Co multilayers studied by means of perturbed angular correlation spectroscopy

~

ELSEVIER

Journal of Magnetism and Magnetic Materials 175 (1997) 23 32

Journalof

magneUsm , i ~ and magnetic. ,~ materials

Structure and magnetism of BCC-Fe/Co multilayers studied by means of perturbed angular correlation spectroscopy B. Swinnen*, J. Dekoster, J. Meersschaut, S. Demuynck, S. Cottenier, G. Langouche, M. Rots Instituut voor kern-en stralingsfysica, University of Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium

Abstract We have used perturbed angular correlation spectroscopy to study Fe/Co superlattices grown on (1 - 1 0)-GaAs with a Co thickness around 20 ,~ and Fe thicknesses between 10 and 40 A. We found that all hyperfine fields in these layers are along the [1 1 0]-axis in the plane of the multilayers. Measurements of the temperature dependence of the Cd hyperfine field at the center of the (1 - 1 0)-Co layers were interpreted in terms of gradually changing Co-structure. Below the growth temperature, thermal lattice expansion accounts for the anomalous temperature dependence of the hyperfine field. At higher temperature the monoclinic deformation of the Co lattice gradually relaxes until a nearly undeformed BCC-structure is achieved around 570 K. Further increasing the temperature causes a phase transition of the Co lattice that results in interdiffusion of Fe and Co. These results in accordance with theoretical calculations suggest that the BCC-like Co structure is stabilized by an interfacial energy contribution, particularly by lattice strain and that BCC-Co is not a thermodynamically metastable phase. We resolved satellite hyperfine fields that are unambiguously attributed to probe atoms in plateaus near a sharp interface. In addition, broad frequency distributions associated with a diffuse interface were obvious in the data. Therefore, we proposed a growth model for (1 - 1 0)-Fe/Co where interfaces of Co on top of Fe are sharp and those of Fe on top of Co are diffuse. Within the extended Stearns hyperfine-field model, the hyperfine-field data were interpreted in terms of magnetic moments. The moment profile derived for (1 - 1 0)-Fe/Co reveals a Friedel oscillation of both the Fe and Co near interface moments. The spatial variation of the moments is best described by an amplitude, decaying exponentially with the distance to the interface and modulated by a sine function of the same distance. Between 90 and 570 K, the amplitude, the decay constant and the wave vector of the modulation are constant within the values determined. The Friedel oscillation of the near interface moments is understood as due to spin waves traveling across the interface and interfering with those of the penetrated lattice. The experimental results suggest that the nodes of the spin waves should be pinned to the interface. The resulting oscillation is superimposed on the bulk moment. This picture evidently explains why the experimental moment profile at (1 - 1 0)-Fe/Co is symmetric about the interface. Keywords." Interface magnetism; Multilayers; Hyperfine interactions

*Corresponding author. Tel.: +32 16 327259; fax: +32 16 327985; e-mail: [email protected]. 0304-8853/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 53(97)001 54-6

24

B, Swinnen et al. /Journal c~#Magnetism and Magnetic Materials 175 (1997) 23 32

1. Introduction Ever since scientists are able to grow epitaxial layers with high precision, surface and interface magnetism have been an important subject of both theoretical and experimental studies. New features have been anticipated and the strong promise for possible applications of new features motivated many researchers to accept the challenge of studying two-dimensional (2D) magnetic systems. Thus, both theorists and experimentalists adopted it as a major research topic. Progress on surface and overlayer magnetism until 1991 has been extensively reviewed by several authors

[I~4]. Interface magnetism is an even more difficult topic than surface magnetism for both theorists and experimentalists. Even with modern computers, calculations are restricted to thin slabs consisting of roughly 10 monolayers. For that reason interfaces of semi-infinite structures nowadays cannot be approximated in theoretical investigations. Interface magnetism therefore is one domain in which experimental results are more numerous than theoretical ones. Torsion-oscillation magnetometry (TOM), ferromagnetic resonance (FMR) and more recently also magnetic circular X-ray dichroism (MCXD) have been used to investigate interface magnetism. These macroscopic techniques, however, are rather sensitive to properties averaged over an entire sample or layer. Therefore, a quantitative and layer-specific interpretation of such experiments is often difficult. Hyperfine interaction techniques, on the contrary, are microscopic and allow to probe locally the magnetic features of surfaces and interfaces. The CEMS studies of the Fe-surface by Gradmann and coworkers are probably the bestknown hyperfine-interaction experiments in the field of thin-film magnetism. Since 1992, our research group has used perturbed angular correlation (PAC) spectroscopy in the study of magnetism in epitaxial superlattices. At first this required a thorough refinement both of the spectrometers and of the software for spectrum analysis. Nowadays it is possible to perform experiments and data analysis in an efficient and straightforward way. In this digest we review our most recent results that were obtained from PAC experi-

ments. More extensive reports on these experiments have been given in Refs. [5 7].

2. Sample preparation and PAC experiments Our Fe/Co multilayers were MBE-grown at a substrate temperature of 445 K. The base pressure before growth was better than 3 x 10-~0 Torr. Samples are of the form ( 1 - 10)-GaAs/Fe 200 A/(Co/Fe)lo with a Co thickness of 20 A and Fe thicknesses of 10, 25 and 40 A. We monitored the quality of the lattice during growth with reflection high energy electron diffraction (RHEED) and after growth we checked the multilayer structure with X-ray diffraction (XRD). Result of such characterization are shown in Ref. [8]. For the PAC experiment we implanted trace amounts of 80 keV 1lain atoms (probes) into the multilayers. Ions are stopped in the bulk of the layers as well as near the interfaces: individual monolayers are not populated selectively. The PAC experiment results in a time-dependent anisotropy ratio R(t) which is obtained as described in Ref. [9]. (For a comprehensive introduction to the theory of perturbed angular correlation we refer to Ref. [10]. A more thorough and mathematical description is given in Ref. [11]. Numerous examples on the application of PAC-spectroscopy in physics and chemistry can be found in Ref. [12].) R(t) typically is a superposition of periodic components, each characteristic of one probe environmerit. For pure magnetic interactions those components have a Larmor frequency that occurs together with its second harmonic and a constant contribution. The harmonic frequencies are proportional to the hyperfine field characteristic of the probe's site. The orientation of the hyperfine field relative to the detectors determines the relative amplitude of the harmonics and the constant (see Ref. [5]). Fig. 1 shows room temperature R(t)spectra for one of the multilayers together with a fit to the data. Similar spectra were taken on all samples at various temperatures. The inset in Fig. la shows the Fourier transform (FT) of an experimental curve. Since the FT is calculated from a finite time domain (400 ns), it contains spurious peaks and therefore it only gives an indication for

B. Swinnen et al. / Journal of Magnetism and Magnetic Materials 175 (1997) 23-32

25

8. 0.05 _g o.oo

~ -o.o5

Co-sat3 ~ /L,O-SStZ i"~

O[

-0.10

\ i

0 6

50

5'0

" '

100 150 200 293 Fr~eqLency/aHz) , 150 200

0.05J,

0"05I

-0.05

0,O0

-0.10

-0.05

-0.15l

~" -0.10

-0.10~ -

5o

360

0.00

1

0

230

(ns)

time

100

150

200

0

time (ns)

50

100

J'J

150

time (ns)

2o0

1_

0

50

lOO

time (ns)

Fig. 1. TDPAC spectra as taken on one of the multilayers (Fe 40 ,~) in four inequivalent detector geometries (see Ref. [5]). The data points are at the centers of the displayed error-bars. (a) All hyperfine fields are perpendicular to the detector plane: only second harmonics are observed. A Fourier transform of experimental data is shown in the inset. (b) Hyperfine fields in the detector plane at 45'between two detectors. (c) Partial spectrum for a geometry where the start detector was aligned with the hyperfine fields. (d) Hyperfine fields tilted 4 5 out of the detectorplane. The projection of the fields on the detectorplane is at 45 c between to detectors.

the frequency components of the experimental R(t)-ratio. The R(t) itself, however, is the interference pattern of all present frequencies. It is a complex signal of which the apparent period and amplitude may vary with time. Its frequency-content is found byfitting it to well-known theoretical curves in time domain. The spectrum in Fig. la was obtained in a sample detector geometry where the hyperfine fields all are normal to the detectorplane. For this geometry only second harmonics occur. A large number of periods is available in this R(t) and, hence, values for the hyperfine fields are obtained with very high accuracy from this spectrum. Spectra taken for other field geometries as the ones in Fig. lb-Fig, ld with less periods in the available time-window are used to cross check the fit results and to exclude the presence of a quadrupole perturbation of the magnetic hyperfine interaction. Spectrum analysis was previously discussed in Ref. [-5] and the results are summarized in Fig. 2.

Each spectrum is fitted with eight purely magnetic probe sites. It is the simplest model that accounts for all the R(t) spectra (36) taken on the different samples in a consistent way. For the thinnest sample 75% of the probes (60% for the thickest one) is found in the broad-feld distributions Aco and Ave (Fig. 2c). These cause the fast decay of the anisotropy-curve's amplitude in the first 50 ns of Fig. la but do not contribute beyond this point. They result from many microscopically slightly different probe environments. Since the mean fields of these distributions are between the ones for Cd in bulk Fe and BCC-Co and because their fractions are proportional to the interface density (l/A, with A the bilayer thickness), we assign them to probe atoms in a mixed FeCo environment at a diffuse

interface. Two other contributions, undoubtedly from their hyperfine fields, originate from probes in pure BCC-Fe and pure BCC Co [9] and for each of

26

B. Swinnen et al. /'Journal of Magnetism and Magnetic Materials 175 (1997) 23-32 41-

18.5 hff

~f

B

B

03 4~

(l) 18.0

•

Co

•

Co

•

•

17.0

•

•

38-

m~ J ,,0

37-

;

36

m,

16.5 4[

3716.0 3~

39-

(T)

I

17.5

3~ 3~

•

satellite I Co satellite 21

a.• Fe i • Fe satellite l • Fesatellite21

"'

I• ', • ",m

3~

"'

•

......

2019-

15.5

18-

15.0

lbo 2bo 3bo 4bo 500 6bo

211

17-

lb0 2bo 3bo 4bo 500 8bo

T (K)

T (K)

lbO 2bo 3bo 4bo 5bo 6bo T (K)

Fig. 2. Temperature-dependent hyperfine fields obtained by fitting the experimental R(t) curves on (1 - 1 0)-Fe/Co. (a) Hyperfine field at Cd in Fe and its satellite felds. (b) Same as in (a) for Cd in Co. (c) Mean fields of the distribution sites Avo and Aco.

them we find two additional satellite fields (Fig. 2a and Fig. 2b). These latter six fields are sharply defined: the amplitude of the R(t) in Fig. la does not decay between 50 and 300 ns thus excluding a spread on the field values• The beating in this part of the spectrum allows to resolve the satellite fields even though their fractions are of the order of 5-10% only. The satellite fields are reproducible within 1%. For the CdFe and CdCo fields the reproducibility is better than 0.5%. The satellites correspond to BCC Fe or BCC Co alike configurations. Since there is no distribution or quadrupole interaction on these fields, they cannot result from the diffuse interface nor from step positions at a sharp interface or from defect sites. (A cubic defect as the one in Ref. [,13, 14] is improbable for BCC structures and would involve a larger field shift relative to the bulk CdFe and CdCo fields.) Therefore, the satellite fields are assigned to probe atoms either in Fe or in Co layers in plateaus near a sharp interface• Finally, it is possible that due to radiation damage, a limited fraction of the probes ended up in ill defined defect sites. These may contribute to the missing fraction (4-10%) or to the large frequency distributions Ave and Aco.

3. Growth model for (1 - 1 0)-Fe/Co

The experiments thus evidence a structure model including both diffuse and sharp interfaces. When the multilayer is grown, first a BCC-Fe buffer of good crystal quality is deposited. It is a welldocumented fact that the Co deposited on top of this bufferlayer, grows pseudomorphically on Fe in a BCC-phase up to a thickness of 10 A. Beyond this thickness Co grows in a mixed F C C - H C P structure. Only when Fe is deposited on top of the Co, the upper part of the layer is forced back into a BCC structure [-15]. Due to the lattice mismatch between the two phases, resulting in many defects in the mixed F C C - H C P structure, this phase transition is likely to induce interdiffusion of the Fe into the Co creating a mixed FeCo phase. This growth model explains the coexistence of both sharp (Co on Fe) and diffuse interfaces (Fe on Co) in one sample as shown in Fig. 3, eventually consistent with the 59Co N M R work by Panissod and coworkers [-8, 16]. We stress that the sharp interface is not necessarily flat: the experiments only indicate that plateaus are large enough to allow for well-defined hyperfine fields.

B. Swinnen et al. / Journal qf Magnetism and Magnetic Materials 175 (1997) 23 32

Fe

F..eeCo C_9oFe /Diffuse Co

Sharp

Fe F eCo C oFe }) Diffuse Co

Sharp

Fe

Fig. 3. Model for the structure of the Fe/Co multilayer as derived from the present data.

4. Thermal lattice expansion and relaxation Whereas in Fig. 2a for the Cd hyperfine field in Fe and for its satellite fields, a normal decrease with temperature is found, an anomalous increase of the fields is observed at Cd probes in the Co layers (Fig. 2b). We may rule out interdiffusion of Fe and Co as a possible cause for the effect since the hyperfine fields take their original room temperature value after annealing experiments and their corresponding fractions remain stable within the experimental error. However, at 610 K the probes diffused out of the multilayer and the multilayer structure was lost. The Curie temperature of BCC-Co has never been calculated nor has it been measured. Based on a mean-field approach and considering the coordination number in first shell, one would expect the Curie temperature for BCC-Co to be reduced by a factor 8//12 compared to that for FCC-Co. However, with a Curie temperature around 892 K, the BCC-Co magnetic moment should strongly reduce on going from T = 90 to 570 K; the 111Cd hyperfine field should decrease accordingly by several Tesla. The positive temperature dependence of the experimental hyperfine field therefore indicates that the mean-field approach strongly underestimates the value of T~ cc-c°. The size of the measured hyperfine field increase is comparable to the effect of thermal lattice expan-

27

sion on the 111CdFe hyperfine field at constant magnetic moment that was calculated by Lindgren and Vijay [-17]. Theory also predicts that the BCCCo magnetic moment does not depend strongly on the lattice parameter [18] so that even for an expanding lattice the assumption of a constant magnetic moment is reasonable. We therefore determine the thermal lattice expansion coefficient that accounts for the anomaly assuming that in the considered temperature range, the BCC-Co magnetic moment is constant. We use the hyperfine field model proposed by Stearns [19, 5]. Within this model the transferred hyperfine field at a diamagnetic probe is a sum of two contributions: one negative term due to the polarization of 4s conduction electrons (cep) at the site of the probe (Be) and one positive due to the shielding of the excess charge by the valence selectrons near the probe atom (B,,). The term Be contains all the field contributions ABi induced at the probes site by the lattice atoms i:

B, = 2

AB..> .--7 fL,,,.

<1)

where AB,lil/I,B represents the fieldshift per magnetic moment f~ of a magnetic atom i in the nth nearest-neighbor shell around the probe and in the Lth layer relative to the interface. The value for AB..)/fB depends on the distance r between probe and polarizing atom and is proportional to the RKKY spin density oscillation

ABn(i) fib

oc

2kvr COs(2kFr) -- sin(2kvr) (2kvr) 4

(2)

with k F the Fermi wave vector. Thus, AB,ll)/fB goes to zero rapidly with r and it suffices to take the first few nearest neighbor shells around the probe atom into account. The valence contribution B~, is due to overlap of 5s orbitals of the probe atom with s orbitals of atoms in the host lattice. It is proportional to the volume misfit between the probe and the host lattice: B,, = C ( V z - - Vo),

(3)

where Vo is the volume available upon removal of one atom out of the host lattice. Vz is the volume

28

B. Swinnen et al. / Journal of Magnetism and Magnetic Materials 175 (1997) 23 32

required by the impurity atom and C is a proportionality constant. Within this hyperfine field model and assuming an isotropic thermal expansion of the monoclinicly deformed Co lattice we may calculate the 111CdCo hyperfine field at different temperatures. Since the cep-contributions depend on r, they will be altered if the lattice expands. We write r(T) = a rRv where r(T) is the interatomic distance at temperature T, rRv is the same distance at 290 K; the multiplicative constant a describes the isotropic enhancement of the interatomic distance. We account for the corresponding cep changes by scaling the values of AB,,)/I~B at different temperatures to the inverse cube of r(T) in a first approximation of Eq. (2). Also the volume overlap contribution is affected by an expansion. In the expanded lattice, the volume available upon removal of one host atom Vo(T) is proportional to the volume of the unit cell of the expanded lattice: Vo(T) = a 3 V~ T with V~T = V0 (T = 290 K). We now vary a in order to fit the experimental hyperfine field. Values for the relevant parameters are taken from Refs. [18, 9]. Fig. 4 shows the temperature dependence of the so obtained unit cell volumes. Below 440 K, which is near the growth temperature of the layers, the volume of the unit cell increases linearly with temperature. The volume expansion coefficient, obtained from fitting the unit cell volumes below 440 K (see Fig. 2) is 3 x 10-5/K. This is approxim-

23.4--- 23.21

iii II

23.01 >

22.8~ 2261

e.)

.~

22.4

22.2

100 200"300"400 5 0 0

600"

T/K Fig. 4. BCC-Co unit cell volume at different temperatures obtained from the temperature dependence of the 11 ~CdCo hyperfine field. The straight line fits the temperature dependence of the volumes below 440 K as due thermal lattice expansion.

ately the same value as obtained at room temperature for stable HCP-Co or BCC-Fe. Beyond this temperature, normal thermal lattice expansion is unable to explain the behavior of the hyperfine field. We may, however, account for the steep increase of the hyperfine field beyond 440 K by an additional uniaxial relaxation of the Co lattice along the normal to the sample. The enhanced hyperfine fields at 550 and 570 K then correspond to an increase of the (1 - 1 0) interplanar distance by 4% lifting the monoclinic compression of the lattice. The Co lattice now has a nearly undeformed BCC-structure and the lattice parameter is isotropically enhanced by 2% compared to its room temperature bulk value. One may consider an X-ray diffraction experiment to evidence this relaxation with a direct structure measurement. However, the diffraction peaks of (1 - 1 0)-Fe and Co coincide and in addition they are close to the (2 - 2 0 ) reflection of the GaAs-substrate. This makes it impossible to resolve the relaxation of the Co lattice in an XRDexperiment or with any macroscopic-structure experiment. A microscopic technique thus is the only way to observe this effect. In order to illustrate the sensitivity of the PAC technique to the details of the probes environment we mention that the hyperfine fields at 111Cd in FCC- and BCC-Co, two Co structures with very similar densities, are - 2 3 . 7 and - 1 6 . 4 T, respectively. A typical PAC spectrometer is able to reproduce these fields within 0.3T. While at 570 K there is no indication either for interdiffusion or for migration of the probe atoms, further increasing the temperature by only 40 K destroyed the multilayer stacking and caused a large fraction of the probes to suddenly diffuse out of the sample. In solids diffusion occurs only via a defect mechanism and the diffusion coefficient is a product of the defect-concentration and a factor that depends exponentially on I / T . The abrupt increase of diffusivity thus implies a sudden increase of the defect-concentration. Therefore, the layer instability at 610 K is attributed to the degeneration of the BCC-structure to an energetically more favorable phase. This phase transition creates defects in the lattice and favors interdiffusion of Fe and Co. Indium is not well soluble in Fe or in Co

29

B. Swinnen et al. /'Journal o['Magnetism and Magnetic Materials 175 (1997) 23 32

nor in FeCo alloys and, consequently, the presence of defects will also facilitate migration of the probes towards the sample surface. Due to the interdiffusion the stable phase is not actually reached and we cannot determine to what stacking the Co lattice transforms. The interpretation is consistent with theoretical calculations of Liu and Singh 1-20, 21] that showed that BCC-Co is at a saddle point of the total energy of the lattice versus tetragonal and monoclinic strain: the BCC-Co structure is stable versus monoclinic but unstable versus tetragonal strain that tends to transform it into an FCCstructure.

5. N e a r interface m o m e n t perturbations

Within the same hyperfine field model we interpreted the near interface hyperfine fields in terms of a near interface moment perturbation. In Ref. [5] we used Eqs. (1) and (3) to calculate near interface hyperfine fields and fitted them to the experimental ones by varying the values of less than six near interface magnetic moments. Best fit was obtained by varying three moments in Fe and two moments in Co, consistent with the interpretation by Pizzini et al. [22] of older magnetization experiments. The resulting magnetic moment profile of Fig. 5, shows a Friedel oscillation of the near interface magnetic moments. The amplitude of the perturbation

decays with the distance Idl to the interface. The moment of the first Fe-layer is enhanced and the first Co-layer has a reduced moment. Further away from the interface the sign of the perturbation alternates from one near interface layer to the next one. This perturbation is similar to the Friedel oscillation of the Fe near interface moments, predicted for one and two Ni monolayers on Fe-(0 0 1) 1-23]. Fig. 6 displays the absolute value of the moment perturbation IA/~I in Fig. 5 together with the error on the total moment as a function of the distance Idl. Both an exponentially decaying perturbation magnitude and a variation of the magnitude with the inverse of the distance to the interface are compatible with the data. In order to determine the correct spatial dependence of the perturbation, we once again fit the calculated hyperfine fields to experimental ones asserting different models for the spatial dependence of the moment perturbation. Consequently, we evaluate the quality of the fits obtained. We consider the following models for the near interface moment perturbation: Ia,.I =

Aid 2,

(4)

IA,.I =

A/Idl.

(5)

IA..I = A e x p ( - p Idl),

(6)

with A the amplitude of the perturbation. The extent of the moment perturbation is no longer

138-

t si

3.0

E 2.5

07. 06-

2.4

2.1

05-

o [23

~a4. 2.0

-ff

1.9

o 1.5

02.

/

E

(31-

._

A/el "". ..........

Nd . . . . . . . . . . . .

~_

(X)-

= 1.0

Fe i

-7

-6

i i I i _/1 /:'' i i i i l -5 -4 -3 -2 1 2 3 4 5 Layer number (L) relative to the interface

Co I

6

i

7

Fig. 5. Magnetic moment profile in Fe and Co near the (1 - 1 0) Fe/Co interface obtained without imposing a model for the spatial variation of the near interface moment perturbation.

le Oo~°rn) Fig. 6. Magnetic moment perturbation and error on the total moment for the first few layers near the (1 - 1 0)-Fe/Co interface obtained by fitting the calculated hyperfine fields (Eqs. (1) and (3)) to experimentally determined hyperfinefields using the moments of three Fe- and two Co-layers as free parameters.

30

B. Swimlen et al. / Journal orMagnetism and Magnetic Materials' 175 (1997) 23 32

limited to the first two or three near interface layers. As is suggested by the result in Fig. 5, we assumed that the sign of the perturbation changes from one layer to the next. We define Q as 7.2

Q= N

--

n'

(7)

where 7.2 is the sum of the squared differences between the calculated fields and the closest experimental hyperfine field. N is the number of near interface layers for which the hyperfine field was calculated and n is the number of free parameters allowed when fitting. Up to six layers at each side of the interface were considered. We fitted the calculated hyperfme fields to the experimental ones in each of the above models for the spatial dependence of the moment perturbation. This is done by minimizing Q through adjustment of the free parameters A and for the third model also the decay constant p. The best model is the one that yields a minimal Q-value. Fig. 7 shows the minimized Q-values obtained. Also the Q-values for the original fits using five uncorrelated near interface moments as in Fig. 5, are shown in this plot. The model described by Eq. (6) convincingly yields the best fit at all temperatures. Allowing for different

amplitudes or decay constants at either side of the interface does not improve the fit quality significantly: both A and p are equal at both sides of the interface.While Eq. (6) provides a good model to account for the experimental hyperfine fields, the sign change from one layer to the next one is an artificial feature. We consider the possibility of a sine-modulation of the exponentially decaying amplitude: A~l = A e x p ( - p ]d]) s i n ( - k d),

where k is the wave vector of the modulation, d is defined as positive at the Co-side of the interface. Again, we fit the near interface hyperfine fields now imposing the near interface moments to vary according to Eq. (8) and using A, p and k as free parameters. Because we know from previous fits that the wavelength of the modulation should be approximately two times the interlayer distance along the [1 - 1 0J-axis in Fe (d~-1 o]), we used 2~/2d~ -1°] as a starting value for k. The minimized Q-values obtained with this perturbation model are also shown in Fig. 7. Although there is no significant improvement compared to the values obtained with Eq. (6), we prefer the more physical model of Eq. (8). The room temperature near interface moment configuration obtained using the latter model is shown by the squares in Fig. 8. Fig. 9a

......... iAul=A/oe •

2K)• . . . . . . . . . .

35-

I~=A/Idl

- - • - - 5 free nea'ir~erfaoe rnornents . . . . _ IAul=~em(-P*ldl) - - . - - Au=A*e~(-P*ldl)*sin(k*d)

I

2[:0-

(8)

T=290K

30-

:4 25-

.

..

'.

i

o'" ........ i . .

O

£: ..(" • ...............

•..

-..._

20-

i

o

- •

1.0

• .................

(35. ~o

~0

~ T~

Fig. 7. Comparison ofthc minimized Q-values for the fits of the calculated hyperfine fields at different temperatures to the experimental ones, assuming different models for the spatial variation of the near interface moment perturbation. The best fit corresponds to an exponential decay of the moment perturbations amplitude with the distance to the interface.

Fe

Co Jo d (101°m)

Fig. 8. The data points are the magnetic m o m e n t s found in the best fit of the hyperfine field data (diamonds in Fig. 7). The solid line here shows the spatial dependence of the moment perturbation obtained by using the average values for A, k and p in Eq. (6). The dashed lines mark the bulk ge and bulk BCC-Co magnetic moments.

B. Swinnen et al. /' Journal oflMagnetism and Magnetic Materials 175 (1997) 23--32

12B1.15. 110. 1£5 <

i

(}!]5 Q~O QS~

• -

-

i

a.

:in

4a) " ~

e~

TOq

g

o

b.

T~)

50

4.0 3.5

Y #

.......

30

• t .........................

25 ZO

1.5 1.0 0.5

C

a~ " at:0

~

~

" ~

T(K) Fig. 9. Temperature dependence of (a) the amplitude, (b) the wave vector and (c) the penetration depth of the magnetic m o m e n t perturbation.

and Fig. 9b show the fitted values for the amplitude A of the perturbation and the wave vector k of the harmonic modulation. The error on the amplitude is estimated at 15%. The error on the wave vector was determined by comparing the perturbation obtained with different wave vector values at constant amplitude and decay constant to the actually fitted perturbation. Although the data may suggest an anticipated decrease with temperature of the perturbation amplitude, within the accuracy of the values, both the perturbation amplitude and the wave vector are temperature independent. The penetration depth dA/2 defined as 1

dA/2 = i In 2 P

(9)

31

is plotted versus the temperature in Fig. 9c. There is no clear trend in the da/z-values. The dotted lines in Fig. 5c show the statistical uncertainty on the average penetration depth. Again, the quantity is temperature independent within the considered temperature range. The average values for the fit parameters (dashed lines in Fig. 5) are A = 1.03#B, k = 1.45 x 10 l° m - 1 and da/2 = 3.08 × 10- 10 m (or p = 2.25 x 109 m - 1). The corresponding distancedependent moment perturbation at the Fe/Co interface, obtained using these average values in Eq. (8), is shown by the solid line in Fig. 8. Beyond the third layer in Fe and the second in Co, the magnetic moments are only moderately perturbed consistent with the original result. Above 440 K the out-of-plane relaxation of the Co-lattice pushes the third Co-layer closer to the second minimum of the moment perturbation at the Co side of the interface. Therefore, at 550 and 570 K also the moment of the third Co-layer differs considerably from the bulk Co-moment. This explains why the minimized Q-values increased for temperatures above 440 K in the original fit with uncorrelated moments (see Fig. 7) where only two perturbed Co-moments were allowed. Little is known up to now on the variation of interface magnetization with temperature. Descriptions of the temperature dependence of surface magnetization usually adopt a picture in which the physical origin of the Friedel oscillation of the magnetic moment is a pinned boundary condition for the thermal spin waves [24 26]. The surface is a free end for populated spin waves and, consequently, these become standing waves at the surface. The topmost layer thus probes the squared amplitudes of all the thermally excited spin wave modes in the antinodes whereas bulk layers probe an averaged value of these amplitudes. In fortunate cases the superposition of these spin waves can yield an oscillation of the near surface moment. This oscillation then is superimposed on a monotonous moment variation near the surface which in turn is a consequence of surface energy states that tend to increase the spin density near the surface. The Friedel oscillation of the near interface moments now also could be understood as an interference pattern of spin waves. One could consider spin waves traveling across the interface and interfering

32

B. Swinnen et al. /Journal of Magnetism and Magnetic Materials 175 (1997) 23 32

w i t h t h o s e of the p e n e t r a t e d lattice. T h e results a b o v e suggest t h a t h e r e the nodes of the spin w a v e s s h o u l d be p i n n e d to the interface. T h e r e s u l t i n g o s c i l l a t i o n is s u p e r i m p o s e d o n the b u l k m o m e n t . In s o m e cases the b a n d s t r u c t u r e n e a r the i n t e r f a c e m a y s t r o n g l y differ f r o m t h a t in b u l k d u e to h y b r i d i z a t i o n effects. In s u c h cases a m o r e c o m p l e x m o m e n t b e h a v i o r c a n be e x p e c t e d . T h i s p i c t u r e e v i d e n t l y e x p l a i n s w h y the m o m e n t profile at (1 - 1 0 ) - F e / C o is s y m m e t r i c a b o u t the interface.

References I-l] A.J. Freeman, R.-Q. Wu, J. Magn. Magn. Mater. 100 (1991) 497. [2] U. Gradmann, J. Magn. Magn. Mater. 100 (1991) 481. [3] L.M. Falicov, D.T. Pierce, S.D. Bader, R. Gronsky, K.B. Hathaway, H.J. Hopster, D.N. Lambeth, S.S.P. Parkin, G. Prinz, M. Salamon, I.K. Schuller, R.H. Victora, J. Mater. Res. 5 (1990) 1299. [4] T. Shinjo, Surf. Sci. Rep. 12 (1991) 49. [5] B. Swinnen, J. Meersschaut, J. Dekoster, G. Langouche, S. Cottenier, S. Demuynck, M. Rots, Phys. Rev. Lett. 78 (1997) 362. [6] B. Swinnen, J. Dekoster, S. Cottenier, J. Meersschaut, S. Demuynck, G. Langouche, M. Rots, Europhys. Lett. 37 (1997) 621. [7] B. Swinnen, J. Dekoster, J. Meersschaut, S. Cottenier, S. Demuynck, G. Langouche, M. Rots, Appl. Phys. Lett. 70 (1997) 3302.

[8] J.P. Jay, E. Jedryka, M. W6jcik, J. Dekoster, G. Langouche, P. Panissod, Z. Phys. B 101 (1996) 329. [9] B. Swinnen, J. Dekoster, G. Langouche, M. Rots, Phys. Rev. B 52 (1995) 5962. [10] G. Schatz, A. Weidinger, in: Nuclear Condensed Matter Physics, Wiley, Chicheser, 1996, p. 63. [11] H. Frauenfelder, R.M. Stefl'en, in: K. Siegbahn (Ed.), Alpha-, Beta-, and Gamma-Ray Spectroscopy, vol. 2, North-Holland, Amsterdam, 1965, p. 997. [12] H.H. Rinneberg, Atomic Energy Rev. 17 (1979) 477. [13] C. Hohenhemser, A.R. Arends, H. De Waard, H.G. Devaere, F. Pleiter, S.A. Drentje, Hyperfine Interactions 3 (1977) 297. [14] F. Raether, G. Weyer, K.P. Lieb, J. Chevallier, Phys. Lett. A 131 (1988) 471. [15] J. Dekoster, E. Jedryka, C. M6ny, G. Langouche, Europhys. Lett. 22 (1993) 433. [16] P. Panissod, J.P. Jay, C. Meny, M. W6jcik, E. Jedryka, Hyperfine Interactions 97/98 (1996) 75. [17] B. Lindgren, Y.K. Vijay, Hyperfine Interaction 9 (1981) 379. [18] D.J. Singh, Phys. Rev. B 45 (1992) 2258. [19] M.B. Stearns, Phys. Rev. B 8 (1973) 4383. [20] A. Liu, D.J. Singh, J. Appl. Phys. 73 (1993) 6189. [21] A. Liu, D.J. Singh, Phys. Rev. B 47 (1993) 8515. [22] S. Pizzini, A. Fontaine, E. Dartyge, C. Chappert, F. Baudelet, J.P. Kappler, P. Boher, F. Giron, Phys. Rev. B 50 (1994) 3779. [23] J.I. Lee, S.C. Hong, A.J. Freeman, C.L. Fu, Phys. Rev. B 47 (1993) 810. [24] J. Mathon, Rep. Prog. Phys. 51 (1988) 1. [25] G.T. Rado, J.C. Walker, J. Appl. Phys. 53 (1982) 5088. [26] D.L. Mills, A.A. Maradudin, J. Phys. Chem. Solids 28 (1967) 1855.