pubs.acs.org/NanoLett
New Type of Magnetic Tunnel Junction Based on Spin Filtering through a Reduced Symmetry Oxide: FeCo|Mg3B2O6|FeCo Derek A. Stewart* Cornell Nanoscale Science and Technology Facility, Ithaca, New York 14853 ABSTRACT Magnetic tunnel junctions with high-tunneling magnetoresistance values such as Fe|MgO|Fe capitalize on spin filtering in the oxide region based on the band symmetry of incident electrons. However, these structures rely on magnetic leads and oxide regions of the same cubic symmetry class. A new magnetic tunnel junction (FeCo|Mg3B2O6|FeCo) is presented that uses a reduced symmetry oxide region (orthorhombic) to provide spin filtering between the two cubic magnetic leads. Complex band structure analysis of Mg3B2O6 based on density functional calculations shows that significant spin filtering could occur in this system. This new type of magnetic tunnel junction may have been fabricated already and can explain recent experimental studies of rf-sputtered FeCoB|MgO|FeCoB junctions where there is significant B diffusion into the MgO region. KEYWORDS Magnetic tunnel junction, tunneling magnetoresistance, Kotoite, Mg3B2O6, complex band structure
T
layers on either side of the oxide10 and provides the epitaxial interface required for spin filtering in the oxide layer.1 In magnetic tunnel junctions based on Fe|MgO|Fe, cubic symmetry is preserved between the bcc Fe leads and the rock-salt MgO oxide region. Since symmetry filtering is essential for the high tunneling magnetoresistance values observed in these systems, this raises the question of whether a oxide layer with a lower symmetry than the leads could provide improved symmetry filtering properties. To address this question, in this work we will examine a potential new magnetic tunnel junction based on the orthorhombic mineral Kotoite (Mg3B2O6). The mineral Kotoite (Mg3B2O6) (space group Pnmn) is an orthorhombic crystal11 where each Mg atom is surrounded by an octahedron of oxygen atoms, shown in green in Figure 1. Boron atoms are surrounded by three oxygen atoms, BO3, in a triangular configuration shown as blue triangles. The single BO3 triangles link chains of oxygen octahedral.12 While it has a reduced symmetry crystal structure compared to the cubic materials, MgO and body-centered cubic (bcc) FeCo, based on its lattice dimensions, it should be possible to incorporate Kotoite into FeCo/MgO based MTJs. The (100) face of Kotoite is rectangular and the lattice match with (001) MgO in this direction is very good. The b lattice vector of Kotoite is 8.416 Å which is very close to twice the MgO lattice constant (2aMgO ) 8.422 Å). The c lattice vector for Kotoite, 4.497 Å, is slightly larger than the MgO lattice vector, 4.211 Å. The Mg atomic positions on the (100) face of Kotoite also mimic those found in (001) MgO for almost all sites (see the inset in Figure 4). This indicates that Kotoite, in a manner similar to MgO, could template neighboring FeCo regions as crystalline bcc layers, a condition essential for TMR based on symmetry spin filtering.
he development of robust magnetic tunnel junctions with high tunneling magnetoresistance values has led to rapid advances in magnetic sensing and memory applications. Magnetic tunnel junctions (MTJs) consist of two ferromagnetic leads separated by a thin oxide barrier region. The electrical resistance of the MTJ depends on the relative orientation of the magnetic moments of the ferromagnetic leads and can be controlled by an applied magnetic field. The tunneling magnetoresistance (TMR) provides a measure of the quality of a magnetic tunnel junction and is given by TMR ) (GP - GAP)/(GAP) where GP and GAP are the conductances when the magnetic leads are aligned parallel and antiparallel, respectively. In 2001, two groups1,2 independently predicted that Fe|MgO|Fe magnetic tunnel junctions would have very high tunneling magnetoresistance values due to symmetry selective filtering by the complex band structure of MgO that strongly favored majority carriers. Soon after this prediction was confirmed in room temperature devices3,4 and symmetry based filtering has also been shown in other MTJ systems such as CoFe|MgO|CoFe5 and Co|SrTiO3|Co.6 Magnetic tunnel junctions based on this principle have come to dominate the magnetic memory device industry. Recent magnetic tunnel junctions based on sputtered amorphous CoFeB leads and MgO tunnel barriers have exhibited record TMR values up of 604% at room temperature.7 Boron ensures that deposited CoFe leads are amorphous, which reduces interface roughness8 and allows the MTJs to grow on synthetic antiferromagnets.9 Upon annealing, MgO acts as a template for the growth of bcc FeCo
* To whom correspondence should be addressed. E-mail:
[email protected]. Received for review: 10/14/2009 Published on Web: 12/17/2009 © 2010 American Chemical Society
263
DOI: 10.1021/nl9034362 | Nano Lett. 2010, 10, 263-267
consider for magnetic tunnel junctions based on a reduced symmetry oxide region. Density functional calculations were performed using both a pseudopotential plane wave approach (as implemented in Quantum Espresso21,22) and a full potential augmented spherical wave approach.23 Since very little work has been done on the electronic structure of Kotoite, using multiple ab initio techniques provides an additional accuracy check. All calculations were done within the local density approximation. A 100 Ryd cutoff energy was used for the plane wave calculations. Monkhorst-Pack k-point grids of 12 × 12 × 12 and 8 × 4 × 12 were used for MgO and Mg3B2O6, respectively. Mg and B ions were described using von Barth Car pseudopotentials,24 while an ultrasoft pseudopotential was used for O atoms.25 Lattice constants and atomic positions were relaxed based on Hellman-Feynman forces. For augmented spherical wave calculations, empty spheres were added to ensure a proper description of open regions in the crystal structure. The calculated lattice vectors for Mg3B2O6 (a ) 5.339 Å, b ) 8.354 Å, c ) 4.465 Å) agree well with the experimentally measured values11 (a ) 5.398 Å, b ) 8.416 Å, c ) 4.497 Å). Density functional calculations in the local density approximation are well-known to overbind and predict smaller lattice constants.26 The atomic positions in the crystal are also in good agreement with experiment and are listed in the Supporting Information (Table S1). Both the plane wave and augmented spherical wave band structure calculations predict that Kotoite should have an indirect band gap of 5.415 eV. Recently, a research group estimated an indirect gap of 6.2 eV based on the transmission spectrum of single crystals of Kotoite grown using the Czochralski method.27 The difference in the predicted and measured band gaps is not surprising, since density functional approaches are known to severely underestimate the band gap of a material.26 The calculated band diagram for Kotoite is available in the Supporting Information (Figure S1). By comparing the density of states of MgO and Kotoite, we can determine how the presence of boron will affect states that contribute to tunneling. In Figure 2, the total DOS of Kotoite is compared to that of MgO. The valence DOS in both systems consists of a p band just below the Fermi energy and another deep energy s band. The s valence band in Kotoite is split in two which could be due to the different oxygen bonding configurations with boron and magnesium. The MgO conduction band DOS gradually decreases as it approaches the conduction band edge. In contrast, Mg3B2O6 shows two sharp peaks at the conduction band edge. By examining the localized density of states, we can determine which orbitals will affect transport in magnetic tunnel junctions based on Kotoite. Figure 3 shows the localized density of states for inequivalent atoms in Kotoite resolved into s and p angular momentum channels. From panels a and c of Figure 3, it is clear that the density of states on the magnesium atoms is fairly small and there is no sign
FIGURE 1. The crystal structure for Kotoite (Mg3B2O6) is shown. The oxygen atoms are given in red and magnesium atoms are located at the center of the green octahedra. Boron atoms are located at the center of the blue triangles connecting oxygen atoms.
There is also some evidence that magnetic tunnel junctions based on a crystalline Mg-B-O region such as Kotoite have already been fabricated. In the development of FeCoB|MgO|FeCoB junctions, it was originally assumed that all boron diffused away from the MgO layer during annealing. This would leave isolated FeCo layers at the MgO interface, resulting in high TMR values. However, recent work indicates that the movement of boron can depend strongly on deposition and annealing conditions. Recent experimental studies provide evidence that boron oxide does form during sputtering deposition13-15 and that a significant amount of boron can diffuse into MgO during annealing and enhance TMR for magnetic tunnel junctions with thin oxide layers.16 Mg and O K-edge EELS data from these studies indicates that Mg and O coordination is different from that of MgO, indicating the presence of Mg-B oxides. Boron K-edges in the oxide region show that boron is oxidized with a BO3 configuration that is present after deposition and remains even after annealing.17 Boron in BO3 triangles links together the oxygen octahedral in Kotoite. Experimental studies of MTJs with Mg-B-O regions show that boron incorporation into the oxide region (1) preserves a high TMR value upon annealing, (2) provides MTJs with the low RA product needed for industrial applications, and (3) still acts to template the neighboring FeCo leads to grow in bcc crystalline layers. While it is possible that other Mg-B-O compounds such as monoclinic18 or triclinic19 Mg2B2O5 could form in the oxide region during deposition, Kotoite is the only one that has a sufficient lattice match to template the FeCo bcc layers. The measured boron concentration in the Mg-B-O regions is also low (5-10%),16,20 and this favors Kotoite, which has the lowest boron concentration (18%) of the magnesium borates. The strong experimental evidence makes Kotoite a perfect candidate to © 2010 American Chemical Society
264
DOI: 10.1021/nl9034362 | Nano Lett. 2010, 10, 263-267
FIGURE 2. The total density of states is shown for (a) MgO and (b) Kotoite Mg3B2O6. The Fermi energy level is represented by a vertical dashed red line in each case.
FIGURE 3. The local density of states (LDOS) is shown for Kotoite (Mg3B2O6) (panels a-e) and for MgO (panel f). The LDOS of Kotoite is shown for inequivalent atoms, two magnesium atoms (panels a,c), two oxygen atoms (panels b,d), and boron (panel e). In these panels, the s- and p-resolved LDOS are denoted by black and blue lines, respectively. The corresponding fractional coordinates of the atoms can be found in the Supporting Information. In panel f, the LDOS for MgO are shown for Mg (black line, s channel; blue line, p channel) and O (orange line, s channel; green line, p channel). In all panels, the Fermi energy is denoted by a red dashed line. © 2010 American Chemical Society
265
DOI: 10.1021/nl9034362 | Nano Lett. 2010, 10, 263-267
FIGURE 4. The complex band structure of MgO and Kotoite (Mg3B2O6) are shown in panels a and b, respectively. K-vector components are shown in terms of positive and negative regions of the plot to indicate real and imaginary components, respectively. Real bands are denoted by black lines. Purely imaginary bands are given by blue lines and complex bands are denoted by orange lines. The (001) MgO surface and the (100) Kotoite surface are shown as insets in panels (a) and (b), respectively. Mg atoms are denoted by green circles.
for the ∆1 and the ∆5 complex bands that leads to efficient majority spin filtering. The complex band structure for Kotoite in the (100) direction is shown in Figure 4b. The band symmetry group along the Γ to X line is C2v. Two different ˜ 4 intersect the Fermi ˜ 1 and ∆ imaginary bands labeled ∆ energy at -0.28i (2π/a) and -0.46i (2π/a) respectively. These imaginary bands are continuations of real conduction bands based on the boron p states. The imaginary component of the two bands determines how effectively electrons tunnel through the barrier. Similar to a free electron potential step, a smaller imaginary component or decay rate will result in greater transmission through the barrier. The large separation in the imaginary components in these two bands indicates that electrons that can couple to the orthorhombic ˜ 1 band should dominate transport through the oxide ∆ region. Introducing FeCo leads on either side of the oxide region will cause the position of the Fermi level to change. However, over the entire energy range in the band gap, the ˜ 4. ˜ 1 is significantly smaller than ∆ imaginary component of ∆ This interface presents an interesting problem in terms of symmetry filtering in MTJs. The FeCo bcc layers and (001) MgO all possess cubic symmetry.1 However, Kotoite is orthorhombic and possesses C2v symmetry along the [100] direction. This raises the question of how cubic symmetry ˜ 1 and ∆ ˜ 4 bands states (∆1, ∆5, and ∆2) will couple into the ∆ in this lower symmetry region. The cubic C4v ∆1 band transforms as linear combinations of functions with 1, z, and ˜ 1 bands in orthorhombic systems 2z2 - x2 - y2. The C2v ∆ transforms as linear combinations of 1, z, x2, y2, and z2. Of ˜ 1 should the symmetry states available in Kotoite, the ∆ couple most effectively with the majority spin ∆1 in the FeCo magnetic leads. For the minority carriers, the cubic C4v ∆5 band transforms as linear combinations of zx and zy symmetry. The closest analogue in the orthorhombic system is ˜ 4 band which transforms as zy and has a much larger the ∆ ˜ 1 band. On imaginary component than the orthorhombic ∆
of peaks at the valence or conduction band edges. In the case of both oxygen atoms (panels b and d), there is a low energy s band roughly 19 eV below the Fermi energy. The oxygen valence band is dominated by p states and there is evidence of two p orbital density of states peaks near the conduction band edge. For boron (Figure 3, panel e), there is a fairly large s band at the same energies as oxygen, indicating oxygen-boron bonding. The p channel DOS for boron reveals the origin of the sharp DOS peaks at the conduction band edge found in the total DOS. We will show later that these boron p states play an important role in the tunneling behavior of MTJs based on Kotoite. Figure 3 also shows the localized density of states of MgO in panel f. A few things are worth noting. Similar to Kotoite, the low energy valence band is primarily due to the s oxygen orbital. However, in this case, the orbital is not split since all oxygens in MgO experience the same bonding environment in contrast to the case of Kotoite. The conduction band DOS of MgO is dominated by the p orbital of Mg and decays gradually to the conduction band edge. Zhang and Butler5 showed that the high TMR in FeCo|MgO|FeCo MTJs relies on symmetry selective filtering in MgO. In particular, the FeCo majority carrier ∆1 band couples efficiently with the ∆1 complex band in MgO, while minority carriers can only couple through the ∆5 and ∆2 bands, which decay much faster. For Kotoite to provide high TMR values, it must provide similar symmetry selective filtering to that of MgO. To determine whether this is the case, the complex band structures for both the (001) direction in MgO and (100) direction in Kotoite were calculated using the approach of Choi and Ihm28 as implemented in the Quantum Espresso package.29 The complex band structure for the tetragonal unit cell of (001) MgO is shown in Figure 4a. In the (001) direction for MgO, the band symmetry is C4v. As has been reported in previous studies,1,5 there is a substantial difference in the imaginary component © 2010 American Chemical Society
266
DOI: 10.1021/nl9034362 | Nano Lett. 2010, 10, 263-267
REFERENCES AND NOTES
the basis of this symmetry analysis and the complex band structure, Kotoite should serve as an effective spin filter similar to MgO. While the complex band structure indicate that magnetic tunnel junctions based on Kotoite (Mg3B2O6) should have high TMR values, it is important to note that previous works30,31 have shown that metal/oxide interface states can, in some cases, play an important role in the MTJ spin polarization and TMR value. The role of interface states can be resolved by a full transmission calculation for the junction and this will be addressed in a future study. In this letter, I have used density functional approaches to show that magnetic tunnel junctions based on Kotoite (Mg3B2O6) are strong candidates for spin filtering by a reduced symmetry oxide. Complex band structure analysis shows that the cubic (001) ∆1 band should couple with the ˜ 1 band in Kotoite, while the cubic ∆5 orthorhombic (001) ∆ bands should partially couple with the orthorhombic (100) ˜ 4 bands. There is sufficient difference in the decay rates of ∆ the imaginary bands so that spin filtering should be expected. Recent experimental evidence indicates magnetic tunnel junctions with Kotoite oxide regions may have already been formed during rf-sputting of FeCoB|MgO|FeCoB tunnel junctions. In addition, the diffusion of boron into the MgO region may also help passivate Mg or O vacancies that would otherwise reduce the TMR in the magnetic tunnel junctions.32,33 However, additional experimental research is required to determine conclusively whether Kotoite is indeed in the barrier region of these devices. Regardless of this issue, the current study shows that an experimental effort focused on forming MTJs based on Kotoite barriers is worthy of exploration. Using a lower symmetry oxide region between two cubic symmetry magnetic leads could provide a new route for enhanced spin filtering and possibly a new generation of high TMR devices.
(1) (2) (3) (4) (5) (6) (7)
(8)
(9) (10) (11) (12) (13) (14) (15) (16)
(17) (18) (19) (20)
(21) (22) (23) (24)
Acknowledgment. Calculations were done on the Intel Cluster at the Cornell Nanoscale Facility, part of the National Nanotechnology Infrastructure Network (NNIN) funded by the National Science Foundation. Special thanks to John Read and Judy Cha for advice on MgBO magnetic tunnel junction issues, Alexander Smogunov for advice on complex band structures, and Volker Eyert for access to his Augmented Spherical Wave code.
(25) (26) (27) (28) (29) (30)
Supporting Information Available. Table comparing calculated fractional coordinates of atoms in Mg3B2O6 in comparison to experimental values. Band diagram of Mg3B2O6 calculated using the augmented spherical wave approach and associated calculation details. This material is available free of charge via the Internet at http:// pubs.acs.org.
© 2010 American Chemical Society
(31) (32) (33)
267
Butler, W. H.; Zhang, X-.G.; Schulthess, T. C.; MacLaren, J. M. Phys. Rev. B 2001, 63, 054416. Mathon, J.; Umerski, A. Phys. Rev. B 2001, 63, 220403. Parkin, S. S. P.; Kaiser, C.; Panchula, A.; Rice, P. M.; Hughes, B.; Samant, M.; Yang, S.-H. Nat. Mater. 2004, 3, 862–867. Yuasa, S.; Nagahama, T.; Fukushima, A.; Suzuki, Y.; Ando, K. Nat. Mater. 2004, 3, 868–871. Zhang, X.-G.; Butler, W. H. Phys. Rev. B 2004, 70, 172407. Velev, J. P.; Belashchenko, K. D.; Stewart, D. A.; van Schilfgaarde, M.; Jaswal, S. S.; Tsymbal, E. Y. Phys. Rev. Lett. 2005, 95, 216601. Ikeda, S.; Hayakawa, J.; Ashizawa, Y. M.; Miura, K.; Hasegawa, H.; Tsunoda, M.; Matsukura, F.; Ohno, H. Appl. Phys. Lett. 2008, 93, 082508. Dyajaprawira, D. D.; Tsunekawa, K.; Tsunekawa, K.; Nagai, M.; Maehara, H.; Yamagata, S.; Wantanabe, N.; Yuasa, S.; Suzuki, Y.; Ando, K. Appl. Phys. Lett. 2005, 86, 092502. Yuasa, S.; Djayaprawira, D. D. J. Phys. D: Appl. Phys. 2007, 40, R337-R354. Yuasa, S.; Suzuki, Y.; Katayama, T.; Ando, K. Appl. Phys. Lett. 2005, 87, 242503. Effenberger, H.; Pertlik, F. Z. Kristallogr. 1984, 166, 129–140. Christ, C. L.; Clark, J. R. Phys. Chem. Miner. 1977, 2, 59–87. Bae, J. Y.; Lim, W. C.; Kim, H. J.; Lee, T. D.; Kim, K. W.; Kim, T. W. J. Appl. Phys. 2006, 99, 08T316. Read, J. C.; Mather, P. G.; Buhrman, R. A. Appl. Phys. Lett. 2007, 90, 132503. Pinitsoontorn, S.; Cerezo, A.; Petford-Long, A. K.; Mauri, D.; Folks, L.; Carey, M. J. Appl. Phys. Lett. 2008, 93, 071901. Read, J. C.; Cha, J. J.; Egelhoff, W. F.; Tseng, H. W.; Huang, P. Y.; Li, Y.; Muller, D. A.; Buhrman, R. A. Appl. Phys. Lett. 2009, 94, 112504. Cha, J. J.; Read, J. C.; Buhrman, R. A.; Muller, D. A. Appl. Phys. Lett. 2007, 91, 062516. Guo, G. C.; Cheng, W.-D.; Chen, J.-T.; Zhuang, H.-H.; Huang, J.S.; Zhang, Q.-E. Acta Cryst. C 1995, 51, 2469–2471. Guo, G.-C.; Cheng, W.-D.; Chen, J.-T.; Zhuang, H.-H.; Huang, J.S.; Zhang, Q.-E. Acta Cryst. C 1995, 51, 351–353. Cha, J. C.; Read, J. C.; Egelhoff, W. F.; Huang, P. Y.; Tseng, H.W.; Li, Y.; Buhrman, R. A.; Muller, D. A. Appl. Phys. Lett. 2009, 95, 032506. Gianozzi, P.; et al. J. Phys.: Condens. Matter 2009, 21, 395502. Giannozi, P.; et al. http://www.quantum-espresso.org (accessed Oct 12, 2009). Eyert, V. Int. J. Quantum Chem. 2000, 77, 1007–1031. von Barth, U.; Car, R. Unpublished work. For a brief description of this method, see. Dal Corso, A.; Baroni, S.; Resta, R.; de Gironcoli, S. Phys. Rev. B 1993, 47, 3588. Vanderbilt, D. Phys. Rev. B 1990, 41, 7892. Martin, R. M. Electronic Structure: Basic Theory and Practical Methods; Cambridge University Press: New York, 2005. Wang, H.; Jia, G.; Wang, Y.; You, Z.; Li, J.; Zhu, Z.; Yang, F.; Wei, Y.; Tu, C. Opt. Mater. 2007, 1635–1639. Choi, H. J.; Ihm, J. Phys. Rev. B 1999, 59, 2267. Smogunov, A.; Dal Corso, A.; Tossati, E. Surf. Sci. 2003, 532535, 549–555. Belashchenko, K. D.; Tsymbal, E. Y.; van Schilfgaarde, M.; Stewart, D. A.; Oleynik, I. I.; Jaswal, S. S. Phys. Rev. B 2004, 69, 174408. Tsymbal, E. Y.; Belashchenko, K. D.; Velev, J. P.; Jaswal, S. S.; van Schilfgaarde, M.; Oleynik, I. I.; Stewart, D. A. Prog. Mater. Sci. 2007, 52, 401–420. Mather, P. G.; Read, J. C.; Buhrman, R. A. Phys. Rev. B 2006, 73, 205412. Velev, J. P.; Belashchenko, K. D.; Jaswal, S. S.; Tsymbal, E. Y. Appl. Phys. Lett. 2007, 90, 072502.
DOI: 10.1021/nl9034362 | Nano Lett. 2010, 10, 263-267
