ARTICLE pubs.acs.org/JPCC
Tunneling Magnetoresistance of Bilayer Hexagonal Boron Nitride and Its Linear Response to External Uniaxial Strain M. L. Hu, Zhizhou Yu, K. W. Zhang, L. Z. Sun,* and J. X. Zhong Laboratory for Quantum Engineering and Micro-Nano Energy Technology, Xiangtan University, Xiangtan 411105, China ABSTRACT: Using density functional theory and nonequilibrium Green’s function method, we investigate the tunneling magnetoresistance (TMR) of the magnetotunnel junctions (MTJs) based on bilayer hexagonal boron nitride and its response to external uniaxial strain. The TMR ratio increases linearly with the increasing uniaxial strain because the increasing uniaxial strain reduces the bandgap of bilayer hexagonal boron nitride gradually. Interestingly, the TMR ratio exceeds 95% when the uniaxial strain increases to 2.51%, which is close to that of the perfect spin filter. Our results indicate that the bilayer hexagonal boron nitride is a promising candidate for the spacer of MTJs. Moreover, its TMR ratio can be linearly modulated by external uniaxial strain.
’ INTRODUCTION The discovery of large tunneling magnetoresistance (TMR) in the magnetotunnel junctions (MTJs) whose transmission through the interface between insulator (or semiconductor) and ferromagnetic metals (FM) is spin dependent has shown fascinating applications in spintronics, such as sensors, magnetic random access memory, and logic circuits.1,2 All electrons with one spin but none with the other spin can tunnel through the ideal spin filter. The TMR ratio can be directly observed in experiments, and it is the most important feature of MTJs.3 It is crucial to achieve a high TMR ratio for promoting practical application of MTJs, which is often restricted by the inability of obtaining well-ordered interfaces.3,4 Recently, many novel nanomaterials, such as two-dimensional layered materials, have attracted great interest as promising spacers in MTJs. For example, Karpan et al.5,6 predicted a perfect spin filter with extremely high magnetoresistance in the magnetoresistive junctions based on multilayer graphene. Analogue to graphite, hexagonal boron nitride (h-BN) is a layered semiconductor, which is widely used as the lubricant and far-ultraviolet devices due to its unique structural, electronic, and optical properties.7,8 The discovery of BN nanotubes made by folded BN sheets motivates much attention to the twodimensional BN materials.9 Recently, monolayer and multilayer boron nitride sheets have been fabricated in experiments successfully.10,11 Using the sonicationcentrifugation technique, the ultimate pure BN sheets have been obtained, and its thickness could be adjusted by the centrifugation speed.12 Moreover, a high-quality BN monolayer can be grown by the chemical vapor deposition (CVD) method on a variety of metallic substrates,13,14 and the covalent bondings of BN sheets are perfectly preserved upon the substrates, which makes the BN sheet r 2011 American Chemical Society
attractive for the spacer of MTJs. Yazyev et al.15 proposed the monolayer BN sheet as the spacer for the magnetoresistive junctions, and they found that the magnetoresistive ratio exceeds 100% for certain chemical compositions. The electronic properties of the bilayer BN sheet (bi-BN) are similar to those of the monolayer BN sheet, but can be easily modulated by uniaxial strain due to the weak interplanar van der Waals bonding. In our present work, we investigate the TMR effect for Ni|bi-BN|Ni MTJs under uniaxial strain along the z axis using the firstprinciples method combined with the nonequilibrium Green’s function. We find that the AA stacking of bi-BN (every atom in one layer sitting atop the same atom in the adjacent layer) is the most stable structure in the MTJs. The TMR ratio increases linearly with the increase in the uniaxial strain because the external strain reduces the bandgap of bi-BN gradually. Thus, the TMR ratio can be linearly modulated by the external uniaxial strain. Moreover, it exceeds 95% when the MTJs are compressed by 2.51%, which approaches that of the perfect spin filter.
’ COMPUTATIONAL DETAILS AND MODELS We sandwich the bi-BN between two semi-infinite Ni(111) electrodes to construct the MTJs, as shown in Figure 1. We adopt Ni for the FM in our prototypical device because the surface lattice constant of Ni(111) well matches the in-plane lattice constant of bi-BN. To gain the stable structures of MTJs, we perform the structural optimization using the Vienna Ab initio Simulation Package (VASP) based on the density functional theory.16,17 The exchange and correlation is approximated by the Received: October 18, 2010 Revised: March 18, 2011 Published: April 06, 2011 8260
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Figure 1. Schematic diagram of Ni|AA|Ni MTJs. The green, pink, and blue balls represent the Ni, B, and N atoms, respectively.
local density approximation (LDA) adapted by Ceperley and Alder.18 A plane wave basis set with the kinetic energy cutoff of 450 eV is employed. The total energy is converged to be 105 eV, and atoms are relaxed with a residual force less than 0.02 eV/Å. The Brillouin zone is sampled by 7 7 3 Γ-centered MonkhorstPack grids. The transport calculations are carried out using the first-principles method within the nonequilibrium Green’s function, as implemented in the Atomistix ToolKit (ATK) package.19 It has been demonstrated that the TMR effect of MTJs with planar contacts such as Fe|MgO|Fe, as well as the electronic properties of the transition metals, can be well described by this method.20,21 The single and double ζ plus polarization numerical orbitals for Ni and B (N) atoms are used in place of the plane wave basis set, respectively. The exchange and correlation potential is approximated by LDA with the PerdewZunger parametrization.18,22 The energy cutoff is set to be 300 Ry, and the convergence of total energy is set to be 105 Ry. The Brillouin zone is sampled by 15 15 100 MonkhorstPack grids. All the computational parameters we used are optimized. In our present work, we define the TMR ratio as TMR ¼
GP GAP G þ GVV 2GvV 100% ¼ vv 100% GAP 2GvV
ð1Þ
where Gvv and GVV are the spin-resolved transmission conductance of majority and minority spins in the parallel (P) configuration, respectively. GvV is the spin-resolved transmission conductance in the antiparallel (AP) configuration which is equivalent for majority and minority spins.
’ RESULTS AND DISCUSSIONS Three high-symmetry sites are possible for B and N atoms adsorbed on the hexagonal Ni(111) surface, and there are 21 possible configurations for bi-BN sandwiched in Ni|bi-BN|Ni MTJs. To obtain the most stable structure of MTJs, we optimize all possible structures and then compare their total energy. We find that the structure of Ni|bi-BN|Ni MTJs with AA stacking of bi-BN whose N atoms sit atop the Ni atoms of the nearest layer and B atoms sit atop the Ni atoms of the third neighboring layer is the most stable one, as shown in Figure 1. The relative position of the interface between Ni(111) and bi-BN in our results agrees well with that of the monolayer BN sheet adsorbed on the Ni(111) surface.23 Thus, we just take this favorable structure as the typical MTJs to study the TMR effect in our present work, and we refer to this system as Ni|AA|Ni. Our optimized system shows that the bonding length of NiN is about 2.1 Å, and the interlayer spacing of bi-BN sandwiched in the MTJs is about 3.33 Å. The bi-BN sheet between Ni(111) electrodes shows very small corrugations (about 0.1 Å), and B atoms of both layers are closer to the Ni(111) surfaces. We also find that the induced
Figure 2. Transmission conductances Gvv, GVV, and GvV for Ni|AA|Ni MTJs in function of the compression ratio ε. Inset: TMR ratios in function of the compression ratio ε.
magnetic moments on B and N atoms of MTJs in the P configuration are about 0.014 μB and 0.019 μB, respectively, due to the strong coupling between Ni and the BN sheet. However, in the AP configuration, the magnetic moments of B (N) atoms in one layer are opposite to that of the adjacent layer. The uniaxial strain for Ni|AA|Ni MTJs is realized by compressing or stretching the electrodes along the z axis of the system. Such a method has been extensively used in both theoretical and experimental studies to simulate the effect of uniaxial strain on transport properties of molecular devices.24,25 The uniaxial strain is defined in terms of the compression ratio derived from the relative change of the distance between two electrodes, which is denoted as ε. The positive and negative values represent the compression and stretch of the system, respectively. We vary ε from 2.79% to 2.79% (the corresponding relative change of the interlayer spacing of bi-BN ranges from about 16.6% to 11.1%) to study the response of TMR effect on the external uniaxial strain. The in-plane lattice constants of bi-BN are not changed under uniaxial strain. The bi-BN spacer would keep physically stable under the uniaxial strain in our present work due to its weak interplane van der Waals bonding and the confinement of the electrodes. We then analyze the transmission conductance of Ni|AA|Ni MTJs under different uniaxial strains, as shown in Figure 2. The results indicate that GVV is always much larger than Gvv and GvV. The transmission conductance is in nearly linear function of the uniaxial strain, and the increasing rate of GVV is faster than that of Gvv and GvV. Thus, the TMR ratio increases linearly with the increasing uniaxial strain, as shown in the inset of Figure 2. We find that the TMR ratio of the equilibrium system is about 51%, which is comparable with that of Ni|monolayer BN| Ni (55%) reported by Yazyev.15 However, it exceeds 95% as the system is compressed by 2.51%, which approaches that of the perfect spin filter. Inversely, the TMR ratio reduces to 25% as the system is stretched by 2.79%. To reveal the physical mechanism of the linear response of TMR ratio to the uniaxial strain, we calculate the band structures of bi-BN with AA stacking to evaluate its electronic properties under uniaxial strain, as shown in Figure 3. We adjust the interlayer distance of bi-BN to realize the uniaxial strain, which has been widely adopted to simulate the electronic properties of graphite as well as bilayer graphene under uniaxial strain in 8261
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Figure 3. Bandgap of bi-BN with AA stacking in function of the compression ratio ξ. Left and right insets represent the band structures of bi-BN with AA stacking under ξ = 0% and ξ = 10%, respectively. Γ, M, and K points denote the high-symmetry k-points within the Brillouin zone of bi-BN.
theoretical studies,26,27 and the change ratio is defined as ξ. The optimized equilibrium interlayer spacing of AA stacking is 3.535 Å. The results indicate that the bi-BN with AA stacking is a direct bandgap semiconductor with the bandgap of 4.03 eV. Both the conduction band minimum (CBM) and the valence band maximum (VBM) are located at the K point, as shown in the inset of Figure 3. The degeneracy of the bands decreases, and the bandwidth increases with increasing uniaxial strain. Moreover, the bandgap decreases exponentially when ξ increases from 16% (the fitted exponential function can be described as Δ(ξ) = 0.66e5.22ξ þ 4.69), and the direct energy gap at Γ and M points also decreases with the increasing uniaxial strain. However, when ξ decreases to 18%, the position of CBM changes from the symmetry point K to Γ, and the VBM is still located at the K point. The band structure of the system becomes indirect. The bandgap slightly decreases when ξ less than 18%, but the direct energy gap at Γ, M, and K points still increases along with the decreasing uniaxial strain. The decrease in direct energy gap of bi-BN with the increasing uniaxial strain is similar to that of h-BN reported by Watanabe.28 The band-edge luminescence (corresponding to the direct energy gap) of biBN is also red-shifted under compression. We then analyze the k||-resolved transmission conductance for Ni|AA|Ni MTJs to further investigate the linear response of the TMR ratio to the uniaxial strain, as shown in Figure 4. As for the equilibrium system, because there is no majority transmission in the Ni(111) systems around Γ and K points, as shown in Figure 4(a), the k||-resolved transmission conductance of the majority spins in the P configuration for Ni|AA|Ni MTJs (Tvv) around Γ and K points must be zero. Although the majority transmission conductance of Ni(111) systems is about 1G0 at M point, Tvv only shows a small value at this point due to the large energy gap between the π and π* bands of bi-BN around the M point, as shown in Figure 4(c). Because the direct energy gap of bi-BN at the M point decreases with increasing uniaxial strain as mentioned above, Tvv increases with the increasing strain at the M point, whereas it decreases and then vanishes with the decreasing strain, as shown in Figure 4(b) and 4(d), respectively. Despite the high minority transmission of the bulk Ni along the (111) direction around Γ and M points, the k-resolved transmission conductance for the minority spins in the P configuration (TVV) vanishes around these k-points owing to the selection rules,29
Figure 4. k||-resolved transmission conductance through (a) bulk Ni along the (111) direction and Ni|AA|Ni MTJs under different uniaxial strains of (b) ε = 2.79%, (c) ε = 0%, and (d) ε = 2.79%. The columns correspond to the majority and minority transmission conductance in the P configuration and to one of the equivalent spin-resolved transmission conductances in the AP configuration, respectively.
namely, due to the incompatibility of wave functions on both sides of the interface. However, TVV is considerably high at the K point due to the high minority transmission conductance of bulk Ni and the Bloch states of bi-BN around this k-point, as shown in Figure 4(c). TVV at the K point increases with the increasing strain due to the decreased bandgap of bi-BN, whereas it decreases and then vanishes as the strain decreases. The results of k||-resolved transmission conductance indicate that the linear response of the TMR ratio to the uniaxial strain is dominated by the change of TVV around the K point. The k||-resolved transmission conductance in the AP configuration (TvV) is mainly determined by the overlap of Tvv and TVV. Consequently, TvV must be lower, and it almost vanishes at Γ, K, and M points. However, we find that the TMR ratio shows two dips at ε = 1.12% and ε = 0.84% along with the increasing uniaxial strain. These two dips mainly originate from the lower value of GVV at ε = 1.12% and the higher value of GvV at ε = 0.84% compared with the corresponding conductances under the strain around 1.12% and 0.84%, respectively. We then compare the band structures for the scattering region of Ni|AA|Ni MTJs under different uniaxial strains to find out the reason for these dips. Because the change of band structures for the systems around ε = 1.12% and ε = 0.84% shows similar characteristics, we just present the results of the former here. GVV mainly originates from TVV around K point as shown in Figure 4. Figure 5(a) and Figure 5(b) present the band structures of the minority spins in the P configuration around the K point for the scattering region of the systems at ε = 0.84% and ε = 1.12%, respectively. We find that the bands of ε = 1.12% become less degenerate than those of ε = 0.84%. Moreover, there are two bands through the Fermi level around the K point for ε = 0.84% but only one band for ε = 1.12% due to the decreased degeneracy. GVV decreases due to the decreased numbers of bands through the Fermi level around the K point, and the TMR ratio then decreases. When the compression 8262
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’ CONCLUSION In summary, we propose bilayer BN sheets as the spacer in the MTJs and investigate the TMR ratio of Ni|AA|Ni MTJs under uniaxial strain by using the first-principles method combined with the nonequilibrium Green’s function. We find that the TMR ratio of the system increases linearly along with the increasing uniaxial strain due to the decreased bandgap of bi-BN. The TMR ratio exceeds 95% when the compression increases to ε = 2.51%, which is close to that of the perfect spin filter. Our present work shows that the bilayer BN sheet is a promising candidate for the spacer of MTJs in the application of spintronics such as magnetic random access memory. Furthermore, its TMR ratio can be linearly modulated by external uniaxial strain. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
Figure 5. Band structures for minority spins in the P configuration for the scattering region of Ni|AA|Ni MTJs under (a) ε = 0.84% and (b) ε = 1.12%. LDOS in the real space for minority spins at the K point of the Fermi level for Ni|AA|Ni MTJs in the P configuration under (c) ε = 0.84% and (d) ε = 1.12%. The green, pink, and blue balls represent the Ni, B, and N atoms, respectively. The red regions represent the LDOS in the real space.
increases to ε = 1.40%, the bands become more degenerate than those of ε = 1.12%, and there are two bands through the Fermi level around the K point. Thus, GVV increases with the increasing strain which results in the increased TMR ratio. Furthermore, we analyze the local density of states (LDOS) in the real space for minority spins at the K point of the Fermi level for Ni|AA|Ni MTJs in the P configuration at ε = 0.84% and ε = 1.12%, as shown in Figure 5(c) and Figure 5(d), respectively. We find that the LDOS distributes homogeneously on N atoms of bi-BN at ε = 0.84%, but it distributes only on the N atoms of one layer of biBN when the compression increases to ε = 1.12%. The localization of the LDOS decreases GVV and the TMR ratio. To this end, it should be emphasized that although the calculated TMR ratio of the equilibrium Ni|bi-BN|Ni MTJs is close to that of the Ni|monolayer BN|Ni MTJs reported by Yazyev15 it can be linearly modulated by the uniaxial strain along the z axis. The modulation can be carried out in experiments due to the weak interplanar van der Waals bonding. Interestingly, the TMR ratio of Ni|bi-BN|Ni MTJs enhances under compression and even approaches that of the ideal spin filter. Owing to the controllable modulation of the TMR ratio under uniaxial strain, bi-BN can serve as an excellent spacer for MTJs. Moreover, the TMR ratio can be directly measured by using the d.c. four-probe method in experiments which is expected to directly confirm our present report. In addition, the controllable multilayer boron nitride sheets have been successfully fabricated in experiments.12 The change of bandgap of bi-BN under uniaxial strain could be observed as the measurement of bandgap of h-BN carried out by using the cathodoluminescence spectroscopy method.28 Such results are expected to further validate our calculated linear response of the TMR ratio of Ni|bi-BN|Ni to external uniaxial strain. We look forward to further experimental reports to confirm our studies.
’ ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (Grant Nos. 10874143, 10974166, and 10774127), Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20070530008), the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (Grant No. 708068), the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 10K065), and the Hunan Provincial Innovation Foundation for Postgraduate (Grant No. CX2010B266). ’ REFERENCES (1) Zhu, J.-G.; Park, C. Mater. Today 2006, 9, 36–45. (2) Heiliger, C.; Zahn, P.; Mertig, I. Mater. Today 2006, 9, 46–54. (3) Yuasa, S.; Nagahama, T.; Fukushima, A.; Suzuki, Y.; Ando, K. Nat. Mater. 2004, 3, 868–871. (4) Heiliger, C.; Zahn, P.; Yavorsky, B. Y.; Mertig, I. Phys. Rev. B 2006, 73, 214441. (5) Karpan, V. M.; Giovannetti, G.; Khomyakov, P. A.; Talanana, M.; Starikov, A. A.; Zwierzyc-ki, M.; van den Brink, J.; Brocks, G.; Kelly, P. J. Phys. Rev. Lett. 2007, 99, 176602. (6) Karpan, V. M.; Khomyakov, P. A.; Starikov, A. A.; Giovannetti, G.; Zwierzycki, M.; Ta-lanana, M.; Brocks, G.; van den Brink, J.; Kelly, P. J. Phys. Rev. B 2008, 78, 195419. (7) Watanabe, K.; Taniguchi, T.; Kanda, H. Nat. Mater. 2004, 3, 404–409. (8) Kubota, Y.; Watanabe, K.; Tsuda, O.; Taniguchi, T. Science 2007, 317, 932–934. (9) Chopra, N. G.; Luyken, R. J.; Cherrey, K.; Crespi, V. H.; Cohen, M. L.; Louie, S. G.; Zettl, A Science 1995, 269, 966–967. (10) Jin, C.; Lin, F.; Suenaga, K.; Iijima, S. Phys. Rev. Lett. 2009, 102, 195505. (11) Han, W.-Q.; Wu, L.; Zhu, Y.; Watanabe, K.; Taniguchi, T. Appl. Phys. Lett. 2008, 93, 223103. (12) Zhi, C.; Bando, Y.; Tang, C.; Kuwahara, H.; Golberg, D. Adv. Mater. 2009, 21, 2889–2893. (13) Oshima, C.; Nagashima, A. J. Phys.: Condens. Matter 1997, 9, 1. (14) Berner, S.; Corso, M.; Widmer, R.; Groening, O.; Laskowski, R.; Blaha, P.; Schwarz, K.; Goriachko, A.; Over, H.; Gsell, S.; Schreck, M.; Sachdev, H.; Greber, T.; Osterwalder, J. Angew. Chem., Int. Ed. 2007, 46, 5115–5119. (15) Yazyev, O. V.; Pasquarello, A. Phys. Rev. B 2009, 80, 035408. (16) Kresse, G.; Furthm€uller, J. Phys. Rev. B 1996, 54, 11169–11186. (17) Kresse, G.; Furthm€uller, J. Comput. Mater. Sci. 1996, 6, 15–50. 8263
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(18) Ceperley, D. M.; Alder, B. J. Phys. Rev. Lett. 1980, 45, 566–569. (19) Brandbyge, M.; Mozos, J.-L.; Ordejon, P.; Taylor, J.; Stokbro, K. Phys. Rev. B 2002, 65, 165401. (20) Stokbro, K. J. Phys.: Condens. Matter 2008, 20, 064216. (21) Stilling, M.; Stokbro, K.; Flensberg, K. J. Comput.-Aided Mater. Des. 2007, 14, 141–149. (22) Perdew, J. P.; Zunger, A. Phys. Rev. B 1981, 23, 5048–5079. (23) Huda, M. N.; Kleinman, L. Phys. Rev. B 2006, 74, 075418. (24) Luo, X.; Lin, S. P.; Wang, B.; Zheng, Y. Appl. Phys. Lett. 2010, 97, 012905. (25) Kim, K. S.; Zhao, Y.; Jang, H.; Lee, S. Y.; Kim, J. M.; Kim, K. S.; Ahn, J.-H.; Kim, P.; Choi, J.-Y.; Hong, B. H. Nature 2009, 457, 706. (26) Nanda, B. R. K.; Satpathy, S. Phys. Rev. B 2009, 80, 165430. (27) Shaw, D. M.; Tse, J. S. J. Phys.: Condens. Matter 2007, 19, 425211. (28) Watanabe, K.; Taniguchi, T.; Kuroda, T.; Kanda, H. Appl. Phys. Lett. 2006, 141902. (29) Xia, K.; Zwierzycki, M.; Talanana, M.; Kelly, P. J.; Bauer, G. E. W. Phys. Rev. B 2006, 73, 064420.
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