- Email: [email protected]
Magnetic and electronic properties of thin iron oxide films
727
Surface Science 126 ( 1983) 727-732 North-Holland Publishing Company
MAGNETIC FILMS
AND ELECTRONIC
M. DOMKE,
B. KYVELOS
Freie Unioersitiit Berlin, Arnimallee Received
24 August
PROPERTIES
OF THIN IRON OXIDE
and G. KAINDL 14, D-1000
Berlin 33, Fed. Rep. of Germany
1982
Conversion electron Mossbauer spectroscopy JCEMS) with the 14.4 keV gamma resonance of 57Fe was employed to study uncovered 5 to 50 A thick iron oxide films grown on single-crystal Fe(l10) and Fe(100) substrates under UHV conditions. For both magnetite (FesO,) and hematite (cu-FesOs) a decrease of the magnetic hyperfine field and of the _Miissbauer isomer shift was observed at room temperature with film thicknesses smaller than 20 A. In addition, the magnetization vector was found to align preferentially normal to the surface with decreasing thickness of the oxide films.
1. Introduction Both the electronic and the magnetic properties of solids are expected to change when going from the bulk to the surface [ 1,2]. While several very powerful methods have been developed for studying electronic properties of surfaces, the experimental situation is less favourable in the case of surface magnetism [3]. Only recently, consistent results have been achieved with spin-polarized photoemission [4], spin-polarized low energy electron diffraction [5], anomalous Hall effect [6], and electron-capture spectroscopy [7]. Despite experimental difficulties due to a rather limited surface sensitivity Mbssbauer spectroscopy particularly with the 14.4 keV gamma resonance of 57Fe offers a rather unique possibility of studying both the local electronic and magnetic properties of surface atoms. Monoatomic surface layers may in principle be studied by Miissbauer emission spectroscopy with 57Co surface films [8] or by depth-selective conversion electron Mossbauer spectroscopy (CEMS) [9]. Very few investigations, however, have been carried out up to now on well-characterized single-crystal surfaces under ultra-high vacuum (UHV) conditions. The quite extensive Mossbauer transmission work on thin magnetic layers covered by various coating films, on the other hand, is not directly relevant to surface magnetism due to the strong influence of the coating materials [ 10,111. In the present paper we report on a CEMS study of uncoated thin iron oxide films (5 to 50 A thick) grown on well-characterized (110) and (100) 0039-6028/83/0000-0000/$03.00
0 1983 North-Holland
728
M. Domke et al. / Properties of iron oxide films
surfaces of 57Fe metal. The different hyperfine parameters of Fe metal and the two oxide phases formed (magnetite and hematite) provide a convenient mean for distinguishing between them. In addition, the chemical inertness of the oxide surface layers is rather favourable for the relatively long data collection times necessary.
2. Experimental The CEMS measurements were performed with a non-dispersive electrostatic analyzer based on a focussing ellipsoidal electron mirror (low-pass) in combination with a retarding grid (high-pass). The spectrometer has been described in detail elsewhere [12]. A 30 mCi 57CoRh source was sinusoidally moved outside of the experimental chamber, which had a base pressure of 1 X lo-” Torr. In the present work the gamma ray direction was normal to the surface, and a wide energy window was used for the detected electrons. The (110) and (100) surfaces of an Fe single crystal of natural abundance were cleaned by Ar ion sputtering at elevated temperatures, and subsequently characterized by LEED and Auger spectroscopy. All contaminants (C, S, Cl, and N) were found to be less than a few percent of a monolayer. Subsequently, 100 A thick epitaxial layers of highly enriched 57Fe metal were grown on both crystal faces and checked by CEMS for bulk chemical purity (no Mossbauer resonance lines other than those of Fe metal were observed). Oxidation of the freshly prepared metal surfaces was carried out in 2 X 10e4 Torr oxygen at 180-250°C for periods from 5 to 200 min, yielding magnetite (Fe,O,) layers from 4 to 15 A thickness. Thicker layers were obtained at a pressure of 2 X lop3 Torr. A 45 min oxidation of Fe(ll0) at 275°C and 2 X 10e3 Torr of 0, resulted in the beginning formation of hematite on a 60 A thick layer of magnetite. A detailed report of the oxidation kinetics will be published elsewhere.
3.Results and discussion On Fe( 100) magnetite forms an ordered p( 1 x 1)-like overlayer after annealing in UHV at 500-600°C. On the other hand, the LEED patterns show that the oxide formed on Fe(ll0) is not well ordered even after annealing at temperatures up to 700°C. In this case facetting cannot be excluded, and the LEED spots disappeared for magnetite layers of more than 8 A thickness as well as during the growth of hematite. Therefore, the quoted thicknesses of the oxide layers, which were obtained from the relative intensities of the CEMS subspectra (see below) should be considered as mean values only. In fig. 1 typical room-temperature CEMS spectra of thin oxide layers on an
M. Domke et al. / Properties of iron oxide firms
-9
-6 -3 RELATIVE Fe1
0
0 VELOCITY I
1
3 (mm/s) 1
6
129
9
,
Fe30~(Alg
I
Fe,O,IBlL a-FezOSt
I
Fig. I. CEMS spectra of (a) an 11 A layer of FesO, and (b) an 11 A layer of a-Fe,O, grown on a thick layer of Fe,O,, both on an Fe( 110) substrate. The horizontal bar diagrams represent the line positions of the four subspectra originating from Fe metal, the A- and B-sites in Fe,O,, and a-Fe,O,, respectively. In (a) the spectra1 intensities from the A-sites (B-sites) of the Fe,O, surface film are represented by the dotted (dashed) subspectra; in (b) those from the cu-FeaO, surface layer are indicated by the dashed subspectrum.
Fe( 110) substrate are presented: in (a) for 11 A of Fe,O, and (b) for 11 A of cr-Fe,O, grown on a thick layer of Fe,O,. In addition to spectral features from the oxide layers all CEMS spectra show the typical six-line pattern of Fe metal caused by a magnetic hyperfine field of 32.95 T. The spectral contribution originating from magnetite (Fe,O,) consists of two six-line subspectra from Fe at tetrahedral (A) and octahedral (B) sites in the oxygen ion lattice, respectively. Thin Fe,O, layers exhibit a B-to-A intensity ratio close to 2, revealing a stoichiometric occupation of the two Fe sites. The six-line pattern from hematite is caused by an additional el~tric-quadrupole interaction of nearly the same size as in bulk ar-Fe,O,. The solid lines in fig. 1 represent the results of least-squares fits of superpositions of Lorentzian lines to the data points. From the splitting of the individual subspectra the magnetic hyperfine fields
730
M. Domke et al. / Properties of iron oxide films
,-
=
+
s
0.5 -
*
c
’ MAGNETITE
(A)
MAGNETITE
lBl Ibl
OXIDE
THICKNESS
IAI
Fig. 2. Least-squares fit results for (a) magnetic hyperfine field, (b) isomer shift, and (c) line intensity ratio .x as a function of the thickness of the oxide layers for A- and B-sites of Fe,O, and for wFe,O,. The solid lines serve only as guides to the eye.
B,, at the various Fe sites are obtained, which are proportional to the local magnetizations. The relative intensities of the 6 resonance lines of each subspectrum reflect the orientation of the magnetization vector relative to the y-ray direction: ratios of 3 : x : 1 : 1 : x : 3 reveal random orientation for x = 2, normal to the surface for x = 0, and in-plane for x = 4. The isomer shift S, which is the shift of the center of gravity of each resonance subspectrum relative to zero relative velocity, is proportional to the total electron density p(O) at the nucleus, and provides information on the oxidation state of iron and its local electronic structure [ 131. Essentially identical results were obtained for the Fe( 100) substrate. The fit results for magnetic hyperfine field, isomer shift, and intensity ratio x are plotted in figs. 2a-2c for the two Fe sites in Fe,O, and for cu-Fe,O, as a function of oxide layer thickness. Both the magnetic hyperfine field and the isomer shift clearly decrease with thicknesses smaller than 20 A of the oxide layers for both the B-site in Fe,O, and for cr-Fe,O,. The effects are much less pronounced in the A-site of magnetite. In all three Fe environments the line intensity ratio x decreases with the oxide layer thickness, which means that the local magnetization vectors align preferentially normal to the surface with decreasing thickness of the oxide layers. The widths of the resonance lines exhibit only very slight increases from typically 0.30 mm/s for thick layers to = 0.40 mm/s for very thin layers, which must be expected from the simultaneous measurement on surface and bulk-like layers. No broad dist~bution of magnetic hyperfine fields is observed as in previous Mossbauer emission work on thin 57Co surface layers [g]. The observed decrease in room-temperature magnetization with the thickness of the oxide films may be compared with theoretical predictions and other experimental results. For weakened magnetic exchange at the surface Binder and Hohenberg [ 141 find a decrease in magnetization in the surface layer, while
A4. Domke et al. / Properties of iron oxide films
731
Wang and Freeman predict a smaller surface magnetization for Ni( 100) and a larger one for Fe(100) on the basis of their ab-initio energy-band calculations for free multilayers [l]. In addition, a stronger (linear) decrease of the spontaneous magnetization with increasing temperature is expected for the outermost surface layer as compared to the bulk [8]. A preliminary study of the temperature dependence of the magnetic hyperfine field B,, for the B-site in thin Fe,O, layers indeed indicates such a steeper decrease with temperature. Therefore, the present room-temperature results do not yet allow a final conclusion concerning the dependence of the saturation magnetization on the layer thickness, since the observed decrease could also be due to the spin wave dynamics at the surface. To clarify this question an extension of the present CEMS measurements to low temperatures is in progress. Depth-selective CEMS measurements on hematite films at room-temperature have also revealed a decrease of B,, by about 2% for the surface and no change in electric-quadrupole interaction in good agreement with the present results [9]. On the other hand, a far stronger decrease of the room-temperature magnetization towards the surface of Fe,O, than observed in the present work has been claimed on the basis of spin-polarized photoemission data [4]. A previous transmission Mossbauer study of thin Fe,O, films prepared on small iron particles, however, revealed a similar decrease of B,, with decreasing film thickness as observed in the present CEMS study [15]. The present observation that the local magnetization vector aligns preferentially normal to the surface for thin iron oxide films is in agreement with previous results by various methods [2,8,10]. It can be attributed to a strong surface anisotropy. The observed decrease of the isomer shift S for very thin oxide layers by at most 0.07 mm/s corresponds to an increase in the total electron density at the nucleus p(O) [13]. Generally, this may be caused either by an increase in the local s-electron population or by a depopulation of d-orbitals due to their shielding effect. The weakening of the lattice potential at the surface presumably leads to an increased localization of both d- and s-orbitals at the surface with the dominant effect of s-electrons on p(O) causing the observed isomer shift change. On the other hand, the observed decrease in S could also be caused by the second-order Doppler effect due to presumably larger meansquare displacements of the surface atoms as compared to the bulk. The expected anisotropy of the latter effect could be used in distinguishing between the two possibilities. It should be noted that previous Mossbauer studies of iron/coating-material interfaces revealed an increase in S towards the outermost Fe layer covered by the coating material [ 111. It is interesting to note that both B,, and S exhibit smaller surface effects for the magnetite A-site as compared to the B-site and to hematite. This may be due to the more densely packed surrounding of the tetrahedral A-sites as compared to the octahedral sites, which may therefore be less sensitive to
hf. Domke et al. / Properties
132
of iron oxide films
surface effects. Similarly, surface relaxation effects are usually pronounced for the less close-packed single-crystal surfaces [ 161.
much
more
Acknowledgement The work was supported by Deutsche Forschungsgemeinschaft.
the
Sonderforschungsbereich-
161 of
the
References [l] [2] [3] [4] [5] [6] [7] [8] (9) [lo] [l l] [ 121 [ 131
[ 141 [ 151 [16]
See, e.g., C.S. Wang and A.J. Freeman, Phys. Rev. B24 (1981) 4364. U. Gradman, J. Magnetism Magnetic Mater. 6 (1977) 173. G. Allan, Surface, Sci. Rept. 1 (1981) 121. SF. Alvarado, Z. Physik B33 (1979) 51. G. Alvarado, M. Campagna and H. Hopster, Phys. Rev. Letters 48 (1982) 51. G. Bergmann, Phys. Rev. Letters 41 (1978) 264. C. Rau, Comments Solid State Phys. 9 (1980) 177, and references therein. U. Gradmann, K. Ullrich, J. Pebler and K. Schmidt, J. Magnetism Magnetic Mater. 5 (1977) 339. T. Yang, K. Krishnan, N. Benczer-Koller and G. Bayreuther, Phys. Rev. Letters 48 (1982) 1292. See, e.g., W. Keune, J. Lauer, U. Gonser and D.L. Williamson, J. Physique 40 (1979) C2-84. A.H. Owens, J. Tyson, G. Bayreuther and J.C. Walker, Hyperfine Interactions 10 (1981) 805. M. Domke, B. Kyvelos and G. Kaindl, Hyperfine Interactions 10 (1981) 1137. See, e.g., P. Giitlich, R. Link and A. Trautwein, Mossbauer Spectroscopy and Transition Metal Chemistry (Springer, Berlin, 1978). K. Binder and P.C. Hohenberg, Phys. Rev. B9 (1974) 2 194. I.P. Suzdalev and A.P. Amulyavichus, Soviet Phys.-JETP 36 (1973) 929. See, e.g., G.A. Somojai and M.A. Van Hove, Adsorbed Monolayers on Solid Surfaces (Springer, Berlin, 1979) p. 105.
Surface Science 126 ( 1983) 727-732 North-Holland Publishing Company
MAGNETIC FILMS
AND ELECTRONIC
M. DOMKE,
B. KYVELOS
Freie Unioersitiit Berlin, Arnimallee Received
24 August
PROPERTIES
OF THIN IRON OXIDE
and G. KAINDL 14, D-1000
Berlin 33, Fed. Rep. of Germany
1982
Conversion electron Mossbauer spectroscopy JCEMS) with the 14.4 keV gamma resonance of 57Fe was employed to study uncovered 5 to 50 A thick iron oxide films grown on single-crystal Fe(l10) and Fe(100) substrates under UHV conditions. For both magnetite (FesO,) and hematite (cu-FesOs) a decrease of the magnetic hyperfine field and of the _Miissbauer isomer shift was observed at room temperature with film thicknesses smaller than 20 A. In addition, the magnetization vector was found to align preferentially normal to the surface with decreasing thickness of the oxide films.
1. Introduction Both the electronic and the magnetic properties of solids are expected to change when going from the bulk to the surface [ 1,2]. While several very powerful methods have been developed for studying electronic properties of surfaces, the experimental situation is less favourable in the case of surface magnetism [3]. Only recently, consistent results have been achieved with spin-polarized photoemission [4], spin-polarized low energy electron diffraction [5], anomalous Hall effect [6], and electron-capture spectroscopy [7]. Despite experimental difficulties due to a rather limited surface sensitivity Mbssbauer spectroscopy particularly with the 14.4 keV gamma resonance of 57Fe offers a rather unique possibility of studying both the local electronic and magnetic properties of surface atoms. Monoatomic surface layers may in principle be studied by Miissbauer emission spectroscopy with 57Co surface films [8] or by depth-selective conversion electron Mossbauer spectroscopy (CEMS) [9]. Very few investigations, however, have been carried out up to now on well-characterized single-crystal surfaces under ultra-high vacuum (UHV) conditions. The quite extensive Mossbauer transmission work on thin magnetic layers covered by various coating films, on the other hand, is not directly relevant to surface magnetism due to the strong influence of the coating materials [ 10,111. In the present paper we report on a CEMS study of uncoated thin iron oxide films (5 to 50 A thick) grown on well-characterized (110) and (100) 0039-6028/83/0000-0000/$03.00
0 1983 North-Holland
728
M. Domke et al. / Properties of iron oxide films
surfaces of 57Fe metal. The different hyperfine parameters of Fe metal and the two oxide phases formed (magnetite and hematite) provide a convenient mean for distinguishing between them. In addition, the chemical inertness of the oxide surface layers is rather favourable for the relatively long data collection times necessary.
2. Experimental The CEMS measurements were performed with a non-dispersive electrostatic analyzer based on a focussing ellipsoidal electron mirror (low-pass) in combination with a retarding grid (high-pass). The spectrometer has been described in detail elsewhere [12]. A 30 mCi 57CoRh source was sinusoidally moved outside of the experimental chamber, which had a base pressure of 1 X lo-” Torr. In the present work the gamma ray direction was normal to the surface, and a wide energy window was used for the detected electrons. The (110) and (100) surfaces of an Fe single crystal of natural abundance were cleaned by Ar ion sputtering at elevated temperatures, and subsequently characterized by LEED and Auger spectroscopy. All contaminants (C, S, Cl, and N) were found to be less than a few percent of a monolayer. Subsequently, 100 A thick epitaxial layers of highly enriched 57Fe metal were grown on both crystal faces and checked by CEMS for bulk chemical purity (no Mossbauer resonance lines other than those of Fe metal were observed). Oxidation of the freshly prepared metal surfaces was carried out in 2 X 10e4 Torr oxygen at 180-250°C for periods from 5 to 200 min, yielding magnetite (Fe,O,) layers from 4 to 15 A thickness. Thicker layers were obtained at a pressure of 2 X lop3 Torr. A 45 min oxidation of Fe(ll0) at 275°C and 2 X 10e3 Torr of 0, resulted in the beginning formation of hematite on a 60 A thick layer of magnetite. A detailed report of the oxidation kinetics will be published elsewhere.
3.Results and discussion On Fe( 100) magnetite forms an ordered p( 1 x 1)-like overlayer after annealing in UHV at 500-600°C. On the other hand, the LEED patterns show that the oxide formed on Fe(ll0) is not well ordered even after annealing at temperatures up to 700°C. In this case facetting cannot be excluded, and the LEED spots disappeared for magnetite layers of more than 8 A thickness as well as during the growth of hematite. Therefore, the quoted thicknesses of the oxide layers, which were obtained from the relative intensities of the CEMS subspectra (see below) should be considered as mean values only. In fig. 1 typical room-temperature CEMS spectra of thin oxide layers on an
M. Domke et al. / Properties of iron oxide firms
-9
-6 -3 RELATIVE Fe1
0
0 VELOCITY I
1
3 (mm/s) 1
6
129
9
,
Fe30~(Alg
I
Fe,O,IBlL a-FezOSt
I
Fig. I. CEMS spectra of (a) an 11 A layer of FesO, and (b) an 11 A layer of a-Fe,O, grown on a thick layer of Fe,O,, both on an Fe( 110) substrate. The horizontal bar diagrams represent the line positions of the four subspectra originating from Fe metal, the A- and B-sites in Fe,O,, and a-Fe,O,, respectively. In (a) the spectra1 intensities from the A-sites (B-sites) of the Fe,O, surface film are represented by the dotted (dashed) subspectra; in (b) those from the cu-FeaO, surface layer are indicated by the dashed subspectrum.
Fe( 110) substrate are presented: in (a) for 11 A of Fe,O, and (b) for 11 A of cr-Fe,O, grown on a thick layer of Fe,O,. In addition to spectral features from the oxide layers all CEMS spectra show the typical six-line pattern of Fe metal caused by a magnetic hyperfine field of 32.95 T. The spectral contribution originating from magnetite (Fe,O,) consists of two six-line subspectra from Fe at tetrahedral (A) and octahedral (B) sites in the oxygen ion lattice, respectively. Thin Fe,O, layers exhibit a B-to-A intensity ratio close to 2, revealing a stoichiometric occupation of the two Fe sites. The six-line pattern from hematite is caused by an additional el~tric-quadrupole interaction of nearly the same size as in bulk ar-Fe,O,. The solid lines in fig. 1 represent the results of least-squares fits of superpositions of Lorentzian lines to the data points. From the splitting of the individual subspectra the magnetic hyperfine fields
730
M. Domke et al. / Properties of iron oxide films
,-
=
+
s
0.5 -
*
c
’ MAGNETITE
(A)
MAGNETITE
lBl Ibl
OXIDE
THICKNESS
IAI
Fig. 2. Least-squares fit results for (a) magnetic hyperfine field, (b) isomer shift, and (c) line intensity ratio .x as a function of the thickness of the oxide layers for A- and B-sites of Fe,O, and for wFe,O,. The solid lines serve only as guides to the eye.
B,, at the various Fe sites are obtained, which are proportional to the local magnetizations. The relative intensities of the 6 resonance lines of each subspectrum reflect the orientation of the magnetization vector relative to the y-ray direction: ratios of 3 : x : 1 : 1 : x : 3 reveal random orientation for x = 2, normal to the surface for x = 0, and in-plane for x = 4. The isomer shift S, which is the shift of the center of gravity of each resonance subspectrum relative to zero relative velocity, is proportional to the total electron density p(O) at the nucleus, and provides information on the oxidation state of iron and its local electronic structure [ 131. Essentially identical results were obtained for the Fe( 100) substrate. The fit results for magnetic hyperfine field, isomer shift, and intensity ratio x are plotted in figs. 2a-2c for the two Fe sites in Fe,O, and for cu-Fe,O, as a function of oxide layer thickness. Both the magnetic hyperfine field and the isomer shift clearly decrease with thicknesses smaller than 20 A of the oxide layers for both the B-site in Fe,O, and for cr-Fe,O,. The effects are much less pronounced in the A-site of magnetite. In all three Fe environments the line intensity ratio x decreases with the oxide layer thickness, which means that the local magnetization vectors align preferentially normal to the surface with decreasing thickness of the oxide layers. The widths of the resonance lines exhibit only very slight increases from typically 0.30 mm/s for thick layers to = 0.40 mm/s for very thin layers, which must be expected from the simultaneous measurement on surface and bulk-like layers. No broad dist~bution of magnetic hyperfine fields is observed as in previous Mossbauer emission work on thin 57Co surface layers [g]. The observed decrease in room-temperature magnetization with the thickness of the oxide films may be compared with theoretical predictions and other experimental results. For weakened magnetic exchange at the surface Binder and Hohenberg [ 141 find a decrease in magnetization in the surface layer, while
A4. Domke et al. / Properties of iron oxide films
731
Wang and Freeman predict a smaller surface magnetization for Ni( 100) and a larger one for Fe(100) on the basis of their ab-initio energy-band calculations for free multilayers [l]. In addition, a stronger (linear) decrease of the spontaneous magnetization with increasing temperature is expected for the outermost surface layer as compared to the bulk [8]. A preliminary study of the temperature dependence of the magnetic hyperfine field B,, for the B-site in thin Fe,O, layers indeed indicates such a steeper decrease with temperature. Therefore, the present room-temperature results do not yet allow a final conclusion concerning the dependence of the saturation magnetization on the layer thickness, since the observed decrease could also be due to the spin wave dynamics at the surface. To clarify this question an extension of the present CEMS measurements to low temperatures is in progress. Depth-selective CEMS measurements on hematite films at room-temperature have also revealed a decrease of B,, by about 2% for the surface and no change in electric-quadrupole interaction in good agreement with the present results [9]. On the other hand, a far stronger decrease of the room-temperature magnetization towards the surface of Fe,O, than observed in the present work has been claimed on the basis of spin-polarized photoemission data [4]. A previous transmission Mossbauer study of thin Fe,O, films prepared on small iron particles, however, revealed a similar decrease of B,, with decreasing film thickness as observed in the present CEMS study [15]. The present observation that the local magnetization vector aligns preferentially normal to the surface for thin iron oxide films is in agreement with previous results by various methods [2,8,10]. It can be attributed to a strong surface anisotropy. The observed decrease of the isomer shift S for very thin oxide layers by at most 0.07 mm/s corresponds to an increase in the total electron density at the nucleus p(O) [13]. Generally, this may be caused either by an increase in the local s-electron population or by a depopulation of d-orbitals due to their shielding effect. The weakening of the lattice potential at the surface presumably leads to an increased localization of both d- and s-orbitals at the surface with the dominant effect of s-electrons on p(O) causing the observed isomer shift change. On the other hand, the observed decrease in S could also be caused by the second-order Doppler effect due to presumably larger meansquare displacements of the surface atoms as compared to the bulk. The expected anisotropy of the latter effect could be used in distinguishing between the two possibilities. It should be noted that previous Mossbauer studies of iron/coating-material interfaces revealed an increase in S towards the outermost Fe layer covered by the coating material [ 111. It is interesting to note that both B,, and S exhibit smaller surface effects for the magnetite A-site as compared to the B-site and to hematite. This may be due to the more densely packed surrounding of the tetrahedral A-sites as compared to the octahedral sites, which may therefore be less sensitive to
hf. Domke et al. / Properties
132
of iron oxide films
surface effects. Similarly, surface relaxation effects are usually pronounced for the less close-packed single-crystal surfaces [ 161.
much
more
Acknowledgement The work was supported by Deutsche Forschungsgemeinschaft.
the
Sonderforschungsbereich-
161 of
the
References [l] [2] [3] [4] [5] [6] [7] [8] (9) [lo] [l l] [ 121 [ 131
[ 141 [ 151 [16]
See, e.g., C.S. Wang and A.J. Freeman, Phys. Rev. B24 (1981) 4364. U. Gradman, J. Magnetism Magnetic Mater. 6 (1977) 173. G. Allan, Surface, Sci. Rept. 1 (1981) 121. SF. Alvarado, Z. Physik B33 (1979) 51. G. Alvarado, M. Campagna and H. Hopster, Phys. Rev. Letters 48 (1982) 51. G. Bergmann, Phys. Rev. Letters 41 (1978) 264. C. Rau, Comments Solid State Phys. 9 (1980) 177, and references therein. U. Gradmann, K. Ullrich, J. Pebler and K. Schmidt, J. Magnetism Magnetic Mater. 5 (1977) 339. T. Yang, K. Krishnan, N. Benczer-Koller and G. Bayreuther, Phys. Rev. Letters 48 (1982) 1292. See, e.g., W. Keune, J. Lauer, U. Gonser and D.L. Williamson, J. Physique 40 (1979) C2-84. A.H. Owens, J. Tyson, G. Bayreuther and J.C. Walker, Hyperfine Interactions 10 (1981) 805. M. Domke, B. Kyvelos and G. Kaindl, Hyperfine Interactions 10 (1981) 1137. See, e.g., P. Giitlich, R. Link and A. Trautwein, Mossbauer Spectroscopy and Transition Metal Chemistry (Springer, Berlin, 1978). K. Binder and P.C. Hohenberg, Phys. Rev. B9 (1974) 2 194. I.P. Suzdalev and A.P. Amulyavichus, Soviet Phys.-JETP 36 (1973) 929. See, e.g., G.A. Somojai and M.A. Van Hove, Adsorbed Monolayers on Solid Surfaces (Springer, Berlin, 1979) p. 105.