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Spin polarized photoemission from gold using circularly polarized light
302
Surface Science 117 (1982) 302-309 worth-Holland Publishing Company
SPIN POLARIZED PHOTOEMISSION CIRCULARLY POLARIZED LIGHT D. PESCIA Luhorutornm
Received
FROM GOLD USING
and F. MEIER fiir
FestkBrperph_vsih.
14 September
ETH-Zijrich,
1981: accepted
CW8U93
for publication
Ziirrc,h, Sn~it:erlutd
4 January
1982
Spin polarized photoemission using circularly polarized light has been performed on the t I I I) surface of a gold single crystal in the photon energy range 2GhuG IO eV. By deposition of potassium on the surface, the workfunction has been varied. Thus it has been possible to investigate the band structure of gold near the L point. Several interband energies have been determined and the symmet~ character of the bands near Er has been unanlbiguously assessed. Thermal effects have been investigated by cooling the sample well below the Debye temperature: they have been found to be irrelevant. The particular applicability of group theoretical arguments to this photoemission technique is shown.
1. In~~ucti~n Gold is among those materials for which the band structure is the subject of intensive experimental studies by means of optical and electron spectroscopic methods. Recently, angle-resolved photoemission experiments [l] showed serious discrepancies with existing band structure calculation f2). In particular the experimentaIly determined position of the first unoccupied band along A differs from the calculated one by about 4eV. Attracted by this puzzling situation, we have tried to investigate this part of the electronic structure of gold by means of spin polarized photoemission. In a crystal, the selection rules governing direct interband transitions by circular@ polarized light may give rise to an overpopulation of a certain spin direction in the excited state. If this state lies above the vacuum level. a part of the electrons is photoemitted and their spin polarization can be measured. The feasibility of such an experiment has been shown before [3,4]. By measuring the spin direction of electrons photoemitted from a [ 11 II-oriented gold single crystal as a function of the photon energy, a careful assignment of the bands involved in the observed transitions has been made. A portion of the 11 direction not accessible to the modern angle-resolved photoemission techniques has been explored. Actually, the position of the vacuum level prevents accurate observation of electrons originating from transitions near the L point. By covering the surface with alkali atoms, the photothreshold can be lotiered, and
0039-6028 /82 /OOOO-0000 /$02.75
0 1982 North-Holland
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from qdd
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these electrons can escape into the vacuum. For the potassium coverages used in our work - between 0.3 and 1.0 monolayer - it is expected, according to ref. [5], that the original momentum distribution of the excited electrons is destroyed by elastic scattering with the potassium atoms, preventing angle-resolved measurements. On the contrary, no evidence for spin-flip scattering with adsorbed alkali metals has been observed so far. The experiment on GaAs [4], shows clearly that such a mechanism does not occur. The decrease of polarization observed on Ni and Co films upon cesiation [6], quoted in ref. [4] as possibly due to spin-flip scattering, has later been recognized to be of completely different origin: it is a typical initial state effect which causes, for instance, the polarization of clean and Cs-covered Ni single crystal surfaces to become negative near the photothreshold [7]. For clean polycrystalline Ni films _ as measured in ref. [6] - the negative polarization is masked by patch effects, which are reduced upon deposition of Cs, leading to a decrease of the spin polarization near the photothreshold. In the k-region considered, agreement has been found with the calculated band structure of Christensen and Seraphin [2] within a few thenths of an eV. As essential result of this experiment, the symmetry character of the bands near E, has been deduced. Actually, this assessement is based on the sign of the polarization, which univocally characterizes the transitions and is an evident experimental quantity. To investigate the contribution of phonon-assisted indirect transitions to the observed polarization spectra, the sample was cooled well below the Debye temperature of gold (0, = 180 K). No evidence for strong thermal effects has been found. Broadening of the observed structures is essentially governed by the typical many body effects of photoemission, life time of the excited electrons and of the hole left behind. The efficacy of spin polarized photoemission in testing the band structure of solids is finally discussed. 2. Experimental A detailed description of the apparatus for measuring the Electron Spin Polarization (ESP) can be found elsewhere [8]. Briefly, the light beam impinges normally to the surface, all electrons leaving the surface inside a full acceptance angle < 80” are sampled, and their polarization is measured as function of the photon energy by the Mott scattering technique. The measured quantity is
where N I‘ (N J) is the number of photoelectrons with spin parallel (antiparallel) to the quantization axis defined by the angular momentum of the light. Circularly polarized light is available in a photon energy range 1.5 < hv < 10.0 eV. It is obtained by passing the unpolarized beam through a linear polarizer followed by a variable MgF, compensator of the Soleil-Babinet type. In the
described geometry, the E vector of the light does not have any component perpendicular to the surface of the irradiated sample. This avoids excitation of the (111) surface state, which has been found to emit very strongly in the used photon energy range [9]. The surface of the [ll l]-oriented gold single crystal was prepared by electropolishing. The sample was then installed in an ultra-high vacuum chamber and cleaned of impurities by a combination of repeated Ar + sputtering and annealing cycles at about 600°C. All contaminations were easily removed and the quality of the surface was then checked by AES and LEED. A clear hexagonal LEED pattern was observed, as expected for a ( 111) surface. The work function was determined with an accuracy of ~0.1 eV by means of a Fowler plot. It varied between 5.3 and 5.6 eV, depending on the details of the cleaning procedure. Varying the amount of potassium deposited on the surface between 0.3 and 1.0 monolayers. a controlled lowering of the work function has been obtained.
3. Theoretical background It is necessary to mention some simple group theoretical arguments which will be used in the next section to interpret the experimental results. According to group theory, the symmetry of an electron wave function &(r) is described by an irreducible representation of the group of the wave vector k. If one takes into account spin-orbit interaction, the irreducible representations of the so-called “double” group must be used. The basis functions consist of a space part and a spin part. These basis functions represent the symmetry of the space and the spin state of the electrons in each energy band. but they do not give information about the radial part of the wave function. Therefore, if in the calculation of transition matrix elements such basis functions are used instead of the complete wave function, the integration is possible for the angular and the spin part but the radial matrix element remains an unknown constant. Because the basis functions describe the symmetry character not only of the space but also of the spin part, the calculation of these matrix elements allows quite general predictions on the spin polarization of a certain transition to be made, without an explicit consideration of the radial part of the wave function. This has recently been performed for cubic crystals in an elegent manner by Wohlecke and Borstel [IO]. who tabulated ESP for transitions along the A and A directions. However, the evaluation of the relative strength of the transitions requires the knowledge of the radial part. In our experimental arrangement, a non-zero ESP can be achieved in direct dipole transitions in a cubic crystal only by circularly polarized light. Energy bands belonging to different representations of the single group may cross accidentally. This crossing may be lifted by spin-orbit interaction. Lifting of band crossing by spin-orbit coupling occurs frequently, because the
number of double group irreducible representations is generally smaller than that of the single group. As a consequence the formation of hybrids must be considered. This means that different spatial parts (single group representations) may contribute to the wave function belonging to the extra representations of the double group in the k region where the crossing has been lifted. Again, the exact composition of the hybrids is determined by the radial part. Experimentally, this feature is not readily accessible to most other spectroscopic techniques that test band structures. In the recent spin polarized photoemission experiments on W [3], hybridization has been found to strongly reduce the magnitude of the polarization. The case of gold is particularly exciting because one of the transitions is in fact due exclusively to hybridization.
4. Results and discussions To interpret our spectra we refer to the band structure of gold calculated in ref. [2]. The A direction is shown in fig. 1. At the L point itself, all transitions with circularly polarized light between bands 1-6 and 7 are forbidden. Comparing the energy scale with the light energies available in the experiment. one notices that only one final state can be reached, namely band 7. The symmetry character of the bands 4, 5, 6, 7 and the ESP for the transition (4, 5, 6) - 7 by right circularly polarized light are summarized in the table at the bottom of fig. 1. The notation is explained in the figure caption. Band 4 and 6 hybridize. because they originate from bands which cross in the non-relativistic band structure [2]. Instead band 7 is of pure Al4 symmetry. Hybridization in this energy range is a typical feature of noble metals, whose rather narrow d bands lie below the Fermi energy but within the range of a nearly free electron like sp band. According to ref. [lo], the transition A’, - Ai is forbidden for circularly polarized light. Therefore transitions from band 6 to band 7 are possible only because A’, mixes with Al. Fig. 2 shows ESP spectra of a (111) gold surface with different K coverages, at room temperature. The results are given for right circularly polarized light. First we explain the clean surface spectrum fig. 2a. It has a large bell-shaped appearance with a flat top between 6.9 and 7.6 eV at P = + 14%. According to the band structure, transitions away from L originating from bands 5 and 6 occur at about the same energies. The separation, being as small as 0.3 eV. is experimentally not resolved. The net result of both bands is a positive polarization, indicating that band 5 prevails. This feature determines the spectrum until band4 begins to contribute, causing the decrease of ESP for hv a 7.6 eV. The described transitions occur along symmetry directions and not at symmetry points. This is the reason for the observed flat maximum. Then the onset of transition 5 --* 7 can be located at 6.9 eV. The width of the flat top, 0.7 eV, measures the spin-orbit splitting between bands4 and 5: this
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/ Spirl polurizd
photoenzissmn
from
2.0 3.0 LO 5.0
gold
6.0 7.0 8.0 9.0 10.0
PHOTON ENERGY [eV] Fig. I. Theoretical band structure of gold along the A direction, from ref. [2]. The different workfunctions used in the experiment are shown as dashed horizontal lines corresponding to +=5.3 eV of the clean surface and +=4.3, 3.4 and 2.4 eV of the potassium covered surfaces. The initial states of the interband transitions, whose energies have been experimentally determined (see text) are indicated by the black dots. The table below shows the ESP of the transition by right circularly polarized light from bands 4. 5, 6 to band 7. The symmetry of the bands is characterized by a superscript for the single group representation and a subscript indicating the double group representation. Fig. 2. Spin polarization versus photon energy for surfaces with different workfunction. Right circularly polarized light is used. In each figure the photothreshold is indicated by a vertical arrow. (a) +=5.3 eV; (b) 4=4.3 eV; (c) +=3.4 eV; (d) +=2.4 eV. The spectra were measured at room temperature.
value agrees with the calculated one. At 7.6 eV the transition 4 - 7 starts. Because of lifetime effects in final and initial states, the ESP extends from 6.9 eV up to the threshold: a FWHM of about 1.6 eV is assigned to the transition 5 - 7. This value includes both hole and electron lifetimes. The first is of the order of 0.5 eV [ 1 l] in noble metals, if the initial state lies in the energy range of the d electrons where the density of states is high. Final state lifetime becomes a serious limit to the sharpness of structures observed by spectroscopies where the photon energy is varied [ 121. This is, for instance, not the case if the photon energy is fixed and the energy of the emitted electrons is analysed 1111.
D. Pesciu, F. Meier / Spin poluri:ed photoemission fronl goid
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The lowering of the workfunction from + = 5.3 eV to + = 3.4 eV does not essentially change the shape of the ESP spectra, as shown in figs. 2b and 2c. This is actually expected for bands which, according to the band structure, extend to the L point remaining approximately parallel. There are two trends: by the transition 5 - 7 in the first, the transition 6 - 7, which is dominated clean spectrum, is resolved if the workfunction is lowered to 3.4 eV. It is revealed by the negative ESP near the threshold (fig. 2~). This is due to the fact that upon approaching L, bands 6 and 5 diverge and become separately resolved. Second, the transition 4 - 7 becomes stronger when the relevant part of the A direction contributing to the transitions approaches L. This results in a negative polarization around 8.0 eV and a decreasing trend of the maximum polarization when going to lower workfunctions: P = 9% for + = 4.3 eV and P = 5% for + = 3.4 eV. The spectrum in fig. 2d, C$= 2.4 eV, is negative over the whole photon energy range considered. This shows that the combined action of bands6 and 4 overcomes the positive contribution of band 5 near L. The spectrum presents two prominent structures, a smaller one around 3.6 eV and a stronger one with minimum at 5.8 eV. At 3.6 eV the transition 6 - 7 starts: this value is in agreement with thermoreflectance measurements [ 131, in which the energy difference between L; and La was found to be 3.6 eV. The small ESP shows that band 6 has predominantly A$ character. Again, ESP extends up to 2.8 eV, mostly because of final state broadening. The FWHM of the transition 6 - 7 near L is about 1.2 eV. The increase of ESP between 3.6 G hv G 4.8 eV is obviously due to the onset of transition 5 - 7 but, instead of becoming positive, the ESP peaks again to the negative values because of the onset of the strong transition 4 - 7. At still higher energies, transitions originating from bands 3 and 2 contribute, stabilizing the ESP at about -4% for hv > 6.5 eV.
-+20
-+I5
-tlO
-t5
7.0
8.0
9.0
PHOTON
ENERGY
[ev]
Fig. 3. Spin polarization line) and at 70 K.
versus photon
energy
for a clean surface,
at room
temperature
(dashed
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D. Pescia. F. Meier / Spin polrnzed
photoemission
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From the measured spectra, the five interband energies shown in fig. 1 are derived. Transition a6_-7: 3.6 (3.8). bS_,: 4.8 (5.2). c,+_,: 5.8 (5.9) d,,_,: 6.9 (7.5). e,_7: 7.6 (8.6). All values are given in eV, the theoretical ones in brackets. The subscripts denote the bands involved in the transition. Recently [ 141, new band structure data have been published by the same authors as in ref. [2]. Essentially, along A, band7 is shifted to higher energies. Our experimental results do not support this upward shift. Photoemission spectra can undergo dramatical changes by cooling the sample from T> 0, to Te O,, as has been shown in fact for the case of gold [9] (0, = Debye temperature = 180 K for gold). Fig. 3 shows the ESP spectrum of the same clean gold surface at room temperature (dashed line) and at T = 70 K. Interestingly, there is only a small difference between the two curves which is entirely due to the different value of the work function at these two temperatures: + = 5.15 eV at T = 70 K and $J = 5.5 eV at room temperature. From this result it is concluded that the contribution of indirect transitions is not significant. Finally, some simplifications made for interpreting the measurements are discussed. Although not angle-resolved, the ESP spectra have been explained in terms of transitions along A. This is strictly true only near the threshold. whereas at higher photon energies, electrons originating from the transitions off the [ll I] direction can escape into the vacuum as well. Evidently, the escape cone of the photoelectrons depends on the work function and the light energy. Wbhlecke and Borstel [ 151 have pointed out that along directions which do not contain at least a threefold rotation as symmetry operation, group theory does no longer help in calculating the spin polarization. Therefore, to appreciate the contribution of direct transitions off the A direction, much more sophisticated computational work than the simple symmetry arguments is needed. This has been recently done for gold by the same authors [ 161 in order to explain the measured spectra. They found that escape cone effects lower drastically the net polarization. but do not at all change their structure. Although the general significance of this result has still to be tested, it shows that spin polarized photoemission by circularly polarized light selects automatically the most interesting parts of the Brillouin zone. namely lines or points of high symmetry. This may have important experimental consequences, for example making apparative angular resolution in spin polarized photoemission less compulsory than in the EDC technique. For the interpretation of the spectra of potassium covered surfaces, it should be taken into account that elastic scattering with the potassium atoms destroys partially the original momentum distribution of the excited electrons [5]. This means that electrons excited originally along a direction outside the escape cone in the sample are also photoemitted, because elastic scattering drives them into a favourable angle. More detailed investigation of this important phenomenon is planned. At present we are not able to appreciate its role in affecting the measured ESP spectra of potassium covered surfaces.
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5.Conclusion Interband energies of gold near the L point have been determined and the symmetry character of the bands near E, experimentally established. It has been possible to evaluate the relative strength of the transitions observed, a feature which is not provided by symmetry arguments and is suitable to be verified by exact calculations. Direct experimental evidence has been obtained for the hybridization properties of the bands involved. The successful application of simple group theoretical methods to interpret spin polarized photoemission with circularly polarized light shows that this experiment is a competitive tool for the investigation of the relativistic band structure of solids.
Acknowledgements We thank H.C. Siegmann discussions. We are grateful cal support. The financial gratefully acknowledged.
for his continuous encouragement and stimulating to M. WBhlecke and G. Borstel for their theoretisupport of the Schweizerische Nationalfonds is
References [I] P. Heimann, H. Miosga and H. Deddermeyer. Solid State Commun. 29 ( IY79) 463: R. Mosei, R. LLsser, N.V. Smith, R.L. Benbow. Solid State Commun. 35 (I 980) 1979. [2] N.E. Christensen and B.O. Seraphin. Phys. Rev. B4 (1971) 3321. [3] P. Ziircher, F. Meier and N.E. Christensen, Phys. Rev. Letters 43 (1979) 54. [4] D.T. Pierce and F. Meier. Phys. Rev. BI 3 (1976) 5484. (51 G.W. Gobeli. F.G. Allen and E.O. Kane, Phys. Rev. Letters I2 (1964) 94. [6] G. Busch, M. Campagna, D.T. Pierce and H.C. Siegmann. Phys. Rev. Letters 2X (1972) 61 I. [7] W. Eib and SF. Alvarado. Phys. Rev. Letters 37 ( 1976) 444. [8] SF. Alvarado, W. Eib. F. Meier. H.C. Siegmann and P. Ziircher. in: Photoemission From Surfaces. Eds. B. Feuerbacher and B. Fitton (Wiley, 1978). [9] K.A. Mills. R.F. Davis, SD. Kevan. G. Thronton and D.A. Shirley, Phys. Rev. B22 (1980) 581. [IO] M. WGhlecke and G. Borstel, Phys. Rev. B23 ( I98 I) 980. [I I] J.A. Knapp, F.J. Himpsel and D.E. Eastman, Phys. Rev. B19 (1979) 4952. [ 121 J.B. Pendry. in: Photoemission and Electronic Properties of Surfaces, Eds. B. Feuerbacher. B. Fitton and R.F. Willis (Wiley, 1978). [I;] W.J. Scouler, Phys. Rev. Letters 18 ( 1967) 445. [ 141 N.E. Christensen and B.O. Seraphin, Solid State Commun. 37 (1981) 57. [ 15) M. Wiihlecke and G. Borstel, Phys. Rev. B. in press. [ 161 G. Borstel and M. Wtihlecke, Surface Sci. I I7 (1982) 310.
Surface Science 117 (1982) 302-309 worth-Holland Publishing Company
SPIN POLARIZED PHOTOEMISSION CIRCULARLY POLARIZED LIGHT D. PESCIA Luhorutornm
Received
FROM GOLD USING
and F. MEIER fiir
FestkBrperph_vsih.
14 September
ETH-Zijrich,
1981: accepted
CW8U93
for publication
Ziirrc,h, Sn~it:erlutd
4 January
1982
Spin polarized photoemission using circularly polarized light has been performed on the t I I I) surface of a gold single crystal in the photon energy range 2GhuG IO eV. By deposition of potassium on the surface, the workfunction has been varied. Thus it has been possible to investigate the band structure of gold near the L point. Several interband energies have been determined and the symmet~ character of the bands near Er has been unanlbiguously assessed. Thermal effects have been investigated by cooling the sample well below the Debye temperature: they have been found to be irrelevant. The particular applicability of group theoretical arguments to this photoemission technique is shown.
1. In~~ucti~n Gold is among those materials for which the band structure is the subject of intensive experimental studies by means of optical and electron spectroscopic methods. Recently, angle-resolved photoemission experiments [l] showed serious discrepancies with existing band structure calculation f2). In particular the experimentaIly determined position of the first unoccupied band along A differs from the calculated one by about 4eV. Attracted by this puzzling situation, we have tried to investigate this part of the electronic structure of gold by means of spin polarized photoemission. In a crystal, the selection rules governing direct interband transitions by circular@ polarized light may give rise to an overpopulation of a certain spin direction in the excited state. If this state lies above the vacuum level. a part of the electrons is photoemitted and their spin polarization can be measured. The feasibility of such an experiment has been shown before [3,4]. By measuring the spin direction of electrons photoemitted from a [ 11 II-oriented gold single crystal as a function of the photon energy, a careful assignment of the bands involved in the observed transitions has been made. A portion of the 11 direction not accessible to the modern angle-resolved photoemission techniques has been explored. Actually, the position of the vacuum level prevents accurate observation of electrons originating from transitions near the L point. By covering the surface with alkali atoms, the photothreshold can be lotiered, and
0039-6028 /82 /OOOO-0000 /$02.75
0 1982 North-Holland
D. Pesciu. F. Merer / Spin poluri~ed photoenlission
from qdd
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these electrons can escape into the vacuum. For the potassium coverages used in our work - between 0.3 and 1.0 monolayer - it is expected, according to ref. [5], that the original momentum distribution of the excited electrons is destroyed by elastic scattering with the potassium atoms, preventing angle-resolved measurements. On the contrary, no evidence for spin-flip scattering with adsorbed alkali metals has been observed so far. The experiment on GaAs [4], shows clearly that such a mechanism does not occur. The decrease of polarization observed on Ni and Co films upon cesiation [6], quoted in ref. [4] as possibly due to spin-flip scattering, has later been recognized to be of completely different origin: it is a typical initial state effect which causes, for instance, the polarization of clean and Cs-covered Ni single crystal surfaces to become negative near the photothreshold [7]. For clean polycrystalline Ni films _ as measured in ref. [6] - the negative polarization is masked by patch effects, which are reduced upon deposition of Cs, leading to a decrease of the spin polarization near the photothreshold. In the k-region considered, agreement has been found with the calculated band structure of Christensen and Seraphin [2] within a few thenths of an eV. As essential result of this experiment, the symmetry character of the bands near E, has been deduced. Actually, this assessement is based on the sign of the polarization, which univocally characterizes the transitions and is an evident experimental quantity. To investigate the contribution of phonon-assisted indirect transitions to the observed polarization spectra, the sample was cooled well below the Debye temperature of gold (0, = 180 K). No evidence for strong thermal effects has been found. Broadening of the observed structures is essentially governed by the typical many body effects of photoemission, life time of the excited electrons and of the hole left behind. The efficacy of spin polarized photoemission in testing the band structure of solids is finally discussed. 2. Experimental A detailed description of the apparatus for measuring the Electron Spin Polarization (ESP) can be found elsewhere [8]. Briefly, the light beam impinges normally to the surface, all electrons leaving the surface inside a full acceptance angle < 80” are sampled, and their polarization is measured as function of the photon energy by the Mott scattering technique. The measured quantity is
where N I‘ (N J) is the number of photoelectrons with spin parallel (antiparallel) to the quantization axis defined by the angular momentum of the light. Circularly polarized light is available in a photon energy range 1.5 < hv < 10.0 eV. It is obtained by passing the unpolarized beam through a linear polarizer followed by a variable MgF, compensator of the Soleil-Babinet type. In the
described geometry, the E vector of the light does not have any component perpendicular to the surface of the irradiated sample. This avoids excitation of the (111) surface state, which has been found to emit very strongly in the used photon energy range [9]. The surface of the [ll l]-oriented gold single crystal was prepared by electropolishing. The sample was then installed in an ultra-high vacuum chamber and cleaned of impurities by a combination of repeated Ar + sputtering and annealing cycles at about 600°C. All contaminations were easily removed and the quality of the surface was then checked by AES and LEED. A clear hexagonal LEED pattern was observed, as expected for a ( 111) surface. The work function was determined with an accuracy of ~0.1 eV by means of a Fowler plot. It varied between 5.3 and 5.6 eV, depending on the details of the cleaning procedure. Varying the amount of potassium deposited on the surface between 0.3 and 1.0 monolayers. a controlled lowering of the work function has been obtained.
3. Theoretical background It is necessary to mention some simple group theoretical arguments which will be used in the next section to interpret the experimental results. According to group theory, the symmetry of an electron wave function &(r) is described by an irreducible representation of the group of the wave vector k. If one takes into account spin-orbit interaction, the irreducible representations of the so-called “double” group must be used. The basis functions consist of a space part and a spin part. These basis functions represent the symmetry of the space and the spin state of the electrons in each energy band. but they do not give information about the radial part of the wave function. Therefore, if in the calculation of transition matrix elements such basis functions are used instead of the complete wave function, the integration is possible for the angular and the spin part but the radial matrix element remains an unknown constant. Because the basis functions describe the symmetry character not only of the space but also of the spin part, the calculation of these matrix elements allows quite general predictions on the spin polarization of a certain transition to be made, without an explicit consideration of the radial part of the wave function. This has recently been performed for cubic crystals in an elegent manner by Wohlecke and Borstel [IO]. who tabulated ESP for transitions along the A and A directions. However, the evaluation of the relative strength of the transitions requires the knowledge of the radial part. In our experimental arrangement, a non-zero ESP can be achieved in direct dipole transitions in a cubic crystal only by circularly polarized light. Energy bands belonging to different representations of the single group may cross accidentally. This crossing may be lifted by spin-orbit interaction. Lifting of band crossing by spin-orbit coupling occurs frequently, because the
number of double group irreducible representations is generally smaller than that of the single group. As a consequence the formation of hybrids must be considered. This means that different spatial parts (single group representations) may contribute to the wave function belonging to the extra representations of the double group in the k region where the crossing has been lifted. Again, the exact composition of the hybrids is determined by the radial part. Experimentally, this feature is not readily accessible to most other spectroscopic techniques that test band structures. In the recent spin polarized photoemission experiments on W [3], hybridization has been found to strongly reduce the magnitude of the polarization. The case of gold is particularly exciting because one of the transitions is in fact due exclusively to hybridization.
4. Results and discussions To interpret our spectra we refer to the band structure of gold calculated in ref. [2]. The A direction is shown in fig. 1. At the L point itself, all transitions with circularly polarized light between bands 1-6 and 7 are forbidden. Comparing the energy scale with the light energies available in the experiment. one notices that only one final state can be reached, namely band 7. The symmetry character of the bands 4, 5, 6, 7 and the ESP for the transition (4, 5, 6) - 7 by right circularly polarized light are summarized in the table at the bottom of fig. 1. The notation is explained in the figure caption. Band 4 and 6 hybridize. because they originate from bands which cross in the non-relativistic band structure [2]. Instead band 7 is of pure Al4 symmetry. Hybridization in this energy range is a typical feature of noble metals, whose rather narrow d bands lie below the Fermi energy but within the range of a nearly free electron like sp band. According to ref. [lo], the transition A’, - Ai is forbidden for circularly polarized light. Therefore transitions from band 6 to band 7 are possible only because A’, mixes with Al. Fig. 2 shows ESP spectra of a (111) gold surface with different K coverages, at room temperature. The results are given for right circularly polarized light. First we explain the clean surface spectrum fig. 2a. It has a large bell-shaped appearance with a flat top between 6.9 and 7.6 eV at P = + 14%. According to the band structure, transitions away from L originating from bands 5 and 6 occur at about the same energies. The separation, being as small as 0.3 eV. is experimentally not resolved. The net result of both bands is a positive polarization, indicating that band 5 prevails. This feature determines the spectrum until band4 begins to contribute, causing the decrease of ESP for hv a 7.6 eV. The described transitions occur along symmetry directions and not at symmetry points. This is the reason for the observed flat maximum. Then the onset of transition 5 --* 7 can be located at 6.9 eV. The width of the flat top, 0.7 eV, measures the spin-orbit splitting between bands4 and 5: this
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6.0 7.0 8.0 9.0 10.0
PHOTON ENERGY [eV] Fig. I. Theoretical band structure of gold along the A direction, from ref. [2]. The different workfunctions used in the experiment are shown as dashed horizontal lines corresponding to +=5.3 eV of the clean surface and +=4.3, 3.4 and 2.4 eV of the potassium covered surfaces. The initial states of the interband transitions, whose energies have been experimentally determined (see text) are indicated by the black dots. The table below shows the ESP of the transition by right circularly polarized light from bands 4. 5, 6 to band 7. The symmetry of the bands is characterized by a superscript for the single group representation and a subscript indicating the double group representation. Fig. 2. Spin polarization versus photon energy for surfaces with different workfunction. Right circularly polarized light is used. In each figure the photothreshold is indicated by a vertical arrow. (a) +=5.3 eV; (b) 4=4.3 eV; (c) +=3.4 eV; (d) +=2.4 eV. The spectra were measured at room temperature.
value agrees with the calculated one. At 7.6 eV the transition 4 - 7 starts. Because of lifetime effects in final and initial states, the ESP extends from 6.9 eV up to the threshold: a FWHM of about 1.6 eV is assigned to the transition 5 - 7. This value includes both hole and electron lifetimes. The first is of the order of 0.5 eV [ 1 l] in noble metals, if the initial state lies in the energy range of the d electrons where the density of states is high. Final state lifetime becomes a serious limit to the sharpness of structures observed by spectroscopies where the photon energy is varied [ 121. This is, for instance, not the case if the photon energy is fixed and the energy of the emitted electrons is analysed 1111.
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The lowering of the workfunction from + = 5.3 eV to + = 3.4 eV does not essentially change the shape of the ESP spectra, as shown in figs. 2b and 2c. This is actually expected for bands which, according to the band structure, extend to the L point remaining approximately parallel. There are two trends: by the transition 5 - 7 in the first, the transition 6 - 7, which is dominated clean spectrum, is resolved if the workfunction is lowered to 3.4 eV. It is revealed by the negative ESP near the threshold (fig. 2~). This is due to the fact that upon approaching L, bands 6 and 5 diverge and become separately resolved. Second, the transition 4 - 7 becomes stronger when the relevant part of the A direction contributing to the transitions approaches L. This results in a negative polarization around 8.0 eV and a decreasing trend of the maximum polarization when going to lower workfunctions: P = 9% for + = 4.3 eV and P = 5% for + = 3.4 eV. The spectrum in fig. 2d, C$= 2.4 eV, is negative over the whole photon energy range considered. This shows that the combined action of bands6 and 4 overcomes the positive contribution of band 5 near L. The spectrum presents two prominent structures, a smaller one around 3.6 eV and a stronger one with minimum at 5.8 eV. At 3.6 eV the transition 6 - 7 starts: this value is in agreement with thermoreflectance measurements [ 131, in which the energy difference between L; and La was found to be 3.6 eV. The small ESP shows that band 6 has predominantly A$ character. Again, ESP extends up to 2.8 eV, mostly because of final state broadening. The FWHM of the transition 6 - 7 near L is about 1.2 eV. The increase of ESP between 3.6 G hv G 4.8 eV is obviously due to the onset of transition 5 - 7 but, instead of becoming positive, the ESP peaks again to the negative values because of the onset of the strong transition 4 - 7. At still higher energies, transitions originating from bands 3 and 2 contribute, stabilizing the ESP at about -4% for hv > 6.5 eV.
-+20
-+I5
-tlO
-t5
7.0
8.0
9.0
PHOTON
ENERGY
[ev]
Fig. 3. Spin polarization line) and at 70 K.
versus photon
energy
for a clean surface,
at room
temperature
(dashed
308
D. Pescia. F. Meier / Spin polrnzed
photoemission
from gold
From the measured spectra, the five interband energies shown in fig. 1 are derived. Transition a6_-7: 3.6 (3.8). bS_,: 4.8 (5.2). c,+_,: 5.8 (5.9) d,,_,: 6.9 (7.5). e,_7: 7.6 (8.6). All values are given in eV, the theoretical ones in brackets. The subscripts denote the bands involved in the transition. Recently [ 141, new band structure data have been published by the same authors as in ref. [2]. Essentially, along A, band7 is shifted to higher energies. Our experimental results do not support this upward shift. Photoemission spectra can undergo dramatical changes by cooling the sample from T> 0, to Te O,, as has been shown in fact for the case of gold [9] (0, = Debye temperature = 180 K for gold). Fig. 3 shows the ESP spectrum of the same clean gold surface at room temperature (dashed line) and at T = 70 K. Interestingly, there is only a small difference between the two curves which is entirely due to the different value of the work function at these two temperatures: + = 5.15 eV at T = 70 K and $J = 5.5 eV at room temperature. From this result it is concluded that the contribution of indirect transitions is not significant. Finally, some simplifications made for interpreting the measurements are discussed. Although not angle-resolved, the ESP spectra have been explained in terms of transitions along A. This is strictly true only near the threshold. whereas at higher photon energies, electrons originating from the transitions off the [ll I] direction can escape into the vacuum as well. Evidently, the escape cone of the photoelectrons depends on the work function and the light energy. Wbhlecke and Borstel [ 151 have pointed out that along directions which do not contain at least a threefold rotation as symmetry operation, group theory does no longer help in calculating the spin polarization. Therefore, to appreciate the contribution of direct transitions off the A direction, much more sophisticated computational work than the simple symmetry arguments is needed. This has been recently done for gold by the same authors [ 161 in order to explain the measured spectra. They found that escape cone effects lower drastically the net polarization. but do not at all change their structure. Although the general significance of this result has still to be tested, it shows that spin polarized photoemission by circularly polarized light selects automatically the most interesting parts of the Brillouin zone. namely lines or points of high symmetry. This may have important experimental consequences, for example making apparative angular resolution in spin polarized photoemission less compulsory than in the EDC technique. For the interpretation of the spectra of potassium covered surfaces, it should be taken into account that elastic scattering with the potassium atoms destroys partially the original momentum distribution of the excited electrons [5]. This means that electrons excited originally along a direction outside the escape cone in the sample are also photoemitted, because elastic scattering drives them into a favourable angle. More detailed investigation of this important phenomenon is planned. At present we are not able to appreciate its role in affecting the measured ESP spectra of potassium covered surfaces.
D. Pescra, F. Meier / Spm polarized photoemrssion from gold
309
5.Conclusion Interband energies of gold near the L point have been determined and the symmetry character of the bands near E, experimentally established. It has been possible to evaluate the relative strength of the transitions observed, a feature which is not provided by symmetry arguments and is suitable to be verified by exact calculations. Direct experimental evidence has been obtained for the hybridization properties of the bands involved. The successful application of simple group theoretical methods to interpret spin polarized photoemission with circularly polarized light shows that this experiment is a competitive tool for the investigation of the relativistic band structure of solids.
Acknowledgements We thank H.C. Siegmann discussions. We are grateful cal support. The financial gratefully acknowledged.
for his continuous encouragement and stimulating to M. WBhlecke and G. Borstel for their theoretisupport of the Schweizerische Nationalfonds is
References [I] P. Heimann, H. Miosga and H. Deddermeyer. Solid State Commun. 29 ( IY79) 463: R. Mosei, R. LLsser, N.V. Smith, R.L. Benbow. Solid State Commun. 35 (I 980) 1979. [2] N.E. Christensen and B.O. Seraphin. Phys. Rev. B4 (1971) 3321. [3] P. Ziircher, F. Meier and N.E. Christensen, Phys. Rev. Letters 43 (1979) 54. [4] D.T. Pierce and F. Meier. Phys. Rev. BI 3 (1976) 5484. (51 G.W. Gobeli. F.G. Allen and E.O. Kane, Phys. Rev. Letters I2 (1964) 94. [6] G. Busch, M. Campagna, D.T. Pierce and H.C. Siegmann. Phys. Rev. Letters 2X (1972) 61 I. [7] W. Eib and SF. Alvarado. Phys. Rev. Letters 37 ( 1976) 444. [8] SF. Alvarado, W. Eib. F. Meier. H.C. Siegmann and P. Ziircher. in: Photoemission From Surfaces. Eds. B. Feuerbacher and B. Fitton (Wiley, 1978). [9] K.A. Mills. R.F. Davis, SD. Kevan. G. Thronton and D.A. Shirley, Phys. Rev. B22 (1980) 581. [IO] M. WGhlecke and G. Borstel, Phys. Rev. B23 ( I98 I) 980. [I I] J.A. Knapp, F.J. Himpsel and D.E. Eastman, Phys. Rev. B19 (1979) 4952. [ 121 J.B. Pendry. in: Photoemission and Electronic Properties of Surfaces, Eds. B. Feuerbacher. B. Fitton and R.F. Willis (Wiley, 1978). [I;] W.J. Scouler, Phys. Rev. Letters 18 ( 1967) 445. [ 141 N.E. Christensen and B.O. Seraphin, Solid State Commun. 37 (1981) 57. [ 15) M. Wiihlecke and G. Borstel, Phys. Rev. B. in press. [ 161 G. Borstel and M. Wtihlecke, Surface Sci. I I7 (1982) 310.