Electronic structure of the Mo 1−x Re x alloys studied through resonant photoemission spectroscopy
Shyam Sundar, Soma Banik, L S Sharath Chandra, M K Chattopadhyay, Tapas Ganguli, G S Lodha, Sudhir K Pandey, D M Phase, S B Roy
aa r X i v : . [ c ond - m a t . s up r- c on ] J a n Electronic structure of the Mo − x Re x alloys studiedthrough resonant photoemission spectroscopy Shyam Sundar , , Soma Banik , L S Sharath Chandra , M KChattopadhyay , , Tapas Ganguli , , G S Lodha , Sudhir KPandey , D M Phase and S B Roy , Homi Bhabha National Institute at RRCAT, Indore, Madhya Pradesh 452013, India Materials Research Lab, Indus Synchrotrons Utilization Division, Raja RamannaCentre for Advanced Technology, Indore, Madhya Pradesh 452013, India. Magnetic and Superconducting Materials Section, Raja Ramanna Centre forAdvanced Technology, Indore, Madhya Pradesh 452013, India. School of Engineering, Indian Institute of Technology, Mandi, Kamand, HimachalPradesh-175005, India. UGC-DAE Consortium for Scientific Research, Khandwa Road, Indore, MadhyaPradesh-452001, India.
Abstract.
We have studied the electronic structure of Mo rich Mo − x Re x alloys (0 ≤ x ≤ E F , the d states lie mostly in the range 0 to -6 eV binding energy whereas s states lie in the range-4 to -10 eV binding energy. We have observed two resonances in the photoemissionspectra of each sample, one at about 35 eV photon energy and other at about 45 eVphoton energy. Our analysis suggest that the resonance at 35 eV photon energy isrelated to the Mo 4 p -5 s transition and the resonance at 45 eV photon energy is relatedto the contribution from both the Mo 4 p -4 d transition (threshold: 42 eV) and Re 5 p -5 d transition (threshold: 46 eV). In the CIS plot, the resonance at 35 eV incident photonenergy for binding energy features in the range of E F (B.E. = 0) to -5 eV becomesprogressively less prominent with the increasing Re concentration x and vanishes for x > − x Re x alloys, measured at 47 eV photon energy,reveal that the Re d like states appear near E F when Re is alloyed with Mo. Theseresults indicate that interband s - d interaction, which is weak in Mo, increases with theincreasing x and influences the nature of superconductivity in the alloys with higher x .PACS numbers: 74.25.Jb, 74.70.Ad, 71.20.Be, 79.60.-i lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy
1. Introduction
Discovered in 1960s, the binary Mo-Re alloys are interesting superconductors havingtransition temperature ( T c ) about an order of magnitude higher than their constituentelements [1, 2, 3]. Experimental studies done in mid 1980s and early 1990s suggestedthe possibility of Re influenced softening of the phonon spectrum [4] and a change in theelectron density of states (DOS) [5] in the Mo − x Re x alloys. But these phenomena couldnot completely explain the large non-monotonic enhancement of T C in the Mo − x Re x alloys. The T c in the Mo − x Re x alloys increases slowly from 0.90 K for Mo to about 3 Kfor x = 0.10 and then rises sharply to about 7 K for x = 0.15 [6, 7]. With further increasein x , the T c increases linearly to about 12.6 K for x = 0.40 [6, 7]. The compositionrange in which the T c increases sharply in the Mo − x Re x alloys, corresponds to thesame composition range where the existence of two electronic topological transitions(ETT) have been reported for the critical concentrations x c = 0.05 and x c = 0.11[8, 9, 10, 11, 12, 13, 14]. The ETT is associated with the appearance or the disappearanceof pockets of Fermi surface when an external parameter such as composition, pressure,and/or magnetic field is varied [15]. The coefficient of the thermoelectric power α/T inthe zero temperature limit shows a giant enhancement around x C = 0.11 [8, 11, 12].The T c of the Mo − x Re x alloys with x > x c is reported to oscillate with pressure [6, 12].The oscillations in the temperature derivative of α/T and resistivity were also observedto be maximum at x c = 0.05 and x c = 0.11 [12]. These oscillations were predicted tobe due to the localization of electrons at the newly appeared Fermi pockets [12]. Ourrecent band structure calculation shows that there is substantial changes in the DOSat the Fermi level E F for x > x c [7]. The X ray photoelectron spectroscopy revealedthat the rigid band model is not applicable in the case of the Mo − x Re x alloys, andthe changes in the spectra as a function of x was assigned to the ETT [16]. The directevidence of this ETT has been provided recently by the Okada et. al., with the helpof angle resolved photoemission spectroscopy along the H-N direction of the Brillouinzone [14]. However, their studies could not establish any relation between the ETT andthe superconductivity in Mo − x Re x alloys.In our recent study, we have found the evidence of multiband effects in thetemperature dependence of heat capacity and the superfluid density (estimated fromthe temperature dependence of lower critical field H c ) in the Mo − x Re x alloys with x =0.25 and 0.40 [17]. Our detailed study also reveals that the multiband superconductivityappears above x > − x Re x alloys, Dikiy et. al.,concluded that the new electron sheet that is formed above x > x c differ from the mainsheets in terms of lower velocity and higher effective mass [20]. Resonant photoemissionspectroscopy (RPES) has been shown to be a powerful tool for determination ofpartial density of states in various intermetallic alloys [21, 22, 23]. RPES has beeneffectively used to get the details of the electronic structure near E F and its role onthe superconducting properties in different classes of superconductors, namely, the iron lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy Cu O − δ [28], ZrB [29], PrPt Ge [30], and the heavyFermion superconductors [31]. Therefore, we expect that the RPES studies on theMo − x Re x alloys may provide useful information of the valence band, which in turn willbe helpful in understanding the correlation between the ETT and the superconductingproperties. In the present study, we have therefore performed RPES experiments on the β -phase Mo − x Re x alloys with x > E F which then develops Re 5 d like character. These enhanced DOS at E F ,enhances the interband s - d interaction in these alloys with increasing x , which in turninfluences the nature of superconductivity.
2. Experimental and Details of the band structural calculations
Polycrystalline samples of Mo − x Re x , where x = 0, 0.15, 0.20, 0.25 and 0.40 wereprepared by melting 99.95+ % purity constituent elements in an arc-furnace under99.999 % Ar atmosphere. The samples were flipped and re-melted six times to improvethe homogeneity. The X-ray diffraction study of these alloys shows that the sampleshave formed in the body centered cubic (bcc) phase (space group: Im¯3m) [7, 17, 18].The RPES measurements on the above samples were performed using the angle-integrated photoemission beamline of the Indus-1 synchrotron radiation source [32].The valence band (VB) photoemission spectra were recorded in 23-70 eV photon energyrange. The details of the configuration of the present system and the experimentalconditions are available elsewhere [33]. The spectra were normalized by the photon fluxestimated from the photocurrent obtained from the post mirror of the beam line. Cleansample surface was obtained by sputtering the sample in-situ. Surface cleanliness wasconfirmed by the absence of the oxygen and the carbon contribution in the core levelpeaks of Mo and Re. The experimental resolution was estimated to be from 0.3-0.4eV in the present photon energy range. The X-ray photoelectron spectra (XPS) weremeasured using Mg K α X-ray source (DAR400, Omicron).The ab-initio electronic structure calculations were performed using the spinpolarized Korringa-Kohn-Rostoker (KKR) method [34]. The effect of doping wasconsidered under the coherent potential approximation. The exchange correlationfunctional developed by Vosko Wilk and Nusair was used for the calculation [35]. Thenumber of k -points used in the irreducible part of the Brillouin zone is 72. The muffin-tin radii for Mo and Re atoms used in the calculations are same and equal to 2.576 bohr.For the angular momentum expansion, we have considered l max =2 for each atom. Thepotential convergence criterion was set to 10 − .
3. Results and discussion
Fig. 1 ( a ), and ( b ) show the XPS data corresponding to the Mo 4 p , Re 4 f , and Mo 3 d core-levels in the Mo − x Re x alloys. These core level spectra are also compared with those lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy i n t en s i t y ( a r b . un i t s )
50 45 40 35 30 x = 0 0.15 0.2 0.25 0.4 1 Mo Re x Re 4f
Re 4f
Mo 4p
Mo 4p (a) i n t en s i t y ( a r b . un i t s )
238 236 234 232 230 228 226 224 binding energy (eV)Mo 3d
Mo 3d (b)
Figure 1.
Core level spectra of the Mo − x Re x alloys, where the panel ( a ) shows theRe 4 f and Mo 4 p states and the panel ( b ) shows the Mo 3 d states. The positions ofthe Re 4 f corelevels in alloys which are marked as tick in ( a ) are found to shift withrespect to that of elemental Re. The positions of the Mo 4 p and Mo 3 d corelevels inalloys which are marked as tick in ( a ) and ( b ) respectively remain at the same positionas that of elemental Mo. The compositions x = 0 and 1 represent elemental Mo andRe respectively. of elemental Mo and Re. The inelastic background has been subtracted using standardTougaard method [36]. In Fig. 1( a ), the 4 p / and 4 p / peaks for elemental Mo appearat 37 eV and 35 eV binding energy (BE), respectively, showing a spin orbit splitting of2 eV. On the other hand, the Re 4 f / and 4 f / peaks appear at 42.2 eV and 39.8 eVrespectively, showing a spin orbit splitting of 2.4 eV. The interesting observation hereis that the BE positions of the Mo 4 p / and 4 p / core levels in the Mo − x Re x alloysappear at the same BE positions as that of elemental Mo (Fig 1( a )). However, theRe 4 f / and 4 f / show a shift towards higher binding energy with decreasing x ascompared to elemental Re. Within the instrumental resolution, the shift observed for x = 0.4, is 0.25 eV. For x = 0.15, 0.2 and 0.25, the shift is about 0.4 eV towards higherbinding energy. In a binary disordered metallic alloy, such a shift appears due to thedifference in the local chemical environment and/or the charge redistribution, which isrelated to the hybridization between the valence electron states of the system [37]. InFig. 1( b ), the BE peak positions for the Mo 3 d core levels (Mo 3 d / = 227.8 eV & Mo3 d / = 231.0 eV) in the Mo − x Re x alloys are found at the same BE positions (withinthe experimental resolution) as those reported for elemental Mo [38]. Similar to Mo 3 d core levels (Fig. 1( b )), the peak positions for Re 4 d core levels in the Mo − x Re x alloys lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy ( b ) 60 eV52 eV48 eV45 eV42 eV40 eV37 eV34 eV32 eV30 eV I n t e n s i t y ( a r b . un i t s ) Mo
25 eV ( a ) MoO (Lit.)_Al k MoO (Lit.)_Al k Mo Metal (Lit.)_Al k I n t e n s i t y ( a r b . un i t s ) Mo Metal _Mg k (Our data) ( c ) Mo He IIHe II
MoO MoO binding energy (eV) He II Mo h = 41 eV (Our data) Figure 2. ( a ) Valence band photoelectron spectra (binding energy vs. intensity) forpure Mo in the photon energy range 23 eV to 60 eV. ( b ) Valence band XPS data forMo-oxides and metallic Mo (data extracted from Ref. [38]) in comparison with ourexperimental data for metallic Mo. ( c ) Valence band UPS data (He II source) forMo-oxides and metallic Mo (data extracted from Ref. [39, 40]) compared with ourexperimental data for metallic Mo at 41 eV photon energy. Panels ( b ) and ( c ) clearlyshow the absence of oxygen in this system. (not shown here), are also found to be same as of elemental Re.The VB spectra for pure Mo in the energy range 23 to 60 eV are shown in Fig. 2( a ). The background obtained by the Tougaard procedure [36] has been subtracted fromthe raw data. In Fig. 2 ( b ), we compare the present VB-XPS of elemental Mo measuredusing Mg K α radiation with the XPS results reported in literature for Mo-oxides andelemental Mo where the measurements were done using Al K α radiation [38]. From Fig.2 ( b ), it is clear that the VB-XPS of elemental Mo is in fairly good agreement with thatof the literature and is quite different from that of oxides of Mo. Therefore, we believethat there is no oxygen in the bulk of the samples. Since, the photons with energies lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy c ) thephotoelectron spectrum (PES) of the VB of Mo obtained using photons of 41 eV energywith the reported PES of the VB of elemental Mo and Mo-oxides obtained using He-IIsource [39, 40]. The features corresponding to the VB of elemental Mo are distinctlydifferent from that of Mo-oxides wherein broad hump like features are observed centeredaround -5 eV below E F . Therefore, we believe that the surface of present samples understudy is not contaminated by oxygen. The PES spectra of the VB of Mo measured at41 eV photon energy showing fine features up to about -4 eV below E F , and then abroad hump ranging from -4 eV to -8 eV which is followed by another hump like featurecentered around -10 eV below E F , are in agreement with that measured [40] at 40.8 eVphoton energy (He-II source) as well as other measurements reported in literature [41].The PES spectra of Mo was taken up to BE = -14 eV below E F , consists offive features viz. one feature very close to E F , two features closely spaced around -2 to -3 eV, a broad peak at -6 eV and a broad hump centered around -10 eV below E F . All the peaks are quite broad due to the large dispersion of the bands [14]. Asystematic shift of the positions of these peaks are also observed when the incidentphoton energy is varied. This may be related to the dispersion of the bands along thek z direction of the Brillouin zone. These results are consistent with many theoreticaland experimental studies performed on Mo (110), (011) and (112) face single crystals[42, 43, 44, 45, 46, 47, 48]. Since, the low energy photons are surface sensitive, thesurface density of states also influence the PES. Weng et al., have shown that thereare two peaks centered around -0.7 eV and -3 eV below E F in the density of statescorresponding to the Mo surface [42]. We have also observed the corresponding featuresin the PES, which is probably the admixture of the bulk and surface states. However,we have also observed other features at -2 eV, -6 eV and -10 eV which are mainly fromthe bulk of the sample [42]. The resonant enhancement of the PES of the VB is observedas a function of photon energy which will be discussed later in detail.A systematic evolution of the VB photoemission spectra of the Mo − x Re x alloyswith x = 0.15, 0.2, 0.25 and 0.40 measured at the selected photon energies ranging from25 eV to 60 eV is shown in Fig. 3. In comparison with Mo, the intensity of the BEfeature in the Mo − x Re x alloys at -6 eV decreases monotonically as a function of photonenergy and this reduction of intensity is quite significant for the alloys with higher Recontent. The features around BE = -2 eV become sharp when Re alloyed with the Mo,although the peak positions of these features do not seem to depend on the photonenergy. However, when Re is alloyed with Mo, the features in the PES depends onthe photon energy quite significantly and the average shift in the peak positions as afunction of the photon energy increases with increasing Re content. This is due to theenhancement in the dispersion of the bands along the k z direction of the Brillouin zonewhen Re is alloyed with Mo [14].In order to know the contributions of different orbitals to the PES, we plot in Fig.4, the partial density of states (PDOS) of Re and Mo in the Mo − x Re x alloys. The d and p states of both Mo and Re lie in the BE range E F to -6 eV, and s states of both lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy
60 eV52 eV48 eV45 eV42 eV40 eV37 eV34 eV32 eV30 eV x = 0.2
25 eV (b)
60 eV52 eV48 eV45 eV42 eV40 eV37 eV34 eV32 eV30 eV
25 eV 60 eV52 eV48 eV46 eV42 eV40 eV37 eV34 eV32 eV30 eV
25 eV x = 0.4binding energy (eV)(d) I n t e n s i t y ( a r b . un i t s ) x = 0.15( a )
60 eV51 eV48 eV45 eV42 eV40 eV37 eV34 eV32 eV30 eV
25 eV I n t e n s i t y ( a r b . un i t s ) binding energy (eV) x = 0.25 (c) Figure 3.
Valence band photoemission spectra of Mo − x Re x alloys for x = 0.15, 0.2,0.25 and 0.4 samples, plotted at some selected photon energies across Mo 4 p -4 d andRe 5 p -5 d resonances. Mo and Re lie below -4 eV in the higher BE side. The 4 d states of Mo show threepeaks around BE = -2, -3 and -4 eV below E F , whereas the 5 d states of Re show threepeaks around BE = -2.5, -3.5 and -5 eV below E F . At the Fermi level, a dip is observedin the Mo 4 d PDOS. When Re is alloyed with Mo, the contributions of both Mo andRe d states increase with the increase in x up to x = 0.25. In the case of x = 0.40,however, the d DOS is reduced once again. The Mo 5 s states lie around -5 eV below E F whereas the Re 6 s states lie around -6 eV below E F . However, the contribution of the s states of both Mo and Re in the energy range E F to -4 eV below E F is quite small butfinite. The Mo 5 p and Re 6 p states are evenly distributed from E F to -4 eV below E F but rather quite less in number as compared to the d states. Since the Re (5 d s ) hasone more valence electron per atom than Mo (4 d s ), the PDOS of both Mo and Reshift towards higher binding energy with the increase in Re concentration. Therefore, lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy Mo 4d(a)
Re 5d(b) ( s t a t e s / e V f. u . ) Mo 5s(c) P D O S Re 6s(d)
Mo 5p (e) x= 0 0.15 0.2 0.25 0.4 w.r.t. E F (eV) Re 6p (f)
Figure 4.
Partial DOS showing Mo 4 d , Re 5 d , Mo 5 s , Mo 5 p , Re 6 s , 6 p states in ( a )to ( f ) respectively. features up to about -4 eV below E F in the PES is dominated by the d like states andfeatures below -4 eV towards higher binding energy represents the s like states.Fig. 2 and Fig. 3 show the resonance enhancement of the features in the PES mea-sured using photons with different energies. In all the samples, the feature around BE= -6 eV below E F resonates around 35 eV photon energy, whereas the feature aroundBE = -2 eV below E F resonates around 45 eV photon energy. A clear picture can beobtained by plotting the constant initial state (CIS) intensities of the VB features as afunction of photon energies as shown in Fig. 5. The CIS plots of all the samples showtwo resonances with the peak positions at around 35 eV and 45 eV incident photonenergy. In the case of Mo, the resonance corresponding to the incident photon energyof around 35 eV is observed over the entire valance band, whereas, the resonance corre-sponding to the incident photon energy of around 45 eV is observed only below the 5 eVbinding energy of the V B. From the Fig. 1, it is clear that the resonance of the VBoccurred across the Mo 4 p threshold. The band structure calculation (Fig. 4) suggeststhat the features of the PES in the BE range from E F to -5 eV below E F are mainly lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy
30 40 50 60 7030 40 50 60 7030 40 50 60 7030 40 50 60 7030 40 50 60 70 3.01 eV2.12 eV1.46 eV0.24 eV10.29 eV6.88 eV5.28 eV3.27 eV2.39 eV1.55 eV0.23 eV0.2 eV(b)X = 0 (a) 1.56 eV2.65 eV C I S I n t e n s i t y ( a r b . un i t s ) X = 0.15 9.69 eV6.69 eV4.88 eV(c)
X = 0.20 3.29 eV2.19 eV1.2 eV0.22 eV9.56 eV6.82 eV5.25 eV3.72 eV2.42 eV1.38 eV0.28 eV(d)
X = 0.25 9.36 eV6.65 eV4.98 eV(e)
Photon Energy (eV)
X = 0.40
Figure 5.
The constant initial state (CIS) of the valence band features for Mo − x Re x alloys (where x = 0, 0.15, 0.2, 0.25 and 0.4) as a function of incident photon energy.The valence band features at different binding energy positions are staggered for theclarity of presentation. lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy d like states where the features of the PES in BE range from -5 eV below E F to -8 eV below E F are mainly derived from s like states. Therefore, the resonancearound 35 eV photon energy is from Mo 4 p -5 s transition via:1)Direct photoemission:4 p d s + hν → p d s + e − and2) Auger emission:4 p d s + hν → p d s → p d s + e − .whereas the resonance around 45 eV photon energy is from Mo 4 p -4 d transition via:1)Direct photoemission:4 p d s + hν → p d s + e − and2) Auger emission:4 p d s + hν → p d s → p d s + e − .The angle resolved photoemission spectroscopy (ARPES) study on the Mo(100) sur-face at various photon energies by Weng et al., revealed four resonances at about 15 eV,30 eV, 38 eV and 45 eV photon energies [42, 43]. They have argued that the resonancesof the features observed at B.E. = -0.3 eV and -3.3 eV below E F for the photon energiesof about 15 eV, 30 eV, and 38 eV are related to surface states. In the present case,both the resonances are observed in the entire VB indicating that these resonances arerelated to bulk states. However, the resonances around BE = -0.3 eV and -3.3 eV be-low E F are to be used with care as they might be influenced by the surface states aswell. It is worth mentioning that the surface resonance feature is extremely sensitiveto the surface contamination [42, 43]. Both the polycrystalline nature of the samplesand the appearance of these resonances in the alloys suggest that these resonances aremainly related to the bulk states. Similar to Mo, we have observed two resonances inthe Mo − x Re x alloys. As the Re content is increased (from x = 0), the resonance cor-responding to the incident photon energy of around 35 eV diminishes below 5 eV andbecome non existent for x ≥ p -5 d transition (46 eV) is expected for the resonance at around 45 eV photon energy.This additional contribution originates from the Re 5 p -5 d transition (46 eV) via:1) Direct photoemission:5 p d s + hν → p d s + e − and2) Auger emission:5 p d s + hν → p d s → p d s + e − .In order to know the effect of alloying Re with Mo on the PES we plot in Fig. 6, thedifference between the spectra for the Mo − x Re x alloys and pure Mo at 47 eV photonenergy. The positive contribution implies the enhancement in the intensity of the PESfeatures with respect to that of Mo introduced by the Re states. On the other hand, the lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy x = 0.15 0.20 0.25 0.40 I n t e n s i t y ( a r b . un i t s ) (a) x = 0.15 0.20 0.25 0.40 I n t e n s i t y ( a r b . un i t s ) Binding Energy (eV)(b)
Figure 6.
Mo and Re contribution extracted by taking the difference betweenphotoemission spectra of Mo − x Re x alloys and pure Mo at 47 eV photon energy. Thedetails are explained in the text. negative contribution corresponds to the loss of Mo states due to alloying and/or theabsence of Re states at the corresponding BE. The expanded portion of the differencespectra up to -5 eV below E F is shown in panel ( b ) of Fig. 6. This figure suggests thatthe contribution of DOS from the Re d states increases near E F with the increase in x up to 0.25. The width of the Re d states near E F also increases with the increase in x upto 0.25. For x =0.15 and 0.20, the Re d states are observed up to about -0.5 eV below E F , whereas for x = 0.25, the Re d states are observed up to about -1 eV below E F .On the other hand, the difference spectra for x = 0.40 is quite different from the rest ofthe alloys. In this case, the contribution to the difference spectra around E F is negativewhich indicates the loss of DOS in spite of the higher Re content. These results are inagreement with the DOS calculation for x = 0.4 (Fig. 4) which also indicate a decreasein the d partial DOS of Mo and Re as compared to the Mo − x Re x alloys. Additionally,in the higher binding energy side from -2 to -5 eV, there is significant contribution fromthe Re d states.The ARPES study performed by Okada et al. [14] shows that an extra band appearsat the Fermi surface of the Mo − x Re x alloys above 10 at.% of Re as a result of ETTin these alloys. When these results are compared with the difference spectra shown inFig. 6, it is clear that the extra band that appeared at the Fermi surface above 10 at.% lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy
30 40 50 60 7030 40 50 60 7030 40 50 60 70 30 40 50 60 7030 40 50 60 7030 40 50 60 70
Around 0.3 eV (a) I n t e n s i t y ( a r b . un i t s ) Around 2 eV (b)
Photon Energy (eV)Around 3 eV (c) x = 0 0.15 0.20 0.25 0.40 Around 5 eV (d)
Around 6 eV (e)
Around 10 eV (f)
Figure 7.
Comparison of the area normalized intensities as a function of incidentphoton energy at different binding energies of the valance band (indicated in the figure)for Mo − x Re x alloys with x = 0, 0.15, 0.2, 0.25 and 0.4. of Re has Re d like character. Recently we have shown that this extra band contributedistinctly to the superconductivity [18]. The temperature dependence of the normalstate resistivity of these alloys indicated that the phonon-assisted s - d scattering in Mois weak as compared to the intra-band s - s scattering, and that the s - d scattering isenhanced with the increase in x above 10 at.% of Re [7]. In the case of s - d scattering,the resistivity is proportional to N d ( E F ) /N s ( E F ) [49] where N d ( E F ) and N s ( E F ) arethe partial DOS of the d and s states at the Fermi level. In order to get further insightinto it, we have compared in Fig. 7, the area normalized intensities as a function ofincident photon energy at different binding energies of the valance band for the presentMo − x Re x alloys. The figure reveals that the resonance corresponding to the incidentphoton energy of around 35 eV is present in Mo over the entire valance band. However,when Re is alloyed with Mo, the resonance corresponding to the incident photon energyof around 35 eV diminishes below BE = -5 eV and vanishes for x ≥ ≥ -5 eV, this resonance is present in all the alloy compositions. Note that the d statesare present in the range E F to -5 eV below E F along with a small contribution from the s states. This indicates that in Mo, the photon energy corresponding to the resonanceof PES involving the s states of the VB is distinctly different from that involving the d states implying negligible s - d interaction. The present study reveals that there is an lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy d DOS in the vicinity of the Fermi surface when Re is alloyed withMo which results in the enhancement of s - d scattering in the alloy compositions. Then,the final state 4 p d s formed due to the Auger process at about the incident photonenergy of 35 eV can return to the original state via s - d scattering. This results in thediminishing of the resonant features below BE = -5 eV for the incident photon energyof 35 eV when Re is alloyed with Mo up to x = 0.20 and its subsequent disappearancefor x ≥ T c in these alloys is related to the s - d scattering. A specialmention is needed here for the Mo . Re . alloy, as the present photoemission as wellas band structure calculations showed the decrease in the density of states at the E F ascompared to x = 0.25, but, the T c enhanced to 12.6 K compared to 9.6 K for x = 0.25.This can be understood in terms of the dispersion of bands along the H-N direction ofthe Brillouin zone. The momentum k separation between the band that appeared in theH-N direction after alloying and the other band with Mo-like character reduces with theincrease in x . Therefore, for the alloys with higher concentrations of Re, the low energyphonons (small k ) can help in s - d scattering. Thus, the multi-band effect is smearedout and the T c is enhanced in the Mo . Re . alloy.
4. Conclusion
We have performed resonant photoemission spectroscopy experiments on the Mo − x Re x alloys with x = 0, 0.15, 0.2, 0.25, and 0.4 in the photon energy range 23-70 eV. Aresonance enhancement of intensity of the photo-electron spectra corresponding to Mo4 p -4 d and/or Re 5 p -5 d transitions at about 45 eV incident photon energy is observedin all the alloys. We have observed another resonance in Mo and low x alloys at about35 eV incident photon energy. Our analysis reveals that the resonance at 35 eV is relatedto the Mo 4 p -5 s transition. The two separate resonances at E F for pure Mo and lowerRe content alloys indicate the lack of s - d interaction in these alloys. The PES of allthe alloys are in agreement with the theoretical DOS estimated from band structurecalculations. The analysis suggests that experimentally observed enhancement of the d like states at the Fermi level and its dispersion upon alloying Re with Mo governs thephysical properties of the both normal and superconducting states.
5. Acknowledgement
We thank Shri R. K. Meena for sample preparations and Shri A. D. Wadikar for hishelp in the photoelectron spectroscopy experiments.
References [1] Hulm J K and Blaugher R D 1961
Phys. Rev.
Phys. Rev. lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy [3] Vonsovsky S V, Izyumov Y A and Kurmaev E Z 1982 Superconductivity of Transition Metals: TheirAlloys and compounds (Translated by E. H. Brandt and A. P. Zavarnitsyn) (Berlin: SpringerVerlag) and the references therein[4] Shum D P, Bevolo A, Staudenmann J L and Wolf E L 1986
Phys. Rev. Lett. Solid state Commun. Pi´sma Zh. Eksp. Teor. Fiz New J. Phys. Pi´sma Zh. Eksp. Teor. Fiz. Phys. Stat. Sol. (b)
Pi´sma Zh. Eksp. Teor. Fiz. Low Temp. Phys. Phys. Solid state
403 [Fiz. Tve. Tela 49, 389][13] Skorodumova N V, Simak S I, Blanter Y M and Vekilov Y K 1998
Phys. Rev. B New J. Phys. Phys. Rep.
Fiz. Met. Metalloved. J. Phys.: Condens. Matter Usp. Fiz. Nauk
427 [Sov. Phys. Usp. 22, 193 (1979)][20] Dikiy N P and Igna´teva T A 2006
Phy. Solid State
24 [Fiz. Tver. Tela 48, 25 (2006)][21] Banik S, Chakrabarti A, Joshi D A, Thamizhavel A, Phase D M, Dhar S K and Deb S K 2010
Phys. Rev. B J. Phys.: Condens. Matter Phys. Rev. B Phys. Rev. B Phys. Rev. B Sci. Technol. Adv. Mater. Phys. Rev.B Phys. Rev.B Physica B
J. Phys. Soc. Japan Phys. Rev. B lectronic structure of the Mo − x Re x alloys studied through resonant photoemission spectroscopy [32] Chaudhari S M, Phase D M, Wadikar A D, Ramesh G S, Hegde M S and Dasannacharya B A2002 Curr. Sci. J. Alloys Compd. http://kkr.phys.sci.osaka-u.ac.jp/ [35] Vosko S H, Wilk L and Nussair M 1980
Can. J. Phys. Surf. Sci.
Phys. Rev. Lett. J. Phys. C: Solid State Phys. Surface Science
Solid State Commun. Czech. J. Phys. B Phys. Rev. B Phys. Rev. Lett. Surface Science
Phys. Rev. B Phys. Rev. B Phys. Rev. B Phys. Rev. B Phys. Rev. B81