Magnetism and structure of ultrathin Gd films

journal 01 magnetism and ‘1’; magnetic materials

M__ ELSEVIER

Journal

of Magnetism

and Magnetic

Materials

132 (1994) 22-30

Magnetism and structure of ultrathin Gd films A Aspelmeler, Instltut fur

F Gerhardter,

K Baberschke

*

Expenmentalphystk, Frele Umuersltat Berlm, Armmallee 14, D-14195 Berlm, Germany (Recemed

17 August

1993, m rewsed

form 19 November

1993)

Abstract

The magnetic phase transItIon of Gd(OOOl)/W(llO) films m ultrahlgh vacuum down to 5 monolayers thickness IS observed by means of the low field and low frequency ac susceptlblhty technique The magnetism of these films strongly depends on the growth modus and on the annealing preparation procedure that IS necessary to obtain well-ordered mcludmg the hmltatlons of real sample geometry draw a lmk structures and the measured magnetic properties This analysis below a thickness of 15 monolayers show a crossover from 3D to

1. Introduction The

magnetic

behavlour

of ultrathin

films

IS of

wide interest for basic research as well as for industrial apphcatlons [l] While most of the results have been obtained with ultrathin films of 3d transition metals, some recent reports focus on the magnetic properties of thm Gd films [2101 The magnetic order m bulk Gd 1s due to a complex RKKY interaction [ll] with a temperature dependent orientation of the easy axis of magnetization Spm polarized LEED experiments by Weller et al [12] have revealed a surface enhanced magnetic order (SEMO) which persists to about 50 K above the bulk Curie temperature, as confirmed by Tang et al [13] using the spin polarized photoemlsslon technique, they propose a ‘canted’ surface magnetization Wu et al 1141

* Correspondmg

author

0304-8853/94/$07 00 0 1994 Elsewer SSDI 0304.8853(93)EO660-5

Science

temperature We discuss a thxkness dependent films without island formation x(T) slmulatlons between simple geometrical models of the film also indicates that layer-by-layer grown Gd films 2D magnetic behavlour

have calculated a 6% outward relaxation of the topmost layer of a Gd(OOO1) surface and thereby an antlferromagnetlc couplmg between the first layer and the bulk Most of the recent expenmental results however indicate partial or even perfect ferromagnetic surface-to-bulk couplmg [151 We have reported the reduction of the Curie temperature of ultrathin Gd(OOOl)/W(llO) films and its strong dependence on the film preparation [161 A dlscusslon of SEMO, the coupling between the bulk and the surface layer, or outof-plane magnetization, must rely on clear mformatlon on the film structure (e g , the existence of 3D islands much higher than the nominal film thickness has to be ruled out) Here we describe m detail the preparation of smooth and wellordered Gd/W(llO) films (Section 2) Based on a full x(T) slmulatlon m the vlcmlty of T, (Section permit the determma3), the xac measurements tlon of an average island size and thickness (Section 4) Only films with an almost perfect layer-

B V All rights reserved

A Aspelmerer et al /Journal

of Magnetwn and Magnetrc Materials 132 (1994) 22-30

23

by-layer structure show a crossover of the crltlcal exponent y from a 3D to the 2D Ismg value below 1.5 monolayers (SectIon 5)

2. Sample preparation zation

and structural

characteri-

The films were prepared by evaporatmg Gd from a Ta crucible onto a clean W(110) surface (dlam 5 mm) at a substrate temperature of T, = 320 K Gd(138 eV)/W(163 eV> Auger amplitude ratios as function of evaporation time indicate layer-by-layer growth [17,12] Fig 1 shows that evaporation at elevated substrate temperature (open symbols) yields different Auger mtensltles above 2 monolayers (ML) The pressure during evaporation is lo-” mbar and below, resulting m very clean films (Zo(503 eV)/Z,,(138 eV) 2: 0 03 similar as m Ref [131) The hexagonal LEED pattern of the as-grown Gd(0001) surface dlsap-

Fig 1 Growth of Gd(OOOl)/W(llO) at substrate temperatures r, = 720 K (open symbols) and T, = 320 K(full symbols) The peak amphtudes Gd(138 eV) and W(163 eV), as well as their ratlo (lower panel), show the typlcal behavlour of layer-by-layer (FM) and Stranskl-Krastanov (SK) growth, respectively Experlmental evaporation rates were of the order of 1 ML/mm (the vertical arrows mark the completron of the first three layers)

TEMPERATURE

Fig 2 (from Ref [7]) Successive annealing of a 100 ML Gd/W (110) film produces sharper and higher xac peaks T, increases by more than 15 K to reach the (bulk) value that IS expected for this film thickness The four measurements are marked by (e) m Fig 4

pears at a coverage of more than 3 ML Above 5 ML coverage, direct determmatlon of the thlckness by Auger amplitude ratios becomes unrehable due to the vanishing W Auger signal (Fig 0, and the film thicknesses have to be extrapolated based on evaporation times and quartz balance measurements Annealing the as-grown films makes the Gd LEED pattern reappear, its intensity increasing with increasing annealing temperature Slmultaneously, the susceptlblhty peak sharpens, attains larger maximum values, and 1s shifted to higher T, [7] (Fig 2) This effect IS even more striking for thinner films, as Fig 3 illustrates with 7 ML Gd/W(llO) The as-grown film has a T, below 120 K, the shape of the xac curve below 150 K indicates a very broad transition Annealing at only 510 K produces a very high xac peak at a T, that has shifted by at least 50 K The effect of thermal treatment shown m Figs 2 and 3 IS due to a reduction of defects, dlslocatlons, and strain [8] However, the Auger spectra of annealed films show that there 1s a critical annealing temperature above which a clearly detectable signal of W Auger electrons reappears while the susceptlblhty shrinks to a small peak near T, (bulk Gd) Thzs crztzcal annealzng temperature depends on the fzlm thzckness, reaching from 500 K for 5 ML to at

least 800 K for thicker (50-100 ML) films (Fig 4) The detected W Auger amplitudes imply that a

A Arpelmerer et al /Journal

24

I

; 1200 e c 3 1000

-

1

1

I

ANNEALING TEMPERATURES

of Magnetism and Magnetic Matenah 132 (1994) 22-30 1

:’ ,

-

,

,{\b ;___.-; _j

*y--I_

210

190

170

150

TEMPERATURE

(K)

Fig 3 Two xac measurements of a 7 ML Gd/W(llO) fdm The as-grown fdm has a slowly mcreasmg response below 150 temperature range K, but no xlC peak m the measured Annealed at 510 K, the change IS much more slgmflcant than for thicker fdms T, has Increased by at least 50 K, and x,,,&, IS several times higher than m Fig 2 The two measurements correspond to (a) and (b) m Fig 4

large fraction of the W substrate area IS covered with no more than 2 ML Gd Therefore Gd clusters large enough to produce high quality LEED patterns must have been formed When annealing to even higher temperatures, the W Auger amplitude still increases and LEED satel-

i2 ,I200

I

’

”

I

’

”

I

”

1

“‘I

ISLANDS

5

.

hte patterns like e g m Ref [12] are visible, but the fundamental change m film structure occurs m a rather narrow temperature range Fig 4 demonstrates that especially at low film thickness a few 10 K m annealing temperature change an almost perfect layer-by-layer structure mto ISlands These island films (open circles m Fig 4) are very similar to Gd/W(llO) films grown at a substrate temperature of 720 K m the StransklKrastanov (SK) growth modus The detailed analys~s 1s performed m Section 4

3. Susceptlbdity

THICKNESS

(ML)

Fig 4 Dependmg on their thickness, Gd/W(llO) films evaporated at 320 K are rearranged as Islands above a certam anneahng temperature Open symbols represent fdms annealed at ‘too high’ temperatures For the full circles, layerby-layer structure 1s guaranteed Optlmlzed anneahng temperature are located close to the sohd hne The effect of thermal treatment m the shaded region 1s dlsplayed m Fig 2 (e) and Fig 3 (a and b) Auger spectra and susceptlblhty peaks are used to Identify the films Typlcdl results are shown m Fig 7 for two annealmg steps of an 11 ML fdm (c and d)

and simulation

The thm film sensltn$y of classical ac susceptlblhty measurements (H = 1 G, v = 182 Hz) m UHV permits a detailed quantitative analysis of the para- and ferromagnetic contrlbutlons to the xIC signal of Gd monolayers x(T) of a bulk-like Gd(OOOl)/W(llO) film has been shown to be m very good agreement with a theoretical descnptlon [8] of magnetic phase transltlons m real films, which allows the determmatlon of a critical exponent y and, simultaneously, of a consistent critical amplitude ~0’ Here this model will be used to simulate the influence of the film structure on the observable X(T) The main feature5 of the apphed model with respect to real samples are (a) a T, dlstrlbutlon (Gaussian for simplicity reasons), taking mto conslderatlon the observed broadening of phase transltlons m not perfectly homogeneous samples, and/or the finite extent of the lattice 1183, (b) a demagnetizing factor, depending on the sample geometry Thus the measured external susceptlblhty 1s related to the internal one by

FILM

measurement

X 1°C Xext =

1 + NX,nt ’

(1)

If the sample geometry allows for the description of demagnetizing effects by a scalar demagnetlzmg factor N x,“~ ideally diverging at T,, ,yext 1~ thus limited by llm (x,,,) Xlnt+a

= $

(2)

A Aspelmerer et al /Journal

When the magnetic field 1s applied m plane, N of a flat disk 1s given by [19] N,, = (r/4)g

-g2,

(3)

ML

d[ML],

(4)

using the layer spacing of 2 89 w The assumption N,, = 0 would be too slmphstlc, the smallest N,, for a mathematically ideal flat disk 1s given m Eq (4), all values for realistic samples will be larger This will be a key argument m the analysis of very high Xac peaks The assumption of a Gaussian T, dlstrlbutlon is not strictly Justified, but it is supported as a good approxlmatlon of phase transltlon broadenmg by experimental [20] and theoretical [18] results The simulated susceptlblhty of a sample has the form

x,,,(T) =

f-=xext( 7) xe-2((T’-T,)/2d

(b-

2u)-’

&i-‘,

(5)

with xextas m Eq (1) and Xlnt conslstmg of the ideal paramagnetlc susceptlblhty followmg power law m the reduced temperature t, Xpa%i‘x$

t-Y,

a

(6)

and a ferromagnetic contrlbutlon below T, (for more details see Ref [81) The integration mterval [T,&,, Tk,,] IS chosen to contam several times the width 2a of the Gaussian dlstrlbutlon to be numerically precise Fig 5 presents a selection of x(T) measurements of Gd films grown at T, = 320 K, carefully annealed without changing the layer-by-layer structure according to Fig 4, as to produce the sharpest and highest susceptlblhty peaks The finite-size scaling T,(d) 1s itself a strong evidence of layer-by-layer structure of these films [4,16] The observed broadening of the phase transition with decreasing film thickness may be explained by larger mhomogeruty due to higher strains, thus

7

5

9

11

14

1200 -G ; 1000 1 ”

g being the ratio thlckness/dlameter of the disk For ultrathin Gd films on a substrate with 5 mm diameter, g 1s very small, and Eq (3) may be slmphfled to N,, = 4 5 x 10-s

25

of Magnetism and Magnetz Materials 132 (1994) 22-30

800

z ? m F k ii 3 v) :

600

400

200

0 120

160

200

TEMPERATURE

240

280

320

(K)

Fig 5 xac peaks of different film thicknesses, correspondmg to full symbols close to the sohd lme m Fig 4

a larger T, dlstrlbutlon This would result m a considerably reduced peak height But, as Fig 5 demonstrates, the calibrated x(T) peaks of the very thm films are enormously higher than the sharp peaks of the thicker films The analysis of this phenomenon 1s obstructed by the fact that a reliable determination of e g the critical exponent y from the slope of the curve 1s lmposslble when the phase transition IS too broad (2a > 1 K) Nevertheless some statements are possible Fig 6 illustrates the influence of N and y for a fured T, dlstnbutlon, based on the slmulatlon using Eq (5) Small variations of y affect the peak shape as much as variations of N over orders of magnitude (note that N 1s ideally a linear function of film thickness, according to Eq (4) The experlmental x(T) of Gd films below 15 ML cannot be simulated with a 3D Zsmg or Helsenberg exponent y without using unrealistic demagnetizing factors N Using the ideal N from Eq (4) therefore yields a lower limit for the effective critical exponent y These results are generalized by mtroducmg a measure for the susceptlblhty peak area Slmulatlons like m Fig 6 show that m the reduced temperature representation the integral

(the area above T,) 1s nearly independent of the T, dlstrlbutlon width and of reasonably chosen parameters for the ferromagnetic susceptlblhty

A Aspelmeler et al /Journal

26

of Magnetwn and Magnetic Materials 132 (1994) 22-30

has been successfully applied to relaxed quaslbulk (2 40 ML) Gd films [7,8] However, its slmple ansatz for the temperature dependence of the effective amsotropy and domain wall motions below T, cannot be expected to apply for ultrathin films of a few atomic layers A systematic devlatlon from xac measurements of films 5 25 ML 1s observed The magnetic amsotroples of these ultrathin films are currently investigated using ferromagnetic resonance measurements, the results will be presented elsewhere Here we will focus the susceptlblhty peak at T, and the paramagnetlc critical parameters In all slmulatlons the theoretical critical amplitude of Gd (for T,(bulk) = 292 5 K ,yi= 5 X lo-’ [SI] 1n 2D and 3D Ismg models) 1s kept constant, which 1s equivalent to the assumption that all Gd atoms contribute to the magnetic behavlour of the film As explained below, the existence of magnetically ‘dead’ or antlferromagnetlcally aligned layers can be excluded

220

230

240

250

TEMPERATURE

260

270

4 280

(K)

Fig 6 The susceptlblhty slgndl of the 11 ML fdm (1) IS dlsplayed along wth slmulatlons accordmg to Eq (5) xl, the T, dlstrlbutlon width 2a, and the parameters for the ferromagnetic susceptlblhty [8] are not varied The upper panel demonstrates the Influence of y for the Ideal N = 5 X lo-’ the slmulatlona are for (2) 1 75 (2 D Ismg), (3) 1 387 (3 D Helsenberg) and (4) 1 24 (3 D Ismg) The best fit curve (5) IS calculated with an effective y of 1 41 Lower panel y = 1 24 = constant, N = 1OW’ (61, lo-’ (7), lOmy (8) N = lOmy, necessary to obtam approximate agreement with the experiment, 1s more than two order\ of magmtude smaller than the Ideal mmlmum value 5 x lo-’ for 11 ML

This Integral IS called T,' area calculated for zero T, dlstrlbutlon

and

1s directly

which 1s a function of xl, N, and y only This will be exploited m Section 5 The model describing the detectable susceptibility of metallic ferromagnetic samples over the whole temperature range of the phase transltlon

4. Fdm structure

and susceptibility

The susceptlblhty signal of a Gd film evaporated at high (720 K) substrate temperature 1s very similar to that of a film prepared at 320 K and annealed at a temperature m the upper ‘island’ region of Fig 4 It 1s accepted 112,171 that these two standard evaporation temperatures correspond to approximate layer-by-layer (Frank van der Merve, FM), and Stranskl-Krastanov (SK) growth, respectively As stated m Section 2, the LEED and Auger characterlzatlon of films prepared at room temperature and annealed beyond a certain temperature suggests a reconstruction of the films towards SK-like geometry The slmultaneous, drastic changes m the observed susceptlb&y as shown m the upper panel of Fig 7 for an 11 ML film are explained schematically in the lower panel of Fig 7, where an ideally flat 11 ML Gd film 1s simulated usmg the ideal N = 5 X lo-’ (Eq (4)), T,= 249 K and a T, dlstrlbutlon of 2a = 6 1 K according to the experimental peak shape, and the critical parameters that apply for this film thickness The slmulatlon of a configuration of 22 ML thick CT,= 283 K, 2~7 = 3 K), flat

A Aspelmaer et al /Journal

0 230

240

250

260

TEMPERATURE

270

280

2-l

of Magnetrsm and Magnetic Materrals 132 (1994) 22-30

290

(K)

Fig 7 Upper panel x(T) and Auger spectra of 11 ML Gd/W(llO) first annealed at 530 K, then at 710 K, correspondmg to Cc) and (d) m Rg 4 The occurrence of a W Auger signal after annealmg to 710 K 1s accompanied by a drastlcally reduced x peak closer to T,(bulk) Lower panel Eq (5) IS used to simulate xac for the mass equivalent of 11 ML We choose two characterlstlc geometries the ‘Ideal film (11 ML perfectly dlstrlbuted over the whole substrate), and Identical circular Islands covermg half of the substrate area The followmg parameters were adapted to the shape of the N = 0 013, T,(22 ML) = 283 K, 2~(22 ML) = 3 K, islands ~(22 ML) = 124

circular Islands (diameter 500 nm, therefore N = 10P2) covering half of the substrate area shows the typical behavlour of x(T) measurements performed with SK films reduced maximum susceptlblhty due to the larger demagnetlzmg factor of islands, and the (higher) T, that corresponds to the island thickness Note that there 1s no contradiction m the smaller T, dlstrlbutlon for a set of many mdlvldual islands Variations of the Island thickness d m the range of 22 ML have much smaller influence on the island T, than varlatlons of strain m the flat 11 ML film Although the agreement with the experimental data 1s convmc-

mg, this picture of FM and SK morphology 1s of course too simple The space between the islands, for example, is certainly not completely free of Gd, as can also be seen from the Auger amphtude ratio of the annealed film However, a mean cluster thickness of SK films may be deduced from T,, and the lateral extent of these clusters ‘,s considerably greater than the mmlmum of 100 A set by the LEED data, as we conclude from the simple fact that the increase of x around T, would be below the limit of detection of the apparatus, if N is too large (e g 10-l) It is remarkable that the construction of the measurmg device 1s highly selective on the film structure only large, flat, magnetically interacting regions m the substrate plane produce signals huge enough to be reglstrated Approaching T, from below, Gd/W(llO) films with the structural and morphological qualities described above exhibit almost monodomam behavlour (well known from Co/Cu(lOO) monolayers [21,22]), as we conclude from the huge response to the osclllatmg field applied along an

I

i”“““““,,,‘,“i

200

250

350

300

TEMPERATURE

(K)

Fig 8 ,y(T) measurement of a 15 ML film and a slmulatlon of ‘14 ML + SEMO’ with an arbltrardy chosen surface transItion temperature of about 340 K Although a demagnetlzmg factor as large as N = 12X lo-* IS assumed for the surface layer the hypothetically resulting small increase of xac at T,(surface) IS not below the experimental sensltlvlty (this ‘worst case’ N 1s derived by discrete summation of dlpolar fields for an Isolated section of a single Gd hcp basal plane [4] It 1s used as an upper hmlt as it IS difficult to estimate a reahstlc N for the surface of a semt-mfmde system) There 1s no evtdence for SEMO of the topmost Gd layer from xac measurements

28

A Aspelmeler et al /Journal

of Magnetrsm and Magnetic Materials 132 (1994) 22-30

easy dlrectlon xac values of up to 1250 at T + TcJ mean that the magnetization of the film follows the external field of approximately 1 G amplitude up to 60% of the saturation magnetization (2 14 kG for Gd) A thorough analysis including the imaginary part of x below T, shows that this corresponds to an almost completely aligned monodomam As the demagnetizing factor does not vanish, we conclude for a 7 ML film that there are no nonmagnetic or antlferromagnetltally aligned layers close to T, Even the surface layer must contribute to the divergent behavlour with the fact that of Xac at T, This 1s consistent we have never observed any anomaly of x above T, (bulk) (Fig 81, e g an additional susceptlblhty peak mdlcatmg a separate surface transition temperature [12,13] In the slmulatlon of Fig 8 we assume the 2D Ismg model for the surface transltlon The expected experimental xac peak should be clearly detectable, as the slmulatlon uses a demagnetizing factor that 1s very likely to be too large However, if the surface phase transition 1s of first order [13], the slmulatlon of Fig 8 1s not valid

5. Analysis bllity

of the critical

paramagnetic

susceptl-

Section 4 has demonstrated the necessity of well-defined film structure when finite-size or dlmenslonahty effects are to be discussed Applymg a finite-size scaling law to a T,(d) dependence 1s only meaningful if d IS the real rather than a mass equivalent film thickness [161 For the same reason a crossover to 2D critical properties can only be observed on carefully annealed films according to Fig 4 As mentioned m Section 3, the T,’ area has to be considered to obtain mformatlon about the paramagnetlc critical parameters These areas are calculated for hypothetical ideal Gd films with the theoretical XT, y of the 3D Ismg model and N of an ideal disk of thickness d, and compared to the experimental areas For d < 15 ML, the experimental Tz areas A._, are mcreasmgly greater than the calculated values A theo (Table 1) A_, smaller than Atheo can al-

Table 1 Comparison between experlmental and theoretlcal drea of the susceptlblhty peak above T, for different film thicknesses The theoretlcal values are determined accordmg to Eq (8) for a 3D Ismg system (y = 1 24) with Ideal demagnetlzmg factors from Eq (4) The experimental values are obtamed by numerlcdl mtegratlon [ML1

A ttNS! [SI units]

;Zmts]

100 55 15 14 11 9 8 7 7 5

43 48 66 68 75 87 92 110 110 15 2

09 12 54 12 0 17 1 22 5 22 0 42 0 65 0 = 150

Fdm thickness

ways be explained by non-ideal film structure (increasing the effective N) and the fact that not every Gd atom may be involved m the phase transition (decreasing the effective xi> However, experimental areas larger than theoretical 3D model areas must be due to a change of the effective critical exponent y, e g increasing towards the 2D Ismg value 1 75 (the critical amphtudes xl of 2D and 3D Ismg systems being approximately the same [23]) The term effective y means that when approaching T, from above, there 1s a point where the diverging correlation length 5 reaches the order of magnitude of the film thickness, and below this point the restricted dlmenslonahty of the system affects the critical fluctuations Because of the rounding of the phase transition this ‘crossover temperature’ 1241 cannot be identified, but rather a mean increase of y is observed For a 7 ML film this effective y 1s at least 1 5 It 1s worthwhile mentlomng that this result for the effective y definitely represents a lower limit certainly N of a real film is never as small as for the ideal flat disk By using the theoretical critical amplitude m the simulations, the posslblhty of nonmagnetic layers etc 1s not considered Furthermore, the calculated T,’ areas are 20 to 30% smaller when the integration 1s carried out only up to t = 0 2 like the experiments Using th15 reduced Atheo, a reahstlc N, and a smaller mean

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of Magnetism and Magnettc Materials 132 (1994) 22-30

crltlcal amplitude, even larger values of y are necessary to fit the data Especially for the 7 ML measurements a noncrltlcal surface layer 1s hardly m agreement with the giant xac peak Turning the above reasomng around and postulating that y = 1 75 m the whole temperature range for the 7 ML film (and all Gd atoms participate m the phase transition), N does not exceed lop5 (ideal value 3 2 x lo-’ for this film thickness) This demonstrates the supreme purity of UHV films, as m pure bulk ferromagnets demagnetizing effects caused by defects set a lower limit of lop4 to 10e3 for N The polycrystallme picture of a T, distribution as a superposltlon of phase transltlons also appears to be questionable for thm films as we see from the maxlmum N, the macroscopic thm film sample may consist of very few separate magnetic regions (= 30) only, the approxlmatlon of a contmuous T, distribution 1s no longer Justified But a discrete distribution spread over 15 or 20 K would produce separate peaks We have never observed more than one susceptlblhty peak and conclude Gd films of a few ML thickness undergo the magnetic phase transition as a whole, or nearly as a whole, and the observed roundmg is an mtrmslc property of this transition, probably due to the limited size of the lattice

6. Conclusion This mvestlgatlon correlates magnetism and structure of ultrathin Gd(OOOl)/W(llO) films and studies the influence of thermal activation The mam issue 1s summarized m Fig 4, where the borderline between layers and islands results from the thickness dependent effect of thermal treatment As a general feature this may be useful m view of metal cluster physics An approximate island size of SK Gd/W(llO) films 1s deduced from magnetic mformatlon obtained by ,yac measurements Close to T,, well-ordered FM Gd films below 1.5 ML thickness exhlblt a crossover of the critical exponent y towards the 2D Ismg value No surface enhanced magnetic order 1s observed on these films This may be due to the moderate annealing temperatures and larger strain The

application of techniques on thickness range the mvestlgatlon

29

surface sensitive experlmental Gd(OOOl)/W(llO) films m the of 10 ML might be of interest for of Gd(0001) surface magnetism

L'51 Acknowledgement

We would like to thank M Farle and U Stetter for helpful dlscusslons This work was supported m part by DFG, Sfb 6, smce 1993 Sfb 290

References [l] M Fahcov, D T Pierce, S D Bader, R Gronsky, K B Hathaway, H J Hopster, D N Lambeth, S S P Parkm, G Prmz, M Salamon, I K Schuller and R H Vlctora, J Mater Res 5 (1990) 1299 [2] D Weller, S F Alvarado, W Gudat, K Schroeder and M Campagna, Phys Rev Lett 54 (1985) 1555 [3] C Rau and M Robert, Phys Rev Lett 58 (1987) 2714 [4] M Farle and K Baberschke, Phys Rev Lett 58 (1987) 511 [5] D LaGraffe, PA Dowben and M Onelhon, Phys Rev B 40 (1989) 970 [6] D LI, C W Hutchmgs, PA Dowben, C Hwang, R -T Wu, M Onelhon, A B Andrews and J L Erskme, J Magn Magn Mater 99 (1991) 85 [7] U Stetter, M Farle, K Baberschke and W G Clark, Phys Rev B 45 (1992) 503 [8] U Stetter, A Aspelmeler and K Baberschke, J Magn Magn Mater 117 (1992) 183 [9] D LI, J Zhang, P Dowben and M Onelhon, Phys Rev B 45 (1992) 7272 [lo] U Paschen, C Surgers and Hv Lohneysen, Z Phys B 90 (1993) 289 [ll] B Coqblm, The Electromc Structure of Rare-Earth Metals and Alloys The Magnetic Heavy Rare-Earths (Academic, London, 1977) p 121, 371f [12] D Weller and SF Alvarado, J Appl Phys 59 (1986) 2908 1131 H Tang, D Weller, T G Walker, J C Scott, C Chappert, H Hopster, A W Pang, D S Dessau and D P Pappas, Phys Rev Lett 71 (1993) 444 [14] R Wu and A J Freeman, J Magn Magn Mater 99 (1991) 81 1151 GA Mulhollan, K Garrison and J L Erskme, Phys Rev Lett 69 (1992) 3240, K Starke, E Navas, L Baumgarten and G Kamdl, Phys Rev B 48 (1993) 1329 [16] M Farle, K Baberschke, U Stetter, A Aspelmeler and F Gerhardter, Phys Rev B 47 (1993) 11571

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of Magneturn and Magnetic Materials 132 (1994) 22-30

[17] J Kolaczklewlcz and E Bauer, Surf SCI 175 (1986) 487 [18] D P Landau, Phys Rev B 14 (1976) 255 [19] E Kneller, Ferromagnetlsmus (Sprmger, Berhn, 1962), S 539f [20] G H C Wantenaar, S J Campbell, D H Chaphn, T .I McKenna, and GVH Wdson, Phys Rev B 29 (1984) 1419 [21] H P Oepen, M Bennmg, H Ibach, C M Schneider and J Kuschner, J Magn Magn Mater 86 (1990) 137

[22] D Kerkmann, D Pescla and R Allenspach, Phys Rev Lett 68 (1992) 686 [23] A Aharony and PC Hohenberg, Phys Rev B 13 (1976) 3081 [24] Y LI and K Baberschke, Phys Rev Lett 68 (1992) 1208 1251 A first attempt IS reported m E Vescovo and C Carbone, 0 Rader, Phys Rev B 48 (1993) 7731