- Email: [email protected]
Fe multiferroic tunnel junctions
Computational Materials Science 112 (2016) 257–262
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Electron tunneling in Fe/KNbO3/Fe multiferroic tunnel junctions Hu Zhang, Jian-Qing Dai ⇑, Yu-Min Song School of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, PR China
a r t i c l e
i n f o
Article history: Received 17 March 2015 Received in revised form 28 October 2015 Accepted 2 November 2015
Keywords: Fe/KNbO3/Fe junctions Electronic structure Electron tunneling Four resistance states
a b s t r a c t We study the electronic structure and electron tunneling in Fe/KNbO3/Fe multiferroic tunnel junctions (MFTJs) with asymmetric interfaces using density functional theory calculations. There are large induced magnetic moments on interfacial Nb and O atoms, which are related to the direction of the polarization in KNbO3 barriers. The complex band structure of bulk KNbO3 indicates that the evanescent states with D1 and D5 symmetry have the smallest decay rates within the gap. We predict the conductance for the antiparallel and parallel magnetization configuration. The lowest decay rate of the evanescent states in KNbO3 characterizes the conductance for the majority spin channel. The polarization orientation has a large influence on the conductance. The tunneling magnetoresistance in the Fe/KNbO3/Fe MFTJs is small for the two opposite polarization states. However we obtain a high tunneling electroresistance for the two magnetization configurations of the electrodes. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Much effort has been devoted to investigate the phenomenon of electron tunneling due to the potential application to design new spintronics devices [1]. The tunneling magnetoresistance (TMR) can exist in a magnetic tunnel junction (MTJ). A MTJ is constructed with two ferromagnetic electrodes which are separated by insulating barriers [2–4]. The TMR effect in MTJs with MgO tunnel barriers has been extensively studied both theoretically and experimentally. Theoretical studies indicated that the symmetry of the states in the MgO barriers and Fe electrodes dominates the spin-dependent tunneling [5]. A TMR ratio of 1000% has been predicted in Fe/MgO/Fe MTJs [6]. In their reports, the TMR ratio was defined as (RAP RP)/RP. RAP and RP were resistances for antiparallel and parallel magnetization configurations of the two electrodes respectively. Experimentally, Yuasa et al. reported a TMR ratios up to 180% in single crystal Fe (0 0 1)/MgO (0 0 1)/Fe (0 0 1) MTJs [7]. After that a TMR ratio of 1010% at 5 K and of 500% at room temperature were discovered in CoFeB/MgO/CoFeB MTJs [8]. Perovskite oxides such as SrTiO3 have also been used as the tunneling barriers. There existed a negative spin polarization in Co/SrTiO3/Co MTJs [9]. This was due to the efficiently tunneling of minority-spin D5 states and majority-spin D1 states of the Co electrodes through the barriers. The tunneling through other barriers including Al2O3, GaAs, and ZnSe has also been studied [10,11]. ⇑ Corresponding author. Tel.: +86 871 65109902; fax: +86 871 65107922. E-mail address: [email protected] (J.-Q. Dai). http://dx.doi.org/10.1016/j.commatsci.2015.11.003 0927-0256/Ó 2015 Elsevier B.V. All rights reserved.
On the other hand, researchers have recently demonstrated that the ferroelectricity can exist in perovskite ferroelectric films at nanometer scale [12–14]. Therefore, the perovskite ferroelectric oxides can be used as ferroelectric tunneling barriers to construct ferroelectric tunnel junctions (FTJs) which display the tunneling electroresistance (TER) effect i.e. the resistance can be changed by the reversal of ferroelectric polarization [15]. Velev et al. investigated changes in the electric conductance in Pt/BaTiO3/Pt FTJs with polarization reversal using first principles calculations [16]. Experimentally, Gruverman et al. studied the TER effect in BaTiO3 thin films grown on the SrTiO3 substrates with crystalline SrRuO3 bottom electrodes [17]. They obtained BaTiO3 thin films in bidomain-patterned state successfully and showed that the reversal of the polarization can change the tunneling resistance by 2 orders of magnitude at room temperature. In addition, a TER effect reaching 50,000% has been measured in PbTiO3 ultrathin films [18]. A multiferroic tunnel junction (MFTJ) can be constructed by sandwiching a ferroelectric barrier between two ferromagnetic electrodes [15]. In these junctions the spin-dependent transport properties can be controlled by both the ferroelectricity in the tunneling barrier and the configuration of the magnetization in the ferromagnetic electrodes. Therefore the TER and TMR effects can coexist in such MFTJs. The existence of four resistance states has been predicted in SrRuO3/BaTiO3/SrRuO3 MFTJs with asymmetric interfaces by Velev et al. using first-principles calculations [19]. They found that the conductance for the parallel configuration of SrRuO3 electrodes is much larger than that for the antiparallel magnetization. The TER effect was mainly determined by the variations in the decay rate of evanescent states in BaTiO3 with
258
H. Zhang et al. / Computational Materials Science 112 (2016) 257–262
polarization reversal. Garcia et al. investigated the electron tunneling in the artificial Fe/BaTiO3/La0.67Sr0.33MnO3 MFTJs experimentally [20]. The ultrathin films of BaTiO3 showed ferroelectricity at room temperature. The obtained TMR was influenced by the polarization direction of the BaTiO3 barriers which can be switched with the voltage. Researchers have also used the organic ferroelectric materials as the tunneling barriers. They chosen poly(vinylidene fluoride) (PVDF). The spin-dependent tunneling conductance in Co/PVDF/Fe/Co and Co/PVDF/O/Co MFTJs has been studied theoretically [21,22]. In addition a bulk material that is both ferromagnetic and ferroelectric, such as La0.1Bi0.9MnO3, can also be used as the barriers [23]. Other MFTJs such as Co/PbZr0.2Ti0.8O3/La0.7Sr0.3MnO3, Fe/PbTiO3/Fe, La0.7Sr0.3MnO3/Ba0.95Sr0.05TiO3/La0.7Sr0.3MnO3, and La0.6Sr0.4MnO3/BiFeO3/La0.6Sr0.4MnO3 have also been studied [24–28]. These works open a way for the design of four-state devices. In this paper, we investigate the electronic structure and spin-resolved conductance in Fe/KNbO3/Fe MFTJs with asymmetric interfaces using first principles calculations. The tunneling conductance for the minority- and majority-spin channels is predicted. We find that the conductance for the two configurations has different magnitude. In addition, the reversal of polarization of the KNbO3 barrier leads to a large variation of the conductance. These results indicate the coexistence of the TMR and TER effects in Fe/KNbO3/Fe MFTJs. 2. Methods In the Fe/KNbO3/Fe MFTJs, the Fe layers are separated by the KNbO3 layers with six unit cells. We align the body centered cubic Fe [1 1 0] with the [0 0 1] axis of KNbO3. To make the MFTJ asymmetric we assume that the KNbO3 barrier has the NbO2 termination (the O atoms on top of Fe) and the KO termination (the O and K atoms on top of Fe) at left and right interfaces respectively. Thus the polarization of KNbO3 can point to the left (P ) or to the right (P?). We fix the in-plane lattice constant of the junction to be our calculated value (3.996 Å) of KNbO3 with the tetragonal phase, which is consistent with the experimental results (3.997 Å) [29]. The experimental value of lattice constant for bcc Fe is 2.87 Å [30]. Thus the in-plane lattice mismatch between bcc Fe (1 1 0) and KNbO3 is only about 1.5%. The theoretical out-plane lattice constant is of KNbO3 is 4.065 Å. The atomic structure of the MFTJ is shown in Fig. 1(a). The theoretical in-plane lattice parameters for the junctions are a = b = 3.996 Å. While the interface separation distance is obtained by minimizing the total energy of the junction keeping the out-plane separation in KNbO3 and Fe (1 0 0) subunits fixed. We use the Vienna ab initio simulation package (VASP) [31–33] to calculate the atomic and electronic structures of Fe/KNbO3/Fe MFTJs. The Perdew–Burke–Ernzerhof (PBE) [34,35] generalized gradient approximation (GGA) is employed with the energy cutoff 500 eV. We relax the structure until the Hellmann–Feynman forces are less than 20 meV/Å with a 6 6 1 Monkhorst–Pack grid [36]. A 12 12 2 grid is used for the density of states (DOS) calculations. Test calculations performed with PBE+U methods indicate that the considering of the on-site Coulomb term do not qualitatively modify the conclusions (see the supplementary materials for details). The Quantum ESPRESSO package [37] is used to calculate the tunneling conductance of the Fe/KNbO3/Fe MFTJs. The structure shown in Fig. 1(a) is used as the scattering region. Two semiinfinite Fe electrodes are attached on two sides of the junction. The ballistic conductance for the systems is calculated by the Landauer–Büttiker formula [38]:
Fig. 1. (a) Atomic structure of the Fe/KNbO3/Fe MFTJ. The top view of the left and right interface layers is also shown. (b) Displacements of Nb and K atoms with respect to O atoms. Filled (open) red circle symbols denote the Nb–O (K–O) displacements with the polarization pointing to the right. Filled (open) square symbols denote Nb–O (K–O) displacements with the polarization pointing to the left. (c) Schematic double-well for the Fe/KNbO3/Fe MFTJ. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
G¼
e2 X T r K jj h rK
ð1Þ
jj
where Tr(K||) gives the transmission probability for the electron with Bloch wave vector K|| = (kx, kY) and spin r at the Fermi energy. We calculate the conductance with a uniform 100 100K|| mesh in the two dimensional Brillouin zone, which can give convergent results. The TMR ratio is defined as
TMR ¼
GP GAP GP þ GAP
ð2Þ
where GP = G"" + G;; and GAP = G"; + G;" are the conductance for the parallel and antiparallel magnetic configuration respectively. We denote the majority (minority) spin channel by G"" (G;;). On the other hand, G#" and G"; denote minority-to-majority and majorityto-minority spin channels in the antiparallel configuration respectively. The TER ratio is defined as
TER ¼
G! G G! þ G
ð3Þ
where G and G? are the conductance for polarization pointing to the left and right respectively. 3. Results and discussion 3.1. Atomic and electronic structure Firstly we investigate the atomic structure of the MFTJs. After fully relaxation, two polarization states of the KNbO3 barrier in MFTJs are obtained. The total energy of the P? state is 152 meV (25.3 meV per unit cells of KNbO3) higher than that of the P state. The relative displacements of Nb and K with respect to O are
H. Zhang et al. / Computational Materials Science 112 (2016) 257–262
shown in Fig. 1(b). The relative displacements of Nb–O at the left interface are 0.07 and 0.09 Å for the P and P? state, respectively. The sign of the Nb–O displacements for all layers in the KNbO3 barriers changes with polarization reversal. This is easy to understand since the polarization direction is related to the relative displacement of the cation respect to the anion. The sign of the K–O displacements except the layer with l = 6 also changes with the MFTJs transform from the P? state to the P state. Abnormal situations can be found at the right interface (the layer with l = 6). When the polarization points to the left, the displacement of K–O is 0.39 Å at the right interface. This magnitude is much larger than that in the bulk KNbO3 with the relative Nb–O and K–O displacements of 0.15 and 0.08 Å respectively. The large magnitude of the relative displacement results from the right interface bonds. For the KO-terminated right interface, the two interfacial Fe atoms are inequivalent. The Fe1 (Fe2) atom is on top of O (K). The bond lengths of Fe2–K and Fe1–O are 2.71 and 1.81 Å, respectively. Their difference is up to 0.9 Å. This large bond length difference leads to a large magnitude of the displacement of K with respective to the O atom. For the P? state, the displacement of K–O at the right interface still remains negative (0.22 Å). This is unusual since other displacements are all positive under this state. The Fe2–K and Fe1–O bond lengths at the right interface are 2.71 and 1.97 Å respectively. Compared to the P state, the bond length of Fe2–K is identical while the Fe1–O bond length is increased by 0.16 Å. The fact that the bond length difference is still large (0.74 Å) makes the relative displacement of K–O at right interface remains negative although the polarization reverses. The electronic structure of the junctions with two polarization states is also investigated. The orbital-resolved DOS for interfacial atoms at two interfaces are shown in Fig. 2. It is seen that significant minority-spin Nb 4d bonding states are formed just below the Fermi energy (EF). This is due to the strong hybridization of Fe 3d and Nb 4d states (see Fig. 2(a) and (d)), which is similar to that find in Fe/BaTiO3 theoretically and experimentally [39,40]. As a result, a magnetic moment aligned antiparallel to that of Fe is induced on the left interfacial Nb atom. The magnetic moments on Nb at the left interface are 0.38 lB for the P state with the Fe–Nb bond of 2.74 Å and 0.25 lB for the P? state with the Fe–Nb bond of 2.85 Å. We can also find that the minority-spin Nb 4d bonding state lies closer to EF and is reduced at EF for the P? state compared to that for the P state. On the other hand, significant majority-spin O 2p states are induced due to interfacial Fe–O
259
bonds. The magnetic moments on the left interfacial O atoms are all about 0.03 lB for both the P? and P states since the Fe–O bond lengths are nearly identically for two polarization states (about 1.94 Å). The magnetic moments for left interfacial Fe atoms are 2.60 and 2.49 lB for the P? and P states respectively. These values are larger than the magnetic moment of bulk Fe (2.20 lB). The magnetic moments of Fe at the layer with l = 8 (about 2.30 lB) are close to the bulk value. A magnetic moment on the O atom of 0.17 lB is also induced at the right interface of the MFTJ in the P state as a result of the strong Fe1–O bond (1.80 Å). For the P? state, the right interfacial Fe1–O bond is increased to 1.97 Å, which results in a smaller magnetic moment on O (0.05 lB). For both the left and right interfacial O atoms, we can find one high peak for the majority-spin sate at the EF for the P? state as shown in Fig. 2(b) and (c). This peak disappears when the polarization is switched. For the P? state, the magnetic moments on Fe1 and Fe2 are 3.04 and 2.60 lB respectively. For the P state, the magnetic moments on Fe1 and Fe2 are 2.97 and 2.64 lB respectively. Furthermore, the magnetic moment on Fe at the layer with l = 8 is recovered to the bulk value for both two polarization states. Obviously, the strength of the interfacial Fe–Nb(O) bonds determines the magnitude of the induced magnetic moment. The induced interfacial magnetic moments are related to the polarization direction of the KNbO3 layer. Therefore there exists a magnetoelectric effect in Fe/KNbO3/Fe MFTJs. 3.2. TMR and TER effects The conductance for channels in the parallel configuration (G"", G;;) and antiparallel configuration (G;", G";) with the P? and P states is collected in Table 1. For the P? state, the conductance for the parallel configuration (GP) is about 1490 107 e2/h. The GP decreases to 109 107 e2/h for the P state. This large amount of decrease with the polarization reversal leads to a large TER of 86.3%. When the magnetization of electrodes changes from the parallel configuration to the antiparallel configuration, the conductance has a relative small variation. Thus we also obtain a large TER of 93.0% for the antiparallel configuration. The small change of GP and GAP results in a small TMR of 3.8% for the P? state. For the P state, GAP is about half of GP and thus we obtain a medium TMR of 30.2%. We can also find that G;; is much larger than G"" for the P? state. This means that the main contribution to GP comes from the conductance for the minority-spin channel. The spin
Fig. 2. Orbital-resolved DOS for the left interfacial (a) Nb, (b) O and (d) Fe; the right interfacial (c) O, (e) Fe1 and (f) Fe2 in the Fe/KNbO3/Fe MFTJs. The solid black and dashed red lines denote DOS for the polarization of the KNbO3 barrier pointing to the right and left, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
260
H. Zhang et al. / Computational Materials Science 112 (2016) 257–262
Table 1 Conductance per unit cell area (in unit of 107 e2/h) of the Fe/KNbO3/Fe MFTJs with the polarization pointing to the right (?) and left ( ). TMR and TER ratios are also given.
? TER (%)
G""
G;;
GP
G";
G;"
GAP
TMR (%)
208.72 91.49
1282.20 18.08
1490.92 109.57 86.3
376.78 20.99
1231.19 37.74
1607.97 58.73 93.0
3.8 30.2
polarization (SP) of the conductance is defined as P = (G"" G;;)/ (G"" + G;;). Thus a negative SP with the value of 72% is obtained. This is due to the fact that the DOS of bulk Fe has a negative SP at the EF and a large minority-spin state is induced on the interface Nb atom at EF. The tunneling of minority spin electrons of the left electrode dominates the antiparallel conductance GAP. For the P state, G"" is larger than G;;. Thus the SP is altered from negative to positive when the polarization is switched from right to left. This is due to the decrease of the induced minority-spin DOS of the interface Nb atom and the increase of the induced majority-spin DOS of the right interface O atom at EF compared to these of the P? state (shown in Fig. 2(a) and (c)). For the antiparallel configuration, the minority-spin electron of the left electrode has a slightly large conductance than the majority-spin electron. To gain insight into the spin-dependent tunneling we investigate the conductance as a function of K|| as shown in Fig. 3. For the P? state, the area that forming a cross pattern dominates G"". The area around the Brillouin zone center makes the largest contribution to the conductance. For G;;, the main contribution is point. The strongly concentrated in the area centered at the C tunneling has an important connection with the complex band structure (CBS) of the tunneling barrier. The CBS of the bulk KNbO3 is shown in Fig. 4(a). We can find that a doubly degenerate state with D5 symmetry and a state with D1 symmetry have the smallest point (K|| = 0). Thus decay rates in the band gap of KNbO3 at the C the tunneling properties of the Fe electrodes are controlled by the D5 and D1 states that propagating in the tunneling barrier. Similar to bulk KNbO3, two evanescent states with D5 and D1 symmetry in
Fig. 4. (a) Complex band structure (in unit of 2p/a) of bulk P4mm KNbO3 at K|| = 0 in the [0 0 1] direction. The middle panel shows the real bands. The left and right panels represent the evanescent states with Re(kz) = 0 and Re(kz) = 0.5 respectively. (b), (c) Two lowest decay rates (in units of 2p/a) of the evanescent states in bulk P4mm KNbO3 as a function of K|| for energies relative to the valence band maximum 1.5 eV.
the CBS of bulk BaTiO3 (BTO) and SrTiO3 (STO) have the lowest decay rates in the gap [9,41]. These states originate from the C point [Re(kz) = 0]. However the situation is very different for PbTiO3 (PTO) [26]. Previous studies showed that the lowest decay rates for
Fig. 3. The K||-resolved conductance in the 2D Brillouin zone of the Fe/KNbO3/Fe MFTJs for the polarization of the KNbO3 barrier pointing to the right (top panel) and left (bottom panel). (a), (e) G""; (b), (f) G;;; (c), (g) G";; and (d), (h) G;". The color scale is in logarithmic. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H. Zhang et al. / Computational Materials Science 112 (2016) 257–262
261
Fig. 5. The K||-resolved DOS (in arbitrary units) of the minority-spin D5-like states for the Fe/KNbO3/Fe MFTJs with the polarization of the KNbO3 barrier pointing to the right (top panel) and left (bottom panel). (a), (e) layer with l = 7; (b), (f) layer with l = 6; (c), (g) layer with l = 6; (d), (h) layer with l = 7.
PTO is always formed by D1 states. One evanescent state has Re(kz) = 0 while the other has Re(kz) = 0.5. The second state is associated with the Pb 6Pz orbitals. As we can see from the K||-resolved lowest decay rates of evanescent states in KNbO3 shown in Fig. 4 (b) and (c), a cross-shaped area of the Brillouin zone displays the lowest decay rates. This means that the G"" is dominated by the lowest decay rates of evanescent states in the KNbO3 barrier. At the Brillouin zone center, the distributions of G"" and G;; are strongly reduced when the polarization direction of the KNbO3 barrier is turned to the left. The K||-resolved G"" for the P state displays a clearer cross character. This demonstrates the domination of evanescent states in KNbO3 over the tunneling. On the other hand, the feature of the K||-resolved conductance of the minority spin channel G;; can be understood by means of the K||-resolved DOS of interfacial layers. Fig. 5 illustrates the minority-spin D5-like states of the layers at two interfaces. Firstly, we can find that the K||-resolved DOS for the layers at right interface are different from those at the left interface for both the P? and P state. The large distinction of the DOS for the left (l = 7) and right (l = 7) interfacial Fe layer is obviously due to their different bonds with NbO2 and KO terminations. For the left interfacial Fe layer (l = 7), the states mainly locate at the area around the Brillouin zone center and the area near four corners. Secondly, the polarization direction has an important influence on the interface states, especially for states of NbO2 and KO terminations. Dif point ferent from Fig. 5(b), the four long bars far away from the C appear in Fig. 5(f). The states shown in Fig. 5(g) have a more extended distribution than that in Fig. 5(c). Compared to Fig. 5 point shown in Fig. 5(h) are (d), the states in the area near the C reduced and distribute as a ‘‘ring”. We demonstrate that the minority-spin D5-like states of the two interfacial layers characterize G;; for two polarization states. The K||-resolved conductance in the antiparallel configuration has the mixed characteristics of the minority and majority spin conductance in the parallel configuration. This is due to the fact that the tunneling electron must traverse both the left and right interfaces. Therefore the G;" and G"; should be also large at the area around point since the extended area around the Brillouin zone center the C dominates both the G"" and G;; for two polarization states. This is consistent with what we find in Fig. 3. As a result, the difference between GP and GAP is small. Thus we obtain a TMR of 3.8% and
30.2% for the P? and P states respectively. In addition we can find clear decreases for the G;" and G"; in the P state compared to those in the P? state. A significant contribution to the G;" from the areas away from the Brillouin zone center can also be found. 3.3. Discussion It is known that the ferroelectricity in thin perovskite films can sustain above some critical thickness. To obtain the TER effect, the tunneling barriers with a thickness of only several nanometers should have two stable polarization states with opposite directions. In this paper, we obtain two stable polarization states for the KNbO3 barriers containing six unit cells (about 2.4 nm) in Fe/KNbO3/Fe MFTJs with asymmetric interface terminations. For the whole MFTJs, the total energy difference between the P? state and P state is 152 meV, as shown in Fig. 1(c). The displacements of K(Nb) with respect to the O atoms are enhanced at the interfaces due to the bonding effect. We should note that the ferromagnetic Fe has a high Curie temperature of 1043 K. Therefore it is convenient to study the electron tunneling in Fe/KNbO3/Fe MFTJs experimentally. We predict a large TER for both the parallel and antiparallel magnetization configuration although the TMR effect in this system with two polarization states is small. Thus the Fe/KNbO3/Fe system is a candidate for applications in new spintronics devices. Finally, it should be pointed out that there is a sharp peak in the spin-down state at 0.2–0.3 eV above EF for left interfacial Fe atoms which are bound to oxygen atoms of the KNbO3 barrier, as shown in Fig. 2(d) and Fig. S1(a) (see supplementary materials). This peak has no influence for the present study since the conductance is calculated at zero bias voltage. However, when very small bias voltage is applied to Fe/KNbO3/Fe junctions, this sharp peak will create conducting hot-spots in the spin-down channel. This effect will change significantly the characteristics of the interface of junctions. Therefore, further researches for this system may focus on the conductance under finite bias to investigate the additional physical phenomena. 4. Conclusions We have studied the electronic structure and spin-dependent tunneling in Fe/KNbO3/Fe MFTJs with the NbO2 termination at
262
H. Zhang et al. / Computational Materials Science 112 (2016) 257–262
the left interface and the KO termination at the right interface using first principles calculations. We obtain two stable ferroelectric states with opposite polarization direction in MFTJs containing six unit cells of KNbO3. At the right interface, the relative displacement of K with respect to O has the same sign for the P? and P state due to the short interface Fe–O bond length and long Fe–K bond length. The analysis of the electronic structure for the interface atoms indicates that there are sizeable induced magnetic moments on interfacial Nb and O atoms results from the strong Fe–Nb and Fe–O bonds. The magnitude of induced magnetic moments is related to the polarization direction of the KNbO3 barrier. Hence there are magnetoelectric effects in such junctions. According to the CBS of the bulk KNbO3, a D1 singlet and a D5 doublet have the smallest decay rates within the band gap. The TMR in these junctions is small for the two polarization states. On the other hand, there exists high TER for both the antiparallel and parallel magnetization configuration. Thus the Fe/KNbO3/Fe MFTJs are suitable systems for applications that display giant TER at room temperature. We hope that our results will provide assistance for the future experimental works. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant Nos. 51162019 and 51462019). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.commatsci.2015. 11.003. References [1] I. Zˇutic´, J. Fabian, S.D. Sarma, Rev. Mod. Phys. 76 (2) (2004) 323.
[2] P.M. Tedrow, R. Meservey, Phys. Rev. Lett. 26 (4) (1971) 192. [3] J.S. Moodera et al., Phys. Rev. Lett. 74 (16) (1995) 3273. [4] E.Y. Tsymbal, O.N. Mryasov, P.R. LeClair, J. Phys.: Condens. Matter 15 (4) (2003) R109–R142. [5] W.H. Butler, X.-G. Zhang, T.C. Schulthess, Phys. Rev. B 63 (5) (2001) 054416. [6] J. Mathon, A. Umerski, Phys. Rev. B 63 (22) (2001) 220403. [7] S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki, K. Ando, Nat. Mater. 3 (12) (2004) 868–871. [8] Y.M. Lee, J. Hayakawa, S. Ikeda, F. Matsukura, H. Ohno, Appl. Phys. Lett. 90 (21) (2007) 212507. [9] J.P. Velev et al., Phys. Rev. Lett. 95 (21) (2005) 216601. [10] J.M. de Teresa et al., Science 286 (5439) (1999) 507–509. [11] Ph Mavropoulos, N. Papanikolaou, P.H. Dederichs, Phys. Rev. Lett. 85 (5) (2000) 1088. [12] T. Tybell, C.H. Ahn, J.-M. Triscone, Appl. Phys. Lett. 75 (6) (1999) 856–858. [13] J. Junquera, Ph. Ghosez, Nature 422 (6931) (2003) 506–509. [14] D.D. Fong et al., Science 304 (5677) (2004) 1650–1653. [15] E.Y. Tsymbal, H. Kohlstedt, Science 313 (5784) (2006) 181–183. [16] J.P. Velev et al., Phys. Rev. Lett. 98 (13) (2007) 137201. [17] A. Gruverman et al., Nano Lett. 9 (10) (2009) 3539–3543. [18] A. Crassous et al., Appl. Phys. Lett. 96 (4) (2010) 042901. [19] J.P. Velev et al., Nano Lett. 9 (1) (2009) 427–432. [20] V. Garcia et al., Science 327 (5969) (2010) 1106–1110. [21] J.M. López-Encarnación et al., Nano Lett. 11 (2) (2011) 599–603. [22] J.P. Velev et al., Phys. Rev. B 85 (12) (2012) 125103. [23] M. Gajek et al., Nat. Mater. 6 (4) (2007) 296–302. [24] D. Pantel, S. Goetze, D. Hesse, M. Alexe, Nat. Mater. 11 (4) (2012) 289–293. [25] J.-Q. Dai, H. Zhang, Y.-M. Song, J. Appl. Phys. 114 (16) (2013) 163703. [26] J.-Q. Dai, H. Zhang, Y.-M. Song, J. Magn. Magn. Mater. 351 (2014) 29–36. [27] Y.W. Yin et al., J. Appl. Phys. 109 (7) (2011) 07D915. [28] Y.K. Liu et al., Appl. Phys. Lett. 104 (4) (2014) 043507. [29] A.W. Hewat, J. Phys. C: Solid State Phys. 6 (1973) 2559. [30] C. Kittel, Introduction to Solid State Physics, seventh ed., Wiley, New York, 1996. [31] G. Kresse, J. Hafner, Phys. Rev. B 47 (1) (1993) 558. [32] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (16) (1996) 11169. [33] M. Gajdoš, K. Hummer, G. Kresse, Phys. Rev. B 73 (4) (2006) 045112. [34] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (18) (1996) 3865. [35] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 78 (7) (1997) 1396. [36] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (12) (1976) 5188. [37] P. Giannozzi et al., J. Phys.: Condens. Matter 21 (39) (2009) 395502. [38] Y. Imry, R. Landauer, Rev. Mod. Phys. 71 (2) (1999) S306. [39] C.-G. Duan, S.S. Jaswal, E.Y. Tsymbal, Phys. Rev. Lett. 97 (4) (2006) 047201. [40] S. Valencia et al., Nat. Mater. 10 (10) (2011) 753–758. [41] N.F. Hinsche et al., Phys. Rev. B 82 (21) (2010) 214110.
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Electron tunneling in Fe/KNbO3/Fe multiferroic tunnel junctions Hu Zhang, Jian-Qing Dai ⇑, Yu-Min Song School of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, PR China
a r t i c l e
i n f o
Article history: Received 17 March 2015 Received in revised form 28 October 2015 Accepted 2 November 2015
Keywords: Fe/KNbO3/Fe junctions Electronic structure Electron tunneling Four resistance states
a b s t r a c t We study the electronic structure and electron tunneling in Fe/KNbO3/Fe multiferroic tunnel junctions (MFTJs) with asymmetric interfaces using density functional theory calculations. There are large induced magnetic moments on interfacial Nb and O atoms, which are related to the direction of the polarization in KNbO3 barriers. The complex band structure of bulk KNbO3 indicates that the evanescent states with D1 and D5 symmetry have the smallest decay rates within the gap. We predict the conductance for the antiparallel and parallel magnetization configuration. The lowest decay rate of the evanescent states in KNbO3 characterizes the conductance for the majority spin channel. The polarization orientation has a large influence on the conductance. The tunneling magnetoresistance in the Fe/KNbO3/Fe MFTJs is small for the two opposite polarization states. However we obtain a high tunneling electroresistance for the two magnetization configurations of the electrodes. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Much effort has been devoted to investigate the phenomenon of electron tunneling due to the potential application to design new spintronics devices [1]. The tunneling magnetoresistance (TMR) can exist in a magnetic tunnel junction (MTJ). A MTJ is constructed with two ferromagnetic electrodes which are separated by insulating barriers [2–4]. The TMR effect in MTJs with MgO tunnel barriers has been extensively studied both theoretically and experimentally. Theoretical studies indicated that the symmetry of the states in the MgO barriers and Fe electrodes dominates the spin-dependent tunneling [5]. A TMR ratio of 1000% has been predicted in Fe/MgO/Fe MTJs [6]. In their reports, the TMR ratio was defined as (RAP RP)/RP. RAP and RP were resistances for antiparallel and parallel magnetization configurations of the two electrodes respectively. Experimentally, Yuasa et al. reported a TMR ratios up to 180% in single crystal Fe (0 0 1)/MgO (0 0 1)/Fe (0 0 1) MTJs [7]. After that a TMR ratio of 1010% at 5 K and of 500% at room temperature were discovered in CoFeB/MgO/CoFeB MTJs [8]. Perovskite oxides such as SrTiO3 have also been used as the tunneling barriers. There existed a negative spin polarization in Co/SrTiO3/Co MTJs [9]. This was due to the efficiently tunneling of minority-spin D5 states and majority-spin D1 states of the Co electrodes through the barriers. The tunneling through other barriers including Al2O3, GaAs, and ZnSe has also been studied [10,11]. ⇑ Corresponding author. Tel.: +86 871 65109902; fax: +86 871 65107922. E-mail address: [email protected] (J.-Q. Dai). http://dx.doi.org/10.1016/j.commatsci.2015.11.003 0927-0256/Ó 2015 Elsevier B.V. All rights reserved.
On the other hand, researchers have recently demonstrated that the ferroelectricity can exist in perovskite ferroelectric films at nanometer scale [12–14]. Therefore, the perovskite ferroelectric oxides can be used as ferroelectric tunneling barriers to construct ferroelectric tunnel junctions (FTJs) which display the tunneling electroresistance (TER) effect i.e. the resistance can be changed by the reversal of ferroelectric polarization [15]. Velev et al. investigated changes in the electric conductance in Pt/BaTiO3/Pt FTJs with polarization reversal using first principles calculations [16]. Experimentally, Gruverman et al. studied the TER effect in BaTiO3 thin films grown on the SrTiO3 substrates with crystalline SrRuO3 bottom electrodes [17]. They obtained BaTiO3 thin films in bidomain-patterned state successfully and showed that the reversal of the polarization can change the tunneling resistance by 2 orders of magnitude at room temperature. In addition, a TER effect reaching 50,000% has been measured in PbTiO3 ultrathin films [18]. A multiferroic tunnel junction (MFTJ) can be constructed by sandwiching a ferroelectric barrier between two ferromagnetic electrodes [15]. In these junctions the spin-dependent transport properties can be controlled by both the ferroelectricity in the tunneling barrier and the configuration of the magnetization in the ferromagnetic electrodes. Therefore the TER and TMR effects can coexist in such MFTJs. The existence of four resistance states has been predicted in SrRuO3/BaTiO3/SrRuO3 MFTJs with asymmetric interfaces by Velev et al. using first-principles calculations [19]. They found that the conductance for the parallel configuration of SrRuO3 electrodes is much larger than that for the antiparallel magnetization. The TER effect was mainly determined by the variations in the decay rate of evanescent states in BaTiO3 with
258
H. Zhang et al. / Computational Materials Science 112 (2016) 257–262
polarization reversal. Garcia et al. investigated the electron tunneling in the artificial Fe/BaTiO3/La0.67Sr0.33MnO3 MFTJs experimentally [20]. The ultrathin films of BaTiO3 showed ferroelectricity at room temperature. The obtained TMR was influenced by the polarization direction of the BaTiO3 barriers which can be switched with the voltage. Researchers have also used the organic ferroelectric materials as the tunneling barriers. They chosen poly(vinylidene fluoride) (PVDF). The spin-dependent tunneling conductance in Co/PVDF/Fe/Co and Co/PVDF/O/Co MFTJs has been studied theoretically [21,22]. In addition a bulk material that is both ferromagnetic and ferroelectric, such as La0.1Bi0.9MnO3, can also be used as the barriers [23]. Other MFTJs such as Co/PbZr0.2Ti0.8O3/La0.7Sr0.3MnO3, Fe/PbTiO3/Fe, La0.7Sr0.3MnO3/Ba0.95Sr0.05TiO3/La0.7Sr0.3MnO3, and La0.6Sr0.4MnO3/BiFeO3/La0.6Sr0.4MnO3 have also been studied [24–28]. These works open a way for the design of four-state devices. In this paper, we investigate the electronic structure and spin-resolved conductance in Fe/KNbO3/Fe MFTJs with asymmetric interfaces using first principles calculations. The tunneling conductance for the minority- and majority-spin channels is predicted. We find that the conductance for the two configurations has different magnitude. In addition, the reversal of polarization of the KNbO3 barrier leads to a large variation of the conductance. These results indicate the coexistence of the TMR and TER effects in Fe/KNbO3/Fe MFTJs. 2. Methods In the Fe/KNbO3/Fe MFTJs, the Fe layers are separated by the KNbO3 layers with six unit cells. We align the body centered cubic Fe [1 1 0] with the [0 0 1] axis of KNbO3. To make the MFTJ asymmetric we assume that the KNbO3 barrier has the NbO2 termination (the O atoms on top of Fe) and the KO termination (the O and K atoms on top of Fe) at left and right interfaces respectively. Thus the polarization of KNbO3 can point to the left (P ) or to the right (P?). We fix the in-plane lattice constant of the junction to be our calculated value (3.996 Å) of KNbO3 with the tetragonal phase, which is consistent with the experimental results (3.997 Å) [29]. The experimental value of lattice constant for bcc Fe is 2.87 Å [30]. Thus the in-plane lattice mismatch between bcc Fe (1 1 0) and KNbO3 is only about 1.5%. The theoretical out-plane lattice constant is of KNbO3 is 4.065 Å. The atomic structure of the MFTJ is shown in Fig. 1(a). The theoretical in-plane lattice parameters for the junctions are a = b = 3.996 Å. While the interface separation distance is obtained by minimizing the total energy of the junction keeping the out-plane separation in KNbO3 and Fe (1 0 0) subunits fixed. We use the Vienna ab initio simulation package (VASP) [31–33] to calculate the atomic and electronic structures of Fe/KNbO3/Fe MFTJs. The Perdew–Burke–Ernzerhof (PBE) [34,35] generalized gradient approximation (GGA) is employed with the energy cutoff 500 eV. We relax the structure until the Hellmann–Feynman forces are less than 20 meV/Å with a 6 6 1 Monkhorst–Pack grid [36]. A 12 12 2 grid is used for the density of states (DOS) calculations. Test calculations performed with PBE+U methods indicate that the considering of the on-site Coulomb term do not qualitatively modify the conclusions (see the supplementary materials for details). The Quantum ESPRESSO package [37] is used to calculate the tunneling conductance of the Fe/KNbO3/Fe MFTJs. The structure shown in Fig. 1(a) is used as the scattering region. Two semiinfinite Fe electrodes are attached on two sides of the junction. The ballistic conductance for the systems is calculated by the Landauer–Büttiker formula [38]:
Fig. 1. (a) Atomic structure of the Fe/KNbO3/Fe MFTJ. The top view of the left and right interface layers is also shown. (b) Displacements of Nb and K atoms with respect to O atoms. Filled (open) red circle symbols denote the Nb–O (K–O) displacements with the polarization pointing to the right. Filled (open) square symbols denote Nb–O (K–O) displacements with the polarization pointing to the left. (c) Schematic double-well for the Fe/KNbO3/Fe MFTJ. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
G¼
e2 X T r K jj h rK
ð1Þ
jj
where Tr(K||) gives the transmission probability for the electron with Bloch wave vector K|| = (kx, kY) and spin r at the Fermi energy. We calculate the conductance with a uniform 100 100K|| mesh in the two dimensional Brillouin zone, which can give convergent results. The TMR ratio is defined as
TMR ¼
GP GAP GP þ GAP
ð2Þ
where GP = G"" + G;; and GAP = G"; + G;" are the conductance for the parallel and antiparallel magnetic configuration respectively. We denote the majority (minority) spin channel by G"" (G;;). On the other hand, G#" and G"; denote minority-to-majority and majorityto-minority spin channels in the antiparallel configuration respectively. The TER ratio is defined as
TER ¼
G! G G! þ G
ð3Þ
where G and G? are the conductance for polarization pointing to the left and right respectively. 3. Results and discussion 3.1. Atomic and electronic structure Firstly we investigate the atomic structure of the MFTJs. After fully relaxation, two polarization states of the KNbO3 barrier in MFTJs are obtained. The total energy of the P? state is 152 meV (25.3 meV per unit cells of KNbO3) higher than that of the P state. The relative displacements of Nb and K with respect to O are
H. Zhang et al. / Computational Materials Science 112 (2016) 257–262
shown in Fig. 1(b). The relative displacements of Nb–O at the left interface are 0.07 and 0.09 Å for the P and P? state, respectively. The sign of the Nb–O displacements for all layers in the KNbO3 barriers changes with polarization reversal. This is easy to understand since the polarization direction is related to the relative displacement of the cation respect to the anion. The sign of the K–O displacements except the layer with l = 6 also changes with the MFTJs transform from the P? state to the P state. Abnormal situations can be found at the right interface (the layer with l = 6). When the polarization points to the left, the displacement of K–O is 0.39 Å at the right interface. This magnitude is much larger than that in the bulk KNbO3 with the relative Nb–O and K–O displacements of 0.15 and 0.08 Å respectively. The large magnitude of the relative displacement results from the right interface bonds. For the KO-terminated right interface, the two interfacial Fe atoms are inequivalent. The Fe1 (Fe2) atom is on top of O (K). The bond lengths of Fe2–K and Fe1–O are 2.71 and 1.81 Å, respectively. Their difference is up to 0.9 Å. This large bond length difference leads to a large magnitude of the displacement of K with respective to the O atom. For the P? state, the displacement of K–O at the right interface still remains negative (0.22 Å). This is unusual since other displacements are all positive under this state. The Fe2–K and Fe1–O bond lengths at the right interface are 2.71 and 1.97 Å respectively. Compared to the P state, the bond length of Fe2–K is identical while the Fe1–O bond length is increased by 0.16 Å. The fact that the bond length difference is still large (0.74 Å) makes the relative displacement of K–O at right interface remains negative although the polarization reverses. The electronic structure of the junctions with two polarization states is also investigated. The orbital-resolved DOS for interfacial atoms at two interfaces are shown in Fig. 2. It is seen that significant minority-spin Nb 4d bonding states are formed just below the Fermi energy (EF). This is due to the strong hybridization of Fe 3d and Nb 4d states (see Fig. 2(a) and (d)), which is similar to that find in Fe/BaTiO3 theoretically and experimentally [39,40]. As a result, a magnetic moment aligned antiparallel to that of Fe is induced on the left interfacial Nb atom. The magnetic moments on Nb at the left interface are 0.38 lB for the P state with the Fe–Nb bond of 2.74 Å and 0.25 lB for the P? state with the Fe–Nb bond of 2.85 Å. We can also find that the minority-spin Nb 4d bonding state lies closer to EF and is reduced at EF for the P? state compared to that for the P state. On the other hand, significant majority-spin O 2p states are induced due to interfacial Fe–O
259
bonds. The magnetic moments on the left interfacial O atoms are all about 0.03 lB for both the P? and P states since the Fe–O bond lengths are nearly identically for two polarization states (about 1.94 Å). The magnetic moments for left interfacial Fe atoms are 2.60 and 2.49 lB for the P? and P states respectively. These values are larger than the magnetic moment of bulk Fe (2.20 lB). The magnetic moments of Fe at the layer with l = 8 (about 2.30 lB) are close to the bulk value. A magnetic moment on the O atom of 0.17 lB is also induced at the right interface of the MFTJ in the P state as a result of the strong Fe1–O bond (1.80 Å). For the P? state, the right interfacial Fe1–O bond is increased to 1.97 Å, which results in a smaller magnetic moment on O (0.05 lB). For both the left and right interfacial O atoms, we can find one high peak for the majority-spin sate at the EF for the P? state as shown in Fig. 2(b) and (c). This peak disappears when the polarization is switched. For the P? state, the magnetic moments on Fe1 and Fe2 are 3.04 and 2.60 lB respectively. For the P state, the magnetic moments on Fe1 and Fe2 are 2.97 and 2.64 lB respectively. Furthermore, the magnetic moment on Fe at the layer with l = 8 is recovered to the bulk value for both two polarization states. Obviously, the strength of the interfacial Fe–Nb(O) bonds determines the magnitude of the induced magnetic moment. The induced interfacial magnetic moments are related to the polarization direction of the KNbO3 layer. Therefore there exists a magnetoelectric effect in Fe/KNbO3/Fe MFTJs. 3.2. TMR and TER effects The conductance for channels in the parallel configuration (G"", G;;) and antiparallel configuration (G;", G";) with the P? and P states is collected in Table 1. For the P? state, the conductance for the parallel configuration (GP) is about 1490 107 e2/h. The GP decreases to 109 107 e2/h for the P state. This large amount of decrease with the polarization reversal leads to a large TER of 86.3%. When the magnetization of electrodes changes from the parallel configuration to the antiparallel configuration, the conductance has a relative small variation. Thus we also obtain a large TER of 93.0% for the antiparallel configuration. The small change of GP and GAP results in a small TMR of 3.8% for the P? state. For the P state, GAP is about half of GP and thus we obtain a medium TMR of 30.2%. We can also find that G;; is much larger than G"" for the P? state. This means that the main contribution to GP comes from the conductance for the minority-spin channel. The spin
Fig. 2. Orbital-resolved DOS for the left interfacial (a) Nb, (b) O and (d) Fe; the right interfacial (c) O, (e) Fe1 and (f) Fe2 in the Fe/KNbO3/Fe MFTJs. The solid black and dashed red lines denote DOS for the polarization of the KNbO3 barrier pointing to the right and left, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
260
H. Zhang et al. / Computational Materials Science 112 (2016) 257–262
Table 1 Conductance per unit cell area (in unit of 107 e2/h) of the Fe/KNbO3/Fe MFTJs with the polarization pointing to the right (?) and left ( ). TMR and TER ratios are also given.
? TER (%)
G""
G;;
GP
G";
G;"
GAP
TMR (%)
208.72 91.49
1282.20 18.08
1490.92 109.57 86.3
376.78 20.99
1231.19 37.74
1607.97 58.73 93.0
3.8 30.2
polarization (SP) of the conductance is defined as P = (G"" G;;)/ (G"" + G;;). Thus a negative SP with the value of 72% is obtained. This is due to the fact that the DOS of bulk Fe has a negative SP at the EF and a large minority-spin state is induced on the interface Nb atom at EF. The tunneling of minority spin electrons of the left electrode dominates the antiparallel conductance GAP. For the P state, G"" is larger than G;;. Thus the SP is altered from negative to positive when the polarization is switched from right to left. This is due to the decrease of the induced minority-spin DOS of the interface Nb atom and the increase of the induced majority-spin DOS of the right interface O atom at EF compared to these of the P? state (shown in Fig. 2(a) and (c)). For the antiparallel configuration, the minority-spin electron of the left electrode has a slightly large conductance than the majority-spin electron. To gain insight into the spin-dependent tunneling we investigate the conductance as a function of K|| as shown in Fig. 3. For the P? state, the area that forming a cross pattern dominates G"". The area around the Brillouin zone center makes the largest contribution to the conductance. For G;;, the main contribution is point. The strongly concentrated in the area centered at the C tunneling has an important connection with the complex band structure (CBS) of the tunneling barrier. The CBS of the bulk KNbO3 is shown in Fig. 4(a). We can find that a doubly degenerate state with D5 symmetry and a state with D1 symmetry have the smallest point (K|| = 0). Thus decay rates in the band gap of KNbO3 at the C the tunneling properties of the Fe electrodes are controlled by the D5 and D1 states that propagating in the tunneling barrier. Similar to bulk KNbO3, two evanescent states with D5 and D1 symmetry in
Fig. 4. (a) Complex band structure (in unit of 2p/a) of bulk P4mm KNbO3 at K|| = 0 in the [0 0 1] direction. The middle panel shows the real bands. The left and right panels represent the evanescent states with Re(kz) = 0 and Re(kz) = 0.5 respectively. (b), (c) Two lowest decay rates (in units of 2p/a) of the evanescent states in bulk P4mm KNbO3 as a function of K|| for energies relative to the valence band maximum 1.5 eV.
the CBS of bulk BaTiO3 (BTO) and SrTiO3 (STO) have the lowest decay rates in the gap [9,41]. These states originate from the C point [Re(kz) = 0]. However the situation is very different for PbTiO3 (PTO) [26]. Previous studies showed that the lowest decay rates for
Fig. 3. The K||-resolved conductance in the 2D Brillouin zone of the Fe/KNbO3/Fe MFTJs for the polarization of the KNbO3 barrier pointing to the right (top panel) and left (bottom panel). (a), (e) G""; (b), (f) G;;; (c), (g) G";; and (d), (h) G;". The color scale is in logarithmic. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H. Zhang et al. / Computational Materials Science 112 (2016) 257–262
261
Fig. 5. The K||-resolved DOS (in arbitrary units) of the minority-spin D5-like states for the Fe/KNbO3/Fe MFTJs with the polarization of the KNbO3 barrier pointing to the right (top panel) and left (bottom panel). (a), (e) layer with l = 7; (b), (f) layer with l = 6; (c), (g) layer with l = 6; (d), (h) layer with l = 7.
PTO is always formed by D1 states. One evanescent state has Re(kz) = 0 while the other has Re(kz) = 0.5. The second state is associated with the Pb 6Pz orbitals. As we can see from the K||-resolved lowest decay rates of evanescent states in KNbO3 shown in Fig. 4 (b) and (c), a cross-shaped area of the Brillouin zone displays the lowest decay rates. This means that the G"" is dominated by the lowest decay rates of evanescent states in the KNbO3 barrier. At the Brillouin zone center, the distributions of G"" and G;; are strongly reduced when the polarization direction of the KNbO3 barrier is turned to the left. The K||-resolved G"" for the P state displays a clearer cross character. This demonstrates the domination of evanescent states in KNbO3 over the tunneling. On the other hand, the feature of the K||-resolved conductance of the minority spin channel G;; can be understood by means of the K||-resolved DOS of interfacial layers. Fig. 5 illustrates the minority-spin D5-like states of the layers at two interfaces. Firstly, we can find that the K||-resolved DOS for the layers at right interface are different from those at the left interface for both the P? and P state. The large distinction of the DOS for the left (l = 7) and right (l = 7) interfacial Fe layer is obviously due to their different bonds with NbO2 and KO terminations. For the left interfacial Fe layer (l = 7), the states mainly locate at the area around the Brillouin zone center and the area near four corners. Secondly, the polarization direction has an important influence on the interface states, especially for states of NbO2 and KO terminations. Dif point ferent from Fig. 5(b), the four long bars far away from the C appear in Fig. 5(f). The states shown in Fig. 5(g) have a more extended distribution than that in Fig. 5(c). Compared to Fig. 5 point shown in Fig. 5(h) are (d), the states in the area near the C reduced and distribute as a ‘‘ring”. We demonstrate that the minority-spin D5-like states of the two interfacial layers characterize G;; for two polarization states. The K||-resolved conductance in the antiparallel configuration has the mixed characteristics of the minority and majority spin conductance in the parallel configuration. This is due to the fact that the tunneling electron must traverse both the left and right interfaces. Therefore the G;" and G"; should be also large at the area around point since the extended area around the Brillouin zone center the C dominates both the G"" and G;; for two polarization states. This is consistent with what we find in Fig. 3. As a result, the difference between GP and GAP is small. Thus we obtain a TMR of 3.8% and
30.2% for the P? and P states respectively. In addition we can find clear decreases for the G;" and G"; in the P state compared to those in the P? state. A significant contribution to the G;" from the areas away from the Brillouin zone center can also be found. 3.3. Discussion It is known that the ferroelectricity in thin perovskite films can sustain above some critical thickness. To obtain the TER effect, the tunneling barriers with a thickness of only several nanometers should have two stable polarization states with opposite directions. In this paper, we obtain two stable polarization states for the KNbO3 barriers containing six unit cells (about 2.4 nm) in Fe/KNbO3/Fe MFTJs with asymmetric interface terminations. For the whole MFTJs, the total energy difference between the P? state and P state is 152 meV, as shown in Fig. 1(c). The displacements of K(Nb) with respect to the O atoms are enhanced at the interfaces due to the bonding effect. We should note that the ferromagnetic Fe has a high Curie temperature of 1043 K. Therefore it is convenient to study the electron tunneling in Fe/KNbO3/Fe MFTJs experimentally. We predict a large TER for both the parallel and antiparallel magnetization configuration although the TMR effect in this system with two polarization states is small. Thus the Fe/KNbO3/Fe system is a candidate for applications in new spintronics devices. Finally, it should be pointed out that there is a sharp peak in the spin-down state at 0.2–0.3 eV above EF for left interfacial Fe atoms which are bound to oxygen atoms of the KNbO3 barrier, as shown in Fig. 2(d) and Fig. S1(a) (see supplementary materials). This peak has no influence for the present study since the conductance is calculated at zero bias voltage. However, when very small bias voltage is applied to Fe/KNbO3/Fe junctions, this sharp peak will create conducting hot-spots in the spin-down channel. This effect will change significantly the characteristics of the interface of junctions. Therefore, further researches for this system may focus on the conductance under finite bias to investigate the additional physical phenomena. 4. Conclusions We have studied the electronic structure and spin-dependent tunneling in Fe/KNbO3/Fe MFTJs with the NbO2 termination at
262
H. Zhang et al. / Computational Materials Science 112 (2016) 257–262
the left interface and the KO termination at the right interface using first principles calculations. We obtain two stable ferroelectric states with opposite polarization direction in MFTJs containing six unit cells of KNbO3. At the right interface, the relative displacement of K with respect to O has the same sign for the P? and P state due to the short interface Fe–O bond length and long Fe–K bond length. The analysis of the electronic structure for the interface atoms indicates that there are sizeable induced magnetic moments on interfacial Nb and O atoms results from the strong Fe–Nb and Fe–O bonds. The magnitude of induced magnetic moments is related to the polarization direction of the KNbO3 barrier. Hence there are magnetoelectric effects in such junctions. According to the CBS of the bulk KNbO3, a D1 singlet and a D5 doublet have the smallest decay rates within the band gap. The TMR in these junctions is small for the two polarization states. On the other hand, there exists high TER for both the antiparallel and parallel magnetization configuration. Thus the Fe/KNbO3/Fe MFTJs are suitable systems for applications that display giant TER at room temperature. We hope that our results will provide assistance for the future experimental works. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant Nos. 51162019 and 51462019). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.commatsci.2015. 11.003. References [1] I. Zˇutic´, J. Fabian, S.D. Sarma, Rev. Mod. Phys. 76 (2) (2004) 323.
[2] P.M. Tedrow, R. Meservey, Phys. Rev. Lett. 26 (4) (1971) 192. [3] J.S. Moodera et al., Phys. Rev. Lett. 74 (16) (1995) 3273. [4] E.Y. Tsymbal, O.N. Mryasov, P.R. LeClair, J. Phys.: Condens. Matter 15 (4) (2003) R109–R142. [5] W.H. Butler, X.-G. Zhang, T.C. Schulthess, Phys. Rev. B 63 (5) (2001) 054416. [6] J. Mathon, A. Umerski, Phys. Rev. B 63 (22) (2001) 220403. [7] S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki, K. Ando, Nat. Mater. 3 (12) (2004) 868–871. [8] Y.M. Lee, J. Hayakawa, S. Ikeda, F. Matsukura, H. Ohno, Appl. Phys. Lett. 90 (21) (2007) 212507. [9] J.P. Velev et al., Phys. Rev. Lett. 95 (21) (2005) 216601. [10] J.M. de Teresa et al., Science 286 (5439) (1999) 507–509. [11] Ph Mavropoulos, N. Papanikolaou, P.H. Dederichs, Phys. Rev. Lett. 85 (5) (2000) 1088. [12] T. Tybell, C.H. Ahn, J.-M. Triscone, Appl. Phys. Lett. 75 (6) (1999) 856–858. [13] J. Junquera, Ph. Ghosez, Nature 422 (6931) (2003) 506–509. [14] D.D. Fong et al., Science 304 (5677) (2004) 1650–1653. [15] E.Y. Tsymbal, H. Kohlstedt, Science 313 (5784) (2006) 181–183. [16] J.P. Velev et al., Phys. Rev. Lett. 98 (13) (2007) 137201. [17] A. Gruverman et al., Nano Lett. 9 (10) (2009) 3539–3543. [18] A. Crassous et al., Appl. Phys. Lett. 96 (4) (2010) 042901. [19] J.P. Velev et al., Nano Lett. 9 (1) (2009) 427–432. [20] V. Garcia et al., Science 327 (5969) (2010) 1106–1110. [21] J.M. López-Encarnación et al., Nano Lett. 11 (2) (2011) 599–603. [22] J.P. Velev et al., Phys. Rev. B 85 (12) (2012) 125103. [23] M. Gajek et al., Nat. Mater. 6 (4) (2007) 296–302. [24] D. Pantel, S. Goetze, D. Hesse, M. Alexe, Nat. Mater. 11 (4) (2012) 289–293. [25] J.-Q. Dai, H. Zhang, Y.-M. Song, J. Appl. Phys. 114 (16) (2013) 163703. [26] J.-Q. Dai, H. Zhang, Y.-M. Song, J. Magn. Magn. Mater. 351 (2014) 29–36. [27] Y.W. Yin et al., J. Appl. Phys. 109 (7) (2011) 07D915. [28] Y.K. Liu et al., Appl. Phys. Lett. 104 (4) (2014) 043507. [29] A.W. Hewat, J. Phys. C: Solid State Phys. 6 (1973) 2559. [30] C. Kittel, Introduction to Solid State Physics, seventh ed., Wiley, New York, 1996. [31] G. Kresse, J. Hafner, Phys. Rev. B 47 (1) (1993) 558. [32] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (16) (1996) 11169. [33] M. Gajdoš, K. Hummer, G. Kresse, Phys. Rev. B 73 (4) (2006) 045112. [34] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (18) (1996) 3865. [35] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 78 (7) (1997) 1396. [36] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (12) (1976) 5188. [37] P. Giannozzi et al., J. Phys.: Condens. Matter 21 (39) (2009) 395502. [38] Y. Imry, R. Landauer, Rev. Mod. Phys. 71 (2) (1999) S306. [39] C.-G. Duan, S.S. Jaswal, E.Y. Tsymbal, Phys. Rev. Lett. 97 (4) (2006) 047201. [40] S. Valencia et al., Nat. Mater. 10 (10) (2011) 753–758. [41] N.F. Hinsche et al., Phys. Rev. B 82 (21) (2010) 214110.