We give experimental and theoretical evidence of the Rashba effect at the
magnetic rare-earth metal surface Gd(0001). The Rashba effect is substantially
enhanced and the Rashba parameter changes its sign when a metal-oxide surface
layer is formed. The experimental observations are quantitatively described by
ab initio calculations that give a detailed account of the near-surface charge
density gradients causing the Rashba effect. Since the sign of the Rashba
splitting depends on the magnetization direction, the findings open up new
opportunities for the study of surface and interface magnetism.Comment: 4 Fig

E. I. Rashba

G. Bihlmayer

G. Kaindl

J. E. Prieto

K. Döbrich

K. Starke

O. Krupin

S. Blügel

S. Gorovikov

V. Moruzzi

English

arXiv

Crossref

Rashba effect at magnetic metal surfaces

Exchange-split two-dimensional electronic states at the magnetic Gd(0001) surface change their energy dispersion upon magnetization reversal owing to the Rashba effect. The Rashba parameter is found to be substantially enhanced and to change sign when an epitaxial metal-oxide surface layer is formed. The experimental observations are quantitatively described by ab initio calculations giving a detailed account of the near-surface charge-density gradients that are responsible for the Rashba effect

Krupin, O.

Bihlmayer, G.

Starke, K.

Gorovikov, S.

Prieto, K. C.

Döbrich, K.

Blügel, S.

Kaindl, G.

Juelich Shared Electronic Resources

Rashba effect at magnetic metal surfacesO. Krupin,1 G. Bihlmayer,2 K. Starke,1,* S. Gorovikov,3 J. E. Prieto,1 K. Döbrich,1 S. Blügel,2 and G. Kaindl11Institut für Experimentalphysik, Freie Universität Berlin, Germany2Institut für Festkörperforschung, Forschungszentrum Jülich, Germany3MAX-Lab, Lund University, SwedensReceived 28 March 2005; published 31 May 2005dExchange-split two-dimensional electronic states at the magnetic Gds0001d surface change their energydispersion upon magnetization reversal owing to the Rashba effect. The Rashba parameter is found to besubstantially enhanced and to change sign when an epitaxial metal-oxide surface layer is formed. The experi-mental observations are quantitatively described by ab initio calculations giving a detailed account of thenear-surface charge-density gradients that are responsible for the Rashba effect.DOI: 10.1103/PhysRevB.71.201403 PACS numberssd: 73.20.2r, 71.70.Ej, 72.25.2b, 85.75.2dA key topic in condensed-matter research aiming at futurespintronic devices is concerned with the control and manipu-lation of the electron spin in a two-dimensional electron gass2DEGd without the need to apply an external magneticfield.1 Rashba had realized early on2 that this can beachieved by an electric field that acts as a magnetic field inthe rest frame of a moving electron. The interaction betweenthe spin s of an electron, moving with momentum "k in anelectric field oriented along the z axis ez, is described by theRashba HamiltonianHR = aRsez 3 kd · s . s1dHere, aR is the so-called Rashba parameter, which is propor-tional to the electric field and depends further on the effec-tive, material-dependent, spin-orbit coupling sSOCd strength.A precondition for the Rashba effect is structural inversionasymmetry sSIAd, which naturally exists at any crystal inter-face or surface, and Rashba splittings have indeed been ob-served for surface states of Aus111d sRefs. 3 and 4d and othernonmagnetic surfaces.5,6 Although there is a close analogybetween the Rashba effect revealed by free-electron-likessp-d surface states and a 2DEG sRef. 7d, crystalline surfaceshave been found to exhibit no Rashba effect without thepresence of high-Z elements that give rise to substantialintra-atomic SOC sRefs. 3 and 4d. This indicates that thesurface-potential gradient alone is not a good measure of theeffective electric field that is responsible for the effect.3Experimental studies of the Rashba effect so far havebeen limited to semiconductor heterostructures8 and non-magnetic metal surfaces. This is surprising when one consid-ers sid the essential role of magnetic materials for spin injec-tion in the suggested spintronic devices and siid theindispensible ferromagnetic/nonmagnetic interfaces sFM/NMd in hybrid structures.9This Communication presents an experimental investiga-tion of two-dimensional electronic states in which exchangeinteraction and the Rashba effect coexist. We use the surfacestate of ferromagnetic Gd metal, as well as a FM/NM inter-face state between ferromagnetic Gd and a nonmagneticmetal-oxide surface layer, as examples to demonstratethat—in cases of dominant exchange interaction—theRashba contribution to the electron binding energy changessign upon magnetization reversal. We also find that theRashba parameter is substantially enhanced and reversedupon formation of the metal-oxide surface layer. These ob-servations are quantitatively described by ab initio calcula-tions, elucidating the role which charge-density gradient andorbital character of a two-dimensional state play for size andsign of the Rashba effect in real systems.To investigate the Rashba effect at magnetic surfaces, it isadvantageous to choose a ferromagnet that contains a high-Zelement, like the close-packed s0001d surface of Gd metal,which has large intra-atomic SOC together with a substantialvalence-band exchange splitting on the order of 0.5 eV sRef.10d. Angle-resolved photoemission sPEd experiments wereperformed using display-type electron analyzers at the I-311undulator beamline at MAX-Lab and the BUS beamline atBESSY II. The overall energy resolution was set to 30 meVfull width at half maximum sFWHMd, and the angular reso-lution to 0.5°. Gds0001d films were prepared in situ by metalvapor deposition on a Ws110d single crystal. The film thick-ness was 10 nm as determined by a quartz balance. Duringevaporation the pressure in the UHV chamber rose from 5310−11 to 5310−10 mbar. The epitaxial surface monoxidelayer was prepared on Gds0001d according to the recipegiven in Ref. 11 with a two-Langmuir oxygen exposure; itwas controlled in situ by PE and low-energy electron diffrac-tion sLEEDd. The PE spectra were recorded using rema-nently magnetized samples in the experimental geometry ofFig. 1scd.At the ferromagnetic Gds0001d surface, only the majoritycomponent S↑ of the d-derived surface state is occupied;12see PE spectrum in Fig. 1sad. At off-normal emission angles,the S↑ peak shifts significantly upon magnetization reversal.From a series of angle-resolved spectra for opposite magne-tization directions fcf. Fig. 1scdg, we derived the dispersionaround the center of the surface Brillouin zone sSBZd. It ispresented in Fig. 2sad, where red and black symbols mark theS↑ peak positions for opposite magnetization directions. Theenergy difference Deskd=Esk ,Md−Esk ,−Md, plotted in Fig.2scd, increases with k, in agreement with the triple-vectorproduct in the Rashba Hamiltonian fsee Eq. s1dg. We attributethe separation between peak positions for opposite M to thePHYSICAL REVIEW B 71, 201403sRd s2005dRAPID COMMUNICATIONS1098-0121/2005/71s20d/201403s4d/$23.00 ©2005 The American Physical Society201403-1Rashba interaction of electrons in the majority-spin surfacestate of Gds0001d. Although the states for opposite M do notexist simultaneously, De in Fig. 2scd is equivalent to theRashba splitting at a nonmagnetic surface, and we shall referto it as Rashba “splitting” in the following.The ps131dO/Gds0001d surface oxide exhibits anexchange-split pair of occupied two-dimensional bands,11shown as S↑ and S↓ in Fig. 1sbd. Their dispersions are pre-sented in Fig. 2sbd, revealing that the peak positions, upon Mreversal, shift into opposite directions and antisymmetricallywith respect to the SBZ center. Figure 2sbd shows as wellthat DEex is much larger than the Rashba splitting De, i.e.,HR can be regarded as a k-dependent sperturbatived energycorrection. Thus, basically the spin remains a good quantumnumber and the spin polarization of the two-dimensionalstates are discussed either as spin up or down states.The qualitative differences in appearance between theRashba effect in magnetic and nonmagnetic systems arehighlighted in Fig. 3, using the nearly-free-electron sNFEdmodel. In nonmagnetic systems, the Rashba interaction splitsthe spin-degenerate surface state irrespective of the orienta-tion of the in-plane momentum, fsee Fig. 3sadg. In magneticsystems, by contrast, the electron spins are oriented along aquantization axis by exchange interaction—we chose the yaxis in Figs. 3sbd–3sdd and 3sfd—and HR in Eq. s1d becomesanisotropic; the Rashba interaction vanishes for k i s sk iMd,and only the exchange splitting remains along ky fsee Fig.3scdg. Yet, for any other k, both exchange and Rashba split-ting become visible, most pronounced along kx fsee Fig.3sbdg. When the magnetization is reversed, the spin s andwith it the triple-vector product in Eq. s1d change sign; thedispersion changes from black to sdottedd red fsee Fig. 3sddg.Hereby the NFE model qualitatively reproduces the experi-mental behavior shown in Fig. 2sbd.The corresponding Fermi contours are compared in Figs.3sed and 3sfd. In nonmagnetic systems, the Rashba effectresults in an isotropic splitting of the NFE parobola and theFermi contour splits into a pair of concentric rings.3 The spinis, in absence of any other interaction, always oriented per-pendicular to the k vector fcf. Fig. 3sedg. By contrast, inmagnetic systems with dominant exchange interaction as inGds0001d and ps131dO/Gds0001d, it is the exchange split-ting that leads to a pair of concentric Fermi contour rings ofmajority slargerd and minority ssmallerd spin electrons. Thespin polarization remains practically 100% as in the limitingcase of vanishing Rashba interaction. A finite Rashba inter-action simply shifts the majority and the minority Fermi con-tours into opposite directions fcf. Fig. 3sfdg.For direct comparison, we plot in Fig. 2scd the Rashbasplitting De for S↑ and S↓ of ps131dO/Gds0001d togetherFIG. 1. sColor onlined sad and sbd Angle-resolved PE spectrarecorded at 6° electron-emission angle with respect to the surfacenormal ez: sad Majority-spin surface state S↑ of Gds0001d sexcitedwith hn=36 eVd; sbd exchange-split two-dimensional states S↑ andS↓ of ps131dO/Gds0001dshn=45 eVd. Owing to the Rashba ef-fect, all peak positions change upon magnetization reversal sseetextd. scd Experimental geometry.FIG. 2. sColor onlined Experimental dispersion of the sadmajority-spin surface state of Gds0001d along G¯ -M¯ and sbdexchange-split majority spin sS↑d and minority spin sS↓d states ofps131dO/Gds0001d along G¯ -K¯ . The exchange splitting DEex is450 meV at the SBZ center. Red and black symbols: opposite mag-netization directions. scd Rashba “splitting” De obtained from thedata in sad and sbd; , snd symbols refer to majority sminorityd spinstates.FIG. 3. sColor onlined NFE model showing the qualitative dif-ference between the Rashba effect at sad and sed a nonmagnetic andsbd-sdd and sfd a FM surface sinterfaced in the x ,y plane, with anin-plane magnetization M iy. For details, see text.KRUPIN et al. PHYSICAL REVIEW B 71, 201403sRd s2005dRAPID COMMUNICATIONS201403-2with the one for S↑ of Gds0001d. De shows a substantialenhancement sby a factor of 3d upon oxide-layer formation.Moreover, the Rashba parameters of the majority O/Gd in-terface states and of the majority metal surface state haveopposite signs. Obviously, electrons in the interface state aresubject to an effective sspatially averagedd crystal electricfield that is significantly larger and opposite to the effectivefield responsible for the Rashba effect at Gds0001d. We findfurther that the Rashba “splitting” is opposite for the S↑ andS↓ states of ps131dO/Gds0001d, supporting that it is reallythe Rashba effect that we observed.To understand the Rashba effect for Gds0001d andps131dO/Gds0001d and their strikingly different splittingsin a quantitative way, we performed ab initio calculationsusing density-functional theory sDFTd in the local-densityapproximation sLDAd.13 We used the full-potential linearizedaugmented-plane-wave method in film geometry,14,15 whereSOC was included self-consistently according to Ref. 16. Fora proper description of the 4f electrons, the LDA+U methodwas applied.17 The Gd surface was simulated by a structur-ally relaxed 10-layer film embedded in two semi-infinitevacua. A plane-wave cutoff of kmax=3.8 a .u.−1 was used, andthe irreducible part of the SBZ was sampled at 36 k points. Itis important to note that the in-plane magnetization lowersthe p3m1 symmetry of hcp Gds0001d to cm symmetry. Usinga pseudohexagonal notation, one can still label the high-symmetry points of the SBZ as M¯ and K¯ , keeping in mindthat opposite points of the hexagonal SBZ in Fig. 4sad areequivalent if one interchanges spin-up and spin-down bands.The magnetization was assumed to point in the direction ofthe in-plane nearest neighbors.The calculated dispersion of the states of Gds0001d andps131dO/Gds0001d, presented in Figs. 4sad and 5sad, is ingood agreement with the experimental data ssee Fig. 2d evenin details18 such as the curvature of the states, the size of theRashba splitting, and the sign reversal of the Rashba constantupon oxide-layer formation fcompare Fig. 2scd with left partsfor clean Gdd or right part sfor 0/Gdd of Fig. 5sbdg.In Figs. 4sbd and 5scd the charge-density distributions ofthe two-dimensional states are displayed in a plane perpen-dicular to the surfaces. In the calculation ofps131dO/Gds0001d, the O atoms were “adsorbed” on thefcc site, and their relaxed positions were found 0.78 Å abovethe plane of the Gd surface atoms, s-Gd. The s-Gd layershows a strong s18%d outward relaxation upon O adsorption,while the positions of the inner layers remain almost thesame. We note that similar results were obtained for O ad-sorbed on the energetically slightly less favorable hcp site. Inother words, ps131dO/Gds0001d consists of an O/Gd mon-oxide layer that is quite separated from the nearly unper-turbed Gds0001d metal.The charge-density distribution in Fig. 4sbd shows that theGds0001d surface state is localized almost exclusivelysto ,89%d in the metal surface layer, s-Gd. It appears to bealmost symmetric with respect to the surface plane, reflectingthe rather pure dz2 character.17 In fact, the charge gradient issmall: the calculation yields an admixture of pz charactersantisymmetric with respect to the surface planed with a d : pratio in the s-Gd layer of approximately 8:1 sintegrated overthe muffin-tin sphered.Upon oxide-layer formation, the charge distribution of theentire near-surface region changes drastically. Figure 5scdshows that the two-dimensional state of ps131dO/Gd is dis-tributed over the whole region between the O/Gd surfacemonoxide layer and the ss−1d-Gd layer; hence, this state canbe conceived as an interface state. The electronegative Oatom attracts charge not only from the s-Gd atom but alsofrom the interface region so that steep charge-density gradi-FIG. 4. sColor onlined sad Calculated majority-spin surface-statedispersions of Gds0001d along two different high-symmetry direc-tions sshown as red linesd of the magnetic SBZ, given as inset.Hatched areas indicate bulk band regions. sbd Charge-density distri-bution for S↑ at the SBZ center in a plane perpendicular to thesurface. The linear color scale ranges from red shigh charge den-sityd, yellow smediumd, green slowd, blue svery lowd, to white sneg-ligibled. Isolines: log scale.FIG. 5. sColor onlined sad Calculated surface-state dispersions ofps131dO/Gds0001d along the high-symmetry directions G¯ -M¯sleft-hand sided and G¯ -K¯ sright-hand sided of the SBZ. sbd Rashba“splittings” De for majority and minority bands. Symbols and no-tation are as in Fig. 4.RASHBA EFFECT AT MAGNETIC METAL SURFACES PHYSICAL REVIEW B 71, 201403sRd s2005dRAPID COMMUNICATIONS201403-3ents arise in both the s-Gd layer and the subsurface layer. Toidentify the main contribution to the Rashba effect, weswitched off the SOC in the calculation for individual layers.In this way we found that the ss−1d-Gd layer accounts forover 70% of the total Rashba splitting at ps131dO/Gd. Thedominant role of the ss−1d-Gd layer becomes obvious fromthe asymmetric probability distribution in Fig. 5scd; the cal-culation gives a high admixture of pz character fd : p<5:1,integrated over the ss−1d-Gd muffin-tin spheresg.With the present results, we arrive at the following physi-cal picture of the Rashba effect: The charge-density profilesof Gds0001d and ps131dO/Gds0001d show that there is aclose link between the Rashba effect of a two-dimensionalstate and the asymmetry of the charge distribution. Theasymmetry directly reflects the effective electric field anelectron experiences in that state; it is responsible for theRashba effect. The small positive effective electric field inthe s-Gd layer of Gds0001d gives rise to the small Rashbasplitting. At ps131dO/Gds0001d, the rather asymmetriccharge distribution of the interface state in the ss−1d-Gdlayer directly reveales the presence of a high effective elec-tric field in this layer. The charge gradient is negative, i.e.,opposite to the uncovered metal surface. We are led to con-clude that it is this reversed effective electric field in thess−1d-Gd layer that causes the sign change of the Rashbaparameter when going from Gds0001d to ps131dO/Gds0001d.In summary, we present here an experimental and theoret-ical study of the Rashba effect in systems where Rashba andexchange interaction coexist. We demonstrated that theRashba effect is closely linked to the asymmetry of the wavefunction that serves as a monitor of the value of the effectivepotential gradient causing the Rashba effect. We suggest toutilize the spin sensitivity of the Rashba effect in magneti-cally ordered systems to study two-dimensional spin struc-tures at surfaces and interfaces. The present findings can beof interest for spintronic devices, especially at FM/NM inter-faces where Rashba and exchange interaction together con-trol the electron spin.We gratefully acknowledge experimental support by J.Andersen sMAX-Labd and R. Püttner sBUS beamline,BESSYd. The work in Berlin was supported by BMBF, Con-tract No. 05 KS1 KEC/2, and DFG sSfB-290d.*Corresponding author: Electronic address: starke@physik.fu-berlin.de1 S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton,S. von Molnar, A. Y. Chtchelkanova, M. L. Roukes, and D. M.Treger, Science 294, 1488 s2001d.2 E. I. Rashba, Sov. Phys. Solid State 2, 1109 s1960d.3 S. LaShell, B. A. McDougall, and E. Jensen, Phys. Rev. Lett. 77,3419 s1996d.4 F. Reinert, G. Nicolay, S. Schmidt, D. Ehm, and S. Hüfner, Phys.Rev. B 63, 115415 s2001d.5 E. Rotenberg and S. D. Kevan, Phys. Rev. Lett. 80, 2905 s1998d.6 M. Hochstrasser, J. G. Tobin, E. Rotenberg, and S. D. Kevan,Phys. Rev. Lett. 89, 216802 s2002d.7 J. Henk, A. Ernst, and P. Bruno, Phys. Rev. B 68, 165416 s2003d.8 I. Zutic, J. Fabian, and S. D. Sarma, Rev. Mod. Phys. 76, 323s2004d.9 C. H. Li, G. Kioseoglou, O. van’t Erve, A. T. Hanbicki, B. T.Jonker, R. Mallory, M. Yasar, and A. Petrou, Appl. Phys. Lett.85, 1544 s2004d.10 The large exchange splitting allows one to avoid the natural limi-tation in studies of nonmagnetic systems, where the Rashbasplitting of a state, to be observed, must be on the order of itswidth sRef. 4d.11 C. Schüssler-Langeheine, R. Meier, H. Ott, Z. Hu, C. Mazumdar,A. Y. Grigoriev, G. Kaindl, and E. Weschke, Phys. Rev. B 60,3449 s1999d.12 E. Weschke, C. Schüssler-Langeheine, R. Meier, A. V. Fedorov,K. Starke, F. Hübinger, and G. Kaindl, Phys. Rev. Lett. 77, 3415s1996d.13 V. Moruzzi, J. Janak, and A. Williams, Calculated ElectronicProperties of Metals sPergamon, New York, 1978d.14 E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, Phys.Rev. B 24, 864 s1981d.15 For program description see http://www.flapw.de16 C. Li, A. J. Freeman, H. J. F. Jansen, and C. L. Fu, Phys. Rev. B42, 5433 s1990d.17 P. Kurz, G. Bihlmayer, and S. Blügel, J. Phys.: Condens. Matter14, 6353 s2002d.18 The exchange splitting is somewhat larger than the experimentalvalue, an overestimation that had been noted before forGds0001d sRef. 17d.KRUPIN et al. PHYSICAL REVIEW B 71, 201403sRd s2005dRAPID COMMUNICATIONS201403-4

Rashba Effect at Magnetic Metal Surfaces

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