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[Keisuke Masuda](https://orcid.org/0000-0002-6884-6390), [Shinya Kasai](https://orcid.org/0000-0001-7149-4800), [Yoshio Miura](https://orcid.org/0000-0002-5605-5452), [Kazuhiro Hono](https://orcid.org/0000-0001-7367-0193)

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[Giant interfacial perpendicular magnetic anisotropy in Fe/CuIn1−xGaxSe2 beyond Fe/MgO](https://mdr.nims.go.jp/datasets/6b31ae99-9a82-4e74-8215-79f0f04953ac)

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PHYSICAL REVIEW B 96, 174401 (2017)Giant interfacial perpendicular magnetic anisotropy in Fe/CuIn1−xGaxSe2 beyond Fe/MgOKeisuke Masuda,1 Shinya Kasai,1 Yoshio Miura,1,2,3,4 and Kazuhiro Hono11Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science (NIMS),1-2-1 Sengen, Tsukuba 305-0047, Japan2Kyoto Institute of Technology, Electrical Engineering and Electronics, Kyoto 606-8585, Japan3Center for Materials Research by Information Integration, National Institute for Materials Science (NIMS),1-2-1 Sengen, Tsukuba 305-0047, Japan4Center for Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka University,Machikaneyama 1-3, Toyonaka, Osaka 560-8531, Japan(Received 10 July 2017; revised manuscript received 28 September 2017; published 1 November 2017)We study interfacial magnetocrystalline anisotropies in various Fe/semiconductor heterostructures by meansof first-principles calculations. We find that many of those systems show perpendicular magnetic anisotropy(PMA) with a positive value of the interfacial anisotropy constant Ki. In particular, the Fe/CuInSe2 interfacehas a large Ki of ∼ 2.3 mJ/m2, which is about 1.6 times larger than that of Fe/MgO known as a typical systemwith relatively large PMA. We also find that the values of Ki in almost all the systems studied in this workfollow the well-known Bruno’s relation, which indicates that minority-spin states around the Fermi level providedominant contributions to the interfacial magnetocrystalline anisotropies. Detailed analyses of the local densityof states and wave-vector-resolved anisotropy energy clarify that the large Ki in Fe/CuInSe2 is attributed to thepreferable 3d-orbital configurations around the Fermi level in the minority-spin states of the interfacial Fe atoms.Moreover, we have shown that the locations of interfacial Se atoms are the key for such orbital configurations ofthe interfacial Fe atoms.DOI: 10.1103/PhysRevB.96.174401I. INTRODUCTIONMagnetic tunneling junctions (MTJs), in which an insulatorbarrier is sandwiched between two ferromagnetic electrodes,are the most important practical spintronic devices. Theyare currently used in nonvolatile magnetic random accessmemories (MRAM), read heads of hard disk drives (HDD),and other magnetic sensors. For all these applications, highmagnetoresistance (MR) ratios are required for high-voltageoutput as magnetic sensors. Second, low resistance-area prod-ucts (RA) are essential for achieving high recording densitiesin HDD and MRAM. Moreover, we have an additionalrequirement for spin transfer torque MRAM (STT-MRAM)[1] and voltage-controlled MRAM [2] applications that MTJsneed to have perpendicular magnetic anisotropy (PMA) atinterfaces between the electrode and the barrier layers. Inparticular, for STT-MRAM, PMA is indispensable to reducethe critical current for STT switching with sufficient thermalstability [1]. Such MTJs with interfacial PMA [3–6] arereferred to as p-MTJs.In the early stages of research on interfacial magnetocrys-talline anisotropy, magnetization measurements showed thatthe interfaces of Co/Pt and Co/Pd heterostructures exhibitPMA with an interfacial anisotropy constant Ki smaller than1 mJ/m2 [7–9]. It has also been clarified from x-ray magneticcircular dichroism (XMCD) spectroscopy that the PMA isattributed to the enhanced orbital moment of Co, which isinduced by the hybridization between Co 3d and Pt 5d (Pd 4d)states [10,11]. Thus, it has been believed that heavy elementswith 5d or 4d electrons are required to obtain interfacial PMA.In the past two decades, PMA has also been observed inheterostructures with oxide barriers [12–18]. Several studieshave found perpendicular magnetic anisotropy at the interfaceof Co(Fe)/MOx (M = Al, Mg, Cr, Ta, Ru, etc.) underappropriate oxidation conditions [12–15]. Moreover, largePMA with Ki > 1 mJ/m2 has been achieved in Fe/MgO[16,17] and Fe-rich CoFeB/MgO [18]. These results suggestthat the coupling between O and Co(Fe) atoms at interfacesof heterostructures plays a crucial role in PMA, which wasactually confirmed by x-ray photoelectron spectroscopy (XPS)measurements [14].Recently, Kasai et al. [19] succeeded in fabricating novelMTJs where semiconductor CuIn0.8Ga0.2Se2 (CIGS) is sand-wiched between ferromagnetic electrodes. They found that theCIGS-based MTJs have both high MR ratios (100% at 8 K and40% at room temperature) and low RA values (0.3–3 �μm2)[19]. Such high MR output was explained theoretically as aresult of the spin-dependent coherent tunneling of �1 wavefunctions [20]. In a more recent study, Mukaiyama et al.demonstrated large voltage outputs under bias voltages, whichindicated that the CIGS-based MTJ is particularly attractive forread-head applications [21]. To consider potential applicationsto STT-MRAM cells, the possibility of obtaining large PMAon CIGS-based MTJs must be investigated; however, noexperimental and theoretical studies have been done on thisissue.In the present work, we investigate interfacial mag-netocrystalline anisotropies of various Fe/semiconductorheterostructures including Fe/CuIn1−xGaxSe2 by meansof first-principles calculations. We found that all of theFe/CuIn1−xGaxSe2 heterostructures show PMA. In particular,the Fe/CuInSe2 system exhibits a quite large Ki ≈ 2.3 mJ/m2,which is approximately 1.6 times as large as that of theFe/MgO system that is currently used for p-MTJs. We alsofound that Bruno’s relation [22], which states that magne-tocrystalline anisotropy is proportional to the anisotropy in theorbital magnetization of a ferromagnet, holds for almost allthe systems considered in this study. This suggests that mag-netocrystalline anisotropies can be described by second-order2469-9950/2017/96(17)/174401(7) 174401-1 ©2017 American Physical Societyhttps://doi.org/10.1103/PhysRevB.96.174401MASUDA, KASAI, MIURA, AND HONO PHYSICAL REVIEW B 96, 174401 (2017)TABLE I. List of in-plane lattice constants a of the heterostruc-tures, k points used in the calculations of Ki, and the obtained valuesof Ki.X in Fe/X(001) a (Å) k points Ki (mJ/m2)ZnSe 4.013 15 × 15 × 1 1.701ZnS 3.823 15 × 15 × 1 1.151GaAs 3.998 15 × 15 × 1 0.210CuInSe2 5.782 10 × 10 × 1 2.305CuIn0.75Ga0.25Se2 5.726 10 × 10 × 1 2.069CuIn0.5Ga0.5Se2 5.698 10 × 10 × 1 1.712CuIn0.25Ga0.75Se2 5.670 10 × 10 × 1 1.575CuGaSe2 5.614 10 × 10 × 1 1.266CuInS2 5.523 10 × 10 × 1 − 0.373CuGaS2 5.356 10 × 10 × 1 0.776AgInSe2 6.109 10 × 10 × 1 0.721AgGaSe2 5.985 10 × 10 × 1 1.257AgInS2 5.872 10 × 10 × 1 0.841AgGaS2 5.754 10 × 10 × 1 0.027MgO 2.982 20 × 20 × 1 1.396perturbation theory with respect to spin-orbit interactions, inwhich electron scatterings only in minority-spin states areconsidered. By analyzing the local density of states (LDOS)and wave-vector-resolved interfacial anisotropy, we show thatthe large Ki in Fe/CuInSe2 can be understood naturally fromthe orbital configurations in the minority-spin states near theFermi level.II. CALCULATION METHODWe carried out first-principles calculations on the basisof density-functional theory (DFT) including spin-orbit in-teractions, which is implemented in the Vienna ab initiosimulation program (VASP) [23]. For the exchange-correlationenergy, we adopted the spin-polarized generalized gradientapproximation (GGA) proposed by Perdew, Becke, and Ernz-erhof [24]. The projector augmented wave (PAW) potential[25,26] was also used to take into account the effect ofcore electrons properly. In this work, we considered 14 typesof Fe/semiconductor(001) heterostructures, the list of whichis given in Table I. We also considered an Fe/MgO(001)heterostructure to obtain a benchmark of Ki under thepresent calculation conditions. First, we prepared a supercellFe(7)/X(17) for each heterostructure with semiconductor X asshown in Figs. 1(a) and 1(b), where each number in parenthesesrepresents the number of layers. For the Fe/MgO(001)heterostructure, we used a supercell Fe(7)/MgO(13) [seeFig. 1(c)] because the thickness of MgO(13) is close to thoseof the semiconductors X(17). Since the barrier is sufficientlythicker than the Fe electrode in all the supercells, the in-plane lattice constant a of each supercell was fixed to theexperimental lattice constant of the barrier abarrier shown inTable I. Note here that we can set a = abarrier/√2 in the casesof ZnSe, ZnS, GaAs, and MgO barriers due to the high sym-metry of the structures. As experimental lattice constants ofternary chalcopyrite semiconductors, we adopted the values inRef. [27]. We also used the equation aCuIn1−xGaxSe2 = (1 − x) ×aCuInSe2 + x × aCuGaSe2 to set the experimental lattice constantFe O Mgxyz(c)Fe Cu InGaxyz(b) SeFe InSeCuxyz(a)FIG. 1. Supercells of (a) Fe(7)/CuInSe2(17), (b) Fe(7)/CuIn0.5Ga0.5Se2(17), and (c) Fe(7)/MgO(13).of CuIn1−xGaxSe2. Unfortunately, VASP cannot treat disorderbetween In and Ga atoms in CuIn1−xGaxSe2. Thus, we treatedthis as a percentage of the numbers of atoms in the supercell.For example, in the case of Fe/CuIn0.5Ga0.5Se2(001), weassigned the same number of atomic sites for In and Ga inthe supercell, where the atomic configurations of these atomswere chosen as shown in Fig. 1(b). In all the supercells, weoptimized each atomic position and the distance between thebarrier and the Fe electrode so that the total energy of thesupercell is minimized. Such optimizations reduced the energyof each supercell by 1–3 eV. In addition, we confirmed thatSe, S, or As layers are energetically favored as the interfaciallayers in all the Fe/semiconductor(001) heterostructures, asshown in Figs. 1(a) and 1(b) (see the Appendix for details).The interfacial anisotropy constant Ki was calculated usingthe force theorem as Ki = (E[100] − E[001])/2S, where E[100](E[001]) is the total energy of the supercell for the magnetizationalong the [100] ([001]) direction, S is the cross-sectional areaof the supercell, and the factor 2 in the denominator reflectsthe fact that two interfaces are included in the supercell. In thisdefinition, a positive (negative) Ki shows a tendency towardperpendicular (in-plane) magnetic anisotropy. The list of kpoints used in the calculations of Ki is provided in Table I.We used 10 × 10 × 1 k points for the heterostructures withternary or quaternary chalcopyrite semiconductors. We usedmore k points for other heterostructures due to their smallersupercell sizes.III. RESULTS AND DISCUSSIONWe show the obtained values of Ki in Table I. We findthat all systems except Fe/CuInS2(001) have positive valuesof Ki. In particular, Fe/CuInSe2(001) has the largest Kiof 2.305 mJ/m2, which is about 1.6 times as large as ourbenchmark value 1.396 mJ/m2 in Fe/MgO(001). Similarto our previous study [20], we additionally considered theeffect of the Coulomb interaction U in the Cu 3d statesof Fe/CuInSe2(001) on Ki. We obtained Ki = 2.363 and174401-2GIANT INTERFACIAL PERPENDICULAR MAGNETIC . . . PHYSICAL REVIEW B 96, 174401 (2017) 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 5.73  5.74  5.75  5.76  5.77  5.78Ki [mJ/m2 ]in-plane lattice constant a [Å]FIG. 2. In-plane lattice constant dependence of the interfacialanisotropy constant Ki for Fe/CuInSe2(001).2.403 mJ/m2 for U = 5 and 10 eV, respectively, whichindicates that the interaction U in the barriers does not havesignificant effects on Ki. We also studied the in-plane latticeconstant a dependence of Ki for Fe/CuInSe2(001), as shownin Fig. 2. The possible smallest value of a is considered to betwice the lattice constant of bulk bcc Fe, a = 2aFe = 5.732 Å.Thus, we changed a from 2aFe to aCuInSe2 . Note that this rangeincludes the value of a that is compatible with bcc Cr oftenused as buffer layers, a = 2aCr = 5.768 Å. We see that Kichanges smoothly with the value of a and is over 2 mJ/m2 forall values of a in the considered range.As mentioned in Sec. II, a positive Ki indicates a tendencytoward PMA. However, to be more precise, the followingeffective anisotropy should be used for a more accurateestimation of PMA: Keff teff = Ki − 2πM2s teff , where Ms isthe saturation magnetization and teff is the effective thicknessof a ferromagnetic electrode. The second term 2πM2s teff is thecontribution from magnetic shape anisotropy, which alwaysfavors in-plane magnetization. In our present situation, sincebcc Fe has a magnetization of 2.262μB per atom and teff =tFe/2 ≈ 0.425 nm, the shape anisotropy term is estimatedas 2πM2s teff ∼ 0.85 mJ/m2, which does not exceed Ki inmany systems considered in this study [28]. Therefore, we canconclude that many Fe/semiconductor(001) heterostructuresfavor PMA even if we use Keff teff for an estimation ofinterfacial magnetocrystalline anisotropy.In Fig. 3, we show the correlation between the interfacialanisotropy constant Ki and the anisotropy of the orbitalmagnetic moment in the interfacial Fe atom �Morb,i forheterostructures studied in this work. Here, the anisotropyof the orbital magnetic moment is defined by �Morb,i =M[001]orb,i − M[100]orb,i , where M[001]orb,i (M [100]orb,i ) is the orbital magneticmoment of the interfacial Fe atom for magnetization alongthe [001] ([100]) direction. We clearly see that the so-calledBruno’s relation Ki ∝ �Morb,i [22] holds for almost allsystems considered in this study. A previous theoretical workhas confirmed this relation in the Fe(Co)/MgO interface [31].Note, however, that values of Ki and �Morb,i in Fe-basedheterostructures do not always follow Bruno’s relation, asshown in a systematic theoretical study [32]. Laan [33]indicated that Bruno’s relation is satisfied when no spin-flipscattering occurs and majority-spin states are fully occupied. Insuch a case, the minority-spin scattering between unoccupiedFIG. 3. Correlation between the interfacial anisotropy constantKi and the anisotropy of the orbital magnetic moment at the interfacialFe layer �Morb,i (see the text for details).and occupied states around the Fermi level (EF) provides thedominant contribution to the magnetocrystalline anisotropy[34]. As shown later, Fe/CuInSe2(001) has a suitable LDOSand band structure to yield large PMA through such minority-spin scattering. Figure 4 shows the anisotropy of the orbitalmagnetic moment �Morb resolved into each Fe-layer contribu-tion for Fe/CuInSe2(001) and Fe/MgO(001). In both systems,the interfacial Fe layer has a much larger �Morb compared toother layers. Since the magnetic anisotropy is proportional to�Morb in these systems, as mentioned above, the results inFig. 4 clearly indicate that the anisotropy Ki is mainly due tothe interfacial contribution.Before discussing Fe/CuInSe2(001) with the largest Ki,let us first focus on Fe/MgO(001) for comparison. Previoustheoretical studies [35–38] have shown that this systemhas relatively large PMA with Ki = 1–2 mJ/m2, which is-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.0  1.0  2.0  3.0  4.0Fe/MgO(001)ΔMorb [μ B/atom]distance from the interface [Å]FIG. 4. Anisotropy of the orbital magnetic moment �Morbresolved into each Fe-layer contribution for Fe/CuInSe2(001) andFe/MgO(001). The horizontal axis shows the distance of each Felayer from the interface.174401-3MASUDA, KASAI, MIURA, AND HONO PHYSICAL REVIEW B 96, 174401 (2017)-1-0.5 0 0.5 1E-EF [eV]Projected LDOS [states/eV/orbital]-1.0-0.8-0.6-0.4-0.2 0 0.2-0.4 -0.2  0  0.2  0.4-0.1-0.05 0 0.05 0.1-4 -3 -2 -1  0  1  2  3  4Projected LDOS [states/eV/orbital](a)(b)FIG. 5. The projected LDOSs for (a) Fe 3d states and (b)O 2p states at the interface of the Fe/MgO(001) heterostructure.In each panel, positive and negative values indicate the majority- andminority-spin projected LDOSs, respectively. The inset of panel (a)shows an enlarged view near the Fermi level.consistent with our present results, Ki = 1.396 mJ/m2. Fig-ure 5(a) shows the calculated LDOS for 3d states of an Fe atomlocated at the interface between Fe and MgO layers, whosemain features around EF are consistent with previous resultson similar systems [39,40]. To understand the relationshipbetween the LDOS and the magnetic anisotropy constant Ki,we introduce the following expression for Ki derived fromthe second-order perturbation expansion with respect to thespin-orbit interaction [34]:Ki ≈ ξ 2∑o↓,u↓|〈o↓|Lz|u↓〉|2 − |〈o↓|Lx |u↓〉|2εu↓ − εo↓, (1)where ξ is the coupling constant of the LS spin-orbitinteraction, |o↓〉 (|u↓〉) is an occupied (unoccupied) statewith minority spin, εo↓ (εu↓) is the energy of the |o↓〉 (|u↓〉)state, and Lα (α = x,z) are the usual angular momentumoperators. In Eq. (1), we considered excitation processesbetween the minority-spin occupied and unoccupied states,and we neglected small contributions from spin-flip scatteringprocesses. This approach was shown to be sufficient tounderstand PMA in Fe/MgO(001) systems [35]. We can easilysee that the matrix element of Lz (Lx) provides a positive(negative) contribution to Ki. In addition, the excitation energy�ε ≡ εu↓ − εo↓ is also an important factor: the excitationprocess with smaller �ε contributes more significantly toKi. In the minority-spin LDOS of an interfacial Fe atomin Fig. 5(a), the dxy state has a peak a little below EF(E − EF ≈ −0.4 eV), and the dyz, dzx , and dx2−y2 states havepeaks just above EF (E − EF ≈ 0.2 eV). These states yieldfinite values of 〈dxy |Lz|dx2−y2〉 and 〈dxy |Lx |dyz(dzx)〉. As aresult, positive contributions from 〈Lz〉 exceed negative onesfrom 〈Lx〉, leading to PMA with positive Ki. Figure 5(b)shows the LDOSs of 2p states in an interfacial O atom.Note that finite values of LDOSs occur around EF, althoughbulk MgO is a band insulator. Such states are induced bymetallic states of interfacial Fe atoms and are thus calledmetal-induced gap states (MIGS). The concept of MIGS wasfirst introduced as a way to understand metal/semiconductorinterfaces [41,42], and it was later applied to Cu/MgO [43] andFe/MgO [44] interfaces. By comparing Figs. 5(a) and 5(b),we see that structures of LDOSs around EF are quite similarbetween Fe d3z2−r2 and O pz states, which is due to the stronghybridization between these states at the interface. Such stronghybridization comes from the geometry of the interface, whereO atoms are on top of Fe atoms in the z direction, as seen inFig. 1(c). We also see that in the minority-spin LDOSs, thepeak structure of the Fe dyz(dzx) state just above EF is almostthe same as that of the O py(px) state.Let us now discuss the relationship between the largepositive Ki and LDOSs in Fe/CuInSe2(001). Figure 6(a) showsthe LDOSs for 3d states of an Fe atom located at the interfacebetween Fe and CuInSe2 layers. We can readily identifysome sharp peaks in minority-spin LDOSs both just aboveand just below EF. Such LDOS structures enable excitationswith quite small �ε, which provide large contributions to Kias mentioned above. As seen from the orbital configurationsaround EF shown in the inset of Fig. 6(a), these peaks can yieldfinite values of 〈dxy |Lz|dx2−y2〉, 〈dzx |Lz|dyz〉, 〈dyz|Lz|dzx〉, and〈dxy |Lx |dyz(dzx)〉. Thus, Fe/CuInSe2(001) has more excitationprocesses with positive contributions to Ki than Fe/MgO(001).Moreover, such positive processes have smaller �ε thanthose of Fe/MgO(001). These features in the LDOSs supportour results that Ki of Fe/CuInSe2(001) is about 1.6 timeslarger than that of Fe/MgO(001). We emphasize that suchpreferable LDOSs of interfacial Fe have a close relationshipwith the LDOSs of interfacial Se shown in Fig. 6(b). Similarto the interfacial O LDOSs in Fe/MgO(001), Se LDOSs havefinite values around EF due to the MIGS. In the minority-spinSe LDOSs, we can find some sharp peaks around EF withpz-orbital character, which couple to various minority-spinFe 3d states around EF [see the inset of Fig. 6(a)]. This isin contrast to the Fe/MgO(001) case, in which pz states ininterfacial O atoms couple mainly to d3z2−r2 states in interfacialFe atoms. Such a difference mainly comes from the differencein the geometry at the interface between Fe and barrier layers.In Fe/CuInSe2(001), interfacial Se atoms are not on top ofFe atoms in the z direction, unlike the Fe/MgO(001) case,as shown in Fig. 1(a). Due to such locations of interfacialSe atoms, pz wave functions of interfacial Se can hybridizewith almost all 3d states of interfacial Fe, not only withd3z2−r2 states; this yields favorable orbital configurationsaround EF.174401-4GIANT INTERFACIAL PERPENDICULAR MAGNETIC . . . PHYSICAL REVIEW B 96, 174401 (2017)-1-0.5 0 0.5 1-1.0-0.8-0.6-0.4-0.2 0.0 0.2-0.4 -0.2  0  0.2  0.4E-EF [eV]Projected LDOS [states/eV/orbital]-0.1-0.05 0 0.05 0.1-2 -1.5 -1 -0.5  0  0.5  1  1.5  2Projected LDOS [states/eV/orbital](a)(b)FIG. 6. The projected LDOSs for (a) Fe 3d states and (b) Se 4pstates at the interface of the Fe/CuInSe2(001) heterostructure. Ineach panel, positive and negative values indicate the majority- andminority-spin projected LDOSs, respectively. The inset of panel (a)shows an enlarged view near the Fermi level.We carried out further analysis to obtain more detailedinformation on large Ki in Fe/CuInSe2(001). Figure 7(a)shows the in-plane wave vector (k‖) dependence of �E(k‖) ≡E[100](k‖) − E[001](k‖). Here, Ki is proportional to the sumof �E(k‖) over all k‖ in the Brillouin zone. We obtainedpositive values of �E(k‖) in wide regions of the Brillouinzone, including high-symmetry � and M points. To understandthe origin of the positive �E(k‖), we plotted in Fig. 7(b) theband structure of the Fe/CuInSe2(001) supercell along thehigh-symmetry lines. Around the � point, both the highestoccupied and lowest unoccupied bands are generated bythe hybridization between dyz and dzx states of Fe, whichcan enhance 〈dzx |Lz|dyz〉 and 〈dyz|Lz|dzx〉, giving positivecontributions to Ki. Around the M point, the highest occupiedand lowest unoccupied bands consist of dxy and dx2−y2 statesof Fe, respectively. These bands can enhance 〈dxy |Lz|dx2−y2〉with positive contributions to Ki. On the other hand, wehave small negative values of �E(k‖) around the X point.As shown in Fig. 7(b), since the highest occupied (lowestunoccupied) band around the X point comes from dzx and dxy(dyz and dxy) states, 〈dzx |Lx |dxy〉 and 〈dxy |Lx |dyz〉 contributeto such negative values of �E(k‖ ≈ X). The smallness of�E(k‖ ≈ X) is due to the relatively large energy difference-1.0 -0.8 -0.6 -0.4 -0.2  0  0.2  0.4  0.6  0.8  1.0-1.0-0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1.0-0.006-0.004-0.002 0 0.002 0.004 0.006 0.008-0.2-0.15-0.1-0.05 0 0.05 0.1 0.15 0.2E-E F [eV](b)(a)FIG. 7. The direct microscopic information on PMA in theFe/CuInSe2(001) heterostructure: (a) the in-plane wave-vector(k‖) dependence of �E(k‖) ≡ E[100](k‖) − E[001](k‖) and (b) theminority-spin bands along the high-symmetry lines in the k‖ Brillouinzone. In panel (b), orbital components of each band are indicated bycolors.between the highest occupied and lowest unoccupied bands[see the denominator of Eq. (1)]. All these band structuresaround EF are consistent with the orbital configurations in FeLDOSs shown in the inset of Fig. 6(a).Finally, we show in Fig. 8 the calculated Ki as a functionof the change in the Fermi energy �EF for Fe/CuInSe2(001)and Fe/MgO(001). These curves were obtained by changingthe valence electron number n in each system. We see that Kiin Fe/MgO(001) increases slightly for small hole and electrondopings. On the other hand, Ki in Fe/CuInSe2(001) decreasesa great deal for both hole- and electron-doped cases, which isconsistent with our findings that the large Ki in this system isclosely related to the sharp peaks in the LDOS around EF in Feminority-spin states [see Fig. 6(a)]. In combination with largeKi, the sharp decrease in Ki by dopings in Fe/CuInSe2(001)is useful for the voltage-assisted MRAM applications[1,2].IV. SUMMARYWe investigated interfacial magnetocrystalline anisotropiesof various heterostructures consisting of Fe and nonoxide174401-5MASUDA, KASAI, MIURA, AND HONO PHYSICAL REVIEW B 96, 174401 (2017)-0.5 0 0.5 1 1.5 2 2.5-0.5 -0.4 -0.3 -0.2 -0.1  0  0.1  0.2  0.3  0.4  0.5ΔEF [eV]Fe/CuInSe2Fe/MgOKi [mJ/m2 ]FIG. 8. Calculated Ki as a function of the change in the Fermienergy �EF for Fe/CuInSe2(001) and Fe/MgO(001). The origin ofthe horizontal axis �EF = 0 corresponds to the original Fermi energyin each system. The changes in the valence electron number �n at�EF = ±1 eV are also shown in units of electrons/atom.semiconductor layers by using first-principles calculations. Wefound that most of those systems show PMA with a positiveinterfacial anisotropy constant Ki. In particular, Fe/CuInSe2was found to have the largest Ki ≈ 2.3 mJ/m2, which isapproximately 1.6 times as large as that of Fe/MgO, beinga benchmark system currently used in p-MTJs. We also foundthat Bruno’s relation holds for almost all systems considered inthis study, which means that the interfacial magnetocrystallineanisotropies are determined mainly by minority-spin statesaround EF. By analyzing the LDOS and wave-vector-resolvedanisotropy energy, we clarified that the large Ki in Fe/CuInSe2is due to the preferable 3d-orbital configurations around EF inthe minority-spin states of interfacial Fe atoms. Moreover, wefound that the positions of interfacial Se atoms play a key rolein the appearance of such orbital configurations of interfacialFe atoms.Note added in proof. In Ref. [28], we commented onmagnetic shape anisotropy estimated from the magnetostaticdipole-dipole interaction. After our manuscript was accepted,we found a minor error in our program for calculating themagnetic shape anisotropy. By using the revised program,we obtained the shape anisotropy of around 1.1 mJ/m2 forthe present Fe/semiconductor(001) superlattices, which issufficiently lower than the crystalline magnetic anisotropy inmany of these systems.ACKNOWLEDGMENTSThe authors are grateful to H. Sukegawa and S. Mitanifor useful discussions and critical comments. This work waspartly supported by Grants-in-Aid for Scientific Research(S) (Grant No. 16H06332) and (B) (Grant No. 16H03852)from the Ministry of Education, Culture, Sports, Science andTechnology, Japan, by NIMS MI2I, and also by the ImPACTProgram of Council for Science, Technology and Innovation,Japan. The crystal structures of the supercells were visualizedusing VESTA [45].APPENDIX: INTERFACIAL LAYERS OF SUPERCELLSTo determine the energetically favored interfacial layerof the supercell, we compared formation energies of thesupercell for different termination layers of the semiconductorbarrier. Here, we show the details of the procedure in the caseof Fe/CuInSe2(001). The relative stability between Se- andCuIn-terminated interfaces is estimated by using the followingformation energy [46,47]:Etermform = Etermtot −∑iNiμi, (A1)where Etermtot is the total energy of the optimized supercell foreach termination, Ni is the number of atoms of the element i,and μi is its chemical potential. 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