Journal of Magnetism and Magnetic Materials 343 (2013) 262267Contents lists available at SciVerse ScienceDirectJournal of Magnetism and Magnetic Materials0304-88http://d

n CorrE-mjournal homepage: www.elsevier.com/locate/jmmmSpin reorientation transition of Fe/FeCo/Cu(001)and Fe/FeCo/Co/Cu(001)

Dongyoo Kim, Hashmi Arqum, Jisang Hong n

Department of Physics, Pukyong National University, Busan 608-737, Republic of Koreaa r t i c l e i n f o

Article history:Received 25 February 2013Received in revised form3 May 2013Available online 20 May 2013

Keywords:Spin reorientationFeCoFLAPW53/$ - see front matter & 2013 Elsevier B.V. Ax.doi.org/10.1016/j.jmmm.2013.05.004

esponding author. Tel.: +82 516295573.ail address: hongj@pknu.ac.kr (J. Hong).a b s t r a c t

Using the full potential linearized augmented plane wave method, we have investigated the effect of Feadlayer and Co underlayer on the magnetic properties of Fe/FeCo/Cu(001) and Fe/FeCo/Co/Cu(001)systems. It is found that the magnetic layers display close to half metallic state and this is independent onFe adlayer thickness or Co underlayer. The pure FeCo/Cu(001) has an in-plane magnetic anisotropy andthe Co underlayer induces a perpendicular magnetic anisotropy. Besides, the spin reorientation transitionis realized with increasing Fe adlayer thickness. Both Fe/FeCo/Cu(001) and Fe/FeCo/Co/Cu(001) systemsmanifest similar behavior although the strength of anisotropy energy is different. This result indicatesthat the Fe adlayer plays an important role for the magnetic anisotropy because the direction ofmagnetization is almost independent on the presence of Co underlayer, while the Co underlayer affectsthe magnitude of magnetic anisotropy energy.

& 2013 Elsevier B.V. All rights reserved.1. Introduction

Magnetic anisotropy is one of the most essential quantities intwo dimensional magnetism because it brings many intriguingissues in both scientific point of view and innovative applicationpurposes. For instance, it is necessary to have a large perpendicularmagnetic anisotropy energy for high density magnetic informationstorage and permanent magnet applications because the stabilityof magnetization is related to this magnetic anisotropy. In lowdimensional magnetic system, the magnetic anisotropy stronglydepends on various factors such as film thickness, structuralmodification, interface geometry, or capping layers [14]. Due tothese effects, the direction of magnetization of film changes fromin-plane to perpendicular to the film surface or vice versa and thisphenomenon is called spin reorientation transition (SRT).

One can find numerous systems which manifest SRT accordingto their environment such as Ni/Cu(001), Mn/Ag/Fe(001), Fe/Ni/Cu(001), Fe/Cu or Fe/Co/Cu(001) [58]. For instance, the Fe has a body-centered-cubic (bcc) structure in bulk, but on Cu(001) surface the Fehas a face-centered-tetragonal (fct) phase below four monolayer(ML) coverage and then transforms to a face-centered-cubic (fcc)structure in the range of 511 ML thickness. Beyond that, it turnsinto its original bcc structure. It has also been reported that the fccFe film has a ferromagnetic (FM) state below 4 ML coverage withperpendicular magnetization, whereas an antiferromagnetic (AFM)state is observed in the range of 511 ML [914]. Like Fe/Cu(001), all rights reserved.similar trend is observed in Co/Cu(001) with Co film thickness[15,16]. In addition, it is found that the magnetic properties of Fe/Co/Cu system can be altered by Co underlayer thickness [1724].Here, the Co underlayer induces very complex magnetic behaviorand in most previous studies for Fe/Co/Cu(001), the Co underlaysthickness is in the range of few monolayers (MLs). Since themagnetic anisotropy is significantly dependent on subtle changeof electronic structure, the SRT is likely to be induced by submo-nolayer Co coverage. In particular, the magnetic anisotropy can bealtered according to different interface alloy formations [24].Recently, it has been experimentally observed that the SRT can beaffected by the Co alloy formation type or Co underlayer thicknessat interface at finite temperatures [25]. For instance, it is likely to beformed FeCo alloy on Cu(001) or the FeCo alloy can be grown on Counderlayer according to the amount of Co coverage. Along with theinfluence of alloy formation on the magnetic anisotropy, one mayfind that the magnetization direction or the magnetic anisotropyenergy depends on Fe adlayer thickness for each alloy configuration.Nonetheless, no systematic studies have been performed usingstate-of-the-art density functional theory calculations. Thus, in thisreport, we will explore the magnetic properties of Fe/FeCo/Cu(001)and Fe/FeCo/Co/Cu(001) systems and find the role of surface layercoverage and Co underlayer on the magnetization direction andmagnetic anisotropy energy.2. Numerical method

We have employed the thin film version of full potentiallinearized augmented plane (FLAPW) method. Therefore, no shape

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Fig. 1. A schematic illustration of unit cell structure of: (a) Fe/FeCo/Cu(001) and (b) Fe/FeCo/Co/Cu(001). (For interpretation of the references to color in this figure caption,the reader is referred to the web version of this article.)

Table 1Calculated vertical distance (in ) for Fe/FeCo/Cu(001) films.

Fe thickness 0 ML 1 ML 2 ML 3 ML

d(Fe3Fe2) 1.846d(Fe2Fe1) 1.849 1.899d(Fe1Fea) 1.809 1.857 1.825d(FeaCoa) 0.101 0.005 0.005 0.005d(CoaCuS) 1.756 1.819 1.803 1.803

Table 2Calculated vertical distance (in ) for Fe/FeCo/Co/Cu(001) films.

Fe thickness 0 ML 1 ML 2 ML 3 ML

d(Fe3Fe2) 1.836d(Fe2Fe1) 1.846 1.857d(Fe1Fea) 1.867 1.867 1.796d(FeaCoa) 0.085 0.030 0.037 0.024d(CoaCoS) 1.576 1.730 1.693 1.632d(CoSCuS) 1.857 1.825 1.862 1.769

D. Kim et al. / Journal of Magnetism and Magnetic Materials 343 (2013) 262267 263approximation is assumed in charge, potential, and wavefunctionexpansions [2628]. We treat the core electrons fully relativisti-cally, and the spinorbit interaction among valence electrons aredealt with second variationally [29]. The generalized gradientapproximation is used to describe exchange and correlationpotentials [30]. Spherical harmonics with lmax 8 are used toexpand the charge, potential, and wavefunctions in the muffintin region. Energy cut offs of 225 Ry and 13.7 Ry are implementedfor the plane wave star function and basis expansions in the

D. Kim et al. / Journal of Magnetism and Magnetic Materials 343 (2013) 262267264interstitial region. We use 210 k-mesh points with the MonkhorstPack method [31] and the convergence for all physical quantitiesinvestigated in the present work has been carefully checked. Weassume epitaxially grown sample on Cu(001) substrate, thus theTable 3Calculated spin magnetic moment (in B) of Fe and Co atoms in the muffin-tinregions for Fe/FeCo/Cu(001) films.

Fe thickness 0 ML 1 ML 2 ML 3 ML

Fe3 2.86Fe2 2.85 2.62Fe1 2.85 2.63 2.61Fea 2.99 2.71 2.71 2.69Coa 1.74 1.69 1.64 1.64

Table 4Calculated spin magnetic moment (in B) of Fe and Co atoms in the muffin-tinregions for Fe/FeCo/Co/Cu(001) films.

Fe thickness 0 ML 1 ML 2 ML 3 ML

Fe3 2.86Fe2 2.85 2.62Fe1 2.87 2.63 2.60Fea 2.86 2.58 2.52 2.45Coa 1.76 1.65 1.62 1.59CoS 1.61 1.62 1.63 1.58

-2

-1

0

1

2 Fea Coa

-2

-1

0

1

2 Fea Coa

DO

S(St

ates

/eV

.spin

.ato

m)

-6 -4 -2 2 40

-2

-1

0

1

2 Fea Coa

Energy (eV)

Fig. 2. Calculated m-DOS of: (a) jmj 0, (b) jmj 1, and (c) jmj 2 in FeCo/Cu(001).lattice constant of Cu(001) is used and it is 3.61 in lateraldirection. Nonetheless, the atomic position in the vertical directionis relaxed, and the optimized atomic structure is obtained via forceand total energy minimization procedure. We have changed the Feadlayer thickness from 0 ML to 3 ML, whereas the FeCo alloy isfixed to 1 ML coverage in Fe/FeCo/Cu(001). In order to understandthe role of Co underlayer, we consider 1 ML of Co underlayer in Fe/FeCo/Co/Cu(001). Note that the Cu(001) substrate is simulated byseven layers of slabs.3. Numerical results and discussions

In Fig. 1(a) and (b), we first show schematic illustrations ofFe/FeCo/Cu(001) and Fe/FeCo/Co/Cu(001), respectively. The greyballs stand for Cu atoms and Fe and Co atoms are denoted by redand blue balls, respectively. The Fe and Co atoms in FeCo alloylayer are expressed by Fea and Coa and Fei means ith adlayercounted from the interface between Fe and FeCo alloy layers. TheCu at interface layer is expressed by CuS and the CoS means the Coatom at interface between CuS and FeCo alloy layers in Fe/FeCo/Co/Cu(001) film.

In Tables 1 and 2, the optimized interlayer distances of Fe/FeCo/Cu(001) and Fe/FeCo/Co/Cu(001) are presented as the Fe adlayerthickness changes. One can see that the FeCo alloy layer displaysbuckling state on Cu(001) surface if there is no Fe adlayer and this-2

-1

0

1

2 Fe1 Fea Coa

-2

-1

0

1

2 Fe1 Fea Coa

-6 -4 -2 0 2 4

-2

-1

0

1

2 Fe1 Fea Coa

DO

S(St

ates

/eV

.spin

.ato

m)

Energy (eV)

Fig. 3. Calculated m-DOS of: (a) jmj 0, (b) jmj 1, and (c) jmj 2 in Fe/FeCo/Cu(001).

-2

-1

0

1

2 Fe1 Fea Coa CoS

-2

-1

0

1

2 Fe1 Fea Coa CoS

DO

S(St

ates

/eV

.spin

.ato

m)

1

2 Fe1 Fea Coa

D. Kim et al. / Journal of Magnetism and Magnetic Materials 343 (2013) 262267 265is suppressed in the presence of Fe adlayer because the relativeheight difference between Fea and Coa is negligible.

In Tables 3 and 4, we have presented spin magnetic moment ofFe and Co atoms. In general, the surface Fe atom has enhancedmagnetic moment and this is quite well known surface enhance-ment found in surface magnetism. In addition, the largestmagnetic moment is observed in alloy layer when there is no Feadlayer, i.e. FeCo/Cu(001) system. This is due to the reduction ofcoordination number around Fea and Coa atoms. It is realized thatthe Co underlayer suppresses the magnetic moment in alloy layer.However, the influence of Co underlayer on the magnetic momentis limited because no significant changes have been found in otherlayers. Interestingly, we observed AFM states in FeCo adlayer or Feadlayer depending on Fe adlyer thickness when the surface Felayer had 0.5 ML coverage [24]. But, no AFM spin state is obtainedif the surface Fe has 1 ML coverage as shown in Tables 3 and 4. Thisresult indicates that the magnetic state of Fe/FeCu/Cu(001) andFe/FeCu/Co/Cu(001) is sensitive to the Fe adlayer thickness inultrathin films systems.

We now discuss the m-resolved density of state (m-DOS). Itshould be remarked that no meaningful disparity is observed evenwhen the Fe adlayer thickness increases. Thus, in Figs. 25, the m-DOS of Fe and Co atoms in FeCo/Cu(001), Fe(1 ML)/FeCo/Cu(001),FeCo/Co/Cu(001), and Fe(1 ML)/FeCo/Co/Cu(001) structures isshown, respectively. One can see that both Fe/FeCo/Cu(001) andFe/FeCo/Co/Cu(001) systems have very large spin asymmetry at-2

-1

0

1

2 Fea Coa CoS

-2

-1

0

1

2

DO

S(St

ates

/eV

.spin

.ato

m)

-6 -4 -2 0 2 4

-2

-1

0

1

2

Energy (eV)

Fig. 4. Calculated m-DOS of: (a) jmj 0, (b) jmj 1, and (c) jmj 2 in FeCo/Co/Cu(001).

-6 -4 -2 0 2 4

-2

-1

0 CoS

Energy (eV)

Fig. 5. Calculated m-DOS of: (a) jmj 0, (b) jmj 1, and (c) jmj 2 in Fe/FeCo/Co/Cu(001).

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-600

-400

-200

0

200

400

600

800

MC

A E

nerg

y (

eV/c

ell)

Fe/FeCo/Cu(001) Fe/FeCo/Co/Cu(001)

Fe thickness (ML)

Fig. 6. Thickness dependent MCA energy of Fe/FeCo/Cu(001) and Fe/FeCo/Co/Cu(001). (For interpretation of the references to color in this figure caption, the readeris referred to the web version of this article.)the Fermi level because the DOS of majority spin states are quitesmall. This feature is insensitive to the Fe adlayer thickness and theexistence of Co underlayer. The spin magnetic moment is simply adifference in the number of electrons occupied in both spin bands

D. Kim et al. / Journal of Magnetism and Magnetic Materials 343 (2013) 262267266below the Fermi level and the character of wavefunctions isirrelevant. In contrast, the magnetic anisotropy is closely relatedto the orbital structure and this is the reason why the magneticanisotropy shows quite different behaviors although we find nosignificant change in magnetic moment. We have used the torquemethod [32], which provides very stable results even fewerk-points, to calculate the magnetic anisotropy. In Fig. 6, we havepresented the calculated magnetocrystalline anisotropy (MCA)energy. A positive value of MCA energy stands for perpendicularmagnetization to the film surface, whereas a negative one is for in-plane magnetization. In our previous studies, we investigated theinfluence of half monolayer Fe coverage at surface layer on themagnetic anisotropy [24], thus in this work we show combinedresults. The red open circle is MCA energy for Fe/FeCo/Cu(001) andthe blue one is for Fe/FeCo/Co/C(001), respectively. Without Feadlayer, the FeCo/Cu(001) has an in-plane magnetization, but aperpendicular magnetization is realized due to Co underlayer inFeCo/Co/Cu(001). In the presence of Fe adlayer, the SRT in bothsystems is observed up to 3 ML Fe coverage. One can see that themagnitude of MCA energy is affected by the presence of Counderlayer, but the direction of magnetization is not substantiallyaltered by Co underlayer.

In principles, one can analyze the MCA by calculating theorbital structures of occupied and unoccupied states at every k-point in an irreducible Brillouine zone. As an example, in Fig. 7, weshow the distribution of MCA energies over two-dimensionalBrillouin zone for four different structures. If the spinorbitFig. 7. Distributions of MCA energies of: (a) FeCo/Cu(001), (b) Fe(1 ML)/FeCo/(For interpretation of the references to color in this figure caption, the reader is referreinteraction between the unoccupied and occupied states at a givenk-point has a contribution to perpendicular magnetization, it isrepresented by a red circle, while the blue circle is for thecontribution to in-plane magnetization. The size of the circle isproportional to the magnitude of anisotropy energy. Usually, theanalysis of MCA can be done by exploring the structure of orbitalwave functions along high symmetry directions. However, asshown, the dominant contributions to MCA energy in momentumspace are neither completely localized nor completely dispersed.As a result, due to the uncertainty principle, it is not possible tosingle out a specific atom localized in real space in which the mostimportant contribution to the magnetic anisotropy is originated.Also, no dominant contributions along any particular direction arefound. These features imply that it is difficult to analyze the MCAin a simple manner.

Setting aside the issue of strength of MCA energy, the change ofmagnetization direction can be understood from the calculated m-DOS in a qualitative manner. In general, the perpendicular mag-netic anisotropy comes from two different spinorbit interactions;(i) spinorbit coupling in the same spin states if m 0 (ii) spinorbit coupling in the different states if m 71 and the in-planecontribution to magnetic anisotropy has also two different chan-nels; (i) spinorbit coupling from different spin states if m 0 (ii)spinorbit coupling from same spin states if m 71. As shownin Fig. 6, the FeCo/Cu(001) and the Fe/FeCo/Cu(001) show theopposite magnetic anisotropy. From the m-DOS of Fig. 2 for FeCo/Cu(001), one can see perpendicular magnetic anisotropy from anCu(001), (c) FeCo/Co(1 ML)/Cu(001), and (d) Fe(1 ML)/FeCo/Co(1 ML)/Cu(001).d to the web version of this article.)

D. Kim et al. / Journal of Magnetism and Magnetic Materials 343 (2013) 262267 267interaction between Fea (roughly 0.8 eV above the Fermi level) andCoa (roughly 0.3 eV below the Fermi level) in jmj 0 states andsimilarly in jmj 1 states. The contribution to perpendicularmagnetic anisotropy in jmj 2 states may be weak because thepeaks of DOS are rather suppressed and they are placed relativelyfar away from each other. On the other hand, in-plane contributionis expected from an interaction between jmj 0 and jmj 1 states.These two counteracting effects will be probably canceled outbecause a similar magnitude of magnetic anisotropy is expected.But, another in-plane contribution can be realized from an inter-action between jmj 1 and jmj 2. Consequently, in-plane mag-netization is realized in FeCo/Cu(001). In the presence of one ML ofCo underlayer as shown in Fig. 4, a substantial change occurs injmj 0 and jmj 2 states. The peak of jmj 0 state at 0.3 eV inFeCo/Cu(001) disappears due to Co underlayer and this results inthe suppression of in-plane contribution through m 71 inter-action. In contrast, the peak-to-peak separation in jmj 2 state isgreatly decreased and this causes enhanced perpendicular mag-netic anisotropy. Besides, the local peaks in jmj 1 states arefound near the Fermi level and this also contributes to perpendi-cular anisotropy. Due to these features, the Co underlayer inducesSRT even though the magnetic moment itself does not changesignificantly. For other systems, one can probably analyze thechange of magnetization direction by looking at the change of m-DOS. Overall, we have realized that both MCA energy andmagnetization direction are strongly dependent on film thicknessand interface geometry in low coverage regime.4. Conclusion

In summary, we have investigated the magnetic properties ofFe/FeCo/Cu(001) and Fe/FeCo/Co/Cu(001) films affected by Feadlayer thickness and Co underlayer. The buckling feature is foundin FeCo alloy layer only if there is no Fe adlayer. A typical surfaceenhancement of spin magnetic moment is observed in adlayer Featom. The FeCo alloy layer on Cu(001) has very large spinasymmetry at the Fermi level and this behavior is intact even inthe presence of Fe adlayer or Co underlayer. Despite this stablemagnetic state, the magnetic anisotropy is strongly altered by Fethickness and Co underlayer. For instance, an in-plane magnetiza-tion is observed in FeCo/Cu(001), but the Co under induces aperpendicular magnetic anisotropy in FeCo/Co/Cu(001). It is rea-lized that the magnitude of MCA energy is substantially influencedby Co underlayer, but the Fe adlayer plays an more important rolefor the SRT. This SRT can be nicely analyzed in terms of changes inorbital wavefunctions affected by Fe adlayer and Co underlayer.Acknowledgments

This research was supported by the Converging ResearchCenter Program through the Ministry of Education, Science andTechnology (No. 2012K001312) and by the Korea Center forArtificial Photosynthesis (KCAP) located in Sogang Universityfunded by the Ministry of Education, Science, and Technology(MEST) through the National Research Foundation of Korea (NRF-2011-C1AAA001-2011-0030278).References

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Spin reorientation transition of Fe/FeCo/Cu(001) and Fe/FeCo/Co/Cu(001)IntroductionNumerical methodNumerical results and discussionsConclusionAcknowledgmentsReferences