22 AUGUsr 1977. Dynamical Calculations of Angle-Resolved Ultraviolet Photoemission from c(2 X 2) 0and S on Ni(001). S. Y. Tong, C. H. Li, and A. R. Lubinsky.
VOLUME
$9, +UMBER 8
PHYSICAL REVIEW LETTERS
22 AUGUsr 1977
Dynamical Calculations of Angle-Resolved Ultraviolet Photoemission from c(2 X 2) and S on Ni(001)
0
DePartment
S. Y. Tong, C. H. Li, and A. R. Lubinsky of Physics and Surface Studies Laboratory, University of tVisconsin,
Mila,
oauhee,
Wisconsin 53201
(Received 21 June 1977) Dynamical caluclations which include initial- and final-state scattering effects are presented for c(2&&2) 0- and S-Ni(001). The dependence of emission intensity on polar angle of emission, plane of emission, photon emission, photon incidence, and polarization are reported. Evidence is presented for separating contributions from a& and e symmetry orbitals in S-derived levels with use of polarized light. Results of intensity dependence on azimuthal angle for c'(2&2) S-Ni(001) are shown.
Recently, many experimental results were reported on angle-resolved ultraviolet-photoemission intensity spectra of overlayer systems on transition-metal substrates. ' ' With improved maneuverability of the experimental equipment, measurements are now possible in some systems for a variety of electron-collection angles, photon incident angles, and planes of photon polarization. Two physical systems of particular interest are the c(2 x2) S and 0 overlayers on Ni(001). The surface structures of these systems have been analyzed by low-energy electron diffraction (LEED) intensity analysis, and results of adsorbate-substrate interlayer spacing and adsorbate site registry have been reported. We present here results of dynamical calculations of angle-resolved ultraviolet-photoemission spectroscopy (ARUPS) on both c(2x2) 0-Ni(001) and S-Ni(001) systems. We investigate dependence of the photoemission intensity as a function of angle of collection, plane of collection, photon incidence, and photon polarization. Also, we present for the first time azimuthal p plots of the c(2x2) S-Ni(001) system. One of the purposes of such studies is to separate and assign contributions from surface orbitals with different symmetries that participate in the chemisorption process. If the orbitals have well-separated energy levels, they can be readily resolved experimentaUy. However, in the case where the different orbitals have about the same energy, they show measurements as a sinup in energy-distribution gle peak. In the highly successful c3lculation of it is Davenport for an oriented CO molecule, shown that one way to separate 0 and m prbitals in CO is through different resonance behaviors of the orbitals as a function of incident photon energy. The adsorbate-derived levels of c(2x2) 0- and S-Ni(001) are orbitals with a, and e symmetries. Jacobi et a/. ' have shown that for c(2x2) 0-¹(001),the a, state has energy level
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498
2 eV below the doubly degenerate e state. Thus, the levels in c(2 x 2) 0-Ni(001) may be separable through energy measurement. For the c(2x2) S-Ni(001) system, however, no experimental measurement has succeeded in resolving the a, and e states. Our cluster calculation on the initial states shows that the energy separation of the two levels is of the order 0.1 eV, using the LEED value for the adsorbate-substrate interlayer spacing. If this is true, then the a, and e states may never be resolved through energy measurement. However, because of different coupling factors of these states to polarized light at given incidence and emission plane, we show that contributions from a, and e states in c(2 x2) S-Ni(001) can indeed be separated. The computational procedure" includes generating initial wave functions from a self-consistent Xn multiple-scattering cluster calculation of S or 0 with five nickel atoms. The surface structures of adsorbate-substrate interlayer spacing and adsorbate site registry determined in LEED analyses are used here. From these initial wave functions, the appropriate matrix elements to finalstate wave functions of individual ion-cores are generated. The effect of a positive charged hole on the final state is neglected. The complete "nohole" final state is obtained by solving for multiple scatterings of the final-state electron through a lattice of c(2x2) 0- or S-Ni(001). Symmetry is used in the self-consistent calculation of the initial states to cut down computation time. For the final-state calculation, a dynamical perturbation LEED method in this case, renormalized forward scattering is used. ~ Whereas each computation step involves a number of assumptions and approximations, however, within the accuracy of these and that of the dynamical inputs, our calculation takes into account essential effects of both initial- and final-state processes. We first present results of the c(2 x2) 0-Ni(001)
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PHYSICAL RKVIKW LKTTKRS
VOLUME 39) NUMBER 8
h~=21. 2 eV 8
ph
22 AUGUsr 1977
5~=21.2 eV
=50
c
i ExP.
8
=50 ph
4.0
O ~
~
CO
2.0
11.81 eV)
0.4 0.0
0.0
FIG.
I
90
1.
Polar distribution of emission intensity with unpolarized light from 0-derived levels, parallel-plane emission. The emission quadrant contains the A vector. The experimental intensity has arbitrary scale. ~~
system. We compare the calculations with experimental data of Weeks and Plummer, ' who used unpolarized light at He I energy h~ = 21.2 eV. The light is incident along a symmetry direction of the crystal [i.e. , (100) or (010)]. Using a work function of 5.12 eV for c(2x2) O-Ni(001), and binding energies of 8 eV (a, state) and 8 eV (doubly degenerate e states), we calculate the emission spectra at final electron energies 8.08 eV (a, state) and 10.08 eV (e states), respectively. We show in Fig. 1 the comparison with experiment at photon angle 8 zq = 50 . The experiment of Weeks and Plummer' did not resolve the a, Bnd e states; i.e. , the measured intensity contains photoelectrons from both levels. A number of points are worth mentioning in the comparison. First, there is good agreement in the position and shape of the two peaks, at around 6, =15 and 40'. In the calculation, separate contributions from the individual orbitals are indicated. It is interesting to note that the two peaks observed in the experimental data arise from surface orbiThe peak at 0, =15' tal. s of different symmetries. is predominantly of a, symmetry while the peak at 8, = 40' is of e, symmetry. The two peaks should show different dependences on the photon incident angle. For the c(2x2) S-Ni(001) system, we used a work function of 5.38 eV. ' The calculated energy levels for the a, and e states are only 0.1 eV apart. The calculated values of the electron kinetic energies are 11.71 eV (a, state) and 11.81 eV (e states). The photoemission intensities from a, and e states at 0 ~„= 50' for p-polarized light
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60
30
I
60 Polar Angle of Collection 30
90
Polar Angle of Collection
I'IG. 2. Polar distribution of emission from S-derived levels with p-polarized light, parallel-plane emission. The emission quadrant contains the A~~ vector. The experimental intensity has arbitrary scale.
2 and 3. The light is incident along the (100) direction, and electrons are collected in the plane of incidence. The photon A~~ vector makes an angle of 50' with the (100) direction. The emission spectra as electron angle 8, sweeps through 90' from the surface normal towards the (100) direction is shown in Fig. 2. Figure 3 shows the spectra as 6, sweeps from the surface normal towards the (100) direction. We note that for the c(2x2) S-Ni(001) system, emission from the a, state is rather strong. This is especially true for electrons emitted in the quadrant containing the A~~ vector (i.e. , Fig. 2). For 0, ~35, the emission is almost entirely due to
are shown in Figs.
Ti~=21.2eV
8
„= 50
ph
ll plane emission rn
IC
C
(-)
4.0—
(11.81eV) 0.0
60 30 Polar Angle of Collection
90
FIG. 8. Polar distribution of emission from S-derived levels with p-polarized light, parallel-plane emission. The emission quadrant does not contain the The experimental intensity has arbitrary A~~ vector.
scale.
VOLUME
$9, NUMBER 8
PHYSICAL REVIEW LETTERS
22 AUGUsT 1/77 5m =21.2eV
hu =24.2 eV
eo'
ee =30
I tg
1.0
-
O IX
f=o' (001)
0.0
I
30 Photon
60
90
Incident Angle
FIG. 4. Parallel-plane
emission intensity with unpolarized light from S-derived levels vs photon incidence. The experimental intensity has arbitrary scale.
the a, state. The experimental data" using p-polarized light taken at Oph 45 are shown as broken lines in Figs. 2 and 3. The dominance of the a, state in the emission of the c(2 x2) S-Ni(001) system along the parallel plane can further be observed from a plot of emission intensity versus photon incident angle (Fig. 4). In the plot, contributions from A~~ and A~ polarizations are added together and the electron emission angle is 8, =30'[i e. , 60' from the (100) direction]. The photon A~~ vector makes acute angles with the (100) direction. The calculated emission intensity, coming primarily from the a, state, peaks at about Op& = 40, then decreases to zero at larger photon angles. Such behavior is characteristic of the dependence of an a, state on photon incident angle. The experimental data, ' measured up to Oph~50 with use of unpolarized light, show qualitatively similar features. A plot of the y dependence of photoemission intensity for c(2 x2) S-Ni(001) is shown in Fig. 5. At 8 pp 0 the pattern has C~„symmetry, as diclattices. Expertated by the overlayer-substrate imental data of y dependence are taken at 0» = 50 .' The general qualitative features suggest good correspondence between theory and experiment. The data, however, should not show C4„ symmetry. At 8ph0', there is only a reflection symmetry along the (100) direction (i.e. , plane of incidence of the photon). The data shown here probably are not accurate enough to pick up the
s.
asymmetric In conclusion, results of dynamical calculations of AH UPS on c(2 x2) 0- and S-Ni(001) systems
500
FIG. 5. Azimuthal-angle dependence at 0 b=0' of emission from S-derived levels, with unpolarized light and an electron-collection angle of 0, = 30'. The experimental intensity has arbitrary scale.
are presented and compared with experiment. Since the calculations always separate contributions from orbitals with different symmetries, it is apparent that such calculations, when used to interpret experimental data, provide valuable information in the understanding of individual emission properties of different surface orbitals not readily separable in the data. It is also of interest to note that the 0 and S systems have very different emission properties. For the c(2x2) 0-Ni(001) system, the emissions from a, But and e states are comparable in magnitude. for the c(2 x2) S-Ni(001) system, the emission is frequently dominated by the a, state. This difference can be traced partly to the different amounts of overlap that the 0 2P and S 3P wave functions have with the nickel-substrate wave functions. It is indeed a pleasure to acknowledge the many stimulating discussions with Dr. M. A. Van Hove on various aspects of this work. We are also indebted to Dr. S. P. Weeks, Dr. E. W. Plummer, and Dr. T. Gustafsson for much useful information and the use of some of their experimental data prior to publication. This work was supported in part by the National Science Foundation, Grant No. DMH73-02614. R. J. Smith, J. Anderson, and G. J. Lapeyre, Phys. Bev. Lett. 37, 1081 (1976). G. Apai, P. S. Wehner, B. S. Williams, J. Stohr, and D. A. Shirley, Phys. Bev. Lett. 37, 1497 (1976).
S. P. Weeks
and
21, 695 (1977).
E. W. Plummer,
Solid State Commun.
VOLUME
39, NUMBER 8
PHYSICAL REVIEW LETTERS
C. L. Allyn, T. Gustafsson, and E. W, Plummer, to be published. P. M. Williams, P. Butcher, J. Wood, and K. Jacobi, Phys. Rev. B 14, 3215 (1976). G. Broden and T. N. Rhodin, Solid State Commun. 18, 105 (1976).
S. P. Weeks, E. W. Plummer, and T. Gustafsson, in Proceedings of the Conference on Photoemission from Surfaces, Noordwijk, Netherlands, September, 1976 (to be published). D. E. Eastman and J, E. Demuth, Jpn. J. Appl. Phys. , Suppl. 2, Pt. 2, 827 (1974). E. Demuth, D. W. Jepsen, and P. M. Marcus, Phys. Rev. Lett. 31, 540 (1978). M. A. Van Hove and S. Y. Tong, J. Vac. Sci. Technol.
12,
(1975).
J. W. Davenport,
Phys. Rev. Lett. 86, 945 (1976). K. Jacobi, M. Scheffler, K. Kambe, and F. Forst-
mann, to be published. Hermanson, Solid State Commun. 22, 9 (1977). C. H. Li, A. R. Lubinsky, and S. Y. Tong, to be pub-
J.
lished. 5S. Y. Tong and M. A. 19, 543 (1976).
Van Hove, Solid State Commun.
J. B. Pendry, J. W. Gadzuk,
Phys. Rev. Lett. 27, 856 (1971). Phys. Rev. B 10, 5030 (1974). A. Liebsch, Phys. Rev. Lett. 32, 1203 (1974). G. E. Becker and H. D. Hagstrum, Surf. Sci. 80, 505
J.
Superhyperfine
2SO
22 AUGUsT 1977
(1972).
E. W. Plummer
T. Gustafsson,
and
to be published.
Splitting and the Dynamic Jahn-Teller Effect for the Ferrous Ion in KMgF3
J.
H. Kim and Lange DePa&ment of Physics, Oklahoma State University, Stil/mate~, (Received 20 June 1977)
Oklahoma
74074
Superhyperfine structure for the ferrous ion in KMgF3 has been observed. A JahnTeller energy of 108 cm ' is determined from the magnitude of the g factor as an upper limit, ignoring covalent contributions. The temperature dependence of the width of the normal electronic Zeeman transitions indicates an excited level at 94 cm ' above the ground state. This energy-level separation agrees with the calculated position of the lowest spin-orbit-split excited state reduced by the dynamic Jahn- TelI. er effect.
The superhyperfine (SHF) spectrum has been observed for the ferrous ion as a dilute substitutional impurity in KMgF, . The interaction of the electron spin of the ferrous ion with the nuclear magnetic fields of the six nearest-neighbor Quorine nuclear spins (f =-', ) leads to a splitting of the electronic Zeeman transition. Although it is possible to use the SHF spectra to obtain information concerning the interaction of the electron and its nearest neighbors, we will emphasize in the following the application of the SHF spectra to provide insight into the possibility of a dynamic Jahn-Teller effect (DJTE).' The narrowness of the SHF lines facilitates this approach. The electronic ground state of the ferrous ion is a triplet in an octahedral crystal field. Spin transitions between all the members of the Zeeman-split triplet result in two distinctive features in the EPH spectra. Firstly, there is a spin transition between the m, =O and m, =a 1 Zeeman-split (b. m =+ 1) triplet. This transition is broad due to its sensitivity to linear strains in the lattice. There is a second transition (normally forbidden in a strictly cubic environment) between the m, =+ 1 members of the Zeeman-split triplet (6m = 2) which occurs at approximately half the magnetic field of the "h, m = 1" transition. This transition
is typically narrower
than the b, m = 1 since it is not sensitive to all linear lattice distortions but only to those with orthorhombic symmetry. These two features of the ferrous EPR spectra have been considered in detail for a MgO host lattice' where no superhyperfine structure is observed. The SHF spectrum in Fig. 1 shows this so-called 4m =2 haL. f-fieM line and is only observed in specimens with low impurity concentrations' (Fe'+&30 ppm). Higher impurity concentrations increase the strain broadening to the point that SHF structure is no longer discernible. The SHF spectrum for the ferrous ion displays the characteristic splitting and anisotropy due to the interaction of the electron with six nearestneighbor nuclear spins. The SHF splitting for the ferrous ion in KMgF, show in Fig. 1 exhibits a seven-line splitting of the electronic Zeeman transition which is due to the interaction of the electron with the six equivalent octahedrally coordinated fluorine nuclei (f =-, ) when the field is along the [111jdirection. The relative intensity of the SHF lines agrees with the ratio expected for six nearest-neighbor fluorine atoms. The spectra for various other magnetic-field directions are also consistent with the interpretation that the spectra are due tb SHF interaction with
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