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[Keisuke Masuda](https://orcid.org/0000-0002-6884-6390), Hiroyoshi Itoh, [Yoshio Miura](https://orcid.org/0000-0002-5605-5452)

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[Interface-driven giant tunnel magnetoresistance in (111)-oriented junctions](https://mdr.nims.go.jp/datasets/20678036-52d5-42d4-ba34-efdab0f677ee)

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Interface-driven giant tunnel magnetoresistance in (111)-oriented junctionsPHYSICAL REVIEW B 101, 144404 (2020)Interface-driven giant tunnel magnetoresistance in (111)-oriented junctionsKeisuke Masuda ,1 Hiroyoshi Itoh ,2,3 and Yoshio Miura 1,3,41Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science (NIMS), Tsukuba 305-0047, Japan2Department of Pure and Applied Physics, Kansai University, Suita 564-8680, Japan3Center for Spintronics Research Network, Osaka University, Toyonaka 560-8531, Japan4Center for Materials Research by Information Integration, National Institute for Materials Science (NIMS), Tsukuba 305-0047, Japan(Received 2 December 2019; revised manuscript received 27 February 2020; accepted 28 February 2020;published 6 April 2020)We theoretically study the tunnel magnetoresistance (TMR) effect in (111)-oriented junctionsCo/MgO/Co(111) and Ni/MgO/Ni(111). The Co-based junction is shown to have a TMR ratio over 2000%,which is one order higher than that of the Ni-based one. The high TMR ratio is attributed to the interfacialresonance effect: The interfacial d-p antibonding states are formed close to the Fermi level in the majority-spinchannel and these states in both interfaces resonate with each other. This differs essentially from the conventionalcoherent tunneling mechanism of high TMR ratios in Fe(Co)/MgO/Fe(Co)(001).DOI: 10.1103/PhysRevB.101.144404I. INTRODUCTIONSince the observation of the giant tunnel magnetoresis-tance (TMR) effect in Fe(Co)/MgO/Fe(Co)(001) magnetictunnel junctions (MTJs) [1,2], the TMR effect has long beenexplained by the coherent tunneling mechanism [3,4]: Bulkwave functions of the ferromagnetic electrode are selectivelyfiltered by the MgO barrier and only the �1 wave functionwith half metallicity at the Fermi level passes through thebarrier, leading to the high TMR ratio [Fig. 1(a)]. However,there is a significant discrepancy in the TMR ratio between thetheory and experiments; the highest TMR ratio observed sofar is around 500% at low temperature [5], but is about half ofthe theoretically predicted value over 1000% [3,4]. A possiblekey to understand this gap is interfacial effects. Several studies[6,7] have indicated the importance of interfacial states forexplaining temperature dependencies of TMR ratios [8]. Inthe (001)-oriented MTJs, the interfacial states are formed inthe minority-spin state [3,9] and tend to decrease the TMRratio [10].These motivate us to speculate that interfacialstates provide significant contribution to TMR effectsin real experiments and decrease the TMR ratios inFe(Co)/MgO/Fe(Co)(001) MTJs. In contrast, we canutilize such interfacial states for enhancing the TMR effectsignificantly; this study proposes a quite high TMR ratiodriven by the interfacial resonance effect in an unconventional(111)-oriented MTJ.In the present work, we theoretically examine the TMReffect in two basic (111)-oriented MTJs, Co/MgO/Co(111)[Fig. 1(b)] and Ni/MgO/Ni(111), where (111) directions ofthe MgO barrier and ferromagnetic electrodes (fcc Co or fccNi) are parallel to the stacking direction of the MTJ. It isnatural to consider such (111)-oriented MTJs for fcc ferro-magnetic electrodes because the close-packed (111) plane hasthe lowest surface energy in the fcc lattice [11]. However,TMR effects in these MTJs have not been understood well,since most previous studies have focused on (001)-orientedMTJs with bcc ferromagnetic electrodes. We calculate con-ductances and TMR ratios of the (111)-oriented MTJs bymeans of the first-principles approach combining the density-functional theory (DFT) and the Landauer formula. It is shownthat the obtained TMR ratio of the Co-based MTJ is quitehigh (∼2100%) while that of the Ni-based one is relativelylow (∼250%). From the in-plane wave-vector dependenciesof the conductances, we find that the TMR effect in the(111)-oriented MTJs cannot be understood from the bulk bandstructures of the barrier and electrodes, which is essentiallydifferent from the case of the (001)-oriented MTJs. Detailedanalyses of the local electronic structure and the transmittanceclarify that the resonance of the interfacial d-p antibondingstates in the majority-spin channel is the origin of the highTMR ratio in the Co-based (111)-oriented MTJ.II. CALCULATION METHODWe prepared supercells of Co/MgO/Co(111) andNi/MgO/Ni(111) as shown in Fig. 1(b). The a- and b-axislengths were fixed to a = afcc/√2 and b = √3 afcc/√2,where we used afcc = 3.52 Å for both the supercells. Inthe Co-based (Ni-based) supercell, we chose the Co-O(Ni-O) interface, which is energetically favored comparedto the Co-Mg (Ni-Mg) one. The atomic positions alongthe c direction in the supercells were relaxed using thefirst-principles DFT calculation implemented in the Viennaab initio simulation program (VASP) [12]. Here, we adoptedthe spin-polarized generalized gradient approximation (GGA)[13] for the exchange-correlation energy and used theprojector augmented wave pseudopotential [14,15] to treatthe effect of core electrons properly. A cutoff energy of500 eV was employed and the Brillouin-zone integration wasperformed with the 23 × 13 × 1 Monkhorst-Pack k-pointgrid. The convergence criteria for energy and force were setto 10−5 eV and 10−3 eV/Å, respectively. More details of ourstructure optimization are given in our previous work [16].2469-9950/2020/101(14)/144404(5) 144404-1 ©2020 American Physical Societyhttps://orcid.org/0000-0002-6884-6390https://orcid.org/0000-0001-6577-8313https://orcid.org/0000-0002-5605-5452http://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevB.101.144404&domain=pdf&date_stamp=2020-04-06https://doi.org/10.1103/PhysRevB.101.144404MASUDA, ITOH, AND MIURA PHYSICAL REVIEW B 101, 144404 (2020)zxyCo O MgxzyFe or FeCoO Mg(a) Fe(Co)/MgO/Fe(Co)(001)(b) Co/MgO/Co(111)FIG. 1. Supercells of (a) Fe(Co)/MgO/Fe(Co)(001) and(b) Co/MgO/Co(111). Schematics for the TMR effects in theseMTJs are also shown.Using the optimized supercell, we constructed quantumopen systems by attaching the left and right semi-infiniteelectrodes of Co (Ni) to the Co-based (Ni-based) supercell.In each quantum open system, we calculated conductancesfor both parallel and antiparallel configurations of magne-tization in the electrodes using the PWCOND code [17] inthe QUANTUM ESPRESSO package [18]. First, we obtainedthe self-consistent potential of the quantum open system,where the GGA and the ultrasoft pseudopotentials were usedfor the DFT calculation. The cutoff energies for the wavefunctions and the charge density were fixed to 45 and 450Ry, respectively. The 23 × 13 × 1 k points were used for theBrillouin-zone integration and the convergence criterion wasset to 10−6 Ry. Since our systems are repeated periodically inthe xy plane, the scattering states can be classified by an in-plane wave vector k‖ = (kx, ky). For each k‖ and spin index,we solved the scattering equation derived under the conditionthat the wave function and its derivative of the supercell areconnected to those of the electrodes [17,19]. These calcula-tions and the Landauer formula give the wave-vector-resolvedconductances GP,↑(k‖), GP,↓(k‖), GAP,↑(k‖), and GAP,↓(k‖),which are the majority- and minority-spin conductances inthe parallel and antiparallel configurations of magnetizations,respectively. The averaged conductances are obtained as, e.g.,GP,↑ = ∑k‖ GP,↑(k‖)/N , where N is the sampling number ofk‖ points. In the present study, N was set to 2500 ensuringgood convergence for the conductances. Using the averagedconductances, we calculated TMR ratio (%) = 100 × (GP −GAP)/GAP, where GP(AP) = GP(AP),↑ + GP(AP),↓.III. RESULTS AND DISCUSSIONTable I shows conductances and TMR ratios obtainedin our calculations. In the Co-based MTJ, the parallelconductance GP is much larger than the antiparallel one GAP,leading to a quite high TMR ratio of more than 2000%.On the other hand, the Ni-based MTJ has a smaller TMRTABLE I. Calculated conductances and TMR ratios. The unitsare in e2/h and %, respectively.Co/MgO/Co(111) Ni/MgO/Ni(111)GP,↑ 2.48 × 10−3 5.71 × 10−5GP,↓ 1.42 × 10−3 1.23 × 10−3GAP,↑ 8.73 × 10−5 1.84 × 10−4GAP,↓ 8.75 × 10−5 1.84 × 10−4GP 3.90 × 10−3 1.29 × 10−3GAP 1.75 × 10−4 3.68 × 10−4TMR ratio 2130 250ratio of 250% since the difference between GP and GAP issmaller compared to the Co-based case. One may think thatthe mechanism of such TMR effects is similar to that inthe (001)-oriented MTJs. Previous theoretical studies [3,4]have shown that the TMR effect in Fe/MgO/Fe(001) isdominated by the bulk band structures of Fe and MgOalong the � line corresponding to the (001) direction;in their results, GP,↑(k‖) mainly contributing to the highTMR ratio has a sharp peak at k‖ = (0, 0) = �. If thesimilar mechanism holds for the (111)-oriented MTJs, theTMR effect should be explained by the band structuresalong the � line corresponding to the (111) direction. Inthis case, GP,↑(k‖) or GP,↓(k‖) or both of them shouldhave a large value at k‖ = �, since the � line is equiv-alent to the kz line at k‖ = � in the present supercells[Fig. 1(b)].To see whether or not this scenario is valid, we analyzedthe in-plane wave vector k‖ = (kx, ky) dependencies of theconductances as shown in Fig. 2. Figure 2(a) shows themajority-spin conductance GP,↑(k‖) in the Co-based MTJplaying the key role for the obtained high TMR ratio. Wesee that the conductance at k‖ = � is much smaller than thataround k‖ = �, which is clearly different from the featuresexpected from the above-mentioned mechanism. Figures 2(b)and 2(c) show the minority-spin and antiparallel conductances[GP,↓(k‖) and GAP,↑(k‖)] in the Co-based MTJ [20], whichalso do not have a significant value at k‖ = � and theirvalues spread more widely in the k‖ Brillouin zone thanGP,↑(k‖). In Figs. 2(d)–2(f), we show the k‖ dependenciesof the conductances in the Ni-based MTJ. Although detailedfeatures are different from those in the Co-based MTJ, theconductances also do not have a significant value at k‖ = �.All these results indicate that the TMR effect in the (111)-oriented MTJs cannot be explained by the bulk band structuresof the barrier and electrodes along the � line, in sharp contrastto the previous results on the (001)-oriented MTJs [3,4]. Wealso analyzed bulk band structures of fcc Co, Ni, and MgOalong the � line, which revealed that, although the complexband of MgO(111) consists of the �1 state, both Co andNi do not have a half metallicity in the �1 state. This alsosuggests the inapplicability of the explanation based on bulkband structures.To obtain further insight into the role of the MgObarrier, we additionally analyzed the TMR effect inCo/vacuum/Co(111), where the distance between the left andright interfaces and all the positions of Co atoms were setto be the same as those of Co/MgO/Co(111). We obtained144404-2INTERFACE-DRIVEN GIANT TUNNEL MAGNETORESISTANCE … PHYSICAL REVIEW B 101, 144404 (2020)-1.0-0.5 00.51.0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5×10-1-1.0-0.5 0 0.5 1.0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4×10-1-1.0 -0.5  0  0.5  1.0-1.0-0.5 0 0.5 1.0 0 0.2 0.4 0.6 0.8 1.0 1.2×10-3-1.0-0.5 0 0.5 1.0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0×10-4-1.0-0.5 0 0.5 1.0 0 0.5 1.0 1.5 2.0 2.5 3.0×10-2-1.0 -0.5  0  0.5  1.0-1.0-0.5 0 0.5 1.0 0 0.5 1.0 1.5 2.0 2.5×10-3Co/MgO/Co(111) Ni/MgO/Ni(111)(a)(b)(c)(d)(e)(f)FIG. 2. The k‖ dependencies of conductances inCo/MgO/Co(111) [(a)–(c)] and Ni/MgO/Ni(111) [(d)–(f)].(a),(d) Majority-spin conductances GP,↑(k‖) and (b),(e)minority-spin conductances GP,↓(k‖) in the parallel magnetizationconfigurations. (c),(f) Majority-spin conductances GAP,↑(k‖) in theantiparallel magnetization configurations.a TMR ratio of 320%, which is one order lower than thatof Co/MgO/Co(111). This clearly indicates the necessity ofMgO to achieve a high TMR ratio. From the comparisonof the k‖-resolved conductances between the vacuum andMgO cases, we found that MgO particularly damps the wavefunctions that are distributed away from k‖ = �.Interfacial effects are the key to understand the presentTMR effect. As shown in Figs. 2(a)–2(f), the conductanceshave significant values in a set of k‖ points surroundingk‖ = �. This reminds us of the existence of the inter-facial resonance effect. Examples showing this effect areFe/MgO/Fe(001) [3,21–23], Co/MgO/Co(001) [24], andFeCo/MgO/FeCo(001) [24], which have interfacial statesclose to the Fermi level in the minority-spin channel. Suchstates in the left and right interfaces resonate with each otherand provide non-negligible values of GP,↓(k‖) in the k‖ pointssurrounding �. Furthermore, additional transport between theinterfacial minority-spin states and the bulk majority-spin �1state enhance GAP,↑(k‖) and GAP,↓(k‖). Thus, the interfacialstates itself tend to decrease the TMR ratio in the (001)-oriented MTJ. However, since GP,↑(k‖) has a quite large valueat k‖ = � based on the coherent tunneling mechanism [3,4],the interfacial effect provides a small contribution to the TMRratio. Note that these are the previous theoretical results; theinterfacial effect is sensitive to the interfacial conditions inreal experiments [21].To confirm the existence of interfacial states in the presentMTJs, we show in Figs. 3(a) and 3(b) the projected LDOSs-0.4-0.2 0 0.2 0.4-0.4-0.2 0 0.2 0.4-0.4-0.2 0 0.2 0.4-0.4-0.2 0 0.2 0.4-0.4 -0.2  0  0.2  0.4(a)(b)(c)(d)E-E  [eV]LDOS [states/eV/orbital]LDOS [states/eV/orbital]LDOS [states/eV/orbital]LDOS [states/eV/orbital]Co in Co/MgO/Co(111)O in Co/MgO/Co(111)Ni in Ni/MgO/Ni(111)O in Ni/MgO/Ni(111)FIG. 3. (a),(b) Projected LDOSs at interfacial Co and O atoms inCo/MgO/Co(111). (c),(d) The same as (a) and (b) but at interfacialNi and O atoms in Ni/MgO/Ni(111). In each panel, positive andnegative values indicate the majority- and minority-spin projectedLDOSs.of interfacial Co and O atoms in the Co/MgO/Co(111)MTJ. In Fig. 3(b), we see that the interfacial O atoms havepeaks of the majority-spin LDOSs in the px and py orbitalsclose to the Fermi level (EF), which originates from theantibonding between Co dzx (dyz) and O px (py) states at theinterface. As mentioned below, such interfacial antibondingstates mainly contribute to the high TMR ratio through theinterfacial resonance effect. It should be emphasized that thesemajority-spin interfacial states enhance GP,↑(k‖) but hardlyenhance GAP,↑(k‖) and GAP,↓(k‖), which is because the bulkminority-spin state is not significant in the (111)-orientedMTJ. This is clearly different from the (001)-oriented caseand the reason why we obtained the large TMR ratio in thisMTJ. In the case of the Ni/MgO/Ni(111) MTJ [Figs. 3(c)and 3(d)], on the other hand, the interfacial antibonding statebetween Ni dzx (dyz) and O px (py) states is formed at a lowerenergy compared to the Co-based case, which is owing to thedifference in the valence electron number between Co and Ni.Thus, the interfacial O atoms have small majority-spin LDOSsin the px and py orbitals at E = EF.Conclusive information on the mechanism for the presentTMR effect is given by the k‖-resolved LDOSs ofinterfacial atoms in Co/MgO/Co(111) [Figs. 4(a)–4(h)] andNi/MgO/Ni(111) [Figs. 4(i)–4(p)]. Here, we only showedthe LDOSs at E = EF in the Co (Ni) dzx, Co (Ni) dyz, Opx, and O py orbitals providing essential contributions to theconductances. It is seen that the LDOS in the Co (Ni) dzx144404-3MASUDA, ITOH, AND MIURA PHYSICAL REVIEW B 101, 144404 (2020)Co d Co d O p O pMajority-spin (↑)Minority-spin (↓)Ni d Ni d O p O pMajority-spin (↑)Minority-spin (↓)Co/MgO/Co(111)Ni/MgO/Ni(111)FIG. 4. The k‖-resolved LDOSs at E = EF of interfacial atomsin (a)–(h) Co/MgO/Co(111) and (i)–(p) Ni/MgO/Ni(111). (a)–(d) Contributions from Co dzx , Co dyz, O px , and O py orbitals inthe majority-spin state, respectively. (e)–(h) The same as (a)–(d) butin the minority-spin state. (i)–(l) Contributions from Ni dzx , Ni dyz, Opx , and O py orbitals in the majority-spin state, respectively. (m)–(p)The same as (i)–(l) but in the minority-spin state. In each panel,k‖-resolved LDOSs are normalized by its maximum value.orbital has an almost the same k‖ dependence as that in theO px orbital in each spin state [e.g., Figs. 4(a) and 4(c)],since these orbitals make an antibonding state around E = EFas mentioned above. The same relation holds between theLDOSs of Co (Ni) dyz and O py orbitals [e.g., Figs. 4(b) and4(d)]. Of particular importance is that the k‖ dependenciesof the conductances in Fig. 2 can be understood by thoseof the LDOSs in Fig. 4. In fact, GP,↑(k‖) in the Co-basedMTJ [Fig. 2(a)] can be almost reproduced by mixing the k‖dependencies of majority-spin LDOSs in the O px (Co dzx)and O py (Co dyz) states [Figs. 4(a)–4(d)]. The minority-spin conductance GP,↓(k‖) [Fig. 2(b)] also reflects minority-spin LDOSs in the O px (Co dzx) and O py (Co dyz) states[Figs. 4(e)–4(h)]. In a similar way, we can explain the k‖dependencies of the conductances [Figs. 2(d)–2(f)] by those ofthe LDOSs [Figs. 4(i)–4(p)] in the case of Ni/MgO/Ni(111);e.g., GP,↓(k‖) [Fig. 2(e)] has a similar k‖ dependence to theminority-spin LDOSs in the Ni dzx and O px states [Figs. 4(m)and 4(o)]. All these results clearly suggest that the interfacialantibonding states at E ≈ EF provide the TMR effect in the(111)-oriented MTJs through the interfacial resonance effect.Further evidence for the interfacial resonance effect isobtained from the energy dependence of the transmittance.Figure 5 shows the majority-spin transmittance TP,↑(E ) of theCo/MgO/Co(111) MTJ at (kxa/π, kyb/π ) = (0.04, 0.32),where the conductance GP,↑(k‖) has the maximum value[Fig. 2(a)]. Note that the transmittance is converted to theconductance simply by multiplying e2/h [GP,↑(k‖) =(e2/h) × TP,↑(k‖)] and we showed in Fig. 2 the conductances -4 -3 -2 -1 0-0.4 -0.3 -0.2 -0.1  0  0.1  0.2  0.3  0.4E-EF [eV]FIG. 5. The energy dependence of the majority-spin transmit-tance at (kxa/π, kyb/π ) = (0.04, 0.32) in the Co/MgO/Co(111)MTJ with the parallel configuration of magnetizations.at E = EF. In Fig. 5, we can see sharp peaks close to EF,which are similar to those previously obtained in the minority-spin transmittance in the Fe/MgO/Fe(001) MTJ exhibitingthe interfacial resonance effect [21–23]. Since the resonanceeffect usually occurs in a narrow energy range, such a charac-teristic energy dependence of the transmittance is concludedto originate from the interfacial resonance effect. On the otherhand, when a finite bias voltage (∼0.05 V) is applied to theMTJ, the interfacial resonance could be removed owing to itssmall energy width [21,25], leading to the reduction of theTMR ratio. However, we have many other interfacial statesaround EF as shown in Figs. 3(a) and 3(b). Thus, if we increasethe bias voltage further, these interfacial states may form anew resonance and enhance the TMR ratio [21].Some previous studies have provided partial informa-tion on (111)-oriented MTJs. Hauch et al. [26] fabricatedan Fe(110)/MgO(111)/Fe(110) MTJ with the (111)-orientedMgO barrier and observed a low TMR ratio of 54% atlow temperature. They attributed the low TMR ratio tothe imperfect spin filtering in the �1 state. Belashchenkoet al. [27] theoretically analyzed Co/Al2O3/Co(111) MTJs.Although they revealed the sensitivity of the current spinpolarization to the interfacial atomic configuration, the ob-tained TMR ratios were quite low (∼60%). In the presentwork, by focusing on simpler (111)-oriented MTJs and car-rying out detailed analyses on local electronic structures, wefound a quite high TMR ratio and clarified its underlyingmechanism.IV. SUMMARYWe theoretically investigated the TMR effect in un-conventional (111)-oriented MTJs, Co/MgO/Co(111) andNi/MgO/Ni(111). By estimating their transport propertiesusing the first-principles-based approach, we found that theCo-based MTJ has a TMR ratio over 2000%, which is muchhigher than that of the Ni-based one of 250%. The anal-yses of the LDOSs and the transmittance showed that theobtained high TMR ratio comes from the resonance of theinterfacial d-p antibonding states in the majority-spin chan-nel. This mechanism is essentially different from that in theFe(Co)/MgO/Fe(Co)(001) MTJ and suggests a novel way toachieve a giant TMR ratio.144404-4INTERFACE-DRIVEN GIANT TUNNEL MAGNETORESISTANCE … PHYSICAL REVIEW B 101, 144404 (2020)ACKNOWLEDGMENTSThe authors are grateful to Y. Sonobe, S. Mitani,H. Sukegawa, Y. Kozuka, and K. Nawa for useful dis-cussions and helpful comments. This work was partlysupported by Grants-in-Aid for Scientific Research (S)(Grant No. 16H06332) from the Ministry of Education,Culture, Sports, Science and Technology, Japan and byNIMS MI2I. The crystal structures were visualized usingVESTA [28].[1] S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki, and K. Ando,Nat. Mater. 3, 868 (2004).[2] S. S. P. Parkin, C. Kaiser, A. Panchula, P. M. Rice, B. Hughes,M. Samant, and S.-H. Yang, Nat. 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