Intrinsic and extrinsic plasmons in the hard x-ray photoelectron spectra of nearly free electron metals
Mohammad Balal Shuvam Sarkar Pramod Bhakuni Andrei Gloskovskii Aparna Chakrabarti Sudipta Roy Barman

	

	
	^1UGC-DAE Consortium for Scientific Research, Khandwa Road, Indore 452001, India
	^2Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, D-22607 Hamburg, Germany
^3Raja Ramanna Centre for Advanced Technology, Indore 452013, Madhya Pradesh, India	  
^4Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, Maharashtra, India
	Collective plasmon excitations in solids that result from the process of photoemission are an important area of fundamental research. In this study, we identify a significant number (n) of multiple bulk plasmons (n)  in the hard x-ray photoelectron spectra of the core levels  and  valence bands (VBs)  of two well-known, nearly free electron metals,  aluminum (Al) and magnesium (Mg). On the basis of earlier theoretical works, we estimate the contributions of extrinsic, intrinsic, and interference processes to the intensities of 1s to 2s core level plasmons. The intrinsic contribution  diminishes from  22%  for 1  to 4.4% for  2, and becomes negligible thereafter (0.5% for 3). The extrinsic and intrinsic plasmon contributions  
	 do not vary significantly  across a broad range of photoelectron kinetic energies, and also between the two metals (Al and Mg). The interference contribution varies from negative to  zero as n increases. An asymmetric line shape is observed for the bulk plasmons, which is most pronounced for 1.   Signature of the surface plasmon  is detected in normal emission, and it  exhibits a significantly increased intensity in the grazing emission.  The  VB spectra of Al and Mg, which are dominated by s-like states, exhibit excellent agreement with the calculated VB based on density functional theory. The VB exhibits four multiple bulk plasmon peaks in the loss region, which are influenced by  an intrinsic  process in addition to the extrinsic process. On a completely oxidized aluminum surface, the relative intensity of the Al metal bulk plasmon remains nearly unaltered, while the surface plasmon is completely attenuated. 
	
	Intrinsic and extrinsic plasmons in the hard x-ray photoelectron spectra of nearly free electron metals
    Mohammad Balal^1, Shuvam Sarkar^1, Pramod Bhakuni^1, 
Andrei Gloskovskii^2, Aparna Chakrabarti^3,4,  Sudipta Roy Barman^1* 
    Received September 15, 1996; accepted March 16, 1997
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§ INTRODUCTION



The investigation of plasmon excitations in photoelectron spectra of free electron metals has been a central focus of fundamental research for over four decades, with ongoing theoretical <cit.>  and experimental <cit.> investigations. 
 These investigations have provided valuable insights into the physics of plasmons   in the nearly free electron metals. Furthermore,  continuous interest in this field highlights its relevance and potential for further advancements in our understanding  of collective electronic excitations and  the development of various future applications, such as plasmonics. The bulk and surface plasmons – observed as loss features in the core level photoelectron spectra – are dominated by an extrinsic process that results from the Coulomb interaction of the  conduction electrons with the photoelectron traversing through  the solid from the photoemission site to the surface.  An additional contribution to the plasmon intensity comes from an intrinsic process, where  the sudden change in the potential  due to the formation of a localized core hole attracts the  conduction electrons  to screen it, resulting in a plasmon oscillation.   From the variation of successive multiple bulk plasmon (n)  intensity in Al 2s x-ray photoemission spectrscopy (XPS), the intrinsic plasmon was estimated to be  14-25% of the total  intensity <cit.>.  Furthermore, an interference <cit.> between the intrinsic and extrinsic processes, where virtual plasmons created by one are  absorbed by the other,  plays an important role in determining the shape of the plasmons.   Hedin <cit.> pointed out that  the interference term should decrease as a function of the photoelectron kinetic energy. The coupling of  the Al surface plasmon to the oxygen adsorbed on its surface was observed in the O 1s  core level spectra in XPS <cit.>.   Biswas et al. <cit.> determined the relative contributions of the intrinsic, extrinsic, and interference processes in the  surface plasmon  from the XPS core level spectra of Al metal. The loss region has been studied for  Al and carbon  by XPS to identify both the one electron interband transitions and plasmon excitations  <cit.>. Bulk plasmons have  been observed in the XPS valence band (VB) spectra  of  Al <cit.> and Mg up to n= 2-3 <cit.>,  but their intensities were affected by presence of KLV Auger electron spectroscopy signal and x-ray satellites. The mechanism of instrinsic plasmon production, where, unlike the core level, the photo-hole is delocalized, was related to many-body effects and electron-electron interaction by theory <cit.>. 
 
Hard x-ray photoelectron spectroscopy (HAXPES) has become a vital method to study the bulk electronic structure of materials because of its large inelastic mean free path (8-10 nm) <cit.>.  Previous research has investigated this phenomenon for a limited number of elements, including carbon <cit.>, silicon <cit.>, germanium <cit.>,  phosphorous <cit.>, and  Al films grown on Si <cit.>.  However, the investigation of plasmon excitation in nearly free electron metals remains a captivating subject due to the substantial theoretical research that has been undertaken in this area previously <cit.>.
Notwithstanding this, theoretical investigations of  plasmons in free electron metals in the HAXPES regime are scarce. 
Shinotsuka et al. <cit.> performed a full quantum mechanical calculation, taking the interference term into account, using the model suggested by Hedin et al. <cit.>. Fujikawa et al. have attempted to address this issue through the application of the quantum Landau formula, which accounts for elastic scatterings both prior to and subsequent to the loss <cit.>. These works show that in the HAXPES regime, the extrinsic contribution  is dominant, although  both  the positive intrinsic   and the negative interference  terms are present. The interference and intrinsic contributions decrease very slowly as a function of the photoelectron energy and  are therefore  significant even at a large photon energy of 10 keV. Even the surface plasmon exhibits a peak of significant intensity at this photon energy <cit.>.  The other interesting theoretical result <cit.> is that  the loss features  hardly exhibit any angular dependence i.e., the grazing versus the normal emission spectra are nearly similar. This behavior is different compared to the low photon energy XPS regime <cit.>. The above-discussed intriguing characteristics of the plasmons, as postulated by theory <cit.>, have yet to be empirically investigated. 

HAXPES study of the core-level and VB plasmons in  free electron metals is scarce in previous literature,  despite the fact that this technique  offers unique advantages over XPS due to its deeper probing depths.   Another benefit of HAXPES over XPS is that the former does not  experience interference from the  Auger electron spectroscopy signal. 
A recent study on Al thin films on Si  and that of fractured Al metal reported  Al 1s related plasmons <cit.>.  However, the Si(111) surface was naturally oxidized and  the ex-situ introduced Al films were inhomogeneous  and showed a  large Al-oxide component  in the Al 1s spectrum. Thus, although bulk plasmons for clean bulk Al were observed,  the thin film related Al plasmons were affected by presence of oxide and Si related loss features.   


Here, we present a detailed HAXPES study of  the plasmon excitations in the VB and core level spectra for clean Al and Mg bulk single crystals.  A large number of multiple bulk plasmons (n) up to n= 13 is observed, in addition to a relatively weaker surface plasmon (). We conduct exhaustive multi-parameter curve fitting considering  the plasmons to ascertain the variation of their  intensity and shape. From the intensity variation,  the intrinsic, extrinsic, and interference contributions to n  are determined based on prior theoretical works <cit.>.  Normal and grazing emission properties of the bulk and surface plasmons have been investigated and compared with an oxidized Al surface.  In addition, our work shows  the existence of the  intrinsic process in the VB related bulk plasmons.   






§ METHODS

The experiments were carried out at the P22 beamline in PETRA III, Deutsches Elektronen-Synchrotron, Hamburg, Germany. A post-monochromator was used to improve the resolution and stability of the photon beam. All the spectra were measured using 6 keV photon energy. The electron energy analyzer has an angular acceptance angle of ±15^∘.  The overall energy resolution, including the source and the  analyzer contribution, was set at 0.3-0.4 eV, as measured from the Au Fermi edge  that was in electrical contact with the specimens. The details of  the beamline and the endstation can be found in Ref. P22.  The measurements were carried out at θ=  85^∘ (referred henceforth as normal emission) and 10^∘ (grazing emission), where θ is the angle between the  analyzer axis and sample surface.  
  
  Polished and oriented Al single crystals were cleaned in-situ by sputtering with  Ar^+ ions of energy 3-5 keV for the core-level studies.   In the case of the VB  and some core-level studies, the Al and Mg crystals were mechanically scraped in-situ with a diamond file.   
     The binding energy (E)  scale of both the core level and valence band spectra has been  defined from the Fermi level position of Al/Mg metal (rather than from Au) because of the recoil shift <cit.>; this is discussed later in subsection IIIC. The HAXPES core level main peaks have been fitted using  the least squares error method, where the Doniach-Šunjić (DS) line shape represents the main peak <cit.>.  
    Asymmetric Lorentzian line shapes have been used to represent the plasmon loss peaks <cit.>, as also suggested by the theoretical 1  and 1  line shapes from Ref. Shinotsuka08 shown in Fig. S1 of Supplementary Material (SM) <cit.>. The lifetime broadening of the core level main peak, the DS asymmetry parameter, intensities, peak positions, and the inelastic background have been varied. The half width at half maximum of the life-time broadening  and the DS asymmetry parameter for Al (Mg) 2s, determined from our fitting, are 0.4 (0.32) eV and  0.1 (0.12), respectively. Each of the  plasmon peaks has been simulated by four parameters: intensity, position,  and an asymmetric Lorentzian <cit.> with independently varying left (Γ_L) and right (Γ_R) half width at half maximum.  Besides the n peaks, 2, 1+1, and 2+1 surface plasmons  were also considered for Al 1s.   The inelastic background was simulated by the Tougaard method <cit.>, whereas use of the Shirley method resulted in  unphysically large value of the intrinsic plasmon probability. 
  As in our earlier works <cit.>, all the parameters were not varied simultaneously to avoid unphysical solutions: for example,  the parameters for  plasmons with  n≥7 were varied individually. Thus, the  number of  independently variable parameters for  1s  (2s) was  68 (39).  



The calculation of the electronic properties of the bulk Al and Mg metals has been performed using the all-electron full potential linear augmented planewave (FPLAPW) method, including scalar relativistic corrections, by employing the density functional theory (DFT) based WIEN2k<cit.> program package. For the exchange-correlation functional, we consider the generalized gradient approximation over the local density approximation, given by Perdew, Burke, and Ernzerhof (PBE) <cit.>. Energy cut-off values of about 15 Ry have been used in the calculations. The charge density cut-off is 14. Further, we have used 10 as the maximum value of angular momentum for the (l, m) expansion of wave function and density. The convergence criteria for energy and charge have been taken to be 10^-5 Ry and 0.001 e^-1, respectively. The total density of states (DOS) is calculated from the Kohn-Sham orbitals, and its integration up to the Fermi level gives the total number of valence electrons. The partial DOS (PDOS) is obtained by projecting the total DOS for each orbital (s, p, d). For Al and Mg with delocalized states,  touching muffin-tin sphere was taken to minimize the discrepancy between the total DOS and the sum of all the PDOS.

To calculate the theoretical VB, the angular momentum  projected  PDOS was multiplied by the corresponding photoemission cross sections per electron calculated for 6 keV  photon energy by Trzhaskovskaya et al. <cit.>.  In the case where an energy level is not occupied and so the cross section is not calculated, the closest value is assumed, as in our previous work <cit.>. For example, for Mg p PDOS, the cross-section is taken to be the same as that of Al p.   Furthermore, the partial contributions are  added and multiplied by the Fermi function  and subsequently convoluted with a Gaussian function representing the instrumental resolution. Additionally, an energy dependent Lorentzian broadening given by  μ×E has been used, where E is the binding energy and μ is taken to be  0.15 eV <cit.>. 





 

§ RESULTS AND DISCUSSION

 
 

 §.§ Multiple bulk plasmons in Aluminum core level spectra

Al 1s: The Al 1s core level spectrum  in Fig. <ref>(a)  shows multiple bulk  plasmon  peaks (n) with n as large as 13, as is evident from the magnified spectrum. These plasmons appear on the higher binding energy (E) side i.e. the loss region of the main peak at  1559.3 eV.   The first bulk plasmon   peak (1)  appears at    loss energy, and the subsequent n multiple  plasmons appear at  equal   intervals. The positions of the plasmon peaks thus provide an average estimate of  to be 15.3 eV; a similar value is obtained from Al 2s plasmons in Fig. <ref>(a). 
The reasons that large number of multiple bulk plasmons could be observed are  large photoemission cross-section of  the s states  at high photon energy (6 keV),   the large flux of the photon beam,  the n= 7-13 plasmon region recorded with larger dwell time, and   the absence of any other   photoelectron or Auger peaks 
 that could obfuscate the plasmons.  The 1 surface plasmon  is also distinctly visible, as shown by the blue arrow.  The behavior of this surface plasmon will be discussed further in subsection III B.    
Bulk plasmons up to n= 7 and the 1 surface plasmon the 1s spectrum of Al metal were reported recently <cit.>, but quantitative analysis their shapes and intensities were not performed. 

Here, based on rigorous multi parameter curve fitting,   the normalized intensities [b(n), i.e., area under n divided by that of the main peak] and shapes [left (Γ_L) and right (Γ_R) half width at half maximum of an asymmetric Lorentzian <cit.>] have been determined. Besides taking a realistic shape of the bulk plasmons justified by theory in subsection III B, inclusion of  weak surface plasmon contributions such as  2(red arrow), 1+1 (black tick), and 2+1 (red tick), improves the quality of the fitting.  We find that b(n) determined from the area of the plasmons  obtained from fitting (shaded with different colors)  decreases with n, as  shown by the red open circles in Fig. <ref>(b). This variation can be explained by Equation 1, as discussed later. Figure <ref>(c)  portrays the asymmetric shape of  n,  where  Γ_R  is smaller compared to Γ_L. Both show a nearly similar  increasing trend  with  n.  The  larger width  of (n+1)    compared to n  is because the former is excited by the latter and  can be regarded as the self-convolution of the latter <cit.>.  The asymmetry can be  quantified by the ratio Γ_L/Γ_R (= κ), its variation with n is shown in  Fig. <ref>(d). 



Al 2s: Figure <ref>(a)  shows the Al 2s spectrum   at  normal emission, 
 showing multiple plasmon peaks n up to n= 7 (compared to n= 13 for Al 1s) because of the relatively lesser photoemission cross section of  2s  compared to  1s. The intensity of the former is ∼9 times less, as shown by the Al survey spectrum in Fig. S2 of SM <cit.>. For the same reason, although 1  surface plasmon is also distinctly visible at 10.4 eV loss energy (blue arrow),  the multiple surface plasmons are not apparent.  Another reason for smaller n is that  Ar 2p and 2s peaks  at E= 242.2 and 320.3 eV, respectively  (Fig. S2 of SM <cit.>)  interfere because  a small amount of  Ar is implanted  during  the sputtering  process <cit.>. 

 In particular, Ar 2p peak  coincides with the 8^ th plasmon, and the former has  a larger intensity. Additionally, the Al related plasmons excited by the Ar 2p photoelectrons <cit.>  overlap with   n>7 plasmons.   
 b(n) determined from multi parameter curve fitting is shown in Figure <ref>(b). Figure <ref>(c) shows that the asymmetry of the Al 2s plasmons  is qualitatively similar to that of the Al 1s :  Γ_R is smaller than  Γ_L, and both increase with n.  The asymmetry in the plasmon line shape given by  κ  decreases  from about 2.7  (n= 1)  to about 1.8 for  n≥2-3. 


Bulk plasmon intensity variation: The decrease of b(n)  with n has been studied theoretically by different  groups <cit.>  to ascertain the  contributions of the different processes connected to the bulk plasmon. Based on perturbation theory arguments,  considering only the extrinsic process, it was suggested that  b(n) should vary as α^n, where α is a measure of the extrinsic plasmon probability <cit.>.  But the black dashed curve that is obtained using this expression shows a large systematic deviation, as shown by the residual  in the top panel of Fig. <ref>(b) in same line type. This shows that, in addition to the extrinsic process, the  intrinsic and interference processes could also be significant. So, a modified Langreth equation <cit.> that considers all three terms  has been used to represent b(n) as follows:

    b(n) = α^n∑_m=0^n[(β-cχ)/α]^m/m!                                                                 (1)

where  β is the measure of the probability of  the intrinsic process for the n^ th plasmon <cit.>.  χ is the probability of the interference process <cit.> given by the product of intrinsic and extrinsic plasmon probabilities <cit.>, where  c is the proportionality constant <cit.>. If the above expression is used to fit the experimental b(n) by varying α, β, and c,  the quality of the fitting (blue curve)  improves substantially, which is evident from a  reduction in chi-square error 
by a factor of  about 2.5 and  comparison of  the  residuals (blue solid and black dashed lines)  in the  top panel.  From the fitting, we obtain  α=  0.54±0.05 
 and β=  0.19±0.1. 
 The experimental value of α is in good agreement with the  theoretically suggested value  of 0.5 by Chang and Langreth <cit.>.  The interference term (black dot-dashed curve) is found to be finite but negative, with a rapidly decreasing contribution that becomes nearly zero for n>3.  

 b(n) for Al 2s has been fitted using Equation 1, as shown by the blue curve in Fig. <ref>(b). The residual in the upper panel demonstrates the good quality of the fitting. On the other hand, the fit is worse if  only the extrinsic term is considered. From the fitting, 
 we find that   α=  0.53±0.05
 and β= 0.18±0.1. 
 Thus, the extrinsic and intrinsic  contributions are similar between  2s and 1s,  although for the former,  the kinetic energy (E_k) of the electrons is larger (5831 eV) compared to the latter (4390 eV).  
Al 2s recorded by XPS, where E_k is relatively smaller (1133 eV), gave α (= 0.46 eV) and β (= 0.22 eV) <cit.> that are not significantly different from the HAXPES values.  This shows that, contrary to the expectation that the extrinsic process might be dominant at larger E_k due to larger inelastic mean free path of the photoelectrons, all  three processes have nearly similar contributions over a large range of E_k from  1133 eV (≈ 1 keV) to 5831 eV (≈ 6 keV). This is  in agreement with the theoretical study by Shinotsuka et al. <cit.> that shows hardly any change in the different processes in the 1  bulk plasmon  of Al 
 in the   range of 2 to 5 keV. 

The interference term (black dot-dashed curve) also shows similar trend. Its contribution at n= 1 is also nearly similar:  -0.14±0.05 
 for  1s and -0.17±0.05  for  2s using HAXPES, while it is  reported to be -0.2 for 2s from XPS <cit.>. This is in agreement with the calculation by Shinotsuka et al. <cit.>, who found that the interference term does not decrease in the HAXPES regime, in disagreement with the prediction by Hedin <cit.>. 
 
 








 §.§ Multiple bulk plasmons in  Magnesium core level spectra


Mg 2s spectrum of clean Mg metal at normal emission, as depicted in Fig. <ref>(a), also exhibits multiple plasmon peaks denoted by n (n= 1-7).  of Mg, determined from the average separation of the plasmon peaks from the main peak, is 10.6 eV.  It is considerably smaller  because of the smaller electron number density of Mg, which  has  2 electrons in the outer shell  compared to  3 electrons in Al.  A weak surface plasmon  is  observed  at 7.5 eV loss energy  (blue arrow). 
 Using curve fitting as in case of Al,  b(n) for Mg has been determined [Fig. <ref>(b)]. The residual (blue curve) in the top panel of  Fig. <ref>(b) shows  good quality of the fitting using Equation 1. 
The values of   α  and β   turn out to be 0.55±0.05
 and 0.18±0.1,  
 respectively.    These values are nearly similar to Al. 

 The interference term for Mg (black dot-dashed curve), as in the case of Al, is negative for n= 1 and  decreases to almost zero for n≥ 3. Figure <ref>(c) shows that the asymmetry of the Mg 2s plasmons  given by κ  decreases  from about 4  (n= 1)  to below 2 for  n= 3 [Fig. <ref>(d)]. This was also observed for Al 2s.  Larger κ i.e., asymmetry in the 1  plasmon shape  compared to  n≥2 is because of the sizable  intrinsic and interference plasmon contributions  that are more asymmetric in shape compared to the extrinsic plasmon <cit.>.




The α and β values obtained for Mg 2s are nearly similar to those from Al 1s and 2s, average representative values for these free electron metals being α= 0.54±0.05 and  β=  0.18±0.1.
Considering these values, the ratio of  the  intrinsic to extrinsic plasmon probabilities (e^-ββ:α from Equation 1) for 1   turns out to be 0.28:1. 
 For 
 2    the probability ratio (e^-ββ^2/2!:α^2) is  0.05:1, 
 whereas for 3  it is  0.005:1 (e^-ββ^3/3!:α^3) .  

 Thus, the  intrinsic plasmon contribution decreases rapidly  with n from  22%  (n= 1) to 4.4% (n= 2), and becomes negligible thereafter (0.5% for n= 3). 





 §.§ Surface plasmon behavior  in the Al 2s core level spectra

This subsection is dedicated to an in-depth analysis of the surface plasmon.   Figure <ref>(a, b) shows the 1 along with 1 in Al 2s spectra of  a polished surface cleaned by Ar ion sputtering. 
 Comparison of the 1  intensity  between normal emission in panel a and grazing emission in panel b shows  a sizable enhancement in the latter.   From the curve fitting, we quantify this by the normalized intensity of 1   i.e., s(1) (the intensity of  1  divided by the main peak). s(1) increases from 
 0.13 
 in normal to 0.44 
 
 in grazing emission. However, a direct comparison with the XPS spectra from Ref. Biswas03 [Figs. <ref>(a,b)] shows the surface plasmon is weaker in HAXPES for both normal and grazing emission. This is   attributed to 
	diminished extrinsic contribution  due to larger velocity (v) of the photoelectron <cit.>. 
From Fig. <ref>(a, b),  b(1) decreases from 0.6 
 in normal  to 0.43 
in grazing emission, which was related to the variation of extrinsic bulk plasmon contribution with emission angle in  theory <cit.>.  The intensity ratio R  (= 1/1) is larger in the grazing (1 i.e., the surface plasmon is  as intense as the bulk plasmon) 
compared to normal emission  (0.2). 












The considerable increase of  s(1) 
and R  
 in the grazing emission  discussed above is in disagreement with the theoretical results of  Shinotsuka et al. <cit.> for HAXPES, where hardly any difference in the calculated  1  and 1  

 was observed between normal and grazing emission (Fig. S1 of SM <cit.>).  Nevertheless, to obtain an estimate of R from theory, we have fitted the theoretical spectrum  using asymmetric Lorentzian shapes for  both 1  and 1 from   Ref. Shinotsuka08. A reasonably good  fit of the theoretical shape <cit.> with the asymmetric Lorentzians in Fig. S1 of SM <cit.> post-priori justifies  the use of the latter  to fit the experimental plasmon shapes in Figs. <ref>-<ref>.  From the area under the fitted curves, the theoretical value of R turns out to be close to 0.2, unchanged  for both normal and grazing emission. While R= 0.2 is in excellent agreement with the experimental normal emission value (0.2), it is   conspicuously underestimated  for the grazing emission,  where the experimental value  is 1.
 Enhancement of s(1) in grazing emission has also been reported for XPS. For example,  in Al 2s  from XPS, a ten times increase in s(1) has been reported in the grazing emission, which  was explained by an increase in v parallel to the surface <cit.>. This effect was possibly not considered in Ref. Shinotsuka08. Note that in Fig. <ref>, the shape of the surface plasmon is found to be highly asymmetric, with Γ_R considerably smaller than Γ_L. Their ratio κ is 4.9 (7.9) in grazing (normal) emission (Fig. <ref>). 
 The asymmetric shape of the surface plasmon as well as the bulk plasmons is in agreement with  Ref. Shinotsuka08 and the earlier theoretical works <cit.>. 

Figures <ref>(c,d) show an interesting result that for rough surface obtained by scraping the polished surface with a diamond file,   the enhancement of the surface plasmon in the grazing emission is not as pronounced: s(1)= 0.14 in the normal and 0.17 in grazing emission.  This is because  the emission angle is not well defined for the rough surface.  
Comparison of Figs. <ref>(a,c) shows that both the bulk and surface plasmon intensities in normal emission are however nearly similar between the smooth [b(1)= 0.6, s(1)= 0.14] and the rough surface [b(1)= 0.58, s(1)= 0.14].   
 



 §.§ Plasmons  in the  core level spectra of a fully oxidized Al surface

In  Fig. S3(a) of SM <cit.>, a fully oxidized  Al crystal surface, shows   oxide and  metal-related components in the Al 1s spectrum.    In spite of being fully oxidized, the metal peak is dominant in normal emission compared to the oxide-related peak at 2.7 eV higher E  
 because of the large electron mean free path in HAXPES (80 Å  for Al 1s at 6 keV <cit.>).  The thickness of the oxide film  estimated  from the relative intensity variation of the  metal- and the oxide-related peaks  with θ <cit.> turn out to be  48±2 Å.  In   normal emission, the  metal-related bulk plasmon is observed at 15.3 eV loss energy with  b(1)= 0.5.  At the grazing emission in  Fig. S3(b) of SM, although the oxide-related peak is highly enhanced in intensity (shown truncated),  surprisingly, the 1  corresponding to the metal underneath  is still observed with the same  of 15.3 eV and  a   b(1) value of  0.6.  Both these values of b(1) in oxidized Al are close to that of the clean Al metal [b(1)= 0.6, Fig. <ref>(b)].    Thus, the normalized intensity of the bulk plasmon is  hardly   affected by the oxide layer formed on the  surface.  This is because both the metal's main peak and the bulk plasmon are similarly attenuated by the oxide layer. However, in contrast, the surface plasmon is completely attenuated  because the metal surface is fully covered by the  oxide film.  














 

 §.§ Multiple bulk plasmons in the valence band spectra of Al and Mg



The HAXPES valence band (VB) spectrum of Al metal, along with the loss region shows, multiple bulk plasmons  n up to n= 4 (black arrows) [Fig. <ref>(a)]. The data were recorded for a scraped surface because, for the Ar^+ ions sputtered surface, the Ar 3p signal arising from implanted Ar bubbles <cit.> appears at 9.3 eV and interferes with the VB, as shown in Fig. S4 of SM.  In Fig. <ref>(b), the   theoretical  VB – calculated using the  PDOS shown in Fig. <ref>(c) – exhibits excellent agreement with the experiment:  All the features, such as a peak near the Fermi level at E= 1 eV (blue arrow), a dip at 2 eV (blue tick), a weak feature centered at 3 eV  (black arrow), and the broad hump around 6 eV  (green arrow), are visible at nearly identical energies and possess similar relative intensities.  The VB is largely  dominated by the s-like states because  of their large photoemission cross-section  for hard x-rays <cit.>. The small  contribution from p-like states  is rather featureless.  
 It should be noted  that the interstitial (int) contribution to the total DOS  is significant because a substantial part of the electron density lies outside the atomic sphere that is used to calculate the PDOS [Fig. <ref>(c)]. Another point to note is that the PDOS  of Al previously calculated using the KKR method <cit.> differs considerably from our calculation [e.g., compare Fig. <ref>(c) with the inset of Fig. S5 in SM <cit.>].  We used the PDOS from Ref. Leonard78 to calculate the VB and find that it  differs significantly from the experiment (Fig. S5 of SM <cit.>): a peak at ∼5 eV is  evident. This is absent in the experimental spectrum, while the dip at ∼2 eV (blue tick) is overestimated. These observations show   the shortcomings of the previous calculation, which  is possibly related to unphysical fluctuations on the lower energy side and was performed with constant potential outside the  Muffin tin sphere <cit.>. 


In the case of Mg  metal, the VB spectrum also shows multiple bulk plasmons  n up to n= 4  with  ∼10.5 eV [black arrows in Fig. <ref>(e)].   The VB, shown on an expanded scale in Fig. <ref>(f), exhibits excellent agreement with the theoretical  VB, which is calculated using the  PDOS shown in Fig. <ref>(g). An earlier augmented plane wave calculation <cit.> of  the PDOS for Mg agrees well with  our calculation.   
 A peak close to the Fermi level at 0.3 eV (blue arrow), a dip at 0.7 eV (blue tick), and a broad hump around 3 eV (green arrow) are visible at similar energies and  exhibit comparable relative intensities [Fig. <ref>(f)].  Here also, as in the case of Al, the VB is largely  dominated by the s-like states. 

 



 





 
 



 The plasmon loss spectra of VB have been calculated  for Mg and Na by Penn <cit.>, which drew on the work by Langreth <cit.>. Unlike  the core level  intrinsic plasmon that is created by a localized core hole in the final state,  the photo-hole in the VB is delocalized. So, the mechanism of  intrinsic plasmon production in the VB was proposed to be  related to electron-electron interaction:  a second electron creates the intrinsic plasmon  via its interaction with the  conduction electrons and scatters into the hole left by the photoexcited electron <cit.>.   Although  energy dependence and interference effect were not considered in theory <cit.>, remarkable agreement was obtained with the XPS spectra <cit.> only when  both extrinsic and intrinsic plasmons were considered. On the other hand,  the plasmon intensities were significantly underestimated  if the intrinsic plasmon was not considered. This established the presence of  intrinsic plasmons  in the XPS VB plasmon  in  nearly free-electron metals <cit.>. 



To compare theory and experimental results,   the  shapes of the n^ th VB plasmons for both Al and Mg have been simulated 
 by shifting the calculated VB by n towards higher E, and allowing the  intensity and an additional Gaussian broadening to vary [Figs. <ref>(a,e)]. We find that unlike the core level plasmons, asymmetric broadening is not required, and the FWHM of the Gaussian remains nearly unchanged with n (2 eV and 2.5  eV for Al and Mg, respectively). 
 The b_ VB(n) values of Mg  have also been extracted for  the theoretical calculations by Penn <cit.> for XPS and the the XPS spectrum published in the literature <cit.>   (Fig. S6 of SM <cit.>). This has been done by shifting the calculated XPS VB by n and broadening it by a Gaussian,  as  discussed above.  Figure S6 of SM <cit.> shows good agreement between the calculated and experimental XPS VB. The former is  obtained from the PDOS in Figs. <ref>(c,g) using the photoemission cross-sections for AlK_α (1486.6 eV) radiation <cit.>. 
 
 
 Figure <ref> shows  b_ VB(n), which is the area of the n^ th plasmon  divided by the area of the VB. b_ VB(n) for  Mg and Al HAXPES VB are close, as shown by the red and blue curves.
  
 b_ VB(1)  for Mg  HAXPES  (0.87) and XPS (0.9) are quite similar to each other and  to the theoretical  value (0.9) of Mg  that includes the  intrinsic and extrinsic plasmons (black filled circle-dashed line).  On the other hand, if intrinsic plasmon is not considered, the contribution of only the extrinsic process is significantly less (0.6) (gray filled square-dashed line).  Similarly, b_ VB(2) and b_ VB(3) for both Mg HAXPES and XPS  are closer to the theoretical values that include both  intrinsic and extrinsic plasmons.   Thus, our data   provide  evidence of  the intrinsic plasmon production in the VB related plasmons of Mg  measured by HAXPES. 


 

 §.§ Recoil effect in  the valence band spectra of  Mg


The recoil effect is well known in the HAXPES core level spectra of light elements. When a photoelectron of mass m is emitted with a large kinetic energy (E_kin) from an atom of mass M, the photoelectron delivers a recoil energy (E_R) to that atom, which is given by E_R≈m/M× E_kin <cit.>. The photoelectrons lose this energy, E_R, resulting in a recoil shift towards higher E. This effect has also been observed in the VB  of light metals such as Al (atomic mass 27 u) 
 through a shift of  the Al metal Fermi edge compared to that of Au <cit.>. Au,  being of high mass (197 u),  hardly exhibits this effect.  Recently, such a recoil shift in the VB has been reported in a light complex metallic alloy β-Al_3Mg_2 <cit.>. 
 Here in Fig. <ref>(d),  the recoil shift of Al is, however, smaller (85 meV) compared to 120 meV reported  using 7.94 keV <cit.>. This can be explained by the proportionality of the recoil shift with E_kin i.e., 6  keV/7.94  keV×120 meV= 90.7 meV, which is close to 85 meV. 
 Due to marginally smaller mass  of Mg (24.3 u)  compared to Al, the recoil shift is  found to be slightly larger [90 meV,  Fig. <ref>(h)].





§ CONCLUSION

Multiple bulk plasmons (n) in the valence band (up to n= 4) and core level spectra (up to n= 13)  of free electron metals such as Al and Mg  have been studied by hard x-ray photoelectron spectroscopy (HAXPES).  
 Based on earlier theoretical works <cit.>, estimates of the extrinsic, intrinsic, and interference processes that contribute to the core level plasmon intensities  are obtained from exhaustive multi parameter curve fitting. The probabilities of the extrinsic and intrinsic  processes in the core level plasmons are nearly similar for the two free electron metals,  α  and β being  0.54±0.05 and 0.18±0.1, respectively. 
 These values imply that, as n increases, the intrinsic plasmon contribution decreases  while the interference plasmon changes  from negative to zero.  Despite the larger inelastic mean free path in HAXPES, the intrinsic, extrinsic, and interference processes  remain nearly unchanged across a broad kinetic energy range  (1–6 keV). This finding is consistent with previous theoretical research <cit.>.  The 1  line shape is  more asymmetric because of the presence of  sizable  intrinsic and interference terms.   The 1  surface plasmon has been identified in  both Al and Mg. Its intensity increases  significantly in the grazing emission compared to the normal emission.  In the case of   oxidized aluminum, the surface plasmon is completely suppressed, while the bulk plasmon intensity is almost unaffected compared to the metal's main peak.  

Multiple plasmons are observed in the loss region of the Al and Mg valence bands; the shape of the VB is in excellent agreement with the DFT-based calculated valence band.  Comparison with the theoretical calculation <cit.> after extracting the relative VB plasmon intensities establish the existence of the intrinsic  plasmon, besides the extrinsic plasmon. The recoil shift observed  in both Al and Mg VB is related to the kinetic energy of the photoelectron and the mass of the atom.



§ ACKNOWLEDGMENT

The HAXPES experiments were carried out at PETRA III of Deutsches Elektronen-Synchrotron, a member of Helmholtz-Gemeinschaft Deutscher Forschungszentren. Financial support by the Department of Science and Technology, Government of India, within the framework of the India@DESY collaboration is gratefully acknowledged. We are thankful to  C. Schlueter, R. Choubisa, and D. Sébilleau  for support and encouragement. The Computer division of the Raja Ramanna Centre for Advanced Technology is thanked for installing the DFT codes and providing support throughout. We thank  I. Schostak for  skillful technical support.


^*e-mail address: barmansr@gmail.com












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	[Mandal et al.(2022)Mandal,
		Tricot, Choubisa, and Sébilleau]Mandal22
	author author A. Mandal, author S. Tricot,
		author R. Choubisa, and		author D. Sébilleau, title title Model dielectric functions for fluctuation
			potential calculations in electron gas: A critical assessment, https://doi.org/10.1103/physrevb.105.195424 journal journal Physical Review B volume 105, pages 195424 (year 2022)NoStop
	[Fujikawa et al.(2022)Fujikawa, Niki, and Haniuda]Fujikawa22
	author author T. Fujikawa, author K. Niki,		and author M. Haniuda,	title title Intrinsic and extrinsic losses in
			photoemission spectra, https://doi.org/10.7566/jpsj.91.064708
	journal journal Journal of the Physical Society
				of Japan volume 91, pages 064708
		(year 2022)NoStop
	[Shinotsuka et al.(2008)Shinotsuka, Uwatoko, Konishi, and		Fujikawa]Shinotsuka08
	author author H. Shinotsuka, author T. Uwatoko,
		author T. Konishi, and author T. Fujikawa, title
	title Theoretical study of plasmon loss peaks in core-level
			photoemission spectra: Energy and angular dependence, @noop 
	journal journal Journal of Surface Analysis		volume 14, pages 332 (year
		2008)NoStop
	[Fujikawa et al.(2008)Fujikawa, Kazama, and Shinotsuka]Fujikawa08
	author author T. Fujikawa, author M. Kazama,		and author H. Shinotsuka,	title title Theoretical study of plasmon losses in
			core-level photoemission spectra, https://doi.org/10.1380/ejssnt.2008.263 journal journal e-Journal of Surface Science and Nanotechnology volume 6, pages 263 (year
		2008)NoStop
	[Zhou et al.(2018)Zhou,
		Gatti, Kas, Rehr, and		Reining]Zhou18
	author author J. S. Zhou, author M. Gatti,
		author J. J. Kas, author J. J. Rehr, and author L. Reining, title
	title Cumulant Green’s function calculations of plasmon
			satellites in bulk sodium: Influence of screening and the crystal
			environment, https://doi.org/10.1103/physrevb.97.035137 journal journal Physical Review B volume 97, pages 035137 (year
		2018)NoStop
	[Kazama et al.(2014)Kazama,
		Shinotsuka, Ohori, Niki,
		Fujikawa, and Kövér]Kazama14
	author author M. Kazama, author H. Shinotsuka,
		author Y. Ohori, author K. Niki, author
		T. Fujikawa, and author
		L. Kövér, title
	title Plasmon losses in core-level photoemission spectra studied
			by the quantum Landau formula including full multiple scattering, https://doi.org/10.1103/physrevb.89.045110 journal journal Physical Review B volume 89, pages 045110 (year 2014)NoStop
	[Yubero and Tougaard(2005)]Yubero05
	author author F. Yubero and author S. Tougaard, title title Quantification of
			plasmon excitations in core-level photoemission, https://doi.org/10.1103/physrevb.71.045414 journal journal Physical Review B volume 71, pages 045414 (year 2005)NoStop
	[Schattke and Hove(2003)]Hedin03
	author author W. Schattke and author M. A. v. Hove, https://doi.org/10.1002/9783527602506 title Solid‐State Photoemission and Related Methods: Theory and
				Experiment (publisher Wiley, year 2003) p.	pages 116NoStop
	[Mahan(2000)]Mahan00
	author author G. D. Mahan, https://doi.org/10.1007/978-1-4757-5714-9 title Many-Particle Physics (publisher Kluwer
		Academic, New York, year 2000)NoStop
	[Hedin et al.(1998)Hedin,
		Michiels, and Inglesfield]Hedin98
	author author L. Hedin, author J. Michiels,		and author J. Inglesfield,	title title Transition from the adiabatic to the
			sudden limit in core-electron photoemission, https://doi.org/10.1103/physrevb.58.15565 journal journal Physical Review B volume 58, pages 15565 (year 1998)NoStop
	[Inglesfield(1983)]Inglesfield83
	author author J. E. Inglesfield, title title Plasmon satellites in
			core-level photoemission, https://doi.org/10.1088/0022-3719/16/2/023 journal journal Journal of Physics C: Solid State Physics volume 16, pages 403 (year 1983)NoStop
	[Inglesfield(1981)]Inglesfield83a
	author author J. Inglesfield, title title Plasmon excitation in
			core-level photoemission, https://doi.org/10.1016/0038-1098(81)90863-2 journal
		journal Solid State Communications volume 40, pages 467 (year 1981)NoStop
	[Bose et al.(1983)Bose,
		Prutzer, and Longe]Bose82
	author author S. M. Bose, author S. Prutzer, and		author P. Longe, title title Plasmon satellites in the x-ray photoemission
			spectra of metals and adsorbates, https://doi.org/10.1103/physrevb.27.5992 journal journal Physical Review B volume 27, pages 5992 (year 1983)NoStop
	[Penn(1978)]Penn78
	author author D. R. Penn, title title Role of intrinsic plasmons
			in conduction-band x-ray photoemission from solids, https://doi.org/10.1103/physrevlett.40.568 journal journal Physical Review Letters volume 40,		pages 568 (year 1978)NoStop
	[Penn(1977)]Penn77
	author author D. R. Penn, title title Theory of the electron
			energy-loss spectrum in core-level x-ray photoemission from solids, https://doi.org/10.1103/physrevlett.38.1429 journal journal Physical Review Letters volume 38,		pages 1429 (year 1977)NoStop
	[Baer and Busch(1973)]Baer73
	author author Y. Baer and author G. Busch,	title title X-ray photoemission from Aluminum,	https://doi.org/10.1103/physrevlett.30.280 journal
		journal Physical Review Letters volume
			30, pages 280 (year 1973)NoStop
	[Citrin et al.(1977)Citrin,
		Wertheim, and Baer]Citrin77
	author author P. H. Citrin, author G. K. Wertheim, and author Y. Baer, title title Many-body processes in
				x-ray photoemission line shapes from Li, Na, Mg, and Al metals, https://doi.org/10.1103/physrevb.16.4256 journal journal Physical Review B volume 16, pages 4256 (year 1977)NoStop
	[Šunjić and Šokčević(1974)]Sunjic74
	author author M. Šunjić and author D. Šokčević, title title Inelastic effects in
			x-ray photoelectron spectroscopy, https://doi.org/10.1016/0368-2048(74)85063-2 journal
		journal Journal of Electron Spectroscopy and Related
				Phenomena volume 5, pages 963
		(year 1974)NoStop
	[Langreth(1974)]Langreth74
	author author D. C. Langreth, @noop  title in Collective
				Properties of Physical Systems: Medicine and Natural Sciences edited by B.
				Lundquist (publisher Elsevier, year 1974)	p. pages 210NoStop
	[Mahan(1973)]Mahan73
	author author G. D. Mahan, title title Electron energy loss during
			photoemission, https://doi.org/10.1002/pssb.2220550227 journal journal Physica Status Solidi B volume 55, pages 703 (year 1973)NoStop
	[Chang and Langreth(1972)]Chang72
	author author J.-J. Chang and author D. C. Langreth, title title Deep-hole excitations in
			solids. I. fast-electron-plasmon effects, https://doi.org/10.1103/physrevb.5.3512 journal journal Physical Review B volume 5, pages 3512 (year 1972)NoStop
	[Langreth(1971)]Langreth71
	author author D. C. Langreth, title title Born-oppenheimer
			principle in reverse: Electrons, photons, and plasmons in
			solids—singularities in their spectra, https://doi.org/10.1103/physrevlett.26.1229 journal journal Physical Review Letters volume 26,		pages 1229 (year 1971)NoStop
	[David and Godet(2016)]David16
	author author D. David and author C. Godet,	title title Derivation of dielectric function and
			inelastic mean free path from photoelectron energy-loss spectra of amorphous
			carbon surfaces, https://doi.org/10.1016/j.apsusc.2016.06.044
	journal journal Applied Surface Science		volume 387, pages 1125 (year
		2016)NoStop
	[Özer et al.(2011)Özer, Moon, Eguiluz, and		Weitering]Ozerprl11
	author author M. M. Özer, author E. J. Moon,
		author A. G. Eguiluz, and		author H. H. Weitering,	title title Plasmon response of a quantum-confined
			electron gas probed by core-level photoemission, https://doi.org/10.1103/physrevlett.106.197601 journal
		journal Physical Review Letters volume
			106, pages 197601 (year 2011)NoStop
	[Biswas et al.(2003)Biswas,
		Shukla, Banik, Ahire, and		Barman]Biswas03
	author author C. Biswas, author A. K. Shukla,
		author S. Banik, author V. K. Ahire, and author S. R. Barman, title
	title Plasmons in core-level photoemission spectra of al(111),	https://doi.org/10.1103/physrevb.67.165416 journal
		journal Physical Review B volume 67,		pages 165416 (year 2003)NoStop
	[Santana et al.(2018)Santana, David, de Almeida, and		Godet]Santana18
	author author V. M. d. S.			Santana, author D. David, author J. S. de Almeida, and author C. Godet, title title Photoelectron energy loss
			in Al(002) revisited: Retrieval of the single plasmon loss energy
			distribution by a fourier transform method, https://doi.org/10.1007/s13538-018-0566-8 journal journal Brazilian Journal of Physics volume 48,		pages 215 (year 2018)NoStop
	[Barman et al.(2004)Barman,
		Biswas, and Horn]Barman04
	author author S. Barman, author C. Biswas,		and author K. Horn, title title Electronic excitations on silver surfaces,	https://doi.org/10.1103/physrevb.69.045413 journal
		journal Physical Review B volume 69,		pages 045413 (year 2004)NoStop
	[Barman et al.(2001)Barman,
		Häberle, Horn, Maytorena, and Liebsch]Barman01
	author author S. R. Barman, author P. Häberle,
		author K. Horn, author
		J. A. Maytorena, and author
		A. Liebsch, title title Quantum well behavior without confining barrier observed via
			dynamically screened photon field, https://doi.org/10.1103/physrevlett.86.5108 journal journal Physical Review Letters volume 86,		pages 5108 (year 2001)NoStop
	[Barman et al.(1998)Barman,
		Horn, Häberle, Ishida,		and Liebsch]Barman98
	author author S. R. Barman, author K. Horn,
		author P. Häberle, author H. Ishida, and author
		A. Liebsch, title title Photoinduced plasmon excitations in alkali-metal overlayers,	https://doi.org/10.1103/physrevb.57.6662 journal
		journal Physical Review B volume 57,		pages 6662 (year 1998)NoStop
	[Th. et al.(1978)Th.,
		van Attekum, and Trooster]Attekum78
	author author P. M. Th., author M. van Attekum,		and author J. M. Trooster,	title title Bulk- and surface-plasmon-loss
			intensities in photoelectron, auger, and electron-energy-loss spectra of Al
			metal, https://doi.org/10.1103/physrevb.18.3872 journal journal Physical Review B volume 18, pages 3872 (year
		1978)NoStop
	[van Attekum and Trooster(1979)]Attekum79
	author author P. M. T. M.			van Attekum and author J. M.			Trooster, title title Bulk- and
			surface-plasmon-loss intensities in photoelectron, auger, and
			electron-energy-loss spectra of Mg metal, https://doi.org/10.1103/physrevb.20.2335 journal journal Physical Review B volume 20, pages 2335 (year 1979)NoStop
	[Baird et al.(1978)Baird,
		Fadley, Goldberg, Feibelman,		and Šunjić]Baird78
	author author R. Baird, author C. Fadley,
		author S. Goldberg, author P. J. Feibelman, and author M. Šunjić, title
	title The angular dependence of plasmon loss features in XPS
			spectra from polycrystalline Aluminum: Clean surfaces and effects of oxygen
			adsorption, https://doi.org/10.1016/0039-6028(78)90366-7
	journal journal Surface Science volume 72, pages 495 (year
		1978)NoStop
	[Steiner et al.(1978)Steiner, Höchst, and Hüfner]Steiner78
	author author P. Steiner, author H. Höchst, and author S. Hüfner, title title XPS investigation of
			simple metals: I. core level spectra, https://doi.org/10.1007/bf01320978 journal journal Zeitschrift für Physik B Condensed Matter volume 30, pages 129 (year 1978)NoStop
	[Höchst et al.(1978)Höchst, Steiner, and Hüfner]Hoechst78
	author author H. Höchst, author P. Steiner, and author S. Hüfner, title title XPS investigation of
			simple metals: II. the valence band spectra, https://doi.org/10.1007/bf01320979 journal journal Zeitschrift für Physik B Condensed Matter volume 30, pages 145 (year 1978)NoStop
	[Bradshaw et al.(1977)Bradshaw, Domcke, and Cederbaum]Bradshaw77
	author author A. M. Bradshaw, author W. Domcke,		and author L. S. Cederbaum,	title title Intrinsic and extrinsic plasmon
			coupling in x-ray photoemission from core states of adsorbed atoms, https://doi.org/10.1103/physrevb.16.1480 journal journal Physical Review B volume 16, pages 1480 (year 1977)NoStop
	[Fuggle et al.(1976)Fuggle,
		Fabian, and Watson]Fuggle76
	author author J. Fuggle, author D. Fabian,		and author L. Watson,	title title Electron energy loss processes in
			x-ray photoelectron spectroscopy, https://doi.org/10.1016/0368-2048(76)81022-5 journal
		journal Journal of Electron Spectroscopy and Related
				Phenomena volume 9, pages 99
		(year 1976)NoStop
	[Pardee et al.(1975)Pardee,
		Mahan, Eastman, Pollak,
		Ley, McFeely, Kowalczyk,		and Shirley]Pardee75
	author author W. J. Pardee, author G. D. Mahan,
		author D. E. Eastman, author R. A. Pollak, author
		L. Ley, author F. R. McFeely, author S. P.			Kowalczyk, and author D. A.			Shirley, title title Analysis of
			surface- and bulk-plasmon contributions to x-ray photoemission spectra,	https://doi.org/10.1103/physrevb.11.3614 journal
		journal Physical Review B volume 11,		pages 3614 (year 1975)NoStop
	[Kalha et al.(2021)Kalha,
		Fernando, Bhatt, Johansson,
		Lindblad, Rensmo, Medina,
		Lindblad, Siol, Jeurgens,
		Cancellieri, Rossnagel, Medjanik, Schönhense, Simon,
		Gray, Nemšák, Lömker,
		Schlueter, and Regoutz]Kalha21
	author author C. Kalha, author N. K. Fernando,
		author P. Bhatt, author F. O. L. Johansson, author A. Lindblad, author
		H. Rensmo, author L. Z. Medina, author R. Lindblad, author S. Siol, author L. P. H.			Jeurgens, author C. Cancellieri, author K. Rossnagel, author K. Medjanik,
		author G. Schönhense,
		author M. Simon, author A. X. Gray, author
		S. Nemšák, author
		P. Lömker, author
		C. Schlueter, and author
		A. Regoutz, title title Hard x-ray photoelectron spectroscopy: a snapshot of the
			state-of-the-art in 2020, https://doi.org/10.1088/1361-648x/abeacd
	journal journal Journal of Physics: Condensed
				Matter volume 33, pages 233001
		(year 2021)NoStop
	[Kobayashi(2009)]Kobayashi09
	author author K. Kobayashi, title title Hard X-ray
			photoemission spectroscopy, https://doi.org/10.1016/j.nima.2008.12.188 journal journal Nuclear Instruments and Methods in Physics Research Section A:
				Accelerators, Spectrometers, Detectors and Associated Equipment volume 601, pages 32 (year
		2009)NoStop
	[Fadley(2010)]Fadley2010
	author author C. Fadley, title title X-ray photoelectron
			spectroscopy: Progress and perspectives, https://doi.org/10.1016/j.elspec.2010.01.006 journal
		journal Journal of Electron Spectroscopy and Related
				Phenomena volume 178–179, pages 2
		(year 2010)NoStop
	[Woicik(2016)]Woicik16
	author author J. C. Woicik, https://doi.org/10.1007/978-3-319-24043-5 title Hard X-ray Photoelectron Spectroscopy (HAXPES), Vol.	volume 59 (publisher Springer
		International Publishing, year 2016)NoStop
	[Gray et al.(2011)Gray,
		Papp, Ueda, Balke,
		Yamashita, Plucinski, Minár,
		Braun, Ylvisaker, Schneider,
		Pickett, Ebert, Kobayashi,		and Fadley]Gray
	author author A. X. Gray, author C. Papp, author S. Ueda, author
		B. Balke, author Y. Yamashita, author L. Plucinski, author J. Minár, author J. Braun, author E. R.			Ylvisaker, author C. M.			Schneider, author W. E.			Pickett, author H. Ebert, author K. Kobayashi,		and author C. S. Fadley,	title title Probing bulk electronic structure with
			hard x-ray angle-resolved photoemission, https://doi.org/10.1038/nmat3089 journal journal
			Nature Materials volume 10, pages
		759 (year 2011)NoStop
	[Gray et al.(2012)Gray,
		Minár, Ueda, Stone,
		Yamashita, Fujii, Braun,
		Plucinski, Schneider, Panaccione, Ebert, Dubon, Kobayashi, and Fadley]Gray_a
	author author A. X. Gray, author J. Minár,
		author S. Ueda, author
		P. R. Stone, author
		Y. Yamashita, author
		J. Fujii, author J. Braun, author L. Plucinski, author C. M.			Schneider, author G. Panaccione, author H. Ebert,
		author O. D. Dubon, author K. Kobayashi, and author C. S. Fadley, title
	title Bulk electronic structure of the dilute magnetic
			semiconductor Ga_1-xMnAs_x through hard
			x-ray angle-resolved photoemission, https://doi.org/10.1038/nmat3450 journal journal
			Nature Materials volume 11, pages
		957 (year 2012)NoStop
	[Nayak et al.(2012)Nayak,
		Maniraj, Rai, Singh,
		Rajput, Gloskovskii, Zegenhagen, Schlagel, Lograsso,
		Horn, and Barman]Nayak12
	author author J. Nayak, author M. Maniraj,
		author A. Rai, author
		S. Singh, author P. Rajput, author A. Gloskovskii, author J. Zegenhagen, author D. L.			Schlagel, author T. A.			Lograsso, author K. Horn, and author S. R. Barman, title title Bulk electronic structure
			of quasicrystals, https://doi.org/10.1103/physrevlett.109.216403
	journal journal Physical Review Letters		volume 109, pages 216403 (year 2012)NoStop
	[Ohtsuki et al.(2011)Ohtsuki, Chainani, Eguchi, Matsunami, Takata, Taguchi, Nishino, Tamasaku, Yabashi, Ishikawa, Oura, Senba, Ohashi, and Shin]Ohtsuki11
	author author T. Ohtsuki, author A. Chainani,
		author R. Eguchi, author M. Matsunami, author
		Y. Takata, author M. Taguchi, author Y. Nishino, author K. Tamasaku, author M. Yabashi, author T. Ishikawa, author M. Oura, author Y. Senba, author H. Ohashi, and		author S. Shin, title title Role of Ti 3d carriers in mediating the
			ferromagnetism of CoTiO_2
				Anatase Thin Films, https://doi.org/10.1103/physrevlett.106.047602 journal
		journal Physical Review Letters volume
			106, pages 047602 (year 2011)NoStop
	[Takata et al.(2008)Takata,
		Kayanuma, Oshima, Tanaka,
		Yabashi, Tamasaku, Nishino,
		Matsunami, Eguchi, Chainani,
		Oura, Takeuchi, Senba,
		Ohashi, Shin, and Ishikawa]Takata08
	author author Y. Takata, author Y. Kayanuma,
		author S. Oshima, author S. Tanaka, author
		M. Yabashi, author K. Tamasaku, author Y. Nishino, author M. Matsunami, author R. Eguchi, author A. Chainani, author M. Oura, author T. Takeuchi, author Y. Senba,
		author H. Ohashi, author S. Shin, and author
		T. Ishikawa, title title Recoil effect of photoelectrons in the fermi edge of simple
			metals, https://doi.org/10.1103/physrevlett.101.137601 journal journal Physical Review Letters volume 101, pages 137601 (year
		2008)NoStop
	[Sing et al.(2009)Sing,
		Berner, Goß, Müller,
		Ruff, Wetscherek, Thiel,
		Mannhart, Pauli, Schneider,
		Willmott, Gorgoi, Schäfers, and Claessen]Sing09
	author author M. Sing, author G. Berner,
		author K. Goß, author
		A. Müller, author
		A. Ruff, author A. Wetscherek, author S. Thiel, author J. Mannhart, author S. A.			Pauli, author C. W. Schneider, author P. R. Willmott, author M. Gorgoi,
		author F. Schäfers, and		author R. Claessen, title title Profiling the interface electron gas of
			LaAlO_3/SrTiO_3 heterostructures with hard
			x-ray photoelectron spectroscopy, https://doi.org/10.1103/physrevlett.102.176805 journal
		journal Physical Review Letters volume
			102, pages 176805 (year 2009)NoStop
	[Sarkar et al.(2021a)Sarkar, Sadhukhan, Singh, Gloskovskii,
		Deguchi, Fujita, and Barman]Sarkar21
	author author S. Sarkar, author P. Sadhukhan,
		author V. K. Singh, author A. Gloskovskii, author
		K. Deguchi, author N. Fujita, and author S. R.			Barman, title title Bulk
			electronic structure of high-order quaternary approximants, https://doi.org/10.1103/physrevresearch.3.013151 journal
		journal Physical Review Research volume
			3, pages 013151 (year
		2021a)NoStop
	[Sarkar et al.(2021b)Sarkar, Krajčí,
		Sadhukhan, Singh, Gloskovskii, Mandal, Fournée,
		de Weerd, Ledieu, Fisher,		and Roy Barman]Sarkar21a
	author author S. Sarkar, author M. Krajčí,
		author P. Sadhukhan, author V. K. Singh, author
		A. Gloskovskii, author
		P. Mandal, author V. Fournée, author M.-C.			de Weerd, author J. Ledieu, author I. R. Fisher,		and author S. Roy Barman,	title title Anderson localization of electron
			states in a quasicrystal, https://doi.org/10.1103/physrevb.103.l241106 journal
		journal Physical Review B volume
			103, pages L241106 (year
		2021b)NoStop
	[Sadhukhan et al.(2019a)Sadhukhan, DSouza, Singh, Dhaka,
		Gloskovskii, Dhar, Raychaudhuri, Chainani, Chakrabarti, and		Roy Barman]Sadhukhan19
	author author P. Sadhukhan, author S. W. DSouza, author V. K.			Singh, author R. S. Dhaka, author A. Gloskovskii,
		author S. K. Dhar, author P. Raychaudhuri, author
		A. Chainani, author
		A. Chakrabarti, and author
		S. Roy Barman, title
	title Role of antisite disorder, electron-electron correlations,
			and a surface valence transition in the electronic structure of
			CeMnNi_4, https://doi.org/10.1103/PhysRevB.99.035102 journal journal Phys. Rev. B volume 99, pages 035102 (year 2019a)NoStop
	[Sadhukhan et al.(2023)Sadhukhan, Sarkar, DSouza,
		Gloskovskii, and Roy Barman]Sadhukhan23
	author author P. Sadhukhan, author S. Sarkar,
		author S. W. DSouza, author A. Gloskovskii, and author S. Roy Barman, title title Bulk electronic
			structure of Mn_2NiGa using hard x-ray photoelectron
			spectroscopy and density functional theory, https://doi.org/10.1088/1402-4896/acc616 journal journal Physica Scripta volume 98, pages 055912 (year 2023)NoStop
	[Kunz et al.(2009)Kunz,
		Cowie, Drube, Lee,
		Thiess, Wild, and Zegenhagen]Kunz09
	author author C. Kunz, author B. Cowie,
		author W. Drube, author T.-L. Lee, author
		S. Thiess, author C. Wild, and author J. Zegenhagen, title title
		Relative electron inelastic mean free paths for diamond and graphite at
			8keV and intrinsic contributions to the energy-loss, https://doi.org/10.1016/j.elspec.2009.03.022 journal
		journal Journal of Electron Spectroscopy and Related
				Phenomena volume 173, pages 29
		(year 2009)NoStop
	[Offi et al.(2007)Offi,
		Werner, Sacchi, Torelli,
		Cautero, Cautero, Fondacaro,
		Huotari, Monaco, Paolicelli,
		Smekal, Stefani, and Panaccione]Offi07
	author author F. Offi, author W. S. M. Werner,
		author M. Sacchi, author P. Torelli, author
		M. Cautero, author G. Cautero, author A. Fondacaro, author S. Huotari, author G. Monaco, author G. Paolicelli, author W. Smekal, author G. Stefani, and author G. Panaccione, title title
		Comparison of hard and soft x-ray photoelectron spectra of silicon, https://doi.org/10.1103/physrevb.76.085422 journal journal Physical Review B volume 76, pages 085422 (year 2007)NoStop
	[Novák et al.(2007)Novák,
		Egri, Kövér, Cserny,
		Drube, and Werner]Novak07
	author author M. Novák, author S. Egri,
		author L. Kövér, author I. Cserny, author
		W. Drube, and author
		W. Werner, title title Energy dependence of electron energy loss processes in Ge 2s
			photoemission, https://doi.org/10.1016/j.susc.2007.03.039
	journal journal Surface Science volume 601, pages 2344 (year
		2007)NoStop
	[David et al.(2020)David,
		Godet, Johansson, and Lindblad]David20
	author author D. G. David, author C. Godet,
		author F. O. Johansson, and		author A. Lindblad, title title Quantitative analysis of plasmon excitations in
			hard x-ray photoelectron spectra of bulk black phosphorus, https://doi.org/10.1016/j.apsusc.2019.144385 journal
		journal Applied Surface Science volume
			505, pages 144385 (year 2020)NoStop
	[Konishi et al.(2023)Konishi, Ueda, and Kinoshita]Konishi23
	author author T. Konishi, author S. Ueda, and		author T. Kinoshita, title title Quantitative analysis of energy loss processes for
			the core level intensities in hard x-ray photoemission, https://doi.org/10.1016/j.elspec.2023.147314 journal
		journal Journal of Electron Spectroscopy and Related
				Phenomena volume 264, pages 147314
		(year 2023)NoStop
	[Chang and Langreth(1973)]Chang72a
	author author J.-J. Chang and author D. C. Langreth, title title Deep-hole excitations in
			solids. II. plasmons and surface effects in x-ray photoemission, https://doi.org/10.1103/physrevb.8.4638 journal journal Physical Review B volume 8, pages 4638 (year 1973)NoStop
	[Schlueter et al.(2019)Schlueter, Gloskovskii, Ederer,
		Schostak, Piec, Sarkar,
		Matveyev, Lömker, Sing,
		Claessen, Wiemann, Schneider,
		Medjanik, Schönhense, Amann, Nilsson, and Drube]P22
	author author C. Schlueter, author A. Gloskovskii, author K. Ederer,
		author I. Schostak, author S. Piec, author
		I. Sarkar, author Y. Matveyev, author P. Lömker, author M. Sing, author R. Claessen, author C. Wiemann,
		author C. M. Schneider, author K. Medjanik, author
		G. Schönhense, author
		P. Amann, author A. Nilsson, and author W. Drube, title title The new
			dedicated HAXPES beamline P22 at PETRAIII, in https://doi.org/10.1063/1.5084611 booktitle AIP
				Conference Proceedings, Vol. volume 2054 (year
	2019) p. pages 040010NoStop
	[Doniach and Sunjic(1970)]Doniach70
	author author S. Doniach and author M. Sunjic, title title Many-electron singularity
			in X-ray photoemission and X-ray line spectra from metals, https://doi.org/10.1088/0022-3719/3/2/010 journal journal Journal of Physics C: Solid State Physics volume 3, pages 285 (year 1970)NoStop
	[sup()]supple
	title title See Supplemental Material at
				http://link.aps.org/supplemental/xxx/PhysRevB.xxx for the theoretical plasmon
				line shapes from the literature <cit.>, HAXPES Al survey
				spectrum, completely oxidized Al spectra in normal and grazing emission,  
				comparison of  Al VB for sputtered and scraped surface,  Al
				PDOS from literature <cit.> and the VB calculated with it, and the
				calculation of the Mg XPS VB and the Mg plasmon intensities from XPS
				experiment <cit.> and theory <cit.>. The Supplemental
				Material contains Figs. S1–S6@noop   NoStop
	[Lor()]Lorentzian
	@noop  journal I_o/1+[(E_K-E_K^p) /
				Γ(E)]^2, where the half width at half maximum, Γ(E)= Γ_R
			when E_K > E_K^p (E_K^p is the peak position in the kinetic energy scale,
			E_K) and Γ(E)= Γ_L when E_K < E_K^p, and I_o is the
			intensity NoStop
	[Tougaard(1989)]Tougaard89
	journal   author author S. Tougaard, title title
		Practical algorithm for background subtraction, https://doi.org/10.1016/0039-6028(89)90380-4 journal
		journal Surface Science volume 216,		pages 343 (year 1989)NoStop
	[Jansson et al.(1992)Jansson, Hansen, Yubero, and		Tougaard]Tougaard89a
	author author C. Jansson, author H. Hansen,
		author F. Yubero, and author S. Tougaard, title
	title Accuracy of the Tougaard method for quantitative surface
				analysis. Comparison of the Universal and REELS inelastic cross sections,	https://doi.org/10.1016/0368-2048(92)80025-4 journal
		journal Journal of Electron Spectroscopy and Related
				Phenomena volume 60, pages 301
		(year 1992)NoStop
	[Sadhukhan et al.(2019b)Sadhukhan, Barman, Roy, Singh, Sarkar,
		Chakrabarti, and Barman]Sadhukhan19a
	author author P. Sadhukhan, author S. Barman,
		author T. Roy, author
		V. K. Singh, author
		S. Sarkar, author A. Chakrabarti, and author S. R. Barman, title title
		Electronic structure of Au-Sn compounds grown on Au(111), https://doi.org/10.1103/physrevb.100.235404 journal journal Physical Review B volume 100, pages 235404 (year 2019b)NoStop
	[Blaha et al.()Blaha,
		Schwarz, Madsen, Kvasnicka,		and Luitz]wien
	author author P. Blaha, author K. Schwarz,
		author G. Madsen, author D. Kvasnicka, and author J. Luitz, title
	title User’s Guide, WIEN2k, An Augmented Plane Wave Plus
				Local Orbitals Program for Calculating Crystal Properties, @noop 
	 NoStop
	[Perdew et al.(1996)Perdew,
		Burke, and Ernzerhof]pbe
	author author J. P. Perdew, author K. Burke, and		author M. Ernzerhof, title title Generalized Gradient Approximation made
				simple, https://doi.org/10.1103/physrevlett.77.3865 journal journal Physical Review Letters volume 77, pages 3865 (year
		1996)NoStop
	[Trzhaskovskaya and Yarzhemsky(2018)]Trzhaskovskaya18
	author author M. B. Trzhaskovskaya and author V. G.			Yarzhemsky, title title
		Dirac–Fock photoionization parameters for HAXPES applications, https://doi.org/10.1016/j.adt.2017.04.003 journal journal Atomic Data and Nuclear Data Tables volume
			119, pages 99 (year 2018)NoStop
	[Sadhukhan(2021)]Sadhukhanthesis
	author author P. Sadhukhan, title Electronic Structure and Morphology
			of Manganese Based Alloys and Thin Films, @noop  type
		Phd thesis, school Devi Ahilya Vishwavidyalaya, address UGC-DAE Consortium for Scientific Research, Indore (year 2021), note available at
		<http://hdl.handle.net/10603/393275>NoStop
	[Fujimori and Minami(1984)]Fujimori84
	author author A. Fujimori and author F. Minami, title title Valence-band photoemission
			and optical absorption in nickel compounds, https://doi.org/10.1103/physrevb.30.957 journal journal Physical Review B volume 30, pages 957 (year 1984)NoStop
	[Barman and Sarma(1995)]Barman95
	author author S. R. Barman and author D. D. Sarma, title title Electronic structures of
			gallium and indium across the solid-liquid transition, https://doi.org/10.1103/physrevb.51.4007 journal journal Physical Review B volume 51, pages 4007 (year 1995)NoStop
	[Biswas et al.(2004)Biswas,
		Shukla, Banik, Barman, and		Chakrabarti]Biswas04
	author author C. Biswas, author A. K. Shukla,
		author S. Banik, author S. R. Barman, and author A. Chakrabarti, title title Argon nanobubbles in Al(111): A photoemission
			study, https://doi.org/10.1103/physrevlett.92.115506 journal journal Physical Review Letters volume 92, pages 115506 (year
		2004)NoStop
	[Dhaka et al.(2008)Dhaka,
		Biswas, Shukla, Barman, and		Chakrabarti]Dhaka08
	author author R. S. Dhaka, author C. Biswas,
		author A. K. Shukla, author S. R. Barman, and author A. Chakrabarti, title title Xe and Ar nanobubbles in Al studied by
				photoemission spectroscopy, https://doi.org/10.1103/physrevb.77.104119 journal journal Physical Review B volume 77, pages 104119 (year 2008)NoStop
	[Dhaka and Barman(2010)]Dhaka10
	author author R. S. Dhaka and author S. R. Barman, title title Plasmon excitations by
			photoelectron emission from rare gas nanobubbles in Aluminum, https://doi.org/10.1103/physrevlett.104.036803 journal
		journal Physical Review Letters volume
			104, pages 036803 (year 2010)NoStop
	[bet()]beta
	@noop  journal P_ int(n), the probability of
			intrinsic process for the n^ th plasmon is given by e^-ββ^n/n! NoStop
	[chi()]chi
	journal   @noop  journal χ=
			α^ne^-ββ^n/n! NoStop
	[Tanuma et al.(2011)Tanuma,
		Powell, and Penn]Tanuma
	journal   author author S. Tanuma, author C. J.			Powell, and author D. R.			Penn, title title Calculations of
			electron inelastic mean free paths. IX. data for 41 elemental solids over
			the 50 eV to 30 keV range, https://doi.org/10.1002/sia.3522
	journal journal Surf. Interface Anal. volume 43, pages 689 (year
		2011)NoStop
	[Strohmeier(1990)]Stroheimer90
	author author B. R. Strohmeier, title title An esca method for
			determining the oxide thickness on Aluminum alloys, https://doi.org/10.1002/sia.740150109 journal journal Surface and Interface Analysis volume
			15, pages 51 (year 1990)NoStop
	[Bhattacharya et al.(2023)Bhattacharya, Sadhukhan, Sarkar,
		Singh, Gloskovskii, Barman,		and Chakrabarti]Bhattacharya23
	author author J. Bhattacharya, author P. Sadhukhan, author S. Sarkar,
		author V. K. Singh, author A. Gloskovskii, author
		S. R. Barman, and author
		A. Chakrabarti, title
	title Bulk electronic structure of
			Ni_2MnGa studied by density functional theory and
			hard x-ray photoelectron spectroscopy, https://doi.org/10.1103/physrevb.108.l121114 journal
		journal Physical Review B volume
			108, pages L121114 (year 2023)NoStop
	[Leonard(1978)]Leonard78
	author author P. Leonard, title title Energy bands, densities
			of states and x-ray spectra of Al with superposed self-consistent
			potentials, https://doi.org/10.1088/0305-4608/8/3/015 journal journal Journal of Physics F: Metal Physics		volume 8, pages 467 (year
		1978)NoStop
	[Gupta and Freeman(1976)]Freeman76
	author author R. P. Gupta and author A. J. Freeman, title title Band-structure
			contributions to x-ray emission and absorption spectra and edges in
			magnesium, https://doi.org/10.1103/physrevlett.36.1194 journal journal Physical Review Letters volume 36, pages 1194 (year
		1976)NoStop
	[Langreth(1970)]Langreth70
	author author D. C. Langreth, title title Singularities in the
			x-ray spectra of metals, https://doi.org/10.1103/physrevb.1.471
	journal journal Physical Review B volume 1, pages 471 (year
		1970)NoStop
	[Singh et al.(2022)Singh,
		Krajčí, Sarkar, Balal,
		Barman, Sadhukhan, Gloskovskii, Feuerbacher, Thomas,
		Ebert, Rotenberg, Horn, and		Roy Barman]Singh22
	author author V. K. Singh, author M. Krajčí,
		author S. Sarkar, author M. Balal, author
		S. Barman, author P. Sadhukhan, author A. Gloskovskii, author M. Feuerbacher, author C. Thomas, author P. Ebert, author E. Rotenberg, author K. Horn, and author S. Roy Barman, title title
		Electronic structure of
				Al_3Mg_2 and
				Al_13Fe_4 complex metallic alloys, https://doi.org/10.1103/physrevb.105.205107 journal journal Physical Review B volume 105, pages 205107 (year 2022)NoStop


