PHYSICAL REVIEW 8 VOLUME 43, NUMBER 6 15 FEBRUARY 1991-II

4f -4f transitions in Gd, oxidized Gd, and epitaxial Gd silicide

J. A. D. MatthewDepartment of Physics, University of York, Heslington, York YOI 5DD, England

W. A. Henle, M. G. Ramsey, and F. P. NetzerInstitut fur Physikalische Chemic, Universita tIn'nsbruck, A 6020-Innsbruck, Austria

(Received 28 June 1990)

4f 4f tran-sitions in the rare earths are investigated in a detailed study of the 4f 4f exc-itationsof Gd observed by electron-energy-loss spectroscopy in reflection mode. Consistent quasiatomiclosses are observed in polycrystalline Gd metal, oxidized Gd, and an epitaxially ordered Gd silicidephase. Sharp 4f' 4f transi-tions, whose positions are independent of environment, are superposedon a broad loss background which changes markedly from system to system. Systematic variationsin the intensity of multiplet components with electron primary energy and angle of scattering arepresented, and attempts are made to distinguish contributions which arise from large-angleelectron-exchange collisions without elastic scattering and those which involve both large-angleelastic scattering and inelastic exchange scattering. Theoretical estimates of spin-Rip cross sectionsare consistent with the importance of high-momentum-transfer processes.

I. INTRODUCTION

Dipole-forbidden 4f 4f transitions -in rare earths withpartially filled 4f shells may be readily excited by elec-trons through exchange interaction in the scattering pro-cess. ' The 4f electrons retain their atomic character inthe solid state and sharp features in electron-energy-lossspectroscopy (EELS) in refiection mode have now beenidentified as transitions between 4f" multiplets. DellaValle and Modesti have shown that the observed transi-tion energies agree well with the very weak lines observedin the optical spectra of rare-earth ions trapped in ionicmatrices, and may also be correlated with shake-upfeatures in x-ray photoemission of 4f"+' systems andbremsstrahlung isochromat spectroscopy of 4f" ' sys-tems. This quasiatomic interpretation is confirmed bythe sharpness of the transitions and their insensitivity tochanges in chemical bonding. One anomaly has not beenfully resolved: In contrast to spin-Hip transitions in sim-ple atoms, e.g., He 1s ~1s4s S&, where the total crosssection peaks close to threshold, the intensity of 4f4f-transitions relative to those of conventional valenceand/or plasmon losses in the adjacent loss region appearto increase steadily with increasing primary energy E tobeyond 100 eV before decreasing steadily at higher ener-gy. Some resonant enhancement at the threshold for4d ~4f transitions is also observed, but some difficultyremains in understanding why electrons with energyaround 100 eV are so eScient in promoting spin-Hip tran-sitions of energies 4—7 eV.

Following preliminary results obtained in a study ofthe Gd/Si(111)7X7 interface we examine the electron-energy-loss spectra of polycrystalline Gd metal, Gd ex-posed to oxygen, and epitaxial Gd silicide. Emphasis isplaced on the variation with incident energy and exit an-gle of 4f 4f losses relative to a-djacent dipole-allowed

losses. The results are interpreted in terms of large-angle,high-momentuin-transfer 4f ( S7/2)~4f ( XJ ) transi-tions involving not only spin Hip but also high angular-momentum transfer.

II. EXPERIMENT

The experiments were carried out in a UHV system(base pressure less than 10 ' mbar) equipped with anangle-resolving electron spectrometer (Vacuum Genera-tors VG-ADES-400) with a movable spherical sectoranalyzer: the EELS resolution was 0.3—0.4 eV. It con-tained facilities for low-energy electron diffraction(LEED), thin film evaporation, and film thickness moni-toring via a quartz microbalance. The Gd films wereevaporated onto Si wafers from W coils after careful out-gassing of the evaporator and the Gd sample to obtaincontamination-free Gd films. Epitaxially ordered Gddisilicide surface phases were obtained by heating 10-AGd deposited onto a clean Si(111) 7 X 7 surface to-650 C. Epitaxial order of the silicide was establishedby LEED [(+3X &3)R 30' pattern] and angle-resolved uvphotoemission.

III. RESULTS

Figure 1 shows the variation in the electron-energy-lossspectra in N(E) mode with primary energy E~ of cleanpolycrystalline Gd metal at fixed specular refiectiongeometry (60' angle of incidence). As in the work of Del-la Valle and Modesti the intensity of the 4f-4f excita-tions in the 4.5 —8-eV loss range increases steadily relativeto the rest of the loss structure from E =40 eV toaround 150 eV; thereafter it decreases steadily in relativeimportance. It must be noted, however, that there is alarge overall decrease in absolute loss signal per unit in-

43 4897 1991 The American Physical Society

4898 MATTHEW, HENLE, RAMSEY, AND NETZER 43

E =120eV

NP

N(E)

-10 -6 -4LOSS ENERGY (eV)

-10 -8I I

-6 -4LOSS ENERGY teQ)

l

-2

FIG. 1. Electron-energy-loss spectra in X(E) form at specu-lar geometry for clean polycrystalline Gd at primary energiesE~ in the range 40—220 eV showing transitions to various 4ffinal-state multiplets.

FIG. 2. Electron-energy-loss spectra in X(E) form of cleanpolycrystalline Gd exposed to 02 (E~ =120 eV) under specularconditions.

cident current between E =40 and 120 eV accompaniedby a reduction of order 10 in elastic reAectivity. In addi-tion, the I loss (see Table I) at LE=4.5 eV grows rela-tive to the adjacent D loss with increasing primary ener-gy. Figure 2 shows the modification of the loss profileswith exposure to oxygen. As oxidation progresses thelosses on which the main ( I ) 4f 4f transitions -are super-posed decline in intensity as the oxide band gap emerges;a prominent feature develops at low loss energy, whichshifts steadily and disappears for higher 02 exposures(not shown). As oxidation proceeds there is some declinein the intensity of the 4f 4f losses relatiu-e to the otherloss structures, but the absolute 4f 4f signal change-s lit-tle. Oxidation is accompanied by an increase in elastic

TABLE II. Trends in 4f loss intensities.

Specular lossE 40~120 eV145~220 eV

Absolute4f loss intensity

(a) Clean Gd

increasingdecreasing

4f loss intensityrelative to lossat DE=10 eV

increasingdecreasing

(b) Gd Exposed to 02

refIectivity of more than a factor of 4, and the otherlosses grow significantly in intensity also. Oxidized Gdshows the same trends in energy dependence of the lossesas the clean metal. The significance of these data is that

TABLE I. 4f 4f 7 transitions in Cxd (Re-f. 9).

Energy (eV)

Specular loss0~1 L 021 L 02~50 L Op

—const—const

increasingdecreasing

(enhanced elasticreAectivity)

Cxd 4f'Ground state8S7yz

Multiplet

8S7i2

6p6I6g)6G6F6H

04.04.55.06.26.77.2

(c) Gd+ 50 L 02 (1 L= 10 Torr sec)Increasingscattering angle

0, 35'~120' increasing increasing

(d) Polycrystalline to epitaxial silicideSpecular loss unknown sharp decrease

43 4f 4f-TRANSITIONS IN Gd, OXIDIZED Gd, AND. . . 4899

in the absence of a broad loss background the full rangeof 4f final state multiplets (Table I) shows up well withP clearly isolated for the first time.

Figure 3 shows the dependence of the loss profile in theGd oxide on exit angle 0 for E =120 eV; 0 is definedwith respect to the surface normal, the angle of incidenceis 60' with respect to the surface normal. At near glanc-ing exit 8=85', i.e., 8, =35, the 4f 4f los-ses are veryweak with the D intensity comparable to that of the Ifeature. As the exit angle moves towards normal the Iintensity grows both relative to D and the other losses.Due to the strong diffuse scattering in the polycrystallinesample the other losses also increase in intensity towardsnormal exit (note that the individual curves have been ad-justed to give comparable loss signals at hE = 10 eV), butthe increase with 0, in the I loss is particularly marked.Similar angular dependence is found on polycrystallinemetallic Gd films.

If 10 A of Gd on Si(111)is heated to 650'C an ordered(&3 X &3) disilicide phase is formed; there is now a spec-ular elastic peak with full width at half maximum(FWHM) of 12', in contrast to the polycrystalline sampleswhere elastic scattering is more isotropic. The EELSspectra at exit angles around the specular beam (48 in-cident angle) are shown in Fig. 4. The 4f 4f losses a-re

N(E)

-20 -10LOSS ENERGY {eV)

E =120eV

FIG. 4. Electron-energy-loss spectra in N(E) form for epi-taxial Gd silicide formed by heating 10-A Gd on Si(111) to650'C. Note the very low relative 4f 4f signal under sp-ecular

geometry and its increase for exit angles towards the surfacenormal.

N(E) now relatively much less intense than before, but againbecome more prominent towards the surface normal, i.e.,when the scattering angle from the incident direction, 0„is larger.

The empirical trends in observed 4f intensities aresummarized in Table II, which identifies the issues ad-dressed in the discussion section.

IV. DISCUSSION

The experimental results presented here are in goodagreement with previous data, but show some importantadditional features.

l

-10I I

-6 -4LOSS ENERGY (eV)

FIG. 3. Electron-energy-loss spectra in N (E) form atE~ =120 eV of Gd exposed to 50 L 02 under different experi-mental geometries. Note the increasing relative importance of4f 4f transitions as one goes from ne-ar glancing exit (low 8, ) tonormal exit (large 0, ).

(a) An additional final-state multiplet P.(b) Diff'erences in the behavior of transitions with

different final-state multiplet angular momenta, e.g. , I,D, and P.

(c) Increase in 4f" 4f" intensity with inc-reasingscattering angle in both ordered and polycrystalline sys-tems.

(d) Little change in 4f" 4f" intensity during o-xidationin spite of a large change in elastic reAectivity and dipolarlosses.

These features have to be understood in relation to thepeaking of 4f" 4f" intensity relative to di-pole-allowed

4900 MATTHEW, HENLE, RAMSEY, AND NETZER 43

channels above 100 eV.In Gd all transitions 4f tttt&&&( S7/2)

~4f& t& t& t&( Xz) involve spin Ilip. In the theoretical ar-

gument that follows we adopt an atomistic viewpointwhich has some significant differences from the bandmodels of Bocchetta, Tosatti, and Yin. ' Consider an in-cident electron wave vector k; (energy Ep =

—,'k; a.u. ) scat-tered by a rare-earth atom into wave vector kf with ener-

gy loss AE =—,'(k; —kf ). The differential cross section for

a spin-Aip transition will be of the form

( d cr /d 0 ), ;„„;„(kf /k; ) ~

T'"'"~

where T"'" is the exchange matrix element. Normallythe probability of spin flip through exchange is highestnear threshold and the probability then falls off with in-creasing primary energy. For electron scattering from aquasi-one-electron atom in a 4f state the spatial part ofT'"'" would be in the first Born approximation" of theform

T'"'"=(4fkf ~1/r, ~~k, 4f ) .

Ochkur' examined the leading term in such matrix ele-rnents and showed that for small momentum transferq=k, —kf, i.e., small-angle scattering, (dcr/dA), ;„„,varies as k;, i.e., E, implying that spin-Aip contribu-tions to the specular beam in solids will be small in agree-ment with the conclusions of Ref. 10. T'"" increaseswith the magnitude of momentum transfer q to reach amaximum when q has magnitude of order r, ', where r,is the effective size of the orbital with which the continu-um electron undergoes exchange and will fall off at highq. Here r, is within a factor 2 or 3 of (r&f ) =0.8 a.u.Overall o.

tot f p Q pvaries in the Born approximation ap-

proximately as E," but (d cr /d O),p,„s;p may varymuch more slowly with primary energy if the momentumtransfer is close to the optimum for exchange.

Little change in the intensity of 4f" 4f" transitions a-t

E =120 eV (Fig. 2) was observed on oxidation, whichwas in turn accompanied by a large change in elasticreAectivity. This suggests that the spin-Aip intensity isthen dominated by large-angle single-inelastic-scatteringevents rather than small-angle loss events accompaniedby larger-angle elastic scattering. In comparing spin-Aiploss intensities with those of dipolar losses we would thenhave for loss energy AE ((E,

I,„;„ft;oc (do /d0), „;„„;„d0,

dipole total, dipole P &

where R (E,O)dA is the probability of elastic scatteringinto d A at exit angle 0, and o.„„&d, p, &, is the total dipolarcross section, concentrated within a scattering angle0, =DE/2E, which is very small for AE —5 eV and

E~ ) 100 eV. o tota& dlpo&e is known to vary as(I/Ep )ln(yE /AE) with y —1." We now gain some in-

sight into how spin-Aip losses can compete with dipolarlosses for E above 100 eV.

At low primary energies (E -20 eV) there is a high

2050

120

1.21.93.0

0.71.11.8

1.21.93.0

2. 1

3.35.2

elastic reAectivity and large dipolar cross section. Al-though small-angle spin-Aip transitions are more prob-able at such low energies, the possible momentumtransfer may be too low for optimum exchangescattering —see Table II. As E increases the reAectivitydecreases rapidly, and the dipolar inelastic cross sectionmore slowly, but the overall loss of intensity will bequicker than E ~ In typical geometry the momentumtransfer for spin-Aip transitions will now be closer to op-timum and the overall loss of intensity may be slowerthan for the dipole channel in the 40—150-eV range. Inthe ordered case R(E,O) is enhanced around the specu-lar direction and the 4f" 4f" trans-itions are less prom-inent; oxidation leads to a similar effect. At high primaryenergies the momentum transfer will be sufficiently highfor interference effects to reduce T„,h, explaining therapid fall in intensity observed above 200 eV.

However, a further complication has to be considered.The spin-Aip exchange interaction of the incoming elec-tron involves interaction not with a one-electron atom,but with a highly correlated S7/2 multiplet state. In pro-moting the transition to XJ transfer of angular momen-tum must occur as well as spin Aip. For a given incidentenergy E =

—,'k; the maximum angular momentum forwhich strong interaction will occur at radius ro will begiven through simple quasiclassical arguments by

l,„(l,„+1)=k,r0=2E ro

neglecting any inner-potential effects.The 4f"-4f" transitions involve changes in orbital an-

gular momentum varying from AL =1 to 6. For appre-ciable interaction with the 4f electrons ro ~ 2(ref ) —1.6a.u. The P and D final states satisfy the above conditionat E -20 eV, but the I state will not optimize penetra-tion until above 100 eV. We attribute the steady rise of Iintensity relative to D and P with increasing primaryenergy (Fig. 1) to this effect. Table III analyzes themomentum transfer q for a AE =5 eV loss at E =20, 50,and 120 eV for the scattering angles, 0, of Fig. 3. Withincreasing 0, and increasing q the intensity of the I com-ponent increases in prominence but at normal exit(8, =120') the higher-energy transitions are losing inten-sity, suggesting that the momentum transfer may then begreater than optimum. Of course, elastic scattering hassome inAuence on the spin-Aip loss intensities, but thereappears to be a strong memory of the incident directionin observed angular distributions.

TABLE III. Momentum transfers q for scattering angle 0, atfixed loss AE and various primary energies E~.

pp—2k; sin( 0, /2 ) (a.u. '

)

E~ (eV) k; (a.u. ) 0, =35' 0, =60' 0, =120'

43 4f 4f-TRANSITIONS IN Gd, OXIDIZED Gd, AND. . . 4901

V. SUMMARY

Observations of the energy and angular dependence of4f" 4f"-spin-flip transitions in Gd suggest that large-angle, high-momentum-transfer inelastic transitions dom-inate. The final-state angular momentum is shown to beimportant in determining the variation of intensity withprimary energy and scattering angle.

ACKNOWLEDGMENTS

This work has been supported by the Austrian Fondszur Forderung der wissenschaftlichen Forschung and bythe Science and Engineering Research Council of theUnited Kingdom.

'E. Bauer and J. Kolacdzkiewicz, Phys. Status Solidi B 131, 699(1985).

zS. Modesti, G. Paolucci, and E. losatti, Phys. Rev. Lett. 55,2995 (1985).

A. Stenborg and E. Bauer, Solid State Commun. 66, 561 (1988).4F. Della Valle and S. Modesti, Phys. Scr. T 19, 419 (1987);

Phys. Rev. B 40, 933 (1989).~W. T. Carnall, P. R. Fields, and K. Rajnak, J. Chem. Phys. 49,

4412 (1968).A. H. Gabriel and D. W. O. Heddle, Proc. R. Soc. London Ser.

A 271, 124 {1960}.~W. A. Henle, M. G. Ramsey, and F. P. Netzer, Vacuum. 41,

814 (1990).8W. A. Henle, M. G. Ramsey, F. P. Netzer, R. Cimino, and W.

Braun, Solid State Commun. 71, 657 (1989).F. Gerken, J. Phys. F 13, 703 (1983).

' C. J. Bocchetta, E. Tosatti, and S. Yin, Z. Phys. B 67, 89(1987).

'tC. J. Joachain, Quantum Collision Theory (North-Holland,Amsterdam, 1983).

~2K. I. Ochkur, Zh. Eksp. Teor. Fiz. 45, 734 (1963) [Sov.Phys. —JETP 18, 503 (1964)]; 47, 1746 (1964) [20, 1175(1965)].