Thermal variation and spatial distribution of local magnetization in ultrathin Fe(110) films

Journal of Magnetism and Magnetic Materials 89 (1990) 325-334 North-Holland

325

THERMAL VARIATION AND SPATIAL DISTRIBUTION OF LOCAL MAGNETIZATION IN ULTRATHIN Fe(110) FILMS

j. KORECKI, M. PRZYBYLSKI Solid State Physics Department, Academy of Mining and Metallurgo', 30-059 Cracow, Poland

and

U. G R A D M A N N Physikalisches Institut, Technische Universitiit Clausthai, 3392 Clausthal-Zellerfeld, Fed. Rep. Germany Received 29 November 1989; in revised form 18 April 1990

Epitaxial 57Fe(l10) films on W(II0) of thicknesses between 7 and 40 ,~, were studied using in situ CEMS. A bulk-like T a 2 temperature dependence of the hyperfine magnetic field, which measures local magnetization, is observed for all films in the temperature range 90-350 K. The temperature and thickness dependence of magnetization agree with Green function calculations. Spatial distribution of the reduced magnetization is derived from the M~ssbauer analysis.

1. Introduction An increased activity on the field of surface magnetism induced a renewed interest in the problem of magnetic thin films [1]. An interest observed twenty years ago was weakened by the serious technological difficulties leading to the irreproducible results. The agreement of experimental results with different theoretical calculations for ill-defined samples was often a~cidental. Presently, the experimental situation is much better. Preparation under ultrahigh vacuum combined with different methods of surface characterization and measurements in situ insures enough knowledge on investigated systems. On the other hand, numerous interesting results were achieved in surface magnetism using ab initio tYalZU

KcCllK, I A I I a l k l O I I ~ ~ l l ~I. 1.11111 ~ l a O

a~.J~:ylUMlli~l.tlUll

[z,,[.

Obviously, this technique, describing objects consisting of several atomic layers, applies directly to thin films. Unfortunately, up to now it was not possible to extend these methods for finite temperatures. The subject of this paper is the thermal variation of thin film magnetization for temperatures

well below Curie temperature. For this temperature range magnetization of a bulk ferromagnet follows the T 3/2 Bloch's low as predicted by spin wave arguments. This behavior can be modified in thin ferromagnetic films. The lack of translational symmetry results in changes of the magnetic coupling at the surface and the finite size in z-direction r,~sults in a discrete spectrum of spin wave modes. The above problem was discussed in many theoretical and experimental papers (for review see refs. [3-5]). There are two main experimental findings which are to be interpreted: (i) thickness dependence of magnetization at a finite constant temperature: (ii) temperature dependence of magnetization at a finite film thickness. Both effects can be influenced by tile thickness dependence of the film Curie temperature. It is commonly believed that: (i) The film magnetization decreases with the reduction of the film thickness although the rate of this reduction is very controversial both in experimental and theoretical approach. On the

0304-8853/90/$C3.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

J. Korecki et al. / Local magnetization in ultrathin Fefl lO) films

326

other hand for the very "hard" surface, when the spins are pinned at the surface, the film magnetization higher than in bulk can be expected t3], (ii) Going to the thinnest films a transition from the Bloch like to linear dependence of magnetization on temperature is frequently predicted and experimentally observed [5]. 1"

.

Very often, experimentally observed effects result from the real slructure of imperfect samples. Based on Mt~ssbauer measurements for the monocrystalline flat Fe(ll0) films on W(ll0) we attempt to extract the intrinsic behavior of ultrathin films magnetization. The magnetization should be discussed in two aspects: average film magnetization and local magnetization of monoatomic layers. Any microscopic approach has to be related to the local magnetization, whose spatial distribution determines the average integral value of the film. Consequently, a simple linear temperature dependence of the film magnetization might result from a superposition of more complicated local contributions. However, the basis of the interpretation should be always the local behavior which can be easily derived from the Mrssbauer analysis. As shown below, spatial profiles of magnetization change considerably with changing film thickness.

2. Experimental and methodology of data analysis Flat and continuous Fe(ll0) films can be easily grown epitaxially layer by layer on W(ll0) [6]. By the proper preparation mode [7] the first or the two first atomic layers remain pseudomorphic with tungsten, then periodic lattice distortions due to an interaction with the misfitting W(110) substrate (misfit parameter fre-w = -9.4%) appear. Consequently, the first ten layers of Fe(ll0) films on tungsten are slightly inhomogeneous in the structural sense. For the present studies isotopically pure 57Fe films 3 to 20 atomic layers thick were investigated using in situ Conversion Electron Mt~ssbauer Spectroscopy (CEMS) as described elsewhere [8]. The films were prepared at the UHV conditions (the base pressure below 5 × 10 -1~ mbar, during the evaporation increased to about

5 × 10 -1° mbar) by the molecular beam epitaxy. The film thickness was measured using the quartz oscillator balance which gives the surface density of the mass deposit. Accuracy of the mass density determination was about 10% of the single layer density. By this method the number of atomic layers contained in a film can be given if the atomic spacing in the film layer is known. According to our preparation mode (first layers deposited at the room temperature and then the preparation temperature gradually increased up to 575 K for the thickest films), which results in a flat surface, we assume that the first monolayer has the spacing of tungsten whereas the following layers are bulk Fe-like. To prevent the contamination of the film surface from residual gasses the films were coated with about 50 ~, of silver. Tile measurements could be performed up to the Curie temperature of bulk iron (1043 K). The thinnest films remained stable only up to about 600 K and for any of the investigated films a transition to the paramagnetic state without changing the film structure was possible. The room temperature CEMS spectra for the chosen films are shown in fig. 1. The character of the spectra is retained in the whole discussed temperature range. The thicker fihns reveal a bulk-like one component Zeeman spectrum of iron with the vanishingly small lines 2 and 5. By the given geometry of the experiment this indicates that the magnetization lies in the film plane in the [110] direction, in contrast to the [100] easy axis of magnetization for bulk iron (for discussion of this problem in terms of the in-plane surface anisotropy refer to the paper of Gradmann et al. [9]). Reaching the thinnest films some changes in the spectra are observed, which by the visual inspection could be identified as increasing intensities of lines 2 and 5. This impression is not confirmed by a numerical fit of one six-line spectrum. Clearly, a second Zeeman component arises. It is characterized by a considerably smaller hyperfine magnetic field as shown in fig. 1 for W(110)/3.4/ Ag film. The low field component (LFC) of Bhr 20 T should be interpreted in the same way as for the case of thicker films [10], where it accounts for the W ( l l 0 ) / F e ( l l 0 ) interface. This component is due to the iron atoms in the first atomic layer on

327

J. Korecki et aL / Local magnetization m ultrathin Fe(110) films

tungsten whereas the high field bulk-like one (HFC) is due to all other layers including iron atoms in F e / A g interface [7], Differences in hyperfine magnetic fields for iron atoms contributing to the high field component are small. They could be detected only applying the local analysis with the 57Fe probe layer in films consisting otherwise of 56Fe and are of the order of 1 T [11,12]. Thus the high field component reflects the average magnetic hyperfine field of the film (excluding Fe atoms in the first layer on tungsten) and the low field component is a very local probe of the magnetic hyperfine field B hf for iron atoms interfacing with tungsten. Fig. 2 summarizes ,'he Bhf data as the function of temperature for the chosen films. The low field component varies only weakly as the film thickness changes and so only the data

36

36 HIGH FELD COMPONENT W(110)/8.61Ag o W{110)lS.31Ag o /Ag

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Fig. 2. The temperature dependence of the magnetichyperfine field for films of dii'ferent thicknesses. All data were fitted to Bhr(T) = B h f ( 0 ) ( 1 - bT 3/2 ) as indicated by solid lines.

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Fig. 1 The room temperature spectra of ultrathin Fe(110) films on W(I10) coated by silver. The spectra are labell,-.~ by W ( l l O ) / D / A g , where D denotes the film thickness in atomic layers.

for the thinnest films are presented. For films thicker than several atomic layers tile intensity of this component is too small for the detailed quantitative analysis. The ground state Bhf value for the high field component increases as the film thickness decreases (compare fig. 2). This can be interpreted in terms of the well established enhancement of B~,f for A g / F e interface [13,11], whose contribution to H F C becomes dominant going to the thinnest films. Additionally, the presence of a size effect should be noted: Bhf(0) = 35.6 T for the 3.4-layer film exceeds by 2% the value observed for A g / F e interface in our 21-!ayer film [11]. For any interpretation of the hyperfine field measurement in terms of the magnetization data the proportionality between magnetizatkm and lhc hyperfine magnetic field has to be assumed. At the surface it is not always true for the ground state magnetic properties because the hyperfine magnetic field results in a complicated way from the combination of the core and conduction electron

328

J. Koreckt et ai. / Local magnetization in ultrathin Fe(110) films

in the temperature range 0 K to several hundreds kelvin. It leads to some systematic error because, as it was shown by Vincze and Kollar [17], for Bhf a small T 2 term should be considered. Consequently, the Bhf data fitted only by T 3/2 term seem to have a stronger temperature dependence (a higher value of the spin wave parameter b) than the corresponding magnetization data. This error is eliminated in the present analysis by taking into account a small quadratic correction [17] to eq. (1) if hyperfine field and magnetization data have been compared directly. The bulk value of the spin wave parameter b = 5,2 × 10 -6 K -3/2, used in the present paper, refers to the hyperfine magnetic field and corresponds to 3.4 × 10 -6 K -3/2 for the bulk magnetization data. The data of Bhf vs. temperature were fitted nicely using the bulk-like dependence (1) both for high and low field component as shown with the solid lines in fig. 2. The fitted values of Bhf (0) and the spin wave parameter b are summarized in table 1. Additionally, the results of the probe layer analysis for the 21-layer film [10,11] are included. Other than T 3/2 power dependencies were also tested and always the exponent value between 1.4 and 1.6 gave the best agreement with the experimental data. The fit quality could be only slightly improved by adding the T 2 term to eq. (1). Regardless of a physical significance, it seems that the T 3/2 low is well suitable for a phenomenologi-

contribution. As shown by Ohnishi et al. [14] only the core electron contribution scales with magnetic moment at the surface, thus the total Bhr is no longer proportional to the magnetization. For true interfaces (coated surfaces) existing theoretical calculations are insufficient. From the paper of Ohnishi et al. [15], which deals with the Fe(100) with one monolayer of silver on it, we can learn about the consequences of "sealing" of Fe surface from vacuum. It restores the periodicity making the interfacing Fe atoms more bulk-like and the standard interpretation relating B hf to magnetization should be valid again as discussed in details elsewhere [12,16]. An interpretation of the temperature dependence of the hyperfine magnetic field in terms of the magnetization behavior is plausible if the reduction of the data to 0 K is possible. Thus, the effects of the surface modification of the magnetic ground state can be eliminated. Even for thin films we can assume the proportionality between the reduced Bhr and the reduced magnetization using arguments holding for bulk iron [17], because the character of the hyperfine coupling remains unchanged. It is a common procedure for bulk iron to fit both the magnetization and the hyperfine magnetic field data with the same temperature dependence: B,,f(T)/Bhr(O)= M ( T ) / M ( O ) = 1 - b T 3/2

(1)

Table 1 Ground state hyperfine magnetic fields Bhf(0 ) and spin wave parameters b derived from the numerical fit of the experimental Bhr data to eq. (1) in the temperature range 90-350 K

Film thickness . . . . . . . (in monolayers)

b' (i0 -6 K - 3/~'j HFC a~

LFC b~

Bhf(0) (Ti . . . . . . . . . . . . . . . . . . HFC LFC

3.4 5.3 8.6 20,5

21.6±1.0 13.5±1.0 9.5±0.5 7.8±0.2

21.3±2.0 15.1±2,5 14.0±3.0 -

35.6±0,2 34.7±0.2 34.2±0,1 34.1±0.1

21.8±0,3 21.5±0,3 21.4±0.4

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Film center

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J. Korecki et al. ,/Local magnetization in uhrathm Fe( l l0t fihns

cal description of our experimental data and makes possible a straightforward comparison with other authors using the same data parametrization [18].

3. Temperature dependence of local magnetization

3.1. Average film magnetization The average film magnetization is proportional to the weighted average of the both hyperfine magnetic fields observed experimentally (taking into account different relative contributions of both spectral components for films of different thicknesses). Obviously, a linear superposition of two or more nonlinear (T3/2-1ike) dependencies must give also a Ta/2-1ike result. It means that in contrast to the classical spin-wave approximation of the isotropic Heisenberg model [5] a quasi-linear dependence predicted for thinnest films at low temperatures is not observed. Bayreuther and Lugert [19] suggested that the linear M, vs. T relation is measured only in films without pronounced anisotropy, what can be a consequence of superparamagnetic effects due to the island structure. On the other hand, the linear M, vs. T dependence at low temperature is considered commonly to be an intrinsic feature of two-dimensional magnetism [20-22], both, for amorphous and crystalline systems. The magnetometric measurements for Co(lll) and 4 8 N i / 52Fe(lll) films [21,22] give a linear decrease of the magnetization with temperature in the whole temperature range (up to Curie temperature) for films thinner than two monolayers. Because the spin wave arguments can apply directly only in the narrow temperature range, well below T~, it is plausible that for the thinnest films showing the linear M, vs. T dependence in a wide temperature range the magnetization reversal processes are governed by the effective anisotropy energy as indicated by Levy and Motchane [23]. Often the nature of the linear M, vs. T dependence is easy to explain when the M~ssbauer measurements complement the magnetometry. The MiSssbauer spectra for monocrystalline sample of Fe(ll0) on Ag [19] or Co(lll) [24] in the monolayer range reveal superparamagnetic properties for films dis-

329

playing linear M, vs. T relation in magnetometric results. Quite recently, Qiu et al. [25] interpreted the linear dependence of the hyperfine magnetic field for F e ( l l 0 ) / A g ( l l l ) superlattices (Fe components were 2 atomic layers thick) by a simple model based on the island structure of Fe and resulting magnetic relaxation. For the present case of the Fe(ll0) films on W(ll0), which remain continuous down to one monolayer, no pronounced linear M, vs. T relation is observed [26]. The strong in-plane anisotropies, reported earlier [9], play certainly an important role by the temperature induced spin deviation processes. As a whole we believe that these phenomena should be interpreted taking into account not only the dimensionality of the system but also its structure and the used experimental method. The average values of the two hyperfine magnetic field components normalized to the ground state values obtained from fits to eq. (1) are shown in fig. 3 for the temperature range covering the reversible changes in M~Sssbauer spectra. An attempt has been made to compare these data with some theoretical results. A surprisingly few meaningful papers on this subject has been published in recent times. A forthcoming theoretical progress is only promised by recent finite temperature calculations for itinerant electron model. The method used by Hasegawa [27] for a transition metal (Ni) thin film sandwiched between nonmagnetic metal (Cu) could be easily extended for another systems. Unfortunately, it is a mean field theory and neglects spin waves important at low temperatures. The effect of surface on the low temperature spin wave excitations was discussed for a semi-finite itinerant ferromagnet by Mathon and Ahmad [28]. Some general results concerning the influence of the surface renormalization of the exchange integrals on the temperature deviation of the magnetization should hold also for thin films as will be discussed in the next section. So far the only possibility of giving an interpretation of the low temperature thin film magnetization data is to adopt some old theoretical calculations for a Heisenberg ferromagnet. And so, the numerical calculations of Jelitto [29] (spin wave approximation SW) and Haubenreisser et al. [30] (Green function

J, Korecki et ai. / Local magn.:dzation in uitrathin Fe(l lO) films

330

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Fig. 3. The normalized values of the high field Bhf describing the average film magnetization for the Fe(110) films on W(110) for different film thicknesses. The solid lines are guide-for-eye curves. The dotted and dashed lines are the results of the SW [29] and GF [30] calculations, respectively.

calculation - GF) chosen rather arbitrarily from the variety of data reviewed for example by Gradmann [5] a ' . shown also in fig. 3 as dotted and dashed lines, respectively. The calculated values were corrected by taking into account the difference between the bulk M(T) and Bhf(T ) dependence and so they can be compared directly with the measured hyperfine field data. The calculations were done for model systems, different fl'om that used in experiment: G F results concern the (100) and not (110) orientation, SW theory applies to spin 1/2. The numerical values for both methods differ significantly, although they use the similar Heisenberg model. Haubenreisser et al. [30] mention two possible sources of the observed discrepancy: (i) different parameters taken for the calculations (this concerns mainly the spin) and (ii) a temperature dependent renormalization of the effective anisotropy and exchange fields used in G F calculations and neglected in SW approximation. The experiment definitely diverges from SW calculations, for which the size effect is much too strong. For example, for a film consisting of 8 atomic layers Jelitto predicts fi,at at the given temperature (300 K) the magnetization deviation

exceeds

about

5

times that of the bulk (AMs/AMbulk ~-5), whereas the presented hyperfine magnetic field data yield a much smaller value. As can be seen from table 1 for the 8.6 M L - f i l m bfilm/bbulk is only about 2. Clearly, the isotropic spin wave theory overestimates the temperature size effects observed for our iron films. The improper value of S = 1 / 2 used in SW-calculations is surely to some extent responsible for this divergence, but on the other hand the same approximation gave a satisfactory description of the magnetization in ultrathin cobalt films [22]. There are of course many other factors, like surface anisotropies, dipole-dipole interaction [31] or details of the local electronic structure, which contribute to magnetic properties and should be considered in a complete theory and are neglected in most approximations. Taking into account the complexity of the problem a surprisingly good description of experimental data is given by G F calculations in the wide temperature range as can be seen in fig. 3. It means of course that at low temperatures the GF-data can be also parameterized using a T 3/2 dependence with a set of the spin wave parameter b being close to these describing our experimental data. Really. the experi-

J. Korecki et ai. / Local magnetization in ultrathin Fe(l lO) films

331

reduced hyperfine magnetic field observed by Qiu et al. [25] for 2-layer F e ( l l 0 l films in F e / m g multilayers rmght be attributed to the effect of this type. This remains in an agreement with the authors interpretation involving a 3-dimensional growth mode of iron on silver.

2

tta~

jr~

1.1

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3. 2. Spatial distribution of the magnetization

1ll3 Fig. 4. The values of the spin wave parameters b vs. reciprocal of the film thickness D (in atomic layers) for Fe(ll0) films on W(ll0) (full circles).The open circlesare the b values obtained by fitti'~gT3/2-1ikedependence to the GF calculations[301.

mental values of b (the weighted average for the high and low field component) shown in fig. 4 as full circles coincide very nicely with parameters of G F curves (open circles). The spin wave parameters b show a simple systematics: they are proportional to the reciprocal of the film thickness. In other words, at a given temperature the deviation of the film magnetization from its saturation values increases linearly with a decreasing film thickness. Hence, the reduction of the total film magnetic moment remains independent of the film thickness for thinnest films. This fact has a simple justification based on the picture of spin wave excitations going from a 3-dimensional to a 2-dimensional magnetic system. As the film thickness decreases the size quantization becomes important. The occupancy of the spin wave states with the nonzero discrete wavevector component k_ (perpendicular to the film plane) becomes negligible at low temperatures and so the number of magnons contributing to the magnetization reduction becomes independent of the film thickness. The conclusion is that the low temperature magnetic excitations in ultrathin monocrystalline films have a spin wave character. A scarcity of low temperature magnons reported by Mauri et al. [32] for polycrystalline Ni0.sFe0. 6 films is clearly not a general feature of 2-dimensional magnetic systems. This effect can take place for grained films where not only z but also x and y directions set the limit for the spin wave propagation. A surprisingly small value of a"~l t ~'~' /filrn/Al~bulk 3 for the hf /~Vhf -"

The linear relation between the spin wave parameter b and the reciprocal of the film thickness was reported also by Gang Xiao et al. for Fe70B3o-Ag multilayers [20]. The authors interpretation involves the spatial variation of the thermal reduction of the magnetization: the surface magnetization decreases with increasing tempera~, ~c more rapidly than that of the film interior. One gets the observed b vs. D dependence under the assumption that the spin wave parameter of the surface (interface) layer of a certain constant depth and the spin wave parameter of the interior are independent on the film thickness. This is obviously true for relatively thick film,; as discussed by Mathon [33]. However, for ultrathin films, when the 2-dimensional limit cf the spinwave theory is reached, the mechanism of linear b vs. D dependence certainly changes. Consider first a surface of a semi-infinite ferromagnet. As pointed out by Rado [34] the bulk value of the spin wave parameter b hu~k is determined by the mean value of the square 0rnplitudes of all thermally excited spin waves modes, ,) proportional to (cos-0) = 1/2. Because spin waves are assumed to have antinodes at the surface, the surface value b~u~f,arising from square :~.mplitudes in antinodes, is twice as large as bbu~k-This surface enhancement of the magnetization reduction decays smoothly over few atomic layers towards the film interior. The above consideration assumes the homogeneous magnetization in tile )i.'ound state and does not take into account a possible modification of the surface exchange coupling. Mathon and Ahmad [28] showed that for the "soft" surface (the surface exchange integrals perpendicular to the film plane smaller than in the bulk) the ratio b~u~f/bbulk can considerably exceed 2, although ',he T3/2-1ike character of the te~,~perature magneti,:ation dependence is retained.

332

J. Korecki et a L / Local magnetization in ultrathin Fe(110) films

For thin films size effects overlap the described surface effects. If the excha'age coupling across tile film were the same as in the bulk, the size effects should inevitably dominate over surface effects for very thin films. Because of the discrete spectrum of k., standing waves with k. =~0 simply cannot exist (their energy is too high to be excited at low temperatures). This implies that the reduced magnetization becomes more homogeneous in the zdirection for thinnest films. In other words the difference between spin wave parameters at the film surface bfilm, urr and in the film interior h.film ..,,, vanishes although these both and the resulting average film value bnlm increases as the film thickness approach one monolayer. Summarizing, contrary to the assumption of Gang Xiao et al. [21] ~'.~,rrhfilmshould be strongly thickness dependent in the limit of ultrathin films. This follows also immediately from our experimental temperature dependence of Bhf for the low field component which probes the outermost layer of the Fe films. The corresponding spin wave parameters by no means remain constant: /,,film u~urf is 21 x 10 -6 K -3/2 and 15.1 x 10 -6 K --V2 for 3.4and 5.3-layer film, respectively. For the film of about twenty layers the 57Fe probe layer analysis [10.11] results in the whole spectrum of b values over all atomic layers. In this case one gets b~,,rf = 13.3 × 10 -6 K -3/2 or 12.6 × 10 -6 K -3/2 for F e / A g and Fe/W interfaces, respectively. The spin wave parameter for the film interior shows also the pronounced thickness dependence: /%film is 6.2 x 10 -6 K -3/2 for twenty layers film and about 21 × 10 -6 K -a/~ for 3.4-layer film for which the spin wave parameter does not show any spatial structure. It is then clear that the microscopic reason of the linear dependence observed in fi~. 4 is a complicated interplay of surface and size effects. The earlier monolayer S:'Fe probe profiling of the hyperfine magnetic fields in 20.5-layer Fe(110) film [10,11] provided full information on the spatial distribution of the relative magnetization. In the present analysis of S7Fe films the information is integrated over atomic arrangements (atomic layers) characterized by hyperfine magnetic fields which differ not enough to be resolved in a MS. sbauer experiment. However, the spatial varit.

In

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ation of the magnetization can be deduced assuming smooth magnetization variation and its film center symmetry. Fig. 5 summarizes the magnetic hyperfine fields at the constant temperature (300 K), normalized to the ground state values as measured for films of different thickness. The full points are the experimental values integrated over the film region indicated by the horizontal segments and the straight horizontal lines represent the mean film values. The broken lines are the resulting spatial distribution profiles of the reduced local magnetization. Whereas the shape of the profile for the 20.5-layer film is quite straightforward, these for 8.6- and 5.3-layer films are only a reliable guess matching the experimental observations. The experimental picture coincides nicely with the predictions of GF-calculations [30] depicted by dotted lines in fig. 5 for 4-layer and 8-layer films. A consistent pattern of magnetization profiles in ultrathin films emerges: the surface enhancement of the thermally induced magnetization deviation vanishes but simultaneously a significant reduction of the film mean magnetization

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J. Korecki et aL / Local magnetization in ultrathin Fe( l lO) fibns

is to be noticed. It is illustrated by the inset in the top of fig. 5 as the "model B", contrasted with the "model A" used by Gang Xiao [20]. In contradiction to our results Lugert and Bayreuther [18] have reported a pronounced differentiation of the layer magnetization in 4-layer iron film. The spin wave parameter for the interface layer exceeds by the factor 2.5 that for center layers. Such effect could be explained if the exchange coupling of spins in outer layers to spins in the film center were weak. It can happen easily if the interface layer is imperfect in a structural sense (effected by roughnesses or inhomogeneities of the composition). Otherwise, i.e. for the homogeneous exchange coupling across the film which is cut at the F.,m boundaries, a certain minimum film thickness is needed to allow the differentiation of surface and film i,terior magnetization. In our earlier analysis [11] of the temperature surface ~froo, . . . . . . it was supposed that the ratio Vsurfhfilm/~fiimt /uin~ 2 found for a 21-layer film reflects the situation for a semi-finite ferromagnet. This supposition was criticized by Mathon [33], who claimed, that the 21-layer film is too thin to reproduce in its center the bulk conditions and so that the hfilm//~ftlm ~.,,urf / U i n t cannot be representative for a semi-infinite sample. The question arises what is a minimum film thickness at which the temperature size effects becomes negligible as compared with surface effects. The answer can be deduced from fig. 6. It illustrates the changes of bsurf/Uint film/hfilm ratio derived experimentally (flail circles) and calculated using

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FILM THICKNESS (IN ATOHIC LAYERS) Fig. 6. The surface enhancement of the magnetization de,~iahfilm/hfilra tion measured by the ratio t,surf/,.,in t . The full circles are the experimental values, the open circles are the values predicted by G F calculations [30].

333

G F method [30] (open circles) with an increasing film thickness. The broken curve is only guide-toeye line. It is hard to imagine that the t,~"f'l"~orf/"of'h~',,~, value of about 2 is far frnm saturation for the film thickness D---20 atomic layers. It means that the penetration of the temperature surface effect into the film interior is no deeper than about 10 atomic layers (from each side of the film) in accordance with our direct observation presented in fig. 5. The saturation of the b surf/°'int film/t~film ratio, combined with the fact that the ..t'mmmtapproaches the bulk value for our 21-layer film. implies immediately that our bsfilm film are representative for the semi-inurf and h~int finite ferromagnet. From the present studies b,~f/b~,ul k ratio close to the model value of two can be concluded.

4. Conclusions

The local behavior of the hyperfine magnetic fields Bhf were analyzed in ultrathin Fe(110) films grown epitaxially on tungsten. The temperature dependencies of Bhf could l:e described using a Bloch-like T 3/2 formula. The picture of the temperature variation of the film mean rnagnctizadon could be obtained by the averaging of the reduced local Bhf. The spin wave parameter describing the temperature deviation of the average film magnetization from saturation is inversely proportional to the film thickness, as can be predicted from spin wave approximation. Spatial profiles of the magnetization shows also a pronounced tl'dckness dependence. For thinnest films magnetization reduction is homogeneous across the film. As the film thickness increases, the surface enhancement of the thermally induced reduction of the magnetization is observed. Already for a twenty layer film the reduction of the magnetization at the film surface is twice as big as for the film center. The prefactor in the Bloch's law is for our ~-e(ll0) surface smaiier than it was rcportcu cal,ter ,~,, another systems. 'Fhere is no exact theoretical treatment of the magnetic excitations in ultrathin metallic films. Effects like surface modification of the ground state, surface anisotropies, spin waves have to be considered in a frame of itinerant-electron model

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J, Korecki et al. / Local magnetization in ulo'athin Fe(110) fihns

for a comprehensive description. Anyway, in spite of many inadequacies our observations are in a good agreement with Green function calculations in Heisenberg model.

Acknowledgement This work was supported by CPBP 01.08.

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