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Mössbauer spectroscopic studies on surfaces and thin films
126
Journal of Magnetism and Magnetic Materials 35 (1983) 126-129 North-Holland Publishing Company MOSSBAUER
SPECTROSCOPIC
STUDIES ON SURFACES AND THIN FILMS *
J o h n T Y S O N , A l e x a n d e r O W E N S ** a n d J.C. W A L K E R Department of Physics, The Johns Hopkins University, Baltimore, MD 21218, USA
We have !nvestigated the magnetic properties of surface layers of Fe films using M~ssbauer spectroscopy. (110) epitaxial Fe films were made of 56Fe with appropriate probe layers of 57Fe in the surface region. In this way we were able to profile the magnetism at and near the surface of our films. Studies of the temperature dependence of layers at the surface indicate a quasilinear dependence of magnetization on temperature while the temperature dependence of layers further inside the material show the usual T 3/2 dependence. In addition to this we note that a region of surface thermal spin deviations larger than bulk values extends over 3 to 4 layers at the surfaces. These results are in qualitative agreement with a number of theoretical studies including those of Mathon, Bender and Hohenberg, and Wolfram et al. The quasilinear temperature dependence of the surface layer implies a weakening of the surface exchange. In addition to the unusual temperature dependence of the surface magnetization we have generally observed larger surface magnetic hyperfine fields near T = 0.
1. Introduction
A knowledge of the surface properties of transition metals is important. These materials have interesting magnetic properties and are also useful as catalysts. A large amount of theoretical work in the last decade has focused on transition metal surfaces, but our knowledge is still quite limited, particularly with regard to magnetic properties. Only recently has a significant amount of experimental work relevant to the magnetism of these surfaces been completed. Some findings of these experiments are consistent with existing theoretical models, while other aspects require new theoretical approaches. In this paper we report on a series of measurements of the magnetic hyperfine fields in the surface layers of epitaxial (110) Fe films. We place particular emphasis on the temperature dependence of these hyperfine fields. It has been previously shown that the magnetic hyperfine field is proportional to the local magnetization in metallic Fe. It is also known [I] that the temperature dependence of the magnetic hyperfine field (Hef t) is the same as the temperature dependence of the local magnetization to within 15[ from 0 to 300 K for bulk Fe. We therefore expect that
n, ff(r)
M(T)
Heft(0)
M(0)
to within 1%. In this paper we have often used the more familiar magnetization ratio although the data came originally from M6ssbauer spectroscopic measurements of the magnetic hyperfine field. The magnetic properties of particular layers near the * Work supported by National Science Foundation Grant No. 80-08148. ** Present address: RCA Labs, Princeton, NJ 08540, USA. 0304-8853/83/0000-0000/$03.00
i
\k
\\
MICA
Ag
\\
Fe5s
Fe51 :e56
Aq
\\
Fig. 1. Schematic structure of an Fe film of SrFe with a S7Fe probe layer. The cover layer (right) is Ag in this example. Other materials are also used. surface of the (110) films were measured by producing the films from isotopically pure 56Fe (which produces no Mrssbauer spectrum) with probe layer(s) of 57Fe deposited" at the appropriate position in the film. A transmission Mrssbauer spectrum then yields a measure of H a l ( T ) at this particular layer in the film. High count-rate MOssbauer spectroscopy makes it possible to obtain reasonable spectra from very thin probe layers (4 •A or about 2 atomic layers) in a reasonable time. Fig. 1 shows schematically the structure of a typical (110) film. In much of the work reported here the 57Fe probe was placed at the Fe film surface. This technique for composite 56Fe-57Fe films has also been used profitably by Shinjo and co-workers for polycrystalline films. 2. Structure of the films
The films studied here were grown epitaxially by vapor deposition of Fe on previously prepared ( 111 ) Ag
© 1983 N o r t h - H o l l a n d
J. Tyson et al. / M~ssbauer spectroscopy of surfaces and thin films substrates. This epitaxial system has been well studied [2] and is known to yield (110) Fe films with a high degree of epitaxy. After production of the Fe films, a protective covering layer, usually Ag, is deposited to prevent oxidation of the film surface. As part of the studies reported here, we changed the covering layers for different films to assess the effects, if any, on the magnetic properties of the Fe surface. Altough some differences were observed, the surface magnetic phenomena reported here were generally independent of the choice of covering material. This point is discussed further elsewhere in the paper. In choosing the covering material two criteria must be satisfied: first, there must be negligible interdiffusion of the covering material into the Fe. Secondly, there must be no possibility of the formation of intermetallic compounds between the Fe and the covering layer. These criteria are both well satisfied for Ag and for several non-metallic covering layers such as MnF2, MgO and MgF2. It should be noted that over the temperature range of the present studies the interdiffusion of the 56Fe and 57Fe layers is completely negligible. In the work reported here two different Fe film thicknesses were used. For one set of measurements the films had a total thickness of 30 layers of Fe. For the other measurements the films were 50 layers thick. In both cases the interior of the films show bulk magnetic properties. It is only the Fe within three or four atomic layers of the surface that shows specific surface effects. 3. Theoretical work on Fe surfaces
Until recently, much theoretical work on transition metal surfaces emphasized the different thermal spin deviations at the surface of a ferromagnet rather than magnetic moment differences due to changes in the surface electronic structure. Most of these models [3-6] were based on a Heisenberg Hamiltonian, although anisotropy terms were included in some calculations [3,6]. The majority of the models predict that there would be larger-than-bulk spin deviations (and consequent lower average magnetization) in the surface layers. The spin-wave models yielded a well-defined surface mode which splits off the bottom of the bulk spin-wave band. This model seemed to be reasonable for ferromagnetic insulators, but it may be less appropriate for metals. In particular, most of these models assumed that at T = 0 the magnetism would be uniform right up to the surface. Recent band-structure calculations [7] indicate that this assumption is not valid in transition metals. Additionally, our own recent work [8] shows an increase in the magnetic hyperfine field at the Fe surface at 4.2 K with all covering layers except Cu. Similar results can be inferred from work on polycrystalline films by Shinjo et al. [9] and by Keune et al. [10]. These theoretical problems do not arise in the recent work of Mathon [11]. He gets results similar to those for
127
a Heisenberg ferromagnet using an itinerant electron model with the equivalent of weaker surface exchange. In this model the surface spin waves become localized below the bulk spin-wave band. 4. Detection of surface spin-wave effects in Fe
In previous work we have shown [8] that the surface hyperfine field in Fe is greater than bulk value at 4.2 K and less than bulk value at 295 K. This is also consistent with measurements in other laboratories. We think these results are due to two different phenomena. At 4.2 K there is little excitation of collective magnetic modes. In this case the larger hyperfine field is associated with surface electron densities which are different from bulk values. This is borne out by the increased isomer shifts which we observe at the surface of our composite 56Fe-57Fe films [8]. As the temperature increases, however, the smaller spin-wave stiffness in the surface layers leads to easier thermal excitation of surface spin waves with consequent greater spin deviations in the surface. This yields a lower effective magnetization in the surface layers (and, consequently, a smaller-than-bulk hyperfine field) in spite of the fact that the T = 0 hyperfine field is larger than bulk. In order to separate these two effects, and to determine the attenuation length of these surface spin waves, we have studied a series of 30-layer films in which the 57Fe probe layer was placed at different depths from the surface in different films. For each probe layer depth we have obtained Heff(295 K)/Heff(4.2 K), which we assume equal to M(295)/M(O). By making this normalization of the data, the effects of the variation of Ml(0) near the film surface are suppressed. (Mr(0) is the T = 0 magnetization of the lth layer of the film). Fig. 2 shows the results of these measurements. The larger surface spin deviations decays as one moves in from the surface and are
98" .97
o~
MI(T) 9 6
g
Ml(O) .9.5 .94 .93
295K 15
20 J~(LAYER
25 POSITION)
30
Fig. 2. Normalized magnetization (from hyperfine fields) of the
top 15 layers of the composite 56Fe-STFefilms. The horizontal error bars measure the thickness of the 57Fe probe layers. Spin deviations in the last three layers are clearly larger than the bulk values of 0.976.
128
J. Tyson et al. / Mtssbauer spectroscopy of surfaces and thin films
similar to bulk values by 3-4 layers from the surface. This is consistent with the results of Mathon's model [ 11 ] which predicts an exponential decay away from the surface for surface spin waves. These experimental results are also in agreement with such Heisenberg model calculations as those of Binder and Hohenberg [12]. These measurements represent the first direct experimental evidence of the thermal excitation of surface spin waves in a transition metal feromagnet. It is interesting to compare these results with the recent FMR measurements carried out on thin epitaxial (110) fe films by Prinz et al. [13]. The results of these experiments indicated that the resonance field was dominated by the surface anisotropy, Ks,re, for films less than 25 layers thick. This implies that the Fe spins are at least partially pinned at the surface. In our case, however, measurements of the average spontaneous magnetization shows unpinned (Ks,rf = 0) behavior of the Fe spins. In both cases these results persisted with different covering layers. Clearly, the role of the surface anisotropy is different for thermal surface spin waves than it is for FMR modes. A possible resolution of this problem was recently proposed [14]. From the general exchange boundary condition of Rado and Weertman [15] one obtains 2A Om an -- Ksurtm = O.
The unpinned boundary condition Ore~an = 0 is obtained if K,urf is negligible compared with 2 A ( a m / O n ) . If the spatial dependence of m is exponential then this is equivalent to Ks,rf -"~ 2 A k , where k is the propagation constant of the spin waves. For thermal spin waves the dominant k vector is. - 3 x 107. With a reasonable value of - 3 erg/cm 2 from Ks,rf and A = 2 x 10 -6 erg/cm, one sees that Ks,rf is indeed -'#:2 A k , so tht the surface thermal spin waves would be unpinned. This conclusion does not apply to FMR modes, however, where the effective k is more than ten times smaller. Thus, the apparent contradiction between our results and those of Prinz et al. seems to be reconciled.
5. Temperature dependence of the sudace magnetization Theorists are uncertain about whether the temperature dependence of the surface magnetization of a thick film ( > 30 layers) should be T 3/2, as is the case for bulk, or should be T, as has been predicted [16] and observed [17] for very thin films ( < 15 layers). Fujiwara et al. [4] have found that the low temperature surface magnetization for a Heisenberg ferromagnet depends linearly on temperature, while Mills and Maradudin [5] find that the overall temperature dependence of the surface magnetization remains T 3/2 because the surface spin wave mode modifies the bulk modes. Both Binder and Hohenberg [12] and Wolfram et al. [18] obtain a quasilinear temperature dependence of the surface mag-
1.00 .975 .950 ~(T) .925 .800 .875 0
80
160
T(K)
240
320
Fig. 3. Linear dependence of reduced surface magnetization with temperature.
netization over a wide temperature range for a Heisenberg ferromagnet if the surface exchange is significantly weaker than the bulk exchange. In order to examine this question experimentally, we have produced a (110) epitaxial Fe film of 50 layers thickness with a 57Fe probe layer at the surface. The thickness of the probe layer was 4 .~, which is two atomic layers (i.e., the two atomic layers at the surface of the film were 57Fe, while the rest of the film was 56Fe). Measurements of the magnetic hyperfine field were made at six temperatures from 4.2 K to 295 K. The results are shown in fig. 3, in which hyperfine field ratios are again used to determine the reduced magnetization. The solid line represents the best least-squares fit to a linear temperature dependence. Attempts to fit the data points with the function M ( T ) / M ( O ) = 1 B T 3/2 produced a variance 20 times greater than that for a linear fit. The covering mterial for the fe film was MnF2. From this result it appears that the surface exchange interactions are definitely weaker than bulk values for this case. Whether this is also true for an Fe surface with a vacuum interface or whether the result is significantly influenced by the covering layer cannot be determined at this time. Further experiments on the temperature dependence of the surface magnetism are in progress making use of a variety of covering layers.
6. Conclusions This work indicates that there are, indeed, distinct surface spin-wave modes in Fe metal and that their basic form is in agreement with the results of the simple itinerant exchange model of Mathon [11]. The quasilinear temperature dependence of the surface magnetization implies that the surface exchange is significantly weaker than the bulk exchange. This weaker surface exchange is also a condition for the existence of distinct surface spin-wave modes in ferromagnetic metals in Mathon's model.
J. Tyson et al. / M6ssbauer spectroscopy of surfaces and thin films
References [1] I. Vincze and J. Koilar, Phys. Rev. 6 (1972) 1066. [2] H.C. Snyman and G.H. Olsen, J. Appl. Phys. 44 (1973) 888. [3] R.F. Wallis, A.A. Maradudin, I.P. Ipatova and A.A. Klochikhin, Solid State Commun. 5 (1967) 89. [4] Takeo Fijiwara, Kazuo Ohtaka and Sadaaki Tanagawa, J. Phys. SOc. Japan 25 (1968) 1236. [5] D.L. Mills and A.A. Maradudin, J. Phys. Chem. Solids 28 (1967) 1855. [6] J.C. Levy, J.L. Motchane and E. Gallais, J. Phys. C 7 (1974) 761. [7] C.S. Wang and A.J. Freeman, Phys. Rev. B 19 (1979) 793; J. Magn. Magn. Mat. 15-18 (1980) 869. [8] J. Tyson, A.H. Owens, J.C. Walker and G. Bayreuther, J. Appl. Phys. 52 (1981) 2487. [9] T. Shinjo, S. Hine and T. Takada, J. Phys. Colloq. 40 (1979) C2-86.
129
[10] W. Keune, J. Lauer, U. Gonser and D.L. Williamson, J. Phys. Colloq. 40 (1979) C2-69. [11] J. Mathon, Phys. Rev. B 24 (1981) 6588. [12] K. Binder and P.C. Hohenberg, Phys. Rev. B 9 (1973) 2194. [13] G.A. Prinz, G.T. Rado and J.J. Krebs, J. Appl. Phys. 53 (1982) 2087. [14] G.T. Rado and J.C. Walker, in: Proc. 3rd Joint Intermag-MMM Conf., Montreal (1982) in press. [15] G.T. Rado and J.R. Weertman, J. Phys. Chem.solids I 1 (1959) 315. [16] R.J. Jelitto, Z. Naturforsch. 19a (1964) 1580. [17] J.C. Walker, in: Proc. Internat. Conf. on Mgssbauer Spectroscopy, Jaipur, India (1981) in press. [18] T. Wolfram, R.E. Dewames, W.F. Hall and P.W. Palmberg, Surface Sci. 28 (1971) 45.
Journal of Magnetism and Magnetic Materials 35 (1983) 126-129 North-Holland Publishing Company MOSSBAUER
SPECTROSCOPIC
STUDIES ON SURFACES AND THIN FILMS *
J o h n T Y S O N , A l e x a n d e r O W E N S ** a n d J.C. W A L K E R Department of Physics, The Johns Hopkins University, Baltimore, MD 21218, USA
We have !nvestigated the magnetic properties of surface layers of Fe films using M~ssbauer spectroscopy. (110) epitaxial Fe films were made of 56Fe with appropriate probe layers of 57Fe in the surface region. In this way we were able to profile the magnetism at and near the surface of our films. Studies of the temperature dependence of layers at the surface indicate a quasilinear dependence of magnetization on temperature while the temperature dependence of layers further inside the material show the usual T 3/2 dependence. In addition to this we note that a region of surface thermal spin deviations larger than bulk values extends over 3 to 4 layers at the surfaces. These results are in qualitative agreement with a number of theoretical studies including those of Mathon, Bender and Hohenberg, and Wolfram et al. The quasilinear temperature dependence of the surface layer implies a weakening of the surface exchange. In addition to the unusual temperature dependence of the surface magnetization we have generally observed larger surface magnetic hyperfine fields near T = 0.
1. Introduction
A knowledge of the surface properties of transition metals is important. These materials have interesting magnetic properties and are also useful as catalysts. A large amount of theoretical work in the last decade has focused on transition metal surfaces, but our knowledge is still quite limited, particularly with regard to magnetic properties. Only recently has a significant amount of experimental work relevant to the magnetism of these surfaces been completed. Some findings of these experiments are consistent with existing theoretical models, while other aspects require new theoretical approaches. In this paper we report on a series of measurements of the magnetic hyperfine fields in the surface layers of epitaxial (110) Fe films. We place particular emphasis on the temperature dependence of these hyperfine fields. It has been previously shown that the magnetic hyperfine field is proportional to the local magnetization in metallic Fe. It is also known [I] that the temperature dependence of the magnetic hyperfine field (Hef t) is the same as the temperature dependence of the local magnetization to within 15[ from 0 to 300 K for bulk Fe. We therefore expect that
n, ff(r)
M(T)
Heft(0)
M(0)
to within 1%. In this paper we have often used the more familiar magnetization ratio although the data came originally from M6ssbauer spectroscopic measurements of the magnetic hyperfine field. The magnetic properties of particular layers near the * Work supported by National Science Foundation Grant No. 80-08148. ** Present address: RCA Labs, Princeton, NJ 08540, USA. 0304-8853/83/0000-0000/$03.00
i
\k
\\
MICA
Ag
\\
Fe5s
Fe51 :e56
Aq
\\
Fig. 1. Schematic structure of an Fe film of SrFe with a S7Fe probe layer. The cover layer (right) is Ag in this example. Other materials are also used. surface of the (110) films were measured by producing the films from isotopically pure 56Fe (which produces no Mrssbauer spectrum) with probe layer(s) of 57Fe deposited" at the appropriate position in the film. A transmission Mrssbauer spectrum then yields a measure of H a l ( T ) at this particular layer in the film. High count-rate MOssbauer spectroscopy makes it possible to obtain reasonable spectra from very thin probe layers (4 •A or about 2 atomic layers) in a reasonable time. Fig. 1 shows schematically the structure of a typical (110) film. In much of the work reported here the 57Fe probe was placed at the Fe film surface. This technique for composite 56Fe-57Fe films has also been used profitably by Shinjo and co-workers for polycrystalline films. 2. Structure of the films
The films studied here were grown epitaxially by vapor deposition of Fe on previously prepared ( 111 ) Ag
© 1983 N o r t h - H o l l a n d
J. Tyson et al. / M~ssbauer spectroscopy of surfaces and thin films substrates. This epitaxial system has been well studied [2] and is known to yield (110) Fe films with a high degree of epitaxy. After production of the Fe films, a protective covering layer, usually Ag, is deposited to prevent oxidation of the film surface. As part of the studies reported here, we changed the covering layers for different films to assess the effects, if any, on the magnetic properties of the Fe surface. Altough some differences were observed, the surface magnetic phenomena reported here were generally independent of the choice of covering material. This point is discussed further elsewhere in the paper. In choosing the covering material two criteria must be satisfied: first, there must be negligible interdiffusion of the covering material into the Fe. Secondly, there must be no possibility of the formation of intermetallic compounds between the Fe and the covering layer. These criteria are both well satisfied for Ag and for several non-metallic covering layers such as MnF2, MgO and MgF2. It should be noted that over the temperature range of the present studies the interdiffusion of the 56Fe and 57Fe layers is completely negligible. In the work reported here two different Fe film thicknesses were used. For one set of measurements the films had a total thickness of 30 layers of Fe. For the other measurements the films were 50 layers thick. In both cases the interior of the films show bulk magnetic properties. It is only the Fe within three or four atomic layers of the surface that shows specific surface effects. 3. Theoretical work on Fe surfaces
Until recently, much theoretical work on transition metal surfaces emphasized the different thermal spin deviations at the surface of a ferromagnet rather than magnetic moment differences due to changes in the surface electronic structure. Most of these models [3-6] were based on a Heisenberg Hamiltonian, although anisotropy terms were included in some calculations [3,6]. The majority of the models predict that there would be larger-than-bulk spin deviations (and consequent lower average magnetization) in the surface layers. The spin-wave models yielded a well-defined surface mode which splits off the bottom of the bulk spin-wave band. This model seemed to be reasonable for ferromagnetic insulators, but it may be less appropriate for metals. In particular, most of these models assumed that at T = 0 the magnetism would be uniform right up to the surface. Recent band-structure calculations [7] indicate that this assumption is not valid in transition metals. Additionally, our own recent work [8] shows an increase in the magnetic hyperfine field at the Fe surface at 4.2 K with all covering layers except Cu. Similar results can be inferred from work on polycrystalline films by Shinjo et al. [9] and by Keune et al. [10]. These theoretical problems do not arise in the recent work of Mathon [11]. He gets results similar to those for
127
a Heisenberg ferromagnet using an itinerant electron model with the equivalent of weaker surface exchange. In this model the surface spin waves become localized below the bulk spin-wave band. 4. Detection of surface spin-wave effects in Fe
In previous work we have shown [8] that the surface hyperfine field in Fe is greater than bulk value at 4.2 K and less than bulk value at 295 K. This is also consistent with measurements in other laboratories. We think these results are due to two different phenomena. At 4.2 K there is little excitation of collective magnetic modes. In this case the larger hyperfine field is associated with surface electron densities which are different from bulk values. This is borne out by the increased isomer shifts which we observe at the surface of our composite 56Fe-57Fe films [8]. As the temperature increases, however, the smaller spin-wave stiffness in the surface layers leads to easier thermal excitation of surface spin waves with consequent greater spin deviations in the surface. This yields a lower effective magnetization in the surface layers (and, consequently, a smaller-than-bulk hyperfine field) in spite of the fact that the T = 0 hyperfine field is larger than bulk. In order to separate these two effects, and to determine the attenuation length of these surface spin waves, we have studied a series of 30-layer films in which the 57Fe probe layer was placed at different depths from the surface in different films. For each probe layer depth we have obtained Heff(295 K)/Heff(4.2 K), which we assume equal to M(295)/M(O). By making this normalization of the data, the effects of the variation of Ml(0) near the film surface are suppressed. (Mr(0) is the T = 0 magnetization of the lth layer of the film). Fig. 2 shows the results of these measurements. The larger surface spin deviations decays as one moves in from the surface and are
98" .97
o~
MI(T) 9 6
g
Ml(O) .9.5 .94 .93
295K 15
20 J~(LAYER
25 POSITION)
30
Fig. 2. Normalized magnetization (from hyperfine fields) of the
top 15 layers of the composite 56Fe-STFefilms. The horizontal error bars measure the thickness of the 57Fe probe layers. Spin deviations in the last three layers are clearly larger than the bulk values of 0.976.
128
J. Tyson et al. / Mtssbauer spectroscopy of surfaces and thin films
similar to bulk values by 3-4 layers from the surface. This is consistent with the results of Mathon's model [ 11 ] which predicts an exponential decay away from the surface for surface spin waves. These experimental results are also in agreement with such Heisenberg model calculations as those of Binder and Hohenberg [12]. These measurements represent the first direct experimental evidence of the thermal excitation of surface spin waves in a transition metal feromagnet. It is interesting to compare these results with the recent FMR measurements carried out on thin epitaxial (110) fe films by Prinz et al. [13]. The results of these experiments indicated that the resonance field was dominated by the surface anisotropy, Ks,re, for films less than 25 layers thick. This implies that the Fe spins are at least partially pinned at the surface. In our case, however, measurements of the average spontaneous magnetization shows unpinned (Ks,rf = 0) behavior of the Fe spins. In both cases these results persisted with different covering layers. Clearly, the role of the surface anisotropy is different for thermal surface spin waves than it is for FMR modes. A possible resolution of this problem was recently proposed [14]. From the general exchange boundary condition of Rado and Weertman [15] one obtains 2A Om an -- Ksurtm = O.
The unpinned boundary condition Ore~an = 0 is obtained if K,urf is negligible compared with 2 A ( a m / O n ) . If the spatial dependence of m is exponential then this is equivalent to Ks,rf -"~ 2 A k , where k is the propagation constant of the spin waves. For thermal spin waves the dominant k vector is. - 3 x 107. With a reasonable value of - 3 erg/cm 2 from Ks,rf and A = 2 x 10 -6 erg/cm, one sees that Ks,rf is indeed -'#:2 A k , so tht the surface thermal spin waves would be unpinned. This conclusion does not apply to FMR modes, however, where the effective k is more than ten times smaller. Thus, the apparent contradiction between our results and those of Prinz et al. seems to be reconciled.
5. Temperature dependence of the sudace magnetization Theorists are uncertain about whether the temperature dependence of the surface magnetization of a thick film ( > 30 layers) should be T 3/2, as is the case for bulk, or should be T, as has been predicted [16] and observed [17] for very thin films ( < 15 layers). Fujiwara et al. [4] have found that the low temperature surface magnetization for a Heisenberg ferromagnet depends linearly on temperature, while Mills and Maradudin [5] find that the overall temperature dependence of the surface magnetization remains T 3/2 because the surface spin wave mode modifies the bulk modes. Both Binder and Hohenberg [12] and Wolfram et al. [18] obtain a quasilinear temperature dependence of the surface mag-
1.00 .975 .950 ~(T) .925 .800 .875 0
80
160
T(K)
240
320
Fig. 3. Linear dependence of reduced surface magnetization with temperature.
netization over a wide temperature range for a Heisenberg ferromagnet if the surface exchange is significantly weaker than the bulk exchange. In order to examine this question experimentally, we have produced a (110) epitaxial Fe film of 50 layers thickness with a 57Fe probe layer at the surface. The thickness of the probe layer was 4 .~, which is two atomic layers (i.e., the two atomic layers at the surface of the film were 57Fe, while the rest of the film was 56Fe). Measurements of the magnetic hyperfine field were made at six temperatures from 4.2 K to 295 K. The results are shown in fig. 3, in which hyperfine field ratios are again used to determine the reduced magnetization. The solid line represents the best least-squares fit to a linear temperature dependence. Attempts to fit the data points with the function M ( T ) / M ( O ) = 1 B T 3/2 produced a variance 20 times greater than that for a linear fit. The covering mterial for the fe film was MnF2. From this result it appears that the surface exchange interactions are definitely weaker than bulk values for this case. Whether this is also true for an Fe surface with a vacuum interface or whether the result is significantly influenced by the covering layer cannot be determined at this time. Further experiments on the temperature dependence of the surface magnetism are in progress making use of a variety of covering layers.
6. Conclusions This work indicates that there are, indeed, distinct surface spin-wave modes in Fe metal and that their basic form is in agreement with the results of the simple itinerant exchange model of Mathon [11]. The quasilinear temperature dependence of the surface magnetization implies that the surface exchange is significantly weaker than the bulk exchange. This weaker surface exchange is also a condition for the existence of distinct surface spin-wave modes in ferromagnetic metals in Mathon's model.
J. Tyson et al. / M6ssbauer spectroscopy of surfaces and thin films
References [1] I. Vincze and J. Koilar, Phys. Rev. 6 (1972) 1066. [2] H.C. Snyman and G.H. Olsen, J. Appl. Phys. 44 (1973) 888. [3] R.F. Wallis, A.A. Maradudin, I.P. Ipatova and A.A. Klochikhin, Solid State Commun. 5 (1967) 89. [4] Takeo Fijiwara, Kazuo Ohtaka and Sadaaki Tanagawa, J. Phys. SOc. Japan 25 (1968) 1236. [5] D.L. Mills and A.A. Maradudin, J. Phys. Chem. Solids 28 (1967) 1855. [6] J.C. Levy, J.L. Motchane and E. Gallais, J. Phys. C 7 (1974) 761. [7] C.S. Wang and A.J. Freeman, Phys. Rev. B 19 (1979) 793; J. Magn. Magn. Mat. 15-18 (1980) 869. [8] J. Tyson, A.H. Owens, J.C. Walker and G. Bayreuther, J. Appl. Phys. 52 (1981) 2487. [9] T. Shinjo, S. Hine and T. Takada, J. Phys. Colloq. 40 (1979) C2-86.
129
[10] W. Keune, J. Lauer, U. Gonser and D.L. Williamson, J. Phys. Colloq. 40 (1979) C2-69. [11] J. Mathon, Phys. Rev. B 24 (1981) 6588. [12] K. Binder and P.C. Hohenberg, Phys. Rev. B 9 (1973) 2194. [13] G.A. Prinz, G.T. Rado and J.J. Krebs, J. Appl. Phys. 53 (1982) 2087. [14] G.T. Rado and J.C. Walker, in: Proc. 3rd Joint Intermag-MMM Conf., Montreal (1982) in press. [15] G.T. Rado and J.R. Weertman, J. Phys. Chem.solids I 1 (1959) 315. [16] R.J. Jelitto, Z. Naturforsch. 19a (1964) 1580. [17] J.C. Walker, in: Proc. Internat. Conf. on Mgssbauer Spectroscopy, Jaipur, India (1981) in press. [18] T. Wolfram, R.E. Dewames, W.F. Hall and P.W. Palmberg, Surface Sci. 28 (1971) 45.