MULTIATOM RESONANT PHOTOEMISSION. THEORY AND SYSTEMATICS.pdf

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VOLUME82, NUMBER20 P H Y S I C A L R E V I E W L E T T E R S 17 MAY1999

Multiatom Resonant Photoemission: Theory and Systematics

F. J. Garca de Abajo,1,2 C. S. Fadley,1,3 and M.A. Van Hove1,31Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720

2Departamento de CCIA (Facultad de Informtica), Donostia International Physics Center, Centro Mixto CSIC-UPVEHU,San Sebastin, Spain

3Department of Physics, University of California, Davis, California 95616(Received 2 November 1998)

A first-principles calculation of the recently discovered interatomic multiatom resonant photoemission(MARPE) effect is presented. In this phenomenon, core photoelectron intensities are enhanced when thephoton energy is tuned to a core-level absorption edge of nonidentical neighboring atoms, thus enablingdirect determination of near-neighbor atomic identities. Both the multiatom character of MARPE andretardation effects in the photon and electron interactions in the resonant channel are shown to becrucial. Measured peak-intensity enhancements of 40% in MnO and spectral shapes similar to thecorresponding x-ray absorption profiles are well reproduced by this theory. [S0031-9007(99)09098-5]

PACS numbers: 79.60.Bm, 33.60.Fy, 71.15.Rf

In a recent experimental development, interatomic mul-tiatom resonant photoemission (MARPE) has been shownby Kayet al. [1] to provide a new method for determining

near-neighbor atomic identities in solids. In the specificexample to be considered here, the measured intensity ofO 1sphotoelectrons coming from a single crystal of MnOexhibits significant enhancements when the photon energyis tuned to the 2p!3d absorption resonances of Mn. Inparticular, there is an increase in the O 1speak intensityat the Mn 2p32 edge of 40% [1]. Similar results havebeen seen in other metal oxides [1].

In a first discussion of the theory of MARPE [1],the conventional model used to describe the well-knownintra-atomic single-atom resonant photoemission (SARPE)[2 5] has been generalized to apply to MARPE. Pho-toemission is assumed to occur via absorption of a singlephoton and two different channels that leave the crystalin exactly the same final quantum state, and thus have tobe added coherently: the direct emission channel in whichan O 1selectron absorbs a photon and the resonant emis-sion channel that is assisted by the Mn 2p!Mn 3dreso-nance, as illustrated in Fig. 1(a). In the resonant channel,the photon promotes a Mn 2p electron to a Mn 3d state,from which it decays instantaneously to refill the Mn 2phole, while exciting the O 1s electron to the continuum.This decay can also be termed an interatomic autoioniza-tion process (AI), and it is thus closely related to the muchweaker interatomic Auger processes reported previously

[6 8]. Resonant processes must be summed coherentlyover several Mn neighbors of the emitter [see Fig. 1(b)].A first estimate from such a theoretical treatment gives anenergy-integrated effect of 2.5%, or about 4 times less thanthe 11% of experiment [1]. This analysis also suggestedthat the influence of a given resonating atom should die offas roughly 1R3, ifR is the distance from emitter to thisatom. However, the model used previously did not per-mit treating the precise many-electron states and energiesinvolved, and so could not predict the form of the spectral

enhancements as a function of energy. This model wasalso too simplified as to the electromagnetic interactionsinvolved. The present paper thus presents a significantly

more quantitative first-principles approach to the theoryof MARPE that yields very good agreement with experi-ment in most respects and permits further assessing thesystematics of this new phenomenon. In particular, many-electron configuration interaction states are used to de-scribe the Mn 2p!Mn 3d excitation, retarded effects in

FIG. 1. Schematic representation of multiatom resonant pho-toemission (MARPE) in MnO. (a) O 1s photoemission takesplace via two different interfering channels: direct emission(thin solid arrow) and emission assisted by the excitationof Mn 2p!Mn 3d (thick solid arrow) with subsequent inter-atomic autoionization (broken arrows) due to electron-electroninteraction (dashed line). (b) The resonance involves coherentaddition over several Mn sites in the solid situated at Rj withrespect to O.

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photon excitation and autoionization are included, and thedistance dependence of the effect is assessed in moredetail.

We begin with a muffin-tin model for which all final-state photoelectron scattering is neglected, with suchscattering effects to be added later. The intensity of thephotoelectron then is

Ik ~ jf0krj2 ~X

lm

Ylmkilh1l krMElm2

, (1)

where k is its wave vector, f0kr is its wave functionat the detector,Ylm is a spherical harmonic, h

1l kris a

spherical Hankel function, and

MElm Elm, O 1sjTjg (2)

is the matrix element describing the transition from themany body ground state jg to the final state with aphotoelectron jElm of energy E h2k22m and anO 1shole. The transition matrixTis given by [5]

T V0rad 1Xj,m

VjAI

jm,j m,jj

hv 1 Eg 2 Em 1 iGm2V

jrad,

(3)

where V0rad is the interaction of the radiation with theemitter,V

jradis this interaction with the resonating atomj ,

VjAI is the autoionization interaction between the emitter

and atom j, Eg is the ground state energy, and the sumsare over both Mn neighbors j and their intermediate manybody statesjm,jof energy Emand widthGm.

Relativistic retardation effects are significant in the

present context due to a combination of relatively largephoton energies hv ( 640eV for Mn 2p!Mn 3d inMnO) and the interatomic character of the AI process. Forexample, the phase change experienced by such a photonwhich has traveled across the nearest-neighbor O-Mn dis-tance d 2.23 is vdc 42 in MnO. As a conse-quence, the dipole approximation will be valid only withinthe extension of each atomic orbital, but different phasefactors have to be included for different atoms, so that

Vjrad A r ? e e

ikhn ?Rj A rX

l

Y1lrel eikhn ?Rj , (4)

where Rj

is the position of atom j relative to the emitter,khn is the wave vector of the light, e is its polarizationvector with components el, r is the electron coordinaterelative to the atom nucleus, and A is a normalizationconstant.

Similarly, the autoionization interaction VjAI requires

going beyond the usual e 2R description used in SARPE[5]. The fully relativistic Mller formula used previouslyin high-energy Auger theory [9] has been adopted for theAI interaction here, so that

VjAI

e2

jRj 1 r2 2 r1jeikhnjRj 1r22r1j1 2 k 2hnr1 ? r2

(5)

describes the interaction between electron 1 of coordinater1 relative to the O emitter and electron 2 of coordinater2relative to the j th resonating Mn atom. The first terminside the parentheses describes the retarded interaction

of the two electron densities, whereas the second ~r1 ? r2accounts for the retarded interaction of the two currentsassociated with the transition [9,10].

A multipole expansion of Eq. (5) that should be valid forr1, r2 Rj (i.e., for atoms other than nearest neighbors)has been performed. Only dipole-dipole terms have beenretained, since this analysis shows that higher-order con-tributions account for less than 5% of the total interaction.Thus, the effective interaction can finally be reduced to

VjAI

e2r1r2

R3

j

eikhn RjX

m1m2

Bjm1m2 Y1m1 r1Y

1m2r2 , (6)

whereBjm1m2 are second-order polynomials in khnRj.

Inserting Eqs. (3), (4), and (6) into Eq. (2), and focus-ing on the MnO case discussed above, one finds

MElm A E1jrjO 1sdl,1

3X

l

el

(Y1mjY1lY00

2X

m1 m2

Y1mjY1m1 Y00Fm1m2 am2l

), (7)

where the magnitude of the resonance is dictated by aproduct of a structure-factor type of sum over Mn sites

Fm1m2 X

j

Bjm1m2eikhn Rj 1khn ?Rj

R3

j

(8)

and the Mn21 polarizability tensor

am2l 2e2X

m

gjrY1m2 jm mjrY1ljg

hv 1 Eg 2 Em 1 iGm2. (9)

The dependence of the intermediate states on j has beendropped, since they have been approximated by theiruniform bulk form, thus neglecting surface effects. Theone-electron radial matrix element of O 1sphotoemissionappears as an overall factor in Eq. (7), so that it is notrelevant to the relative magnitude of MARPE.

The polarizabilityam2lhas been obtained using a con-figuration interaction scheme for a central Mn21 ion sur-rounded by six O22 ions in an octahedral cluster, as usedin prior SARPE analyses (see Ref. [5] for further de-tails). Thus, the polarization of nearest-neighbor electroniccharge around intermediate states with a Mn 2p hole isaccurately included. The widthsGm, coming from domi-nant intra-atomic Coster-Kronig decay of the intermediate

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states, have been taken to be constant (0.5eV). More-over, an average over orientations of Mn magnetic mo-ments has been performed, since the experiment was doneabove the MnO Nel temperature, and thus, am2l canbe approximated by the average quantity adm2l, wherea a2121 1 a00 1 a113. The calculated x-ray ab-sorption profile, given by Ima, is in good agreement withexperiment [11], as shown in Fig. 2(a). In addition,Rea

shows characteristic sign variations around the resonance,and agrees excellently with a Kronig-Kramers analysis ofthe experimental absorption coefficient [1].

A small imaginary part has been added to the photonwave vector in both V

jrad and V

jAI to account for inelas-

tic attenuation of the incoming radiation at the Mn 2pedge. This is related to the polarizability viakhn 1 12pnavc[2], wheren is the density of Mn sites, and ityields an attenuation length of148 at the Mn 2p32resonance maximum in MnO, in reasonable agreementwith values inferred from experiment [1].

Multiple scattering effects on the photoelectron havefinally been incorporated using an exact Green-function

cluster formalism [12]. Using MElmas input, the photo-electron wave function fkris constructed in the far-fieldr ! ` limit as the superposition of spherical outgoing di-rect and scattered waves like those of Eq. (1) and centeredaround various atoms (emitter plus scatterers). Clusters of153 atoms distributed over 5 layers have been used, withan electron inelastic mean free path of 4 and an inner po-tential of 25 eV [1,13]. Emitters situated in the first 5 lay-ers have been summed over, with the MARPE summationover Mn sites in Eq. (8) being performed for the full semi-infinite solid using methods described elsewhere [14,15].

The results of our calculations of the MARPE effectfor two different measurement geometries are shown inFigs. 2(b) and 2(c). Plotted is the quantity II0, whereI is the actual O 1s intensity and I0 is the nonresonantbackground under it. Curves are shown for both a fullsum over all Mn atoms, and a sum limited to a dis-tance of hd 10d 22 from the emitter. The pre-dicted enhancements follow quite closely the shape of thex-ray absorption profile, showing little evidence of theconstructive-destructive interference patterns that are of-ten seen in so-called Fano profiles [2], in agreement withexperiment [1]. In general, the limited sum agrees betterwith experiment as to both peak positions and intensities,suggesting an effectively more rapid convergence withdistance in experiment. In magnitude, there is also excel-lent agreement for the geometry in Fig. 2(b) for an x-rayincidence angle of20, although in Fig. 2(c) the principalMn 2p32 peak is predicted to be too weak by a factorof 2 for an incidence angle of40. The possible reasonsfor this discrepancy are inaccuracies in our treatment ofnearest-neighbor effects and the O 1shole state, multiplescattering, and resultant phase averaging and screening ofthe interaction (much enhanced at the resonance), and ne-glect of atomic vibrational motion.

FIG. 2. (a) Real (dashed curve) and imaginary (solid curve)

parts of the average polarizability of Mn21

in MnO, calculatedusing a configuration interaction scheme [5], as compared withthe experimental absorption coefficient [11] and its Kronig-Kramers transformation (dotted curves). (b) Enhancement inthe O 1s photoelectron intensity emitted along the normal ofa MnO(001) surface illuminated with linearly polarized lightincident at an angle of 20 with respect to the surface. Thepolarization vector e lies in the plane containing 100 and001. The experimental result [1] (dotted curve) is comparedwith theoretical curves for a full sum over all Mn atoms ineach plane (solid curve, h `) and for a sum only out to10 nearest-neighbor distances (dashed curve,h 10). (c) Thesame as (b) for an incidence angle of40.

Results obtained using different approximations to VjAI

are illustrated in Fig. 3(a). The nonretarded approxi-mation, consisting of setting khn 0 in V

jrad and V

jAI

[Eqs. (4) and (5)] gives a sizable result (dash-dottedcurve), yet significantly lower in magnitude than the mea-sured effect and of different shape. The results obtainedusing the full Mller expression (solid curve) are verysimilar to those obtained by keeping only the secondterm inside the parentheses of Eq. (5) (dashed curve current-current approximation), so that V

jAI ~ r1 ? r2,

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FIG. 3. (a) MARPE enhancement in O 1s photoemissionfrom MnO calculated under the same conditions as in Fig. 2( b)and using different approximations to the full theory (solidcurve): current-current approximation to the electron-electroninteraction, consisting in neglecting the first term inside theparentheses of Eq. (5) (dashed curve); result of neglecting thesquared term jFaj2 in Eq. (10) (dotted curve); and nonretardedapproximation (dash-dotted curve). (b) MARPE enhancementof O 1s photoemission arising in spheres centered on emitterssummed over different layers up to the 5th, under the sameconditions as in Fig. 2(b). Only Mn sites closer to the emitterthanh d, whered is the nearest-neighbor distance, are includedin the summation over Mn sites in Eq. (8). The result for a fullsum over all atoms in each plane is also shown.

and therefore, Fm1m2 F dm1m2, from which the photo-electron intensity reduces to

I ~ j1 2 Faj2 1 2 2 ReFa 1 jFaj2.

Actually,jFaj2 1, as shown in Fig. 3(a) by the dottedcurve, which neglects that term. Moreover, the current-current interaction provides F with a relatively largeimaginary part, implying that the MARPE enhancementis actually proportional to Ima, that is, to the x-rayabsorption spectrum, in agreement with experiment.

Finally, an estimate of the range of interatomic dis-tances involved in MARPE is shown in Fig. 3(b). Thedegree of enhancement is shown as a function of a radialcutoff in Rj ofh (in units of the O-Mn nearest-neighbordistance d), with intensities summed over emitters in thefirst 5 layers from the surface. That is, only resonating

Mn atoms withinh dof each emitter are included. Near-est and next-nearest neighbors are seen to be capable ofproducing a sizable fraction of15%of the effect, withnearly full convergence being reached at about h 10(i.e., 22 away), which in view of our approximationsis probably a realistic estimate of the maximum MARPErange in MnO. The falloff in influence of resonatingatoms is found to vary roughly as 1R2 for small dis-

tances, and much more rapidly for larger distances.In summary, the theory of MARPE presented here haspermitted explaining both the magnitude of the effect andthe shape of the resonance enhancement. It has also beenshown that retardation effects are relevant in the under-standing of the phenomenon, owing to a combination ofrelatively large transition energies and interatomic dis-tances. The interatomic autoionization decay is dominatedby the interaction between the dipole currents induced ineach of the atoms. The range of the effect has also beenestimated more quantitatively. Future calculations withmore accurate treatment of some of our approximationsshould improve the description of MARPE and further as-

sist with various applications of this new phenomenon.Discussions with E. Arenholz, A. Kay, S. Hfner,

S. Mun, and A. Tanaka are gratefully acknowledged.This work was supported by the U.S. Department ofEnergy, under Contract No. DE-AC03-76SF00098, theUniversity of the Basque Country, and the SpanishMinisterio de Educacin y Cultura (Fulbright GrantNo. FU-98-22726216).

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