Oscillatory magnetic anisotropy and spin-reorientation...

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PHYSICAL REVIEW B 94, 174404 (2016) Oscillatory magnetic anisotropy and spin-reorientation induced by heavy-metal cap in Cu/FeCo/ M ( M = Hf or Ta): A first-principles study P. V. Ong, 1 , * Nicholas Kioussis, 1, P. Khalili Amiri, 2, 3 and K. L. Wang 2 1 Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, USA 2 Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA 3 Inston Inc., Los Angeles, California 90095, USA (Received 25 April 2016; published 3 November 2016) Using ab initio electronic structure calculations we have investigated the effect of the thickness of a heavy-metal (HM) cap on the magnetic anisotropy of the Cu/FeCo/HM(n) thin film where HM = Hf and Ta with thicknesses of n = 0–10 monolayers (MLs). We find that the Hf cap results in a large perpendicular magnetic anisotropy (PMA), which exhibits quasiperiodic oscillation with a period of two MLs. In contrast, the Ta-capped heterostructure exhibits a spin reorientation from out-of-plane to in-plane magnetization orientation at two MLs of Ta. Moreover, the MA remains negative and depends weakly on the Ta-cap thickness beyond the critical thickness. The underlying mechanism of the PMA oscillation is the periodic change in spin-flip spin-orbit coupling between the minority-spin Fe d (xz,yz) and majority Fe d (z 2 ) at , which is induced by the hybridization with Hf at the FeCo/Hf interface. Our results help resolve the contradictory experiments regarding the role of the FeCo/Ta interface on the PMA of the MgO/FeCo/Ta junction. The calculations reveal that the ferromagnet/Hf is promising for spintronic applications and that the capping material and thickness are additional parameters for optimizing the functional properties of spintronic devices. DOI: 10.1103/PhysRevB.94.174404 I. INTRODUCTION Perpendicular magnetic anisotropy (PMA) in trilayers of nonmagnetic metal/ferromagnet/heavy metal (NM/FM/HM) or insulator/ferromagnet/heavy metal (I/FM/HM) is of great interest for spintronic applications, such as spin-transfer-torque random access memory (RAM) [1,2], magnetoelectric RAM [3,4], and spin valves [59]. These perpendicularly magnetized heterostructures where the NM and I layers are usually Cu and MgO, respectively, and the HM layer (Ru, Pd, Hf, Ta, Pt, and Au) has strong spin-orbit coupling (SOC), promise a lower critical current for magnetization switching, faster magnetic switching, smaller magnetic bits, and high thermal stability [1,9,10]. Recently, it was shown that the material type and thickness of the HM layer play crucial roles not only on the MA [1117], but also on the voltage control [18] and magnetotransport behavior [7,14,16,19,20] of these trilayers. In particular, experiments showed that the Hf overlayer enhances the PMA of MgO/Co 20 Fe 60 B 20 /Hf and MgO/Co 40 Fe 40 B 20 /Hf over that of MgO/Co 20 Fe 60 B 20 /W [16] and MgO/Co 40 Fe 40 B 20 /Ta [17], respectively. Similar results have also been predicted from ab initio calculations on Fe/Hf and Fe/Ta superlattices where the thicknesses of each FM and HM layer is nine monolayers (MLs) [21]. On the other hand, experimental results on the effect of Ta on the MA of MgO/CoFeB remain controversial. Worledge et al. [22] showed that the magnetization orientation of MgO/Co 60 Fe 20 B 20 /Ru remains in plane for FM thickness down to 0.5 nm whereas that of MgO/Co 60 Fe 20 B 20 /Ta becomes perpendicular at around 0.9 nm, indicating that the CoFeB/Ta interface provides a PMA contribution. A * [email protected] [email protected] similar conclusion also was drawn from experiments by Liu et al. [17] In contrast, Yamamoto et al. [13] showed that in MgO (1-nm)/Co 20 Fe 60 B 20 /cap the MA decreases when the cap is successively replaced by 5-nm-thick MgO, Ta, and Ru, respectively. Moreover, these experiments reported that there is no PMA in Ta/Co 20 Fe 60 B 20 /Ta, indicating that the CoFeB/Ta interface yields a negative contribution to the MA. Further- more, it has been shown that MgO/Co 60 Fe 20 B 20 /Ta [14] and MgO/Co 20 Fe 60 B 20 /Ta [23] with a 1.2-nm-thick FM layer exhibit in-plane magnetization orientation when the Ta thickness exceeds 0.45 and 2 nm, respectively. Besides the Ta thickness, the annealing time and temper- ature which govern the diffusion of Ta across the interfaces have been shown to have a strong effect on the MA of the MgO/CoFeB/Ta junction [1,7,24,25]. Therefore, given the contradictory results and ill-defined structural characteristics of the I/FM and FM/HM interfaces, current experiments could not provide an unambiguous and consistent interpretation of the role of the FeCoB/Ta interface on the PMA of the magnetic junctions. Furthermore, it is well known that by varying the thickness of the FM thin film or the HM cap can induce shifts of spin-polarized quantum well states, resulting in strong variation of the MA [26] and even a switching of the magnetic easy axis of thin films [27]. This raises another interesting question when comparing the MA of the Hf- and Ta-capped systems, namely, whether the enhancement of the MA of the FM/Hf interface over that of the FM/Ta interface is specific to a certain thickness range of the HM cap, or is it generally true? In this paper, we report ab initio electronic structure calculations of the effect of the HM-cap thickness on the MA in Cu/FeCo/HM (HM = Ta, Hf). Our results show distinct differences in the effect of Ta and Hf cappings on the MA of the trilayers and resolve the above questions. The underlying mechanism is elucidated by mapping the k-resolved MA and analyzing the energy and k-resolved distributions of the d 2469-9950/2016/94(17)/174404(7) 174404-1 ©2016 American Physical Society

Transcript of Oscillatory magnetic anisotropy and spin-reorientation...

PHYSICAL REVIEW B 94, 174404 (2016)

Oscillatory magnetic anisotropy and spin-reorientation induced by heavy-metal cap inCu/FeCo/M (M = Hf or Ta): A first-principles study

P. V. Ong,1,* Nicholas Kioussis,1,† P. Khalili Amiri,2,3 and K. L. Wang2

1Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, USA2Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA

3Inston Inc., Los Angeles, California 90095, USA(Received 25 April 2016; published 3 November 2016)

Using ab initio electronic structure calculations we have investigated the effect of the thickness of a heavy-metal(HM) cap on the magnetic anisotropy of the Cu/FeCo/HM(n) thin film where HM = Hf and Ta with thicknesses ofn = 0–10 monolayers (MLs). We find that the Hf cap results in a large perpendicular magnetic anisotropy (PMA),which exhibits quasiperiodic oscillation with a period of two MLs. In contrast, the Ta-capped heterostructureexhibits a spin reorientation from out-of-plane to in-plane magnetization orientation at two MLs of Ta. Moreover,the MA remains negative and depends weakly on the Ta-cap thickness beyond the critical thickness. Theunderlying mechanism of the PMA oscillation is the periodic change in spin-flip spin-orbit coupling betweenthe minority-spin Fe d(xz,yz) and majority Fe d(z2) at �, which is induced by the hybridization with Hf atthe FeCo/Hf interface. Our results help resolve the contradictory experiments regarding the role of the FeCo/Tainterface on the PMA of the MgO/FeCo/Ta junction. The calculations reveal that the ferromagnet/Hf is promisingfor spintronic applications and that the capping material and thickness are additional parameters for optimizingthe functional properties of spintronic devices.

DOI: 10.1103/PhysRevB.94.174404

I. INTRODUCTION

Perpendicular magnetic anisotropy (PMA) in trilayers ofnonmagnetic metal/ferromagnet/heavy metal (NM/FM/HM)or insulator/ferromagnet/heavy metal (I/FM/HM) isof great interest for spintronic applications, such asspin-transfer-torque random access memory (RAM) [1,2],magnetoelectric RAM [3,4], and spin valves [5–9]. Theseperpendicularly magnetized heterostructures where the NMand I layers are usually Cu and MgO, respectively, andthe HM layer (Ru, Pd, Hf, Ta, Pt, and Au) has strongspin-orbit coupling (SOC), promise a lower critical current formagnetization switching, faster magnetic switching, smallermagnetic bits, and high thermal stability [1,9,10]. Recently,it was shown that the material type and thickness of theHM layer play crucial roles not only on the MA [11–17],but also on the voltage control [18] and magnetotransportbehavior [7,14,16,19,20] of these trilayers. In particular,experiments showed that the Hf overlayer enhances the PMAof MgO/Co20Fe60B20/Hf and MgO/Co40Fe40B20/Hfover that of MgO/Co20Fe60B20/W [16] andMgO/Co40Fe40B20/Ta [17], respectively. Similar resultshave also been predicted from ab initio calculations on Fe/Hfand Fe/Ta superlattices where the thicknesses of each FM andHM layer is nine monolayers (MLs) [21].

On the other hand, experimental results on the effect of Taon the MA of MgO/CoFeB remain controversial. Worledgeet al. [22] showed that the magnetization orientation ofMgO/Co60Fe20B20/Ru remains in plane for FM thicknessdown to 0.5 nm whereas that of MgO/Co60Fe20B20/Tabecomes perpendicular at around 0.9 nm, indicating thatthe CoFeB/Ta interface provides a PMA contribution. A

*[email protected][email protected]

similar conclusion also was drawn from experiments by Liuet al. [17] In contrast, Yamamoto et al. [13] showed that inMgO (1-nm)/Co20Fe60B20/cap the MA decreases when thecap is successively replaced by 5-nm-thick MgO, Ta, and Ru,respectively. Moreover, these experiments reported that there isno PMA in Ta/Co20Fe60B20/Ta, indicating that the CoFeB/Tainterface yields a negative contribution to the MA. Further-more, it has been shown that MgO/Co60Fe20B20/Ta [14]and MgO/Co20Fe60B20/Ta [23] with a 1.2-nm-thick FMlayer exhibit in-plane magnetization orientation when the Tathickness exceeds 0.45 and 2 nm, respectively.

Besides the Ta thickness, the annealing time and temper-ature which govern the diffusion of Ta across the interfaceshave been shown to have a strong effect on the MA of theMgO/CoFeB/Ta junction [1,7,24,25]. Therefore, given thecontradictory results and ill-defined structural characteristicsof the I/FM and FM/HM interfaces, current experiments couldnot provide an unambiguous and consistent interpretation ofthe role of the FeCoB/Ta interface on the PMA of the magneticjunctions. Furthermore, it is well known that by varying thethickness of the FM thin film or the HM cap can induceshifts of spin-polarized quantum well states, resulting in strongvariation of the MA [26] and even a switching of the magneticeasy axis of thin films [27]. This raises another interestingquestion when comparing the MA of the Hf- and Ta-cappedsystems, namely, whether the enhancement of the MA of theFM/Hf interface over that of the FM/Ta interface is specific toa certain thickness range of the HM cap, or is it generally true?

In this paper, we report ab initio electronic structurecalculations of the effect of the HM-cap thickness on the MAin Cu/FeCo/HM (HM = Ta, Hf). Our results show distinctdifferences in the effect of Ta and Hf cappings on the MA ofthe trilayers and resolve the above questions. The underlyingmechanism is elucidated by mapping the k-resolved MA andanalyzing the energy and k-resolved distributions of the d

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ONG, KIOUSSIS, AMIRI, AND WANG PHYSICAL REVIEW B 94, 174404 (2016)

states of the minority- and majority-spin bands. The restof this paper is organized as follows: Sec. II describes themethodology used to calculate the MA. In Sec. III A weconsider the limit of zero-cap thickness, i.e., Cu/FeCo/vacuumand investigate the origin in the electronic structure of thePMA in the uncapped system. In Sec. III B, we demonstratethat the PMA of the Cu/FeCo/Hf trilayer oscillates with Hfthickness and elucidate the mechanism of the oscillatorybehavior. In Sec. III C, we show that Ta capping induces a spinreorientation in Cu/FeCo/Ta and discuss the mechanism of thethickness-induced magnetic switching. Finally, conclusionsare summarized in Sec. IV.

II. COMPUTATIONAL METHODS AND MODELS

There are different approaches for calculating the MA inmagnetic alloys. For example, one approach for calculating theMA and its thermal variation is based on the relativistic exten-sion of the Korringa-Kohn-Rostoker multiple scattering theorywithin the coherent potential approximation (CPA) using themagnetic torque [28]. In this paper, the ab initio calculationshave been carried out within the framework of the projectoraugmented-wave (PAW) formalism [29] as implemented inthe Vienna ab initio simulation package [30,31]. It has beenshown that MA values calculated from the supercell approachwithin the PAW methodology with SOC are in good agreementwith those calculated within the CPA and other full potentialmethods and for Fe-Co alloys very well describe experimentaldata for tetragonally distorted thin films [32]. The generalizedgradient approximation (GGA) [33] is employed to treatthe exchange-correlation interaction. For Fe1−xCox alloyswith x ∼ 0.5, the MA values calculated at the levels of thelocal density approximation and GGA exhibit no significantdifference [32]. Cu/FeCO/Hf(Ta) trilayers are modeled by aslab supercell approach along [001] consisting of four MLs offcc Cu rotated by 45◦ on the (001) plane, three MLs of B2-typeFeCo, zero to ten MLs of Hf or Ta, and a 15-A-thick vacuumseparating the periodic slabs (Fig. 1). In experiment, HM caps

FIG. 1. (a) Schematic of the Cu/FeCo/HM(n) trilayer, whereHM = Hf or Ta and n = 0–10 MLs. (b) Tetragonal pyramidalstructure at the FeCo/HM interface.

grow on the FM layer in an amorphous form [19,34]. In thepresent paper, we assume the Hf layer has a fcc or bcc structure.We denote with Fe1 and Fe2 the iron atoms at the Fe/Cu andFe/Hf(Ta) interfaces, respectively. The in-plane lattice constantis fixed at the calculated value of the bulk FeCo lattice constant(2.840 A). The magnetic and electronic degrees of freedomand atomic-z positions are relaxed until the forces acting onthe ions become less than 2 × 10−3 eV/A and the change inthe total energy between two ionic relaxation steps is smallerthan 10−6 eV. The plane-wave cutoff energy is 500 eV, and theMonkhorst-Pack k mesh was 17 × 17 × 1 for the relaxations.SOC of the valence electrons is then included using thesecond-variation method [35] employing the scalar-relativisticeigenfunctions of the valence states and a 41 × 41 × 1 k-pointmesh. The MA per unit interfacial area A is determined fromMA = [E[100] − E[001]]/A, where E[100] and E[001] are the totalenergies with magnetization along the [100] and [001] direc-tions, respectively. Test calculations with 51 × 51 × 1 k meshindicate that the calculated MA values are converged within10%. For comparison, we also employ the force theorem [36]to calculate the MA ≈ ∑

k MA(k)/A, where the k-resolvedMA MA(k) = ∑

n∈occ[ε(n,k)[100] − ε(n,k)[001]] with the bandindex n runs over all occupied (occ) states. Here, the sumwith respect to k is taken over the two-dimensional Brillouinzone (2D BZ), and ε(n,k)[100]([001]) are the eigenvalues ofthe Hamiltonian for magnetization along the [100] ([001])directions, respectively.

III. RESULTS AND DISCUSSION

A. Perpendicular magnetic anisotropy of Cu/FeCo/vacuum

Figures 2(a) and 2(b) show MA(k) in the 2D BZ and along�M , respectively. We also show in Figs. 2(c) and 2(d) the

FIG. 2. Cu/FeCo/vacuum: (a) and (b) MA(k) (in meV) in the 2DBZ and along �M , respectively. In (a), I and II indicate the BZ k‖points where there are large positive contributions to MA. (c) and(d) Energy- and k-resolved distributions of the orbital character ofminority-spin (↓) bands along �M for the Fe1- and Fe2-derived dxy

and dx2-y2 states, respectively.

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FIG. 3. (a) Cap-thickness dependence of MA of Cu/FeCo/Hf, calculated using the total energy difference (circles) and the force theorem(triangles). The stars indicate MA of MgO/FeCo/Hf(n) for n = 0 and three MLs. (b) Cap-thickness dependence of the orbital momentdifference �mo = m[001]

o − m[100]o of the Fe1 and Fe2 interfacial atoms. (c) MA(k) contours (in meV) in the 2D BZ for Hf thickness nHf = 1–4.

For the sake of clarity, MA(k) is magnified by factors of 6 and 2 for nHf = 1 and 2, respectively.

energy- and k-resolved distributions of the minority-spin (↓)Fe1 and Fe2 d states, respectively, along �M .

The main PMA contributions occur at BZ points I and II[(BZP-I) and (BZP-II), respectively] along �M [Figs. 2(a)and 2(b)]. Within second-order perturbation theory the MAcan be expressed as [37]

MCA ∝ ξ 2∑

k

o,u

|〈�↓ko|Lz|�↓

ku〉|2 − |〈�↓ko|Lx |�↓

ku〉|2E

↓ku − E

↓ko

,

+ ξ 2∑

k

o,u

|〈�↑ko|Lx |�↓

ku〉|2 − |〈�↑ko|Lz|�↓

ku〉|2E

↓ku − E

↑ko

.

(1)

Here, �↓ko (E↓

ko), �↑ko (E↑

ko), and �↓ku (E↓

ku) are occupiedminority-, occupied majority-, and unoccupied minority-spinstates (energies); ξ is the SOC constant, and Lx(z) is thex(z) component of the orbital angular momentum operator.Note that the contribution from the spin-flip SOC term has anopposite sign from the SOC term between states of the samespin.

The origin of the positive MA at BZP-I and BZP-II is mainlydue to the SOC of the occupied Fe1 ↓ d(x2 − y2) state to theunoccupied d(xy) states and that of the occupied Fe1 ↓ d(xy)to the unoccupied d(x2 − y2) states, respectively, through Lz

[Fig. 2(c)]. At BZP-I, there is also SOC of the occupiedFe2 ↓ d(x2 − y2) states to the unoccupied d(xy) states, givingpositive MA contributions. The separation in energy betweenthe occupied and the unoccupied Fe2 ↓ d states is large and

out of the energy window at BZP-II [Fig. 2(d)]. Consequently,the MA contribution of the Fe2 atom at this k point is notsignificant.

B. Oscillatory magnetic anisotropy in Cu/FeCo/Hf(n)

Figure 3(a) shows the variation of MA with Hf-capthickness (nHf) in the Cu/FeCo/Hf trilayer. The MAs de-termined from: (i) total energy calculations (circles) and(ii) the force theorem (triangles) are in excellent agree-ment. For comparison, we also display the MA values ofMgO/FeCo/vacuum and MgO/FeCo/Hf(3). The first Hf MLinduces a large decrease in MA from 1.49 erg/cm2 for theCu/FeCo/vacuum to 0.62 erg/cm2 for Cu/FeCo/Hf(1). For thinfilms, the contribution of the shape anisotropy can be estimatedby MAshape/t = −(μ0/2)M2

S (SI units) [38,39], where t is thethickness of the FeCo layer and μ0 = 4π × 10−7 N A−2. Thesaturation magnetization is estimated by MS = M/V , whereM = MFe + MCo and V are the total magnetic moment andvolume of the unit cell of the B2-type FeCo, respectively.

Using V ∼ 23 A3, MFe ∼ 2.7μB , and MCo ∼ 1.7μB , we find

MS = 1774 × 103 A m−1, which is in good agreement withthe experimental value of 1950 × 103 A m−1 [40]. Thus, thecontribution of the MAshape of about −0.6 erg/cm2 is smallerthan the MA values for the range of Hf thickness consideredin this paper.

Except for nHf = 1 ML, the MA values are larger for oddnumbers of Hf layers, resulting in a quasiperiodic oscillationperiod of two MLs, which shows no sign of damping up to

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FIG. 4. DOS of minority-spin (↓) Fe2-derived d(xz,yz) (leftpanel) and d(z2) (right panel) states. Numerals in the left panelindicate Hf thickness nHf = 0–10 MLs. The Fermi level is set atzero energy. The arrows indicate enhancement of d(xz,yz) and d(z2)DOS which occur periodically near the Fermi level for odd and evennHf’s, respectively.

ten-ML Hf. The MA(k) in the 2D BZ is plotted for nHf =1–4 MLs [Fig. 3(c)]. One can clearly see that the enhancementin MA originates from the hot spot at �, which appearsperiodically for odd values of nHf.

We have also calculated the effect of cap thickness on theorbital moment difference �mo = m[001]

o − m[100]o . The results

for the interfacial Fe1 and Fe2 atoms are shown in Fig. 3(b).For the Co and Hf atoms the variation of �mo is much weakerand is not shown. Interestingly, the thickness dependence of�mo for Fe1 and Fe2 correlates very well with that of MA andoscillates with the same period of two MLs. Note that �mo

is positive and negative for Fe1 and Fe2, respectively. Forsingle atomic species FM with large exchange splitting wherethe spin-flip SOC between states of opposite spins vanishes,Bruno has shown that the MA is proportional to �mo [41].However, for the Cu/FeCo/Hf trilayer the spin-flip term cannotbe ignored due to hybridization of Fe2 with the nonmagneticHM cap. Therefore, the fact that �mo is negative for Fe2does not necessarily imply an in-plane magnetic orientationat the FeCo/Hf interface. On the contrary, we show below theFeCo/Hf interface provides a large contribution to PMA dueto the spin-flip SOC induced by hybridization of Fe2 and Hforbitals.

Figure 4 shows the evolution of density of states (DOS) ofthe minority-spin Fe2-derived d(xz,yz) and d(z2) states withHf thickness. The data clearly show that the d(xz,yz) DOSaround the Fermi level is periodically enhanced for odd valuesof nHf, except for nHf = 1 ML (left panel in Fig. 4). On theother hand, the unoccupied d(z2) DOS is increased for evennHf [right panel in Fig. 4]. This periodic behavior is consistentwith the MA oscillation discussed above. The unoccupiedFe2(↓)d(z2) and occupied d(xz,yz) are coupled through theLx operator. Therefore, the increase in the unoccupied d(z2)

FIG. 5. DOS of majority-spin (↑) Fe2-derived d(z2) states (leftpanel) and Hf1-derived hybridized d2p3 = d(xy) + d(z2) + p(x) +p(y) + p(z) states, averaged over the number of the componentorbitals (right panel). Numerals in the right panel indicate Hfthickness nHf = 0–10 MLs. The Fermi level is set at zero energy.The arrows indicate enhanced DOS of the d(z2) or hybridized d2p3

states that occur periodically near the Fermi level for odd nHf. For thesake of clarity, the d2p3 DOS is magnified by a factor of 2.

DOS leads to a decrease in the negative MA term, giving riseto a trough in the MA variation for even nHf.

Figure 5 shows the evolution of the DOS of majority-spin Fe2-derived d(z2) and Hf1-derived hybridized d2p3 =d(xy) + d(z2) + p(x) + p(y) + p(z) states, averaged over thenumber of the component orbitals. Since the FeCo/Hf interfacehas a tetragonal pyramidal structure [Fig. 1(b)], the Hf1-derived hybrid d2p3 state is allowed [42]. The consistency inbehavior and peak positions of Fe2 ↑ d(z2) and Hf1 ↑ d2p3

clearly indicates that there is a strong hybridization betweenthe two orbitals. Note that the DOS of Fe2 ↑ d(z2) is enhancednear the Fermi level for odd nHf, in contrast to that ofFe2 ↑ d(z2), which increases for even Hf thickness. Thecalculated energy- and k-resolved distributions of the orbitalcharacters of majority-spin states shows that the Fe2 ↑ d(z2)states occur exclusively around the � point. The spin-flip SOCbetween Fe2 ↑ dz2 and Fe2 ↓ dxz,yz through the Lx operator,leads to an enhancement in the positive MA contribution. Thisgives rise to the MA hot spot in MA(k) contours at the �

point and explains the peak in MA variation for odd nHf

[Fig. 3(c)].

C. Cap-thickness-induced spin reorientation in Cu/FeCo/Ta(n)

Figure 6(a) shows the variation of MA with Ta-cap-thickness (nTa) in the Cu/FeCo/Ta trilayer. The MA valuescalculated using the total energy method and the force theoremare in excellent agreement. In contrast to the oscillatorybehavior in the Hf-capped system, the MA of Cu/FeCo/Ta(n)abruptly drops to a negative value at nTa = 2 MLs, leadingto a switching of magnetization vector from out-of-plane toin-plane orientation. Using the same method as in Sec. III B,the contribution of the shape anisotropy is calculated to beabout −0.6 erg/cm2, whose absolute value is significantly

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FIG. 6. The same as Fig. 3 but for a Ta cap. In the MA(k) contours for nTa = 2 and 4, points I and II indicate the BZP where there are largenegative contributions to MA.

smaller than the MA at nTa = 1 (1.0 erg/cm2). Consequently,the spin reorientation still persists. For the one-ML-thick Tacap the MA increases sharply but remains thereafter negativeand exhibits only weak dependence on Ta-cap thickness.For comparison, the MA values of MgO/FeCo/vacuum andMgO/FeCo/Ta(3) also are presented. More specifically, theMA decreases from 2.70 erg/cm2 for MgO/FeCo/vacuumto 1.43 erg/cm2 for MgO/FeCo/Ta(3). Note that the MAvalues of the MgO-supported systems are consistently largerthan those of the Cu-supported one. This indicates thatMgO/FeCo induces PMA, whereas FeCo/Ta favors in-planeMA. Figure 6(b) shows the orbital moment difference �mo

for the Fe1 and Fe2 atoms versus the thickness of the Tacap, which correlates well with that of the MA. �mo rapidlydecreases at one and two MLs for Fe1 or Fe2, respectively,and thereafter increases and becomes weakly dependent onnTa. The MA(k) in the 2D BZ is plotted for nTa = 1–4 MLs[Fig. 6(c)]. In contrast to the MA hot spots found for odd MLsfor the Hf cap, we find that the MA vanishes at � for all Tathicknesses considered in this paper.

The electronic configurations of Hf (5d2) and Ta (5d3) differby one electron. Addition or removal of an electron from thesystem will lead to an increase or decrease in the Fermi level,respectively. Within the rigid band model, the Fermi-levelshift leads to the extinction of certain SOC matrix elementsand/or the establishment of new ones. Since the MA energy isdetermined mainly from spin-orbit-coupled pairs of occupiedand unoccupied bands in the vicinity of the Fermi level, theseshifts can result in a dramatic change in the MA. Therefore,the distinct behavior of the Hf- and Ta-capped systems can beunderstood in terms of the band filling effect.

In order to elucidate the underlying mechanisms of the spin-reorientation and in-plane (negative) MAs of the Ta-cappedsystem we have calculated the energy- and k-resolved distri-butions of the orbital characters of minority- and majority-spinbands for the Fe1 and Fe2 interfacial atoms for nTa = 1 whichare shown in Fig. 7. The unoccupied Fe2 ↑ d(z2) states stilloccur near the Fermi level at �, and they couple to the occupiedFe2 ↓ d(xz,yz) states via spin-flip SOC of Lx yielding apositive MA contribution. However, this is counterbalancedby the same-spin SOC between the occupied Fe2 ↓ d(xz,yz)

FIG. 7. Energy- and k-resolved distributions of orbital characterof minority-spin (↓) (left panel) and majority-spin (↑) bands (rightpanel), respectively, along k ‖ �X for the interfacial Fe2 atom d statesfor nTa = 1.

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FIG. 8. Left panel: energy levels of Fe1-derived minority-spin (↓)states at BZPs I and II for nTa = 4. Middle and right panels: energylevels of Fe1- and Fe2-derived minority-spin (↓) states, respectively,at BZP I for nTa = 4. The vertical lines connecting pairs of occupiedand unoccupied states denote nonvanishing SOC matrix elementswhere the line color matches that of the occupied state.

and the unoccupied Fe2 ↓ d(xy) states and d(x2 − y2) throughLx , which yields a negative MA contribution. We find a similarbehavior for the thicker Ta cap. The mutual cancellation ofMA contributions from the spin-flip and same-spin SOCs isresponsible for the disappearance of the hot spots at � inMA(k) for the Ta-cap trilayers [Fig. 6(c)].

Figure 8 shows the energy levels of the Fe1-derivedminority-spin states at the BZP-I and BZP-II for nTa = 2(left panel) and those of Fe1- and Fe2-derived minority-spinstates at the BZP-I for nTa = 4 (middle and right panels). Theassociated nonvanishing SOC matrix elements are representedby vertical lines connecting pairs of occupied and unoccupiedstates. Because the MA of the Cu/FeCo/Ta system is negativefor nTa = 2 and 4 MLs, we only focus on the BZP whereMA(k) < 0 [Fig. 6(c)]. For nTa = 2, the SOC of the occupiedFe1 ↓ d(xz) states with the unoccupied Fe1 ↓ d(z2) states atpoint I and that of the occupied Fe1 ↓ d(yz) states with theunoccupied Fe1 ↓ d(z2) states at II through Lx gives rise tothe negative MA(k) at BPZ-I and BPZ-II, respectively [leftpanel in Fig. 8]. For nTa = 4, the occupied Fe1 ↓ d(x2 − y2)states (middle panel in Fig. 8) is coupled to the unoccupiedFe1 ↓ d(xz) states and d(yz) through Lx and to the unoccupied

Fe1 ↓ d(xy) states through Lz. For the Fe2 site the occupiedFe2 ↓ d(yz) states at point I is coupled to the unoccupied Fe2 ↓d(xy), d(x2 − y2), and d(z2) states through Lx and to theunoccupied Fe2 ↓ d(xz) states through Lz. The competitionbetween the negative and the positive MA contributions due tothese SOCs through Lx and Lz, respectively, renders MA(k) <

0 at the BZP-I [right panel in Fig. 8].

IV. CONCLUSION

To summarize, using electronic structure calculations wehave studied the effects of the HM cap on the MA of aCu/FeCo/HM(n) thin film where HM = Hf and Ta withthicknesses n = 0–10 MLs. We showed that the Hf capinduces large PMA, which exhibits quasiperiodic oscillationwith cap thickness. The oscillation has a period of twoMLs and shows no sign of damping up to ten MLs ofcap thickness. The underlying mechanism of the oscillatorybehavior is the periodic change in the spin-flip SOC at �

between the minority-spin Fe d(xz,yz) and majority-spin Fed(z2) states, which is induced by the hybridization with Hfat the FeCo/Hf interface. On the contrary, the Ta cap inducesa spin reorientation from the perpendicular to the in-planedirection at a Ta thickness of two MLs. Moreover, the MAremains negative and exhibits weak thickness dependence forthe thicker Ta cap. We showed that the effect of spin-flipSOC is suppressed in the Cu/FeCo/Ta trilayers due to themutual cancellation of MA contributions from the same-spin SOC at �. The results unambiguously indicate thatthe FeCo/Ta interface favors in-plane MA and helps resolvethe contradictory experimental results regarding the roles ofthe FeCo/Ta and FeCo/MgO interfaces on the PMA of theMgO/FeCo/Ta junctions. Furthermore, our results imply thatmagnetic multilayers employing the Hf cap have large PMAand hence would be promising for spintronic applications.

ACKNOWLEDGMENTS

This research was supported by NSF Grant No. 1160504,ERC Translational Applications of Nanoscale MultiferroicSystems (TANMS), by Inston Inc. and by NSF Grant No.DMR-1532249.

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