The origin of satellites in 2p core level of late transition metal compounds are studied using plasmon theory. The calculated values of energy separation and relative intensity agree well with the experimental values and the theoretical calculations by Kozo Okada et al. The excitation of surface plasmons in 2p core level X-ray photoemission spectra of transition metal dihalides is discussed.Proučavamo nastanak satelita 2p sredice spojeva kasnih prijelaznih metala primjenom plazmonske teorije. Izračunate vrijednosti pomaka energije i relativnih intenziteta u dobrom su skladu s eksperimentalnima i s teorijskim vrijednostima Kozo Okade i sur. Raspravljamo uzbudu površinskih plazmona rentgenskim zračenjem u fotoemisijskim spektrima 2p sredice dihalida prijelaznih metala

Badahur, Amar

Srivastava, Sanjay Kumar

English

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Printed ISSN 1330–0008Online ISSN 1333–9125CD ISSN 1333–8390CODEN FIZAE4SURFACE PLASMON SATELLITES IN CORE-LEVEL X-RAYPHOTOEMISSION SPECTRA OF LATE TRANSITION-METALCOMPOUNDSSANJAY KUMAR SRIVASTAVA and AMAR BAHADURa,1Department of Physics, Kamla Nehru Institute of Physical and Social Sciences,Sultanpur, U.P., IndiaaE-mail address: amar.b.007@gmail.com, me.amar07@yahoo.co.inReceived 17 June 2008; Revised manuscript received 20 November 2008Accepted 3 December 2008 Online 28 January 2009The origin of satellites in 2p core level of late transition metal compounds are stud-ied using plasmon theory. The calculated values of energy separation and relativeintensity agree well with the experimental values and the theoretical calculationsby Kozo Okada et al. The excitation of surface plasmons in 2p core level X-rayphotoemission spectra of transition metal dihalides is discussed.PACS numbers: 79.60.-i, 78.70.En, 33.60.-q UDC 535.215Keywords: X-ray satellite spectra, plasmon, energy separation, relative intensity, intrinsicand extrinsic effects1. IntroductionX-ray photoemission spectra of core levels in many transition metal compoundsshow intense satellites occurring on high binding-energy side of the main line [1 –5]. Such satellites have been observed in gas phase molecules as well as in solids.Although many models attempting to explain origin of the core-level satellites inhalides [6 – 10] have appeared in the literature, yet at the first sight it appears thatthese satellites may be due to plasmon excitation processes because their energyseparations are in the range of plasmon excitation, and plasmon theory is supposedto be the most suitable theory in this energy range. The existence of bulk and sur-1Corresponding author: A. BahadurFIZIKA A (Zagreb) 17 (2008) 3, 117–124 117srivastava and badahur: surface plasmon satellites in core-level x-ray . . .face plasmon in X-ray satellite spectra are well known since the theoretical work ofPines and Bohm [11 – 13]. Pines [14] defined plasmons as quanta of energy of thesecollective oscillations. In X-ray photoemission spectra, a valence electron, whilefilling core vacancy, excites a plasmon, then transition energy is shared betweenplasmon and photoelectron. This process gives rise to low-energy X-ray satellitesthat have been observed by a large number of workers experimentally and consid-ered theoretically [15 – 16]. However, if a plasmon pre-exists, then during the X-rayemission process it transfers its energy to the transiting valance electron beforeit annihilates the core vacancy. Thus the energy of emitted X-ray photon will behigher than the energy of the main line. This process gives rise to high-energy satel-lites. Although, the excitation of surface plasmon is well known in oxides [17 – 18]of various metals and compounds, yet the literature is silent about the excitation ofsurface plasmons even in halides. Since halogens are very near to oxygen in the peri-odic table and more electronegative than oxygen, the possibility of surface plasmonexcitation in halogens can not be ignored. Therefore, we have, for the first time,tried to examine the excitation of surface plasmons [19] in the satellite spectra oftransition metal halides.2. Energy separationExperimental data were taken from published literature from Refs. [20 – 22].Although the origin of satellite transition metal halides may also be analyzed byapplying different analytical techniques [23], we have applied plasmon theory. Inthis we applied some modified terms which proved superiority over old plasmonmethods [24 – 27]. We calculated energy separation from the main line using thefollowing formula given by Marton [28]Bulk plasmon energy, h̄ωp = 28.8(Z ′σ/W)1/2(1)where Z ′ is the effective number of electrons taking part in plasma oscillation, σ thespecific gravity and W the molecular weight of compound. Since at the surface morelocalized oscillations can occur with frequency ωs, depending on the conditions andthe energy of the corresponding peak, surface plasmon may also be seen. Hence wealso calculated surface plasmon energies using formula given by Ritchie [29],Surface plasmon energy, h̄ωs = h̄ωp/√2 (2)This equation is valid for free-electron model to a fairly good approximation. Itcan also be used for semiconductors and insulators. The present calculated valuesof surface plasmon energy in Table 1 are in close agreement with experimental[20 – 22] and previously calculated [23] values.118 FIZIKA A (Zagreb) 17 (2008) 3, 117–124srivastava and badahur: surface plasmon satellites in core-level x-ray . . .TABLE 1. Values of surface plasmon energy.Energy separation (eV)Compound Z ′ σ WPresentwork(h̄ωs)ExperimentalRef. [20 – 22]CalculatedRef. [43]NiF2 2 4.72 96.71 6.4 6.0 6.0CoF2 2 4.46 96.93 6.3 6.0 6.0FeF2 2 4.09 93.84 6.0 6.5 6.4MnF2 2 3.98 92.93 6.0 7.0 7.1FeCl2 3 3.16 126.75 5.6 5.5 5.7MnCl2 3 2.977 125.84 5.4 5.0 5.6FeBr2 3 4.636 215.67 5.2 6.0 5.6MnBr2 3 4.39 214.76 5.04 5.5 5.73. Relative intensitiesFrom the energy considerations alone, the satellite can be regarded as being dueto an excitation of surface plasmon. But for a further confirmation of involvementof surface plasmon in satellites of these compounds, the relative intensity (Is/Im)has also been calculated using plasmon theory in new light. There are two types ofplasmon excitation – extrinsic and intrinsic [30]. In the extrinsic process, excita-tion of plasmon occurs during the transport of electrons through solid (fast electronprocess), while the in intrinsic process, excitation of plasmon takes place simultane-ously with the creation of a hole [31] (slow electron process). In the present work,we have tried to incorporate both these processes, i.e., the relative contributionof the extrinsic process as well as of the intrinsic process in which the number ofslow electrons is conserved. We have gone through detailed survey of the literatureregarding this and found that Pardee et al. [32] have done the remarkable job incombining both extrinsic and intrinsic effects in one equation simultaneously withsome inelastic effects and have given the formula for the combined relative intensityasi = αnn∑m=0(β/α)mm!, (3)whereα =11 + l/L(4)FIZIKA A (Zagreb) 17 (2008) 3, 117–124 119srivastava and badahur: surface plasmon satellites in core-level x-ray . . .is the inelastic loss factor, which gives the relative intensity for extrinsic satellites.Here l is the mean-free path for extrinsic plasmon excitation and L the meanattenuation length for electrons due to processes other than plasmon excitation.The parameter β is a measure for the probability Pi(n) for the intrinsic excita-tion of n plasmons,Pi(n) = e−β βnn!(5)The value of β [33 – 36] is taken asβ = 0.12 rs , (6)which has been used for intrinsic relative intensity by K. S. Srivastava et al. [17]and clearly is an approximation and one term of Eq. (3).But in the present case, Pardee’s Eq. (3) with the same values of α and β givenby Eqs. (4) and (5), respectively, could not be used directly because it does notgive satisfactory results, so it needed some modifications.Therefore we modified α. We have replaced α from inelastic loss factor to theratio of cut-off wave vector Kc to the Fermi wave vector as α = Kc/KF and itsvalue is taken [37] asα = 0.47 r1/2s . (7)Here rs is a dimensionless parameter and is the same as used in Eq. (6), given by[13]rs =(47.11h̄ωp)2/3(8)for volume plasmon, and for surface plasmonrs =(47.11h̄ωs)2/3. (9)Using the new values of α, Eqn. (7), and β, Eqn. (6), in Eqn. (3), we have calculatedseveral excellent results [38 – 41].The beauty of Eqn. (3) is that it contains a series of terms which include bothextrinsic and intrinsic contributions along with their relative coupling terms. Thefirst term is purely extrinsic, while the second term is purely intrinsic. The otherterms give both extrinsic and intrinsic relative contributions. The speciality of thisformula is that each term alone or simultaneously [42] with other terms is able togive the relative intensity. It is the type of excitation which decides which and howmany terms will be used. This formula also includes both categories mentionedby Bradshaw [31] for intrinsic contributions and gives better results as comparedto that and than traditional methods for the calculation of the relative intensity.Using Eqs. (3), (5), (6) and (7), we calculated the values of relative intensity that120 FIZIKA A (Zagreb) 17 (2008) 3, 117–124srivastava and badahur: surface plasmon satellites in core-level x-ray . . .are given in Table 2, including the experimentally observed values. Earlier work-ers [17 – 18, 24 – 27] used different terms of this form alone to explain successfullythe relative intensities of many satellites up to certain extent. But using variousterms of this formula or their combination, we are able to calculate not only therelative intensity of existing satellites, but it is also possible to predict those satel-lites which are yet to be discovered. It is also the beauty of the method that therelative intensity of higher-order satellites can easily be calculated without goinginto much mathematical detail. One can also separate the relative contributionsof extrinsic and intrinsic excitations in total intensity. No method is known in theliterature which gives the intensities of much higher satellites and separates thesecontributions with such an accuracy.TABLE 2. Relative intensities.Relative intensityComp. rs αIntensityassign.ThisworkExptl.Ref. [20-22]Calc.Ref. [43]Exptl.Ref. [43]NiF2 3.8 0.92 β + β2/(2α) 0.55 0.60 0.60CoF2 3.83 0.92 β − 0.1 0.36 0.40 0.40 0.18FeF2 3.94 0.93 β2/(2α) 0.1 0.20 0.26 0.10MnF2 3.97 0.94 β2/(2α) 0.11 0.10 0.15 0.06FeCl2 4.15 0.96 β + β2/(2α) 0.62 0.65 0.64MnCl2 4.22 0.97 β − 0.1 0.41 0.35 0.35FeBr2 4.36 0.98 β + β2/(2α) 0.66 0.85 0.79MnBr2 4.45 0.99 β − 0.1 0.43 0.45 0.47 0.384. ConclusionAuthors calculated the values of surface plasmon energies which are in closeagreement with the experimentally observed values of energy separation. For thecalculation of relative intensity, compounds are treated microscopically [45]. Whentreated in this way, the satellites of different compounds slightly differ in assignmentfrom one another in natural way as types of halides differ. The calculated values ofrelative intensity are in close agreement with the observed values [20 – 22, 46] andcalculated values [23]. So it can be concluded that the core-level satellites of latetransition metal dihalides may be due to surface plasmon excitation.AcknowledgementsWe are greatly thankful to Prof. K. S. Srivastava of Physics Department, Luc-know University, Lucknow U.P. and Dr. A. K. Srivastava, Physics Department,FIZIKA A (Zagreb) 17 (2008) 3, 117–124 121srivastava and badahur: surface plasmon satellites in core-level x-ray . . .Kamla Nehru Institute of Physical and Social Sciences, Sulatnpur, U.P., for theirfruitful conversations and valuable suggestions.References[1] B. Wallbank, J. S. H. Q. Parera, D. C. Frost, and C. A. Mc Dowell, J. Phys Chem.Phys. 69 (1978) 5405.[2] D. C. Frost, C. A. Mc Dowell and B. Wallbank, Chem. Phys. Lett. 40 (1976) 189.[3] S. K. Sen, J. Riga and J. Verbist, Chem. Phys. Lett. 39 (1976) 560.[4] K. S. Kim and N. Winogard, Chem. Phys. Lett. 31 (1975) 312.[5] D. K G. de Boer, C. Hass and G. A. Sawatzky, Phys. Rev. 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Lett. 17 (1972) 320.FIZIKA A (Zagreb) 17 (2008) 3, 117–124 123srivastava and badahur: surface plasmon satellites in core-level x-ray . . .POVRŠINSKI PLAZMONSKI SATELITI U SPEKTRIMA FOTOEMISIJE IZSREDICA U SPOJEVIMA KASNIH PRIJELAZNIH METALAProučavamo nastanak satelita 2p sredice spojeva kasnih prijelaznih metala prim-jenom plazmonske teorije. Izračunate vrijednosti pomaka energije i relativnih inten-ziteta u dobrom su skladu s eksperimentalnima i s teorijskim vrijednostima KozoOkade i sur. Raspravljamo uzbudu površinskih plazmona rentgenskim zračenjem ufotoemisijskim spektrima 2p sredice dihalida prijelaznih metala.124 FIZIKA A (Zagreb) 17 (2008) 3, 117–124

Povrsinški plazmonski sateliti u spektrima fotoemisije iz sredica u spojevima kasnih prijelaznih metala

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