AFM-II state ↑↓↓↑ are analogous. Similarly, it is not surprising that there is little band structure difference between the FIM-I ↑↑↑↓ and FIM-II ↑↑↓↑ states and that between the FIM-III ↓↑↑↑ and FIM-IV ↑↓↑↑ states. It is worth noting that similar band structures do not guarantee a similar spin-polarized transport property. As shown in the calculated TMR results below, despite there being only five distinguishable band structures, five distinguishable TMR values can still be produced by the eight magnetic states.The schematic diagram of the MTJ device is shown in Fig. 1(f), where the Cr2Ge2Te6/CrI3 heterojunction is sandwiched between two multilayer graphene electrodes. The ATK software was used to calculate the spin-polarized transport property. Figure 3 shows the calculated spin-resolved transmission spectra of the eight magnetic states in an energy range of [−2, 2] eV. A common feature is that the transmission spectra difference between spin-up and spin-down electrons of all the eight magnetic states is very small below the Fermi level (EF), whereas it becomes significantly large above EF. This phenomenon can be understood from the spin-resolved band structures. As shown in Fig. 2, the energy bands of both spin-up and spin-down electrons in the heterojunction largely overlap below EF, so there is almost no isolated spin-polarized state in an energy range of [−2, 0] eV. However, above EF, the isolated spin-polarized states of CrI3 appear, which can lead to a significant difference in the spin-resolved transmission spectra. Note that the transmission spectra profiles of the eight magnetic states are distinguishable from each other above EF, owing to the multiplex spin-polarized band alignments in the Cr2Ge2Te6/CrI3 heterostructure. Furthermore, the transmission spectra difference has a strong dependence on the interlayer magnetic order of bilayer CrI3. When the bilayer CrI3 is in FM interlayer coupling, there is a significant transmission difference between spin-up and spin-down electrons, whereas, when the CrI3 is in the AFM interlayer coupling state, the transmission difference is tiny. This phenomenon mainly resulted from the more compatible energy levels of FM CrI3 with that of Cr2Ge2Te6, which leads to a large energy band overlap region in the conduction bands (Fig. 2).This plentiful transmission spectrum means that multiple TMR values can be obtained in the MTJ device, which motivated us to explore the I-V curve characteristics of all eight magnetic states. At a bias-voltage Vb, the spin-resolved current can be calculated as follows: Iσ(Vb)=eh∫−∞+∞dE[f(E, μL)−f(E, μR)]Tσ(E,Vb),(1)where f(E, μL) and f(E, μR) are the Fermi–Dirac distribution of the left and right electrodes, respectively. μL and μR are the electrochemical potential of the left and right electrodes, respectively, and Tσ(E) is the transmission probability for an electron at energy E with spin σ. The linear response current originated from the equilibrium transmission spectrum at zero bias is considered in the calculations.As shown in Fig. 4, the flour-layered magnetic heterojunction can lead to a novel distribution of I-V curves. The I-V curves can be divided into three groups. That is, the FM, FIM-III, and AFM-III states have the largest current, the FIM-I, FIM-II, and AFM-I states have the smallest current, and the current of remaining FIM-IV states is in between. Note that the current difference among these magnetic states becomes more and more significant with the bias-voltage increasing, with the most significant difference appearing in region of 0.8–1.0 V. Interestingly, different from conventional concept that the current of the FM state is the largest,1–51. M. N. Baibich, J. M. Broto, A. Fert, F. N.van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988). https://doi.org/10.1103/PhysRevLett.61.24722. G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn, Phys. Rev. B 39, 4828(R) (1989). https://doi.org/10.1103/PhysRevB.39.48283. S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki, and K. Ando, Nat. Mater. 3, 868 (2004). https://doi.org/10.1038/nmat12574. I. Žutić, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004). https://doi.org/10.1103/RevModPhys.76.3235. S. Ikeda, J. Hayakawa, Y. Ashizawa, Y. M. Lee, K. Miura, H. Hasegawa, M. Tsunoda, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 93, 082508 (2008). https://doi.org/10.1063/1.2976435 the FIM-III and AFM-III states have the largest current in the low (0.7 V) bias-voltage regions, respectively. The variation of I-V curves of these magnetic states can be understood from the transmission spectra shown in Fig. 3, i.e., the state with a larger current has a larger T(E) in energy range of [−Vb/2, Vb/2]. Particularly, a direct comparison of T(E) for AFM-III, FIM-III, and FM states which have very similar current values is shown in Fig. S2. One can see that the larger current value under Vb corresponds to a larger integration of T(E) in [−Vb/2, Vb/2].To reveal the intrinsic correlations between the T(E) and magnetic states, we further calculated the projected local density of states (PLDOS) at zero bias along the MTJ device. As marked by the black lines in Fig. 5, the shape of the tunneling barrier in the magnetic heterojunction region (central region) strongly depends on the interlayer magnetic configuration. In the following, we will show that the shape of the tunneling barrier directly correlates with the electric resistance, and thus the I-V curves. According to the Wentzel–Kramers–Brillouin (WKB) formula, the tunneling transmission function T can be written as19,3019. J. Yang, S. Fang, Y. Peng, S. Liu, B. Wu, R. Quhe, S. Ding, C. Yang, J. Ma, B. Shi, L. Xu, X. Sun, G. Tian, C. Wang, J. Shi, J. Lu, and J. Yang, Phys. Rev. Appl. 16, 024011 (2021). https://doi.org/10.1103/PhysRevApplied.16.02401130. Y. B. Band and Y. Avishai, Quantum Mechanics with Applications to Nanotechnology and Information Science ( Academic Press, Amsterdam, 2013), pp. 303–366. where U−EF represents the tunneling barrier height in the magnetic system, μ is the effective mass of electrons, B(x) is the electric field related to x, and ℏ is Planck's constant. Note that U−EF+B(x)σ is equivalent to the height of the tunneling barrier with respect to EF, which is defined as h hereafter. The tunneling barrier in the central region can be divided into n discrete rectangles, so that T≈ exp (−42μℏ∑i=1nddhi)=exp (−42μℏd∑i=1nsi),(3)where d is the center-to-center distance of two adjacent magnetic layers, i represents the index of magnetic layers, and si = dhi with hi being the height of ith layer's tunneling barrier. From the aforementioned transmission formula, the difference in T mainly lies in S = ∑si in this study, that is, the area of potential barrier, which directly corresponds to the transmission barrier shapes in the center region.According to the spin-polarized PLDOS shown in Fig. 5, if one simply considers a spin-polarized electron transporting across the four magnetic layers, e.g., in an order of Cr2Ge2Te6-Cr2Ge2Te6-CrI3-CrI3, three features on the transmission barrier can be obtained: (1) the transmission barrier is low/high when an electron transports across CrI3 layers with the magnetization direction parallel/antiparallel to its spin polarization direction, due to the appearance/absence of isolated spin-polarized electronic states nearby EF as indicated by the band structures in Fig. 2; (2) the transmission barrier is much lower when an electron transports across the Cr2Ge2Te6 layer than that across the CrI3 layer with opposite spin polarization, owing to the much smaller spin dependent band gaps in Cr2Ge2Te6; (3) the transmission barriers between two Cr2Ge2Te6 layers are basically identical (except for the FIM-IV and AFM-I states with small transmission barrier difference between two Cr2Ge2Te6 layers) in both FM and AFM states. This is because FM and AFM states of bilayer Cr2Ge2Te6 have similar band gaps with either spin-up or spin-down electrons (Fig. 2), which is responsible for electron transmission. Note that such band gaps can be affected by the interlayer coupling from CrI3 to a certain extent, which depends on the specific magnetic states. As a result, the transmission barrier across the bilayer Cr2Ge2Te6 slightly depends on the magnetic states of the heterojunction.The variation of the transmission barrier can lead to a significant change in the area of potential barrier S, which is inversely proportional to transmission probability. Note that the total current is contributed by both spin-up and spin-down electrons, whereas only the one with a larger transmission probability (smaller electronic resistance) is expected to contribute the most from the viewpoint of the two-current model.29,31,3229. M. Julliere, Phys. Lett. A 54, 225 (1975). https://doi.org/10.1016/0375-9601(75)90174-731. N. F. Mott, Adv. Phys. 13, 325 (1964). https://doi.org/10.1080/0001873640010104132. S. Shen, P. R. Ohodnicki, S. J. Kernion, and M. E. McHenry, J. Appl. Phys. 112, 103705 (2012). https://doi.org/10.1063/1.4765673 To this end, via the variation of S for a spin polarization with a larger transmission probability (Fig. 5), one can naturally understand the relationship between total current and PLDOS for all eight magnetic states. As shown in Fig. 5, four magnetic states (FM, AFM-III, FIM-III, and FIM-IV) have obviously smaller S than the remaining four (AFM-I, AFM-II, FIM-I, and FIM-II), due to the absence of high transmission barrier induced by CrI3 layers. This result means that the former four states have smaller electronic resistances, and thus larger currents, which is in good agreement with the calculated I-V curves shown in Fig. 4. It is noticed that the AFM-III state has the smallest S (spin-down electrons) among all the magnetic states, and its PLDOS above the potential energy barrier (0.35 eV) is also the largest. This feature explains why it has the largest current value with Vb > 0.7 V. Since S is a product of PLDOS, the aforementioned results confirm that the electronic resistance of a multilayer magnetic vdW heterojunction strongly correlates with its microscopic band structures, which are determined by the magnetic state. In addition, the PLDOS of all the eight magnetic states with the spin polarization of smaller transmission probability is shown in Fig. S3, most of which have obviously larger S than that in Fig. 5.To further unveil the applicability of magnetic vdW heterojunction in the MTJ device, we calculated the bias-voltage dependent TMRs with different magnetic states, where AFM-I was adopted as the reference state. The TMR is defined as TMR=|Ix−I↑↓↑↓I↑↓↑↓|×100%,(4)where Ix represents an electronic current of the magnetic states except for AFM-I. As shown in Fig. 6, eight magnetic states give rise to five distinguishable TMR curves, where two features can be obtained: (1) almost all TMR values (except for the FIM-I and AFM-II states) increase first and then decrease with the bias-voltage increasing, which reaches the maximum at about 0.8 V; (2) the TMR values become the most distinguishable at 0.8 V. It is noted that the TMR values of all the magnetic states (except for the FIM-I and AFM-II states) are quite sizable at 0.8 V, i.e., 300%, 17 000%, 35 000%, 110 000%, and 620 000% for FM-II, FIM-IV, FM, FIM-III, and AFM-III states, respectively. This result clearly shows that six distinguishable memories can be realized via a four-layered magnetic heterojunction, which is two times larger than the homojunction case.1616. T. Song, M. W. Tu, C. Carnahan, X. Cai, T. Taniguchi, K. Watanabe, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, and X. Xu, Nano Lett. 19, 915 (2019). https://doi.org/10.1021/acs.nanolett.8b04160Finally, we discuss the electric field controllability on the magnetic state of the vdW heterojunction. We propose that the magnetic state can be efficiently modulated by using the one-dimensional (1D) contact technique. As shown in attached Fig. S4(a), the very thin monolayer/multilayer graphene can be used to contact the edge of magnetic layers. In this way, various electric fields can be applied to CrI3 bilayers, Cr2Ge2Te6 bilayers, and CrI3-Cr2Ge2Te6 bilayers by changing the external voltages V1, V2, and V3, respectively. In addition, we have calculated the electric field dependent energy difference between AFM and FM states for the aforementioned three bilayer structures. As shown in Figs. S4(b)–S4(d), efficient magnetic state switching can be realized under the electric field effect for all three bilayer structures. Note that in the bilayer Cr2Ge2Te6, the switching is realized with an interlayer distance of 2.90 Å, which is a little smaller than its equilibrium distance (3.26 Å).3333. T. Song, Z. Fei, M. Yankowitz, Z. Lin, Q. Jiang, K. Hwangbo, Q. Zhang, B. Sun, T. Taniguchi, K. Watanabe, M. A. McGuire, D. Graf, T. Cao, J. Chu, D. H. Cobden, C. R. Dean, D. Xiao, and X. Xu, Nat. Mater. 18, 1298–1302 (2019). https://doi.org/10.1038/s41563-019-0505-2 This result means that efficient switching among the eight magnetic states can be realized by the 1D contact technique.3434. B. Huang, G. Clark, D. R. Klein, D. MacNeill, E. Navarro-Moratalla, K. L. Seyler, N. Wilson, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, P. Jarillo-Herrero, and X. Xu, Nat. Nanotech. 13, 544 (2018). https://doi.org/10.1038/s41565-018-0121-3In conclusion, based on the MTJ composed of bilayer CrI3/bilayer Cr2Ge2Te6 heterojunction, we have theoretically demonstrated that the multilayer vdW magnetic heterojunctions can make much more plentiful TMR values than the widely studied vdW homojunctions. The density functional theory (DFT) calculations show there are eight stable magnetic states in the four-layered magnetic heterojunction, more than two times larger than the homojunction case. Spin-polarized transport calculations further show that the eight magnetic states can lead to six distinguishable electronic resistances. Despite the weak interlayer interactions, the interlayer magnetic configurations can effectively influence the spin-polarized band alignments and band gaps near EF. The variation of band structures can lead to significant change in transmission barrier, and thus the transmission probability, which is responsible to the formation of multi-state magnetic resistances. Consequently, five distinguishable TMRs that are larger than 300% are obtained, with the maximum value up to 620 000%. Moreover, the magnetic states, and thus TMRs, can be efficiently modulated by an external electric field. This result shows that the multi-state TMRs in such heterojunction MTJ device can be effectively realized with low operation energy, which has great potential applications in the electrically coupled spintronic devices.
We acknowledge financial support from the Ministry of Science and Technology of the People's Republic of China (Grant No. 2022YFA1402901), the Natural Science Foundation of China (Grant Nos. 12074301 and 12004295), and the Natural Science Foundation of Shaanxi Province (Grant No. 2023-JC-QN-0768). We gratefully acknowledge the computational resources provided by the HPCC platform of Xi'an Jiaotong University.
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Bang Liu: Data curation (lead); Investigation (lead); Methodology (lead). Xiao Xiong Ren: Data curation (supporting); Investigation (supporting); Methodology (supporting). Xian Zhang: Investigation (equal); Supervision (equal). Ping Li: Data curation (supporting); Investigation (supporting). Y. Dong: Funding acquisition (equal); Supervision (equal). Zhi-Xin Guo: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
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