- Email: [email protected]
Calculation of angle-resolved Auger electron diffraction spectra to investigate the surface magnetism of Fe(0 0 1)
3ournal el Magnetism and Magnetic Materiats 177-181 (1998) 1275-1276
~
IDBrnal e|
J~
and
ELSEVIER
magnetism magnetic materials
Calculation of angle-resolved Auger electron diffraction spectra to investigate the surface magnetism of Fe(0 0 1) P. Rennert a'*, Yu Kucherenko b, L.
Niebergall a
~Physics Department, Martin-Luther-University Halle-Wittenberg, D-06099 Halle, Germany blnstitute of Metal Physics, Na~.Acad.Sci. Ukraine, 252142 Kiev, Ulcraine
Abstract Surfaces and low-dimensional systems show a special magnetic structure. A useful method to study this magnetic structure is the spin-polarized Auger electron spectroscopy. We have calculated the angle-resolved Auger emission from the Fe(0 0 1) surface following the creation of a core hole by polarized photons. Diffraction of the escaping Auger electrons has been taken into account. To discuss the Fe L3VV Auger spectrum it is important to consider a multi-band picture. The Auger matrix elements strongly depend on the character of the hands, whether they are tzg-Iike or eg-like, respectively. At the surface the enhanced magnetic moment and the additional splitting contribute a few percent to the spin polarization. :~) 1998 Elsevier Science B.V. All rights reserved. Ke3qvords: Auger electron diffraction; Spin polarization
The spin dependence of angle-resolved photoelectron and Auger electron spectra may be used to analyze the magnetic structure of surfaces [1-31. Auger spectra following a creation of the core hole with polarized photons are intensively investigated experimentally [-2, 4] because the spin polarization of the core hole is transferred to the Auger electron. We present calculations of the spin-polarized Auger electron emission for the Fe(0 0 1) surface. Auger spectra are considered taking into account band-structure effects rather than a simple convolution of the total density of states (DOS). For the valence d-states of different symmetry - t2~ and eg - the partial DOS has a quite different shape, the angular part of the Auger matrix elements is also quite different [5]. Furthermore, a symmetry breaking at the surface removes the degeneration of both tzg and eg states. For details of our methods and for details of our notation, see Ref. E6]. Angular-resolved Auger electron emission is calculated for the excitation of L3VV transitions from the Fe(0 0 1) surface with linearly and circularly polarized X-ray photons. The geometry was chosen similar to that one used in the experiment of Sinkovic et al. [41. We consider the off-resonance case with a photon energy of 820 eV. * Corresponding author. Tel.: + 49 345 552 5430', fax: + 49 345 552 5456; e-mail: [email protected].
Results are presented for an azimuthal scan with a fixed polar angle of 54,7 ° and for normal incidence of the photons. The direction of the inplane magnetization was chosen as the x-axis. The spin polarization of the escaping Auger electrons is given with respect to this direction. Fig. 1 shows the spin polarization of the direct (or primary) wave from an Fe atom in the surface layer and from an atom in the third layer, respectively. Results are shown for two linear polarizations ul = (1 0 0) (parallel to the magnetization) and Ue = (0 1 0) as well as for right (rc) and left (lc) circularly polarized light. Fig. 2 shows the spin polarization (a) and intensity (b) of Auger electrons for a linear photon polarization
.~- 13 -m_
10
0
90
180
270
360
azimuthal angle
Fig. 1. Spin polarization of the L3M~sM¢5 Auger electrons emitted from Fe(0 0 1) after creating a core hole with X-rays of different polarization, ul (full line), u2 (dashed line) and rc/Ic (dotted line).
0304-8853/98/$19.00 ,~ 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 7 7 4 - 9
1276
P. Rennert et al. /Journal o f Magnetism and Magnetic Materials 177-181 (1998) 1275-1276
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Fig. 2. As Fig. i for X-ray polarization ul. The spin polarization (a) and the intensity (b) for spin-up (full line) and spin-down (dashed line) electrons are shown. The results without scattering contributions (thin lines) are given for comparison.
Fig. 3. Contributions to the Fe L3VV spectrum from different orbital combinations: (t2e-t2g) (solid line), (eg--%) (dotted line). (t2g-eg) (dashed line). Spin polarization (a) and intensities for the spin-up Auger electrons (b) are shown for an emitter in the third layer.
parallel to the magnetization. The total intensity is calculated as a sum over contributions from emitters in different layers including scattering contributions. In Fig. 3 we have presented separately the contributions from the t2g and eg parts of the DOS as well as the mixed part. Occupation numbers of these sublevels calculated with the recursion method are 2.676 (t2g ]'), t.865 (% ]'), 1.59 (t2g $) and 0.80 (% $) for the bulk atoms and 2 x 0.961 + 0.972, 0.956 + 0.950, 2 x 0.441 + 0.561, 0.399 + 0.388 for a surface atom. Due to the symmetry breaking at the surface there is an additional splitting into (xz, yz; xy) and (x 2 - y2; 3z 2 _ r2) orbitals, respectively. The main contribution to the spin-polarization results from the valence band polarization. It is stitl present without electron scattering as shown in Fig. 1. The surface atom gives a bigger contribution than the atom in the third layer (a bulk atom) due to the enhanced magnetic moment of about 2,6 PB. The magnetic moment of the iron atoms is involved in the calculation of the wave functions and the matrix elements. We get a dependence on the azimuthal angle due to the mixing of the final channels weighted with different matrix elements, and there remains only one mirror plane, the yz-plane. It is perpendicular to the magnetization and a reflection does not change the (two-component) spinors. In the following figures we show only the region between 90 ° and 270 °. The intensity and the spin polarization is strongly modified by scattering as it can be seen from Fig. 2, For the polar angle of 54.7 ° we get a important forward scattering in the BCC structure for 4~ = 135 °, 225 °. The relatively smooth curve from the direct wave (Fig. 2b) is enhanced by a factor four to five, F r o m the spin polarization (Fig. 2a) it can be seen that there is a strong contribution from the magnetic scattering. Whereas the spin
polarization of the direct wave varies around 12%, including the scattering changes these values from 6% to 20%. The partial DOSs (t2g, %) contribute with different weight to the Auger electron intensity. There are quite different values of the matrix elements and a different shape in dependence on the energy. Therefore, we have analysed these parts separately (here the energy-integrated results are presented). Similar to Fig. 2 we have a strong influence of the forward scattering in all parts of the intensity (Fig. 3b). But, again we find a more differentiated situation in the spin polarization (Fig. 3a) where the values vary between 0% and 30%. Thus, in the energy-resolved measurements it could be possible to separate these contributions, if an energy is chosen where a particular symmetry state dominates in DOS [61. This work was supported under G r a n t No. 436UKR17/2/96 by D F G and by B M B F under Grant No. 332-4006-06 H A L 01 (8).
References [1"] B. Sinkovir, C.S. FadIey, Phys. Rev. B 31 (1985) 4665. [2] N. MfilIer, R. David, G. Snell, R. Kuntze, M. Drescher, N. Brwering, P. Stoppmanns, S.-W. Yu, U. Heinzmann, J. Viefhaus, U. Hergenhahn, U. Becker, J. Electr. Spectr. Relat. Phenom. 72 (t995) 187. [33 P. Rennert, Yu. Kucherenko, J. Electr. Spectr. Relat. Phenora. 76 (1995) 157. [4] B. Sinkovir, E. Shekel, S.L. Hulbert, Phys. Rev. B 52 (1995) R15703. I-5] C. Presilla, F. Sacchetti, J. Phys. F: Met. Phys. 17 (1987) 779. [61 Yu. Kucherenko, P. Rennert, J. Phys.: Condens. Matter 9 (t997) 5003.
~
IDBrnal e|
J~
and
ELSEVIER
magnetism magnetic materials
Calculation of angle-resolved Auger electron diffraction spectra to investigate the surface magnetism of Fe(0 0 1) P. Rennert a'*, Yu Kucherenko b, L.
Niebergall a
~Physics Department, Martin-Luther-University Halle-Wittenberg, D-06099 Halle, Germany blnstitute of Metal Physics, Na~.Acad.Sci. Ukraine, 252142 Kiev, Ulcraine
Abstract Surfaces and low-dimensional systems show a special magnetic structure. A useful method to study this magnetic structure is the spin-polarized Auger electron spectroscopy. We have calculated the angle-resolved Auger emission from the Fe(0 0 1) surface following the creation of a core hole by polarized photons. Diffraction of the escaping Auger electrons has been taken into account. To discuss the Fe L3VV Auger spectrum it is important to consider a multi-band picture. The Auger matrix elements strongly depend on the character of the hands, whether they are tzg-Iike or eg-like, respectively. At the surface the enhanced magnetic moment and the additional splitting contribute a few percent to the spin polarization. :~) 1998 Elsevier Science B.V. All rights reserved. Ke3qvords: Auger electron diffraction; Spin polarization
The spin dependence of angle-resolved photoelectron and Auger electron spectra may be used to analyze the magnetic structure of surfaces [1-31. Auger spectra following a creation of the core hole with polarized photons are intensively investigated experimentally [-2, 4] because the spin polarization of the core hole is transferred to the Auger electron. We present calculations of the spin-polarized Auger electron emission for the Fe(0 0 1) surface. Auger spectra are considered taking into account band-structure effects rather than a simple convolution of the total density of states (DOS). For the valence d-states of different symmetry - t2~ and eg - the partial DOS has a quite different shape, the angular part of the Auger matrix elements is also quite different [5]. Furthermore, a symmetry breaking at the surface removes the degeneration of both tzg and eg states. For details of our methods and for details of our notation, see Ref. E6]. Angular-resolved Auger electron emission is calculated for the excitation of L3VV transitions from the Fe(0 0 1) surface with linearly and circularly polarized X-ray photons. The geometry was chosen similar to that one used in the experiment of Sinkovic et al. [41. We consider the off-resonance case with a photon energy of 820 eV. * Corresponding author. Tel.: + 49 345 552 5430', fax: + 49 345 552 5456; e-mail: [email protected].
Results are presented for an azimuthal scan with a fixed polar angle of 54,7 ° and for normal incidence of the photons. The direction of the inplane magnetization was chosen as the x-axis. The spin polarization of the escaping Auger electrons is given with respect to this direction. Fig. 1 shows the spin polarization of the direct (or primary) wave from an Fe atom in the surface layer and from an atom in the third layer, respectively. Results are shown for two linear polarizations ul = (1 0 0) (parallel to the magnetization) and Ue = (0 1 0) as well as for right (rc) and left (lc) circularly polarized light. Fig. 2 shows the spin polarization (a) and intensity (b) of Auger electrons for a linear photon polarization
.~- 13 -m_
10
0
90
180
270
360
azimuthal angle
Fig. 1. Spin polarization of the L3M~sM¢5 Auger electrons emitted from Fe(0 0 1) after creating a core hole with X-rays of different polarization, ul (full line), u2 (dashed line) and rc/Ic (dotted line).
0304-8853/98/$19.00 ,~ 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 7 7 4 - 9
1276
P. Rennert et al. /Journal o f Magnetism and Magnetic Materials 177-181 (1998) 1275-1276
40f
i~ '
'
=2° I:%", ; ~i ",",i '..-.V ,?:":',,~ :if"
°olI
4 2.5
~
0,5
'
a)
",i~: ';~'";
~
2.0
0,3
.~ "1.5 1.0 o
.~ o,1
_~ 0.5 0.0 90
180
azfmuthal
270
0.0
gO
angle
180
azimuthal
270
angle @
Fig. 2. As Fig. i for X-ray polarization ul. The spin polarization (a) and the intensity (b) for spin-up (full line) and spin-down (dashed line) electrons are shown. The results without scattering contributions (thin lines) are given for comparison.
Fig. 3. Contributions to the Fe L3VV spectrum from different orbital combinations: (t2e-t2g) (solid line), (eg--%) (dotted line). (t2g-eg) (dashed line). Spin polarization (a) and intensities for the spin-up Auger electrons (b) are shown for an emitter in the third layer.
parallel to the magnetization. The total intensity is calculated as a sum over contributions from emitters in different layers including scattering contributions. In Fig. 3 we have presented separately the contributions from the t2g and eg parts of the DOS as well as the mixed part. Occupation numbers of these sublevels calculated with the recursion method are 2.676 (t2g ]'), t.865 (% ]'), 1.59 (t2g $) and 0.80 (% $) for the bulk atoms and 2 x 0.961 + 0.972, 0.956 + 0.950, 2 x 0.441 + 0.561, 0.399 + 0.388 for a surface atom. Due to the symmetry breaking at the surface there is an additional splitting into (xz, yz; xy) and (x 2 - y2; 3z 2 _ r2) orbitals, respectively. The main contribution to the spin-polarization results from the valence band polarization. It is stitl present without electron scattering as shown in Fig. 1. The surface atom gives a bigger contribution than the atom in the third layer (a bulk atom) due to the enhanced magnetic moment of about 2,6 PB. The magnetic moment of the iron atoms is involved in the calculation of the wave functions and the matrix elements. We get a dependence on the azimuthal angle due to the mixing of the final channels weighted with different matrix elements, and there remains only one mirror plane, the yz-plane. It is perpendicular to the magnetization and a reflection does not change the (two-component) spinors. In the following figures we show only the region between 90 ° and 270 °. The intensity and the spin polarization is strongly modified by scattering as it can be seen from Fig. 2, For the polar angle of 54.7 ° we get a important forward scattering in the BCC structure for 4~ = 135 °, 225 °. The relatively smooth curve from the direct wave (Fig. 2b) is enhanced by a factor four to five, F r o m the spin polarization (Fig. 2a) it can be seen that there is a strong contribution from the magnetic scattering. Whereas the spin
polarization of the direct wave varies around 12%, including the scattering changes these values from 6% to 20%. The partial DOSs (t2g, %) contribute with different weight to the Auger electron intensity. There are quite different values of the matrix elements and a different shape in dependence on the energy. Therefore, we have analysed these parts separately (here the energy-integrated results are presented). Similar to Fig. 2 we have a strong influence of the forward scattering in all parts of the intensity (Fig. 3b). But, again we find a more differentiated situation in the spin polarization (Fig. 3a) where the values vary between 0% and 30%. Thus, in the energy-resolved measurements it could be possible to separate these contributions, if an energy is chosen where a particular symmetry state dominates in DOS [61. This work was supported under G r a n t No. 436UKR17/2/96 by D F G and by B M B F under Grant No. 332-4006-06 H A L 01 (8).
References [1"] B. Sinkovir, C.S. FadIey, Phys. Rev. B 31 (1985) 4665. [2] N. MfilIer, R. David, G. Snell, R. Kuntze, M. Drescher, N. Brwering, P. Stoppmanns, S.-W. Yu, U. Heinzmann, J. Viefhaus, U. Hergenhahn, U. Becker, J. Electr. Spectr. Relat. Phenom. 72 (t995) 187. [33 P. Rennert, Yu. Kucherenko, J. Electr. Spectr. Relat. Phenora. 76 (1995) 157. [4] B. Sinkovir, E. Shekel, S.L. Hulbert, Phys. Rev. B 52 (1995) R15703. I-5] C. Presilla, F. Sacchetti, J. Phys. F: Met. Phys. 17 (1987) 779. [61 Yu. Kucherenko, P. Rennert, J. Phys.: Condens. Matter 9 (t997) 5003.