Interference of spin states in photoemission from Sb/Ag(111)

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by  Fabian Meier

Interference of spin states in photoemission from Sb/Ag(111)
Fabian Meier1,2, Vladimir Petrov3, Hossein Mirhosseini4, Luc
Patthey2, Ju¨rgen Henk4, Ju¨rg Osterwalder1, and J. Hugo Dil1,2
1Physik-Institut, Universit¨at Zu¨rich, Winterthurerstrasse 190, CH-8057 Zu¨rich, Switzerland
2 Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen, Switzerland
3St. Petersburg Polytechnical University, 29 Polytechnicheskaya St, 195251 St Petersburg, Russia
4Max-Planck-Institut fu¨r Mikrostrukturphysik, D-06120 Halle (Saale), Germany
(Dated: January 27, 2010)
Usingathree-dimensionalspinpolarimeterwehavegatheredevidencefortheinterferenceofspin
states in photoemission from the surface alloy Sb/Ag(111). This system features a small Rashba-
type spin-splitting of a size comparable to the linewidth of the quasiparticles, thus causing an
0 intrinsic overlap between states with orthogonal spinors. Besides a small spin polarization caused
1 by the spin-splitting, we observe a large spin polarization component in the plane normal to the
0 quantizationaxisprovidedbytheRashbaeffect. Stronglysuggestiveofcoherentspinrotation,this
2 effect is largely independent of the photon energy and photon polarization.

n
PACSnumbers: 73.20.At,71.70.Ej,79.60.-i
a
J

7 Animportantbranchofspintronicsresearchislooking (a) quasi- (b)
2 paricles
for new systems with naturally existing spin polarized up down overlap (:2)
] electronsandwaystomanipulatetheirspins. Thebroken γ
r spacial inversion symmetry at surfaces can induce a spin experimental
e broadening
h splittingofelectronicstatesinnon-magneticsystemsvia
t the spin-orbit interaction. A substantial splitting due to measured measured z
o
. thisso-calledRashbaeffect1 was observedfortheShock- states polarization y x
t ley surface state on Au(111) by angle-resolved photoe-
a
m missionspectroscopy(ARPES)2. Laterspin-resolvedex- (c) -0.4 -0.2 0.0 0.2 0.4 (d) -0.4 -0.2 0.0 0.2 0.4
FIG. 1: (color online) (a) and (b) Sketch of the suggested
periments confirmed the high degree of spin polarization
[cond- oiFofnofnergrtmAhehvegeiel(sein1ucle1arlc1flata)srrcpgoheeinsanr.svsseMptphraiouontrcttertosaupreecrmlicteteesittdnittntaemlgdnys,ug,fsecreunhoxrtmfpaiaatltclotheeittenoaistnlteilghoosnyetasatiwtconeofostmB3hs,bipeoaiinnsbneasdsateprirPoclvihbnt- msselteypixcaepicdncieohts-vassatettpnoariiIntensity (arb. units)olitntasnehmpspei.oxxxnb-s===l0lAtete100a.e2ra...tr076rowcd55ifzn oeieangnre0teglvn.iyn0oocttnlouoehv.taeeis0l2roop.s(4l2nΓapan ieMnp)iVgwnpSt-piiuthmnohpeglPolarizationaatymlar--hl00000in.....dzee11022sdaaipertsiexsiunocp-p0rtni.ee2sinordp-iindlnmsiotp(e0twtve.in0hnicntoetgalrqelaxwtub,20z/4a.iar2-Γdt seopMhaViRalpradaiaknnesrethgntrirbicibnanalyyge--
1 of strong atomic spin-orbit interaction of the heavy met- curve), and a cohkex r(Åe-1n)tly rotated spin polarikzxa (Åt-i1o)n within the
v als with structural effects enhancing the local potential xz-plane(green/lightgraycurve). (b)Illustrationoftheasso-
7 gradients at the surface4,5. ciatedspinpolarizationvectorsinoneregionofthespin-split
2
circular Fermi surface.
9 In this Letter we discuss the structurally related sys-
4 tem of Sb on Ag(111) which has a small but finite spin
. splitting6. The splitting is so small that it cannot be re-
1
0 solved by ARPES in most of the surface Brillouin zone. ized light from magnetized Gd by Mu¨ller et al.7. In this
0 Our spin-polarized ARPES data show nevertheless sub- system,orthogonalspinstatescanbepreparedbythean-
1 stantialspinpolarizationandpermittoquantifythespin gular momentum transfer from the light and spin-orbit
v: splitting. More importantly, the measured spin texture interaction on one hand, and by direct photoemission
i isatstrongvariancewiththatexpectedfromtheRashba from magnetized states in the valence band on the other
X
model and suggests that coherent superposition of spin hand. By tuning the photon energy to the 4d resonance,
ar statesoccurinthephotocurrent. Itisanintriguingprop- the two spin states can be brought to interfere. In our
ertyofquantummechanicsthatspinstatescaninterfere, case it is the Rashba effect that defines the two orthog-
hence the expectation value of the sum of two spinors onal spin states, and we argue that they interfere when
candifferfromthesumoftheindividualexpectationval- their energy or momentum splitting is of the same or-
ues. In particular, the addition of a spin-up and a spin- der as the intrinsic line width of either state, as is illus-
down spinor along some quantization axis does not yield tratedinFig.1. Intheoverlappingregionthequasiparti-
zero polarization, but results in a spinor with an expec- cles formed by the photohole states in the two spin-split
tation value (henceforth spin polarization) placed within bands are indistinguishable in time and space, and the
the plane orthogonal to the quantization axis. This is corresponding photoelectrons should thus represent co-
exactly what we observe. herent superpositions as reflected in spin space.
Spin-state interference has previously been observed Like in the related Bi and Pb surface alloys on
in resonant photoemission induced by circularly polar- Ag(111), the Sb adatoms replace every third Ag atom
2
√ √
ipnerstthreucttouprme8o,9s,thleanyceerfotrothfotremrmead(Sb3/A×g(1131))R.30M◦ixseud- 45° hν sample (a) units) (c )Itot 2Γ4M eV
Stloubyt1se−dxthBbeyixs/BpAii,ng(w1sep1rl1ei)ttalianlsygoercisna,vnwesbhteeigraeetnSehdba.niscIenrda1sn0ud,1co1hm, mlaynixdseudbthsateliy-- e z x ky ntensity (arb. IIyy,,udpn
can therefore serve as a test for our overlap hypothesis. kx I
Finally,photoemissionexperimentswerecarriedoutwith -0.3-0.2-0.10.0 0.1 0.2 0.3
kx (Å-1)
ddonieffrTtethhroeeenspetsrpoppbiahnero-apttmhooenleadtreeienzrpesee.rdngidAeesnRacPneEdoSfpthh(oSetAsopnRinPpEsotlSaa)treizeiaxntptieoernrfiemirneennoctres- ng energy (eV)-0000....2024 (b) spz pxΓyM Polarization-000...101 (d) 2Γ4M eV PPPxyz
were performed at room temperature at the Surface di0.6
and Interface Spectroscopy beamline at the Swiss Light Bin0.8 -0.2
SourceofthePaulScherrerInstituteusingtheCOPHEE -0.3-0.2-0.10.0 0.1 0.2 0.3 -0.3-0.2-0.10.0 0.1 0.2 0.3
kx (Å-1) kx (Å-1)
spectrometer.12 The energy and angle resolution when
measured with the Mott detectors was 80 meV and ± FIG. 2: (color online) (a) Schematic experimental setup.
0.75◦, respectively. The photoemission setup is schemat- (b) Spin integrated surface state band structure of the
ically shown in Fig. 2 (a). There is a 45◦ angle between Sb/Ag(111) surface alloy around 1Γ¯.0. (c) Spin resolved and
24 eV ΓM
the incoming photons and the detected electrons. The spin integrated (inset) MDC inten0s.5ity data for 24 eV pho-
z axis is given by the sample normal and the sample is tons in the directionΓ¯M¯ at Eb =Pz00..06 eV. (d) Simultaneously
obtained spin polarization curves for all three components.
rotated around the y axis. In a momentum distribution
-0.5
curve (MDC) this corresponds to a scan along the k
x -1.0
axis with k =0 as shown in Fig. 2 (a) for schematically -1.0 -0.5 0.0 0.5 1.0
y
Px
drawn circular constant energy surfaces.
showmodulationswithsmalleramplitudes,withthosein
Sample preparation was carried out in situ under ul-
P being rather in phase with those in P . On the other
trahigh vacuum conditions with a base pressure better z x
hand, P crosses the zero line at the peak centers, which
than 2×10−10 mbar. The Ag(111) crystal was cleaned y
is typical of Rashba-type behaviour13. From this latter
by multiple cycles of Ar+ sputtering and annealing. A
curve we can produce the spin-resolved spectra as pro-
total amount of Sb corresponding to 1/3 of a monolayer
jected onto the y axis16, which corresponds to the spin
was evaporated from a calibrated evaporator at a pres-
quantization axis in the Rashba model (Fig. 2 (c)). The
sure below 4×10−10 mbar followed by an annealing at
spin-resolved MDCs I and I show a clear signa-
T ≈ 300◦ C. The sample quality was confirmed by low- y,up y,dn
√ √
tureofaRashba-typespin-orbitsplittingwithamomen-
energyelectrondiffraction,whichshowedsharp 3× 3-
tum shift dk = 2k ∼= 0.01 ˚A−1 between the two bands
spots, and ARPES. For the mixed alloys the deposition 0
(as obtained from fitting the two main peaks).
of Sb and Bi was simultaneous with a total amount of
Another remarkable observation in these data is that
1/3 monolayer.
the measured spin polarization curves violate time-
In Fig. 2 (b) we show the spin integrated surface state
reversal symmetry. According to this symmetry, the two
band dispersion of the Sb/Ag(111) surface alloy around
Γ¯ measured along Γ¯M¯. Similar to the two related sur- spin-split partners of the Kramers pairs should have op-
fbHsamaocnwaedlelasevlrleaorary,ensdtoBhbieis/seAnRrovgate(s1dhr1e,bs1ato)e-ltrvaymenpddeediPnsibpnt/ihnAeangsda(pa1lltoi1atg1ty)oin4f,ag5Fs,1ii3gss,.phtz2we(aroben)sd.emtTpusxhcoyhef.ensity (arb. units) 24peTtc ieruooVhgrsneivieteosmes,fsiPaips.sxeipin.nhagponPotdtoΓli(aMemPkrmiz(cid:107)ezPolarizationi)-aasr-tser000=iie...v101ooenns2r−Γy4sMvr maePeeVllcma(ts−toyeertkmdsr(cid:107)imfec)off.erwetecriYtqtyhe,utisiPPP,rsvixyzenatasclhpPezeesne-t1000tctr....ip0505tmobonti2elno4ga- derrkVeiiiznnxvadge=triiecsona0an--Γ.lM
smaller splitting can be understood as a consequence ofInt symmetry has to h-0o.2ld for the quasiparticl-e1.0wave func-
thesmalleratomicnumberZ ofSb(Z =51)comparedto -1.0 -0.5 0.0 0.5 1.0
-0.3t-i0o.2n-0s..10W.0 e0.1s0u.2gg0.e3st tha-t0.3t-h0.2e-0o.1ri0g.0in0.1o0f.2th0.i3s photoemisPxsion
Bi(83)andPb(82)andasmallersurfacecorrugation6,14. kx (Å-1) kx (Å-1)
effectisthespin-stateinterferencecausedbytheintrinsic
santnernBdutic)/ot.ArutIrghne(os1F1g13oi1,gn)sia..ela2.nttod(hdte)Phwsbep/eieAnglegipcv(to1erl1oaS1nrA)izRmsahPtoioEmownSeniRdstaaumtsmahabion(abPl-yttyayiipncnoeepmdslappfnooiner-nsity (arb. units) (aosd)pvoieTwnrhnlasepspplciiiotnnthoienerrag2el4c.eΓn ehaKVtdKssPolarizationurtpa-o00000me.....10123areps(rbops)siniptaisoitrnataoesfswoaictihsaptaPPPienxyzds-puPwzipn-i1000t....p0505ahno2ltd4ah erVeaizsasmtpiiaonln-ΓlK
S24b/eAVg((1i1.e1.) alitghEtbp=ol0a.r6izeaVtiownitihnpt-hpeolxazrizpeldanpeh)o.toHnseroef,Inte vector normal to th--00e..23spin polarization of t-h1.e0-1.i0n-d0.5iv0i.d0u0a.5l 1.0
the spin polarization component P is dominant, corre- -0.3s-p0.2in-0o.1rs0..0 0F.1o0r.2i0n.3stance-,0.3a-0n.2-e0.l1ec0.t0r0o.1n0.w2i0t.3h its spin aPlxong
atvssrputiaarotstfnhatiodectnieonpsfg.ertaohItktmeopsothtothhoshewieetrisrRoasnladayssirshagotlbeefamdtmhimsreo1e5odcMdtuaielDonaln.dCtiPoosr.nefyxpTtaarhhmenesidspecnliPoisttnzsuisndcatoeasmsmnhtacaperjeopnonnrteceerodnrgenteyds--ensity (arb. units) (c)tw(cid:0)bph1heie,tawh0sp(cid:1)ersoik+ptdxs t(iiÅi(cid:0)nefft-01nis)ev,r1eaae(cid:1)2lsno8zΓ =cn√eKVega2(cid:10)bxty·Polarizationiehs↑(cid:10)te(cid:12)(cid:12)000xw...c+210↑yea(cid:12)(cid:12)e(cid:10)n(and=yx)↓b(cid:10)i(cid:0)(cid:12)(cid:12)sey1,.↑,Srr(cid:12)(cid:12)−eeikamapxi (nd(cid:1)rÅied-il1=na)ser(cid:10)glny(cid:10)y√ty↓,e(cid:12)(cid:12)↑PPPa2d(cid:12)(cid:12)xyzc·s+abp(cid:10)Puzyzies-n1000↑ie....30505(cid:12)(cid:12)tsaπw=l/a2oo82n re(cid:0)(cid:10)gVos1ypt,x↓ai1(cid:12)(cid:12)nt(cid:1)c.ioaor=AnnsΓK
Int -0.1 -1.0
-1.0 -0.5 0.0 0.5 1.0
-0.3-0.2-0.10.0 0.1 0.2 0.3 -0.3-0.2-0.10.0 0.1 0.2 0.3 Px
kx (Å-1) kx (Å-1)
nsity (arb. units) (e) 20Γ eKV Polarization000...210 (f) PPPxyz Pz-1000....0505 20 eV ΓK
e
Int -0.1 -1.0
-1.0 -0.5 0.0 0.5 1.0
-0.3-0.2-0.10.0 0.1 0.2 0.3 -0.3-0.2-0.10.0 0.1 0.2 0.3 Px
kx (Å-1) kx (Å-1)
nsity (arb. units) (g) 24 eV CL ΓM Polarization000...210 (h) 24 eV CL ΓM Pz-1000....0505 24 eV ΓM
e
Int -0.1 Px Py Pz -1.0-1.0 -0.5 0.0 0.5 1.0
-0.3-0.2-0.10.0 0.1 0.2 0.3 -0.3-0.2-0.10.0 0.1 0.2 0.3 Px
kx (Å-1) kx (Å-1)
nsity (arb. units) 24 eV ΓK Polarization000...420 24 eV ΓK Pz-1000....0505 24 eV ΓK
Inte -0.2 -1.0
-1.0 -0.5 0.0 0.5 1.0
-0.3-0.2-0.10.0 0.1 0.2 0.3 -0.3-0.2-0.10.0 0.1 0.2 0.3 Px
kx (Å-1) kx (Å-1)
ensity (arb. units) (a) 24Γ eKV Polarization-0000....4202 (b) PPPxyz Pz-1000....0505 24 eV ΓK
Int -0.4 -1.0
-1.0 -0.5 0.0 0.5 1.0
-0.3-0.2-0.10.0 0.1 0.2 0.3 -0.3-0.2-0.10.0 0.1 0.2 0.3 Px
kx (Å-1) kx (Å-1)
3
of the resulting spin polarization vector in the xz plane. (a) -0.4 -0.2 0.0 0.2 0.4
dswFtiieargTletl.ceh1tdseley(amfiarbn)eo.eedsdWpae,lpleitptielwllrbiueemysrdtee2rdtankot0ouettp∼=dhaebai0ncnl.ea0dFs1teiodg˚Aoosm−w.fe11Snabas(o/unanAr)degtatt(hnhh1ede1ei1uri()npbs.tp)prHeiicnnreaosrnlireecs,fntltaiohnroweeef ntensity (arb. units) xxx===000...02355 24Γ eMV Intensity(arb. units) IICPL (d)
widthofthesepeaksduetoexperimentallimitationsand I
-0.2 0.0 0.2
thelimitedsamplequality,butarealisticlowerboundary
(b) -0.4 -0.2 0.0 0.2 0.4
ifsorgiAveun(1b1y1)avaatluneoromf4a0l emmeiVssiaotnro2o1mmteeVmpweerraeturreep,osrintecde 0.2 ΓM 0.4 (e)
n 24 eV n
(at 30 K)17, and away from normal emission more than atio0.1 atio0.2
4va0lumeetVrawnselraetemseinatsouraendi(nattri6n0sicKm)1o8m. eInntuthmebMroDaCde,ntihnigs Polariz-00..01 Polariz0.0
of 0.01 ˚A−1 when applying the group velocity measured -0.2 Px -0.2 PPxz P
atabindingenergyof0.6eV.Thereisthusclearlyalarge
-0.2 0.0 0.2
intrinsic overlap between the two peaks. The peaks can (c) -0.4 -0.2 0.0 0.2 0.4 0.4 (f)
tshpeinndboewndiavniddedaninovreerglaiopnrsegwioitnh(uppupreelryrisgphint)uinp,orpduerretlyo n0.1 Pz zation0.2
oCbotnasiindetrhiengsctehnaatritoheshcoowhenreonnttahdedliotiwoenrolfefttwoofoFrtigh.o1go(naa).l olarizatio0.0 Polari-00..02 Px CL
spinorshasaspinpolarizationvectorintheplanenormal P ΓM Pz
to the spin polarization of the initial spinors as shown -0.1 24 eV -0.4 -0.2 0.0 0.2 0.4
in Fig. 1 (b), spin polarization curves like those on the -0.2 0.0 0.2 kx (Å-1)
lower right of Fig. 1 (a) are obtained. In particular, the kx (Å-1)
spin polarization of the overlap region has components
FIG. 3: (color online) (a) Spin-integrated MDC data of
P and P with their maxima at the point of maximum
x z Sb Bi /Ag(111) for x = 0, 0.25 and 0.35 at E = 0.6 eV
overlap, i.e. centered on the MDC peak. The direction 1−x x b
(x=1) and 0.9 eV (x=0.25 and 0.35). For better compar-
ofthespinpolarizationinthexz plane, describedbythe
ison, the k scale for the x = 0 sample (top curve) is given
x
angle γ, is defined by the phase difference between the on the upper side of the frame, while the scale for x = 0.25
two orthogonal spin states of the Kramers pair. From and 0.35 samples is given on the lower side . The arrows
theobservationthattheP andP curvesaresymmetric refer to the corresponding k scale. (b) and (c) Spin polar-
x z x
with respect to kx = 0 ˚A−1 (Fig. 2 (d)), we conclude izationdataPx andPz correspondingtothesamesamplesas
that corresponding states of opposite k have equal spin in (a). Note again the different k-scales. (d)-(f) Fully rela-
x
rotationangles. Forthesp stateswemeasureγ =22◦± tivistic spin-resolved one-step photoemission calculations for
z
9◦, for the p states the value is −25◦±10◦. Sb/Ag(111) at Eb = 0.6 eV and hv = 21.2 eV. (d) The to-
xy tal (spin-integrated) photoemission intensity for p-polarized
In Fig. 3 (a)-(c) we show SARPES data for Sb Bi
1−x x (IP)andforcircularleftpolarizedlight(ICL). Spinpolariza-
forx=0,0.25and0.35. Fromthespinpolarizationdata tion curves P and P for (e)p-polarized and (f) circularleft
x z
Py (not shown) we find that the spin-splitting increases polarized light.
asSb/Ag(111)isdopedwithBifrom2k =0.01forx=0
0
to 2k =0.019 ˚A−1 for x=0.35. The amplitudes of the
0
spin polarization curve P (and P ) decrease markedly
x z
as the splitting is increased. We thus observe a decrease polarization curves in the xy plane (cf. Fig. 2 (d)). The
in the measured spin polarization in the plane normal to experimentalspinpolarizationamplitudesarelargerand
the spin quantization axis of the quasiparticles as their the shapes of the curves are very different. A change of
splitting gets larger and the intrinsic overlap is reduced. the photon polarization to circular left leads to drastic
This is fully in line with our model. changes in the predicted spin polarization curves, shown
We performed fully relativistic spin-resolved one-step in Fig. 3 (f).
photoemission calculations for x = 0, with p-polarized Ingeneralsuchcalculationsareingoodagreementwith
and circular left polarized light using the experimental the experimental data19. The dramatic failure in the
geometry. Fig. 3 (d) shows the (spin-integrated) inten- present case indicates that an important ingredient is
sities for these two light polarizations. The two strong missing in the theoretical description. Specifically, the
peaks nearest to k =±0.1 ˚A−1 represent emission from calculations do not capture coherent initial state effects
x
sp states,whilethesplitpeaksat|k |>0.2˚A−1 aredue asthequasiparticlesaredescribedbyanon-localspectral
z x
to p emission. Fig. 3 (e) shows the spin polarization density, which is an incoherent superposition of initial
xy
curves P and P for p-polarized light. While the curve states. Hence, thedisagreementbetweenthedatashown
x z
forP (notshownforbetterviewingclarityofP andP ) in Fig. 2 (d) and the curves in Fig. 3 (e) may also hint
y x z
is in good agreement with the experimental data, there at a coherent effect in the initial states.
is neither quantitative nor qualitative agreement for the Spin polarization observed in photoemission data can
4
Intensity (arb. units) (a) 24Γ eKV (c) 28Γ eKV (e) 20Γ eKV ((gg)) 2244 eeVV CCLL ΓM Ttnphehhegoeatptoleionvacekeasnl(,peeraoxgnstyidrteidvameerpa)eefpnfoodorrseitntPhcivxeeeo((uF(Pntizgee)rg.aa4otrni(evebes)a).,lwf(Todahr)yestahancebdesni(netfnne)cre)eerdruoaflnoednas
Polarization---0000000.......3310122 (b) PPxz -0000....2101 (d) PPxz -0000....2101 (f) PPxz -0000....1021 (h) PPxz ofifrunotamlapst-sapttroeolsan.rgizMceodonstttoriscbtiurrictkuioilnnagroliefsftstphpieonl-fiaornribdzeiitndgcliotguhhpatlti(nFagigci.hn2ant(hdgee)
vs. Fig. 4 (h)) has no significant effect on the measured
-0.3-0.2-0.10.00.10.20.3 -0.3-0.2-0.10.00.10.20.3 -0.3-0.2-0.10.00.10.20.3 -0.3-0.2-0.10.00.10.20.3
kx (Å-1) kx (Å-1) kx (Å-1) kx (Å-1) spin polarization curves, in contrast to the calculations
FIG.4: (coloronline)SARPESdataforSb/Ag(111)atE = shown in Fig. 3 (e) and (f). This corroborates the hy-
b
0.6eVfordifferentphotonenergiesandlightpolarization. (a), pothesis that the measured Px and Pz spin polarization
(c)and(e)MDCintensitydataalongΓ¯K forp-polarizedlight is dominated by the spin structure of the initial state
withphotonenergiesof24eV,28eVand20eV,respectively. quasiparticles.
(b), (d) and (f) Corresponding spin polarization data. (g)
MDCintensitydataalongΓ¯M forcircularleftpolarizedlight Spin-state interference has recently been predicted for
withhν =24eV.(h)Spinpolarizationdatacorrespondingto photoemission from the π states of graphene26, where
(g). photoelectrons from equivalent atoms within the same
unit cell interfere. The authors describe this effect as an
interference between spin and pseudo-spin. In contrast,
for Sb/Ag(111), the interference stems from an intrinsic
havevariousotherorigins19–25,buttheoutcomedepends overlap in k space.
strongly on the symmetry of the solid and of the partic-
In summary, we have presented evidence for a coher-
ular surface, on photon energy as well as on the absolute
ent superposition of spin states in photoemission from a
directions of photon incidence, photon polarization and
Rashba system. Interference is assigned to the intrinsic
electron emission. In order to rule out such effects, we
overlap region of spin-up and spin-down states. Hence
have measured SARPES MDC data for Sb/Ag(111) at
the measured spin polarization is defined by the quasi-
a binding energy of 0.6 eV for different photon energies
particlesintheinitialstatebandsandisnotsignificantly
and different light polarizations (Fig. 4). With respect
modifiedbyfinalstateeffects. Thiswasverifiedbyvary-
to Fig. 2, the sample has been rotated by 90◦ and the
MDCsarethusalongΓ¯K¯ forFig.4(a)-(f),while(g)and ing the sample orientation, the photon energy and the
(h)showagainascanalongΓ¯M¯. Theupperpanelsshow light polarization. These observations are not described
byrelativisticone-stepmodelcalculations. Whatdefines
the MDC intensity data, the lower ones the correspond-
thephasedifferencebetweenthestateswithoppositespin
ing spin polarization curves. We observe that the effect
in the overlap region remains a key issue towards a fur-
is quite robust against variations of these experimental
ther understanding of this effect.
parameters. The sample rotation of 90◦ has no signifi-
cant influence on the spin polarization curves (Fig. 2 (d) Fruitful discussions with T. Greber, M. Hengsberger,
vs. Fig. 4 (b)), in contrast to the effects described by B.Slomski,C.R.AstandI.Gierzaregratefullyacknowl-
Tamura et al.20 Second, although the intensity distribu- edged. We thank C. Hess, F. Dubi, and M. Kl¨ockner for
tioncurveschangeasafunctionofthephotonenergy,the technical support. This work is supported by the Swiss
spin polarization features are qualitatively not affected. National Foundation.
1 Y. Bychkov et al.,JETP Lett. 39, 78 (1984). 15 J. H. Dil, Journal of Physics: Condensed Matter 21,
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