- Email: [email protected]
Tb trilayers
Journal of Magnetism and Magnetic Materials 242–245 (2002) 532–534
Magnetic interactions in MBE grown Fe/x Au/Tb trilayers E. Shypila,*, A. Pogorilyya, Ye. Pogoryelova, T.H. Kimb, G. Bererab, J. Mooderab a
Institute of Magnetism, National Academy of Sciences, 36-b Vernadsky Blvd., 03142 Kyiv, Ukraine b Francis Bitter Magnet Laboratory, MIT, Cambridge, MA, USA
Abstract Indirect exchange coupling between Fe and Tb layers showed oscillatory behaviour through Au layer as a function of its thickness. Trilayers, prepared in the MBE system, were characterized with different experimental tools. Results are analysed to reconstruct the dynamics of Fe and Tb magnetic moments. For the first time, the change of sign in magnetic interaction is shown for Fe/Au/Tb system. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Exchange couplingFoscillations; Thin filmsFtrilayer; Ferromagnetic; Rare-earth
Among the most important advances in the recent years in artificially engineered nano-structured materials is the discovery of coupling between magnetic layers. Interlayer coupling was first observed between Fe layers across Cr layer [1,2] and then in multilayers (Mls) with various ferromagnetic (FM) and spacer layers [3,4]. It was found that the amplitude of the coupling strength depends on the material of interlayer and that the sign of the coupling oscillates with the thickness increase of nonmagnetic layer, that is consistent with RKKY model. The other interesting system to study the coupling is between FM and rare-earth (RE) layers. Exchange coupling between Fe and Tb is known to be antiparallel. Many papers (e.g. [5,6]) are devoted to this coupling, which presents perpendicular magnetic anisotropy (PMA) and already is used in practice for magnetic recording. Although there is the only work where the long range coupling between these layers via nonmagnetic spacer is studied [7]. Authors studied Mls, prepared by sputtering, where after each Fe or Tb layer the Au layer was placed. It was concluded that in contrast to the theory the sign of exchange interaction does not change with interlayer thickness. In this paper we investigate the carefully prepared Fe/ ( bi- and trilayers, grown in the x Au/Tb (x ¼ 0 35 A) MBE system. We will show that oscillations of the net *Corresponding author. Tel.: +380-44-444-9593; fax: +38044-444-1020. E-mail address: [email protected] (E. Shypil).
magnetic moment are well observed in magnetic, magneto-optical and magneto-transport methods and ( We will also demonstrate their periods are 8 and 26 A. for the first time, that the indirect coupling changes the sign with interlayer thickness in the Fe/Au/Tb system. Two sets of Fe/Au/Tb trilayers on quartz and silicon substrates were prepared by electron-beam evaporation in MBE system with a background pressure of 1–5 1010 Torr and maintaining a pressure of 1–3 109 Torr during the film growth. To minimize interdiffusion of layers, the substrate temperature during evaporation was kept no higher than 01C. The rates of ( and were indepenevaporation did not exceed 0.4 A/s dently controlled with quartz crystal monitors. Samples ( thick layer on quartz substrate were protected with 30 A of Al2O3, whereas on Si substrate they were capped ( Au layer. SQUID magnetometer and polar with 30 A magneto-optical Kerr effect (PMOKE), were used to characterize the films magnetically. Extraordinary Hall Effect (EHE) and magneto-resistance (MR) of trilayers were measured using standard techniques. The details of these experiments are published in Ref. [8]. The thickness of the individual layers, dFe and dTb ; were 3 monolayers (ML), which were chosen on the basis of the previous experiments [8], where the ferrimagnetic ordering of Fe/Tb multilayer has been shown; dFe and dTb ( (3 ML) and 12 A ( (3 ML), were maintained at 8 A respectively, while dAu was increased. Theoretical works for noble-metal spacers based on the RKKY model have predicted two oscillations of the
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 1 1 3 6 - 2
E. Shypil et al. / Journal of Magnetism and Magnetic Materials 242–245 (2002) 532–534
interlayer coupling with the spacer thickness reflecting the topological properties of the Fermi surface [9] 1 2pd Jinter ðdÞ ¼ 2 A1 sin þ F1 d L1 2pd ; ð1Þ þ F2 þA2 sin L2
Tb
-6
Au
15
EHE, 10
Fe
Fe /3Å Au/ Tb
0.03
Tb Au Fe Tb Au Fe
(a)
0.00
Tb Fe -0.03
0 0.8
5
10
15
20
25
30
10
15
20
25
30
35
(b)
8Å Fe
MR, %
Q, min.
PMOKE angle, Θ (min.)
6
measured for the Fe/Au/Fe system [11] and also with values of 2.51 and 8.6 ML, extracted [12] from measurements of the Au Fermi surface. The facts that the second oscillation period appears and also the high amplitude ratio, A1max =A1min ; show that the growth conditions for the trilayers were good and the quality of interface was 0 0 high. The amplitude ratio, A1max =A1min ; of PMOKE angle seen in our work, which is proportional to the net magnetic moment, is evaluated as 1.26–1.33 for trilayers on quartz substrate and 1.64 for the silicon substrate. Magneto-transport data plotted in Fig. 2 for trilayers show oscillations of Hall resistivity and MR with dAu : We observed alternate (‘right and left’) loops for EHE for different dAu ; showing the sign change of magnetic interaction (inset at Fig. 2b). MR increase is observed at the periods of EHE-resistivity modulations, where the antiparallel coupling of Fe and Tb magnetic moments occurs. In Fig. 3, we show the magnetization loops measured by SQUID with magnetic field applied parallel to the film plane. The sharp change of susceptibility seen ( can be attributed to for the trilayer with dAu ¼ 9 A remagnetization of one of the magnetic sublattices from the antiparallel state. The sign of EHE loop is observed on antiferromagnetic coupling (AF) of Fe and Tb magnetic moments for this trilayer. M2H loop, that shows AF coupling, can be useful for extracting the exchange coupling constants. In the case of AF coupling, there are three possible phases when H increases, namely, (1) AF, (2) 901, where the angle between external magnetic field, H; and one of the magnetic moments (the smaller) is 901 and (3) saturated, when both magnetic moments are parallel to H: The coupling constant for the trilayer with a spacer between
Ohm cm
where Jinter ðdÞ is the interlayer exchange coupling as a function of the spacer thickness d; A1 ; A2 are amplitudes and L1 ; L2 are periods of energy oscillations. The phases and the amplitude ratio A1 =A2 have been found to depend critically on the sample quality and ferromagnetic layer thickness. It is only for a few trilayers that two periods of oscillations and antiferromagnetic coupling have been observed for spacers thinner than 3–4 ML, e.g., for Fe/Au/Fe [10]. In Fig. 1, oscillations of PMOKE angle in Fe/Au/Tb trilayers (top inset) are shown. PMOKE angle was measured at a kink of the loop (bottom inset). Starting with 1 ML of spacer in ( PMOKE loops showed that magtrilayer (dAu ¼ 3 A), netic moments of Fe and Tb layers are no more perpendicular to the film plane. Instead of a rectangular loop we observed loops with a kink, which connected two regions. The origin of one of them is the rotation of magnetic moments of the layers from the film plane at H ¼ 0; following the increasing perpendicular magnetic field. Position of the kink (values of PMOKE angle and magnetic field) changes the oscillation while dAu increases. The difference of the loops for the control Fe ( and for trilayers shows that an film with dFe ¼ 8 A interaction between Fe and Tb layers still exists. The periods we observed for the Fe/Au/Tb system was about ( that is 2.75 and 8.9 ML, correlate well with 8 and 26 A, the oscillation periods 2.5 and 8.6 ML, which were
533
0
4 -15 -2
0.0 -1
0
1
2
50
55
H, T
0
5
10
15
20
25
30
35
40
45
Au interlayer thickness, Å. Fig. 1. Oscillation of PMOKE angle for Fe/x Au/Tb trilayers as a function of dAu : The top inset: scheme of trilayer, studied in this work. The bottom inset: PMOKE loop for the trilayers, ( Fe film. Arrows show the kink at compared with the control 8 A a critical field.
0
5
35
Au interlayer thickness, Å.
Fig. 2. (a) EHE resistivity and (b) MR (perpendicularF‘white’ and transverseF‘black triangles’) as a function of dAu : Insets: schemes of the antiparallel and parallel orientations of Fe and Tb magnetic moments as a result of coupling via Au spacer (a) the change of sign in EHE loops (b).
E. Shypil et al. / Journal of Magnetism and Magnetic Materials 242–245 (2002) 532–534
534 800 600
Fe/6Å Au/Tb
400 200
Magnetic moment, emu/cm 3
0 -200 -400 -600 -2
-1
0
800
1
2
o
90 phase
Fe/9Å Au/Tb
600 400 200 0 -200 -400 -600 -2
-1
0
1
compensation composition. The vectors of Fe and Tb magnetic moments are antiparallel to one another directed perpendicular to the film plane. Only 1 ML of Au interposed between Fe and Tb layers is sufficient to shield the short-range magnetic interactions. The vectors of Fe and Tb magnetic moments are no more perpendicular to the film plane. It is supported with the change of the loop shape in PMOKE and SQUID data [8]. At a further increase of dAu ; the vectors of magnetic moments change their inter-orientation in keeping with the film plane (EHE data). Further, up to 12 Au MLs this process is shown to be periodical. At the negative periods of modulations the sharp increase of MR is observed, that shows the sign change of the long-range exchange interaction. In conclusion, it is experimentally shown for the first time with different methods, characterization tools, that Fe and Tb layers, separated by thin Au layer, couple their magnetic moments parallel–antiparallel for different Au thicknesses, i.e., the sign of exchange interaction oscillates. The exchange coupling constant is evaluated. Presented results correlate well with the existing experimental and theoretical data. No change in sign [7] could be observed in sputtered multilayers because of the interfacial mixing.
2
H, T. Fig. 3. SQUID loops measured in the parallel magnetic field ( ( ( and Fe (8 A)/Au ( for two trilayers. Fe (8 A)/Au (6 A)/Tb (12 A) ( ( at T ¼ 300 K. For the second sample the point, (9 A)/Tb (12 A) where sharp change of susceptibility is observed, is marked as 901 phase.
two different ferromagnetic layers, one of which is Fe and the second is Tb with induced magnetization is described [7]: 1 m1 m2 A¼ HCR : ð2Þ 2 mðHCR Þ To evaluate it we used the data extracted from the ( Au/Tb trilayer (Fig. 3): M2H loop for Fe/9 A m1 ¼ 457 emu/cm3 and m2 ¼ 42 emu/cm3 are magnetizations of Fe and Tb layers, mðHCR Þ ¼ 634 emu/cm3 and HCR ¼ 0:6 T is a field, at which 901 phase is observed. Accounting the layer thickness, dFe and dTb ; we obtain A ¼ 4 103 erg/cm2. This value is almost one order less than what was observed for the Fe/Au/Fe trilayers (2 102 erg/cm2) [3]. By analysing the data, obtained with different methods, we can reconstruct the change dynamics of Fe and Tb magnetic moments with the increase of dAu : Without Au layer PMA was observed in Fe/Tb interface, similar to amorphous Fe–Tb films closer to
The work was supported by CRDF UP2-2117 and NSF International Collaborative Grant No. 9940368.
References [1] P. Grunberg, . R. Schreiber, Y. Pang, M.B. Brodski, H. Sowers, Phys. Rev. Lett. 57 (1986) 2442. [2] M. Baibich, J.U. Bruto, A. Fert, F. Ngnyen van Dan, F. Petroff, P. Etienne, G. Creuzot, J. Chazeles, Phys. Rev. Lett. 61 (1988) 2472. [3] B. Heinrich, J.F. Cochran, Adv. Phys. 42 (1993) 523. [4] S.S.P. Parkin, Annu. Rev. Mater. Sci. 25 (1995) 357. [5] B. Scholz, R.A. Brand, W. Keune, Phys. Rev. B 50 (1994) 2537. [6] W.S. Kim, W. Kleeman, J. Tappert, W. Keune, J. Appl. Phys. 84 (1) (1998) 4384. [7] H. Hoffmann, R. Scherschlicht, in: R. Helbig (Ed.), . Festkorperprobleme, Vieweg, Braunschweig/Wiesbaden, 1998, p. 275. [8] E. Shypil, A. Pogorilyy, D. Podyalovski, Ye. Pogoryelov, Low Temp. Phys. 27 (8) (2001) 650. [9] A. Ney, F. Wilhelm, M. Farle, P. Poulopoulos, P. Srivastava, K. Baberschke, Phys. Rev. B 59 (1999) R3938. [10] J. Unguris, R.J. Celotta, D.T. Pierce, Phys. Rev. Lett. 79 (1997) 2734. [11] J. Unguris, R.J. Celotta, D.T. Pierce, J. Appl. Phys. 75 (1994) 6437. [12] P. Bruno, L. Chappert, Phys. Rev. Lett. 67 (1991) 1602.
Magnetic interactions in MBE grown Fe/x Au/Tb trilayers E. Shypila,*, A. Pogorilyya, Ye. Pogoryelova, T.H. Kimb, G. Bererab, J. Mooderab a
Institute of Magnetism, National Academy of Sciences, 36-b Vernadsky Blvd., 03142 Kyiv, Ukraine b Francis Bitter Magnet Laboratory, MIT, Cambridge, MA, USA
Abstract Indirect exchange coupling between Fe and Tb layers showed oscillatory behaviour through Au layer as a function of its thickness. Trilayers, prepared in the MBE system, were characterized with different experimental tools. Results are analysed to reconstruct the dynamics of Fe and Tb magnetic moments. For the first time, the change of sign in magnetic interaction is shown for Fe/Au/Tb system. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Exchange couplingFoscillations; Thin filmsFtrilayer; Ferromagnetic; Rare-earth
Among the most important advances in the recent years in artificially engineered nano-structured materials is the discovery of coupling between magnetic layers. Interlayer coupling was first observed between Fe layers across Cr layer [1,2] and then in multilayers (Mls) with various ferromagnetic (FM) and spacer layers [3,4]. It was found that the amplitude of the coupling strength depends on the material of interlayer and that the sign of the coupling oscillates with the thickness increase of nonmagnetic layer, that is consistent with RKKY model. The other interesting system to study the coupling is between FM and rare-earth (RE) layers. Exchange coupling between Fe and Tb is known to be antiparallel. Many papers (e.g. [5,6]) are devoted to this coupling, which presents perpendicular magnetic anisotropy (PMA) and already is used in practice for magnetic recording. Although there is the only work where the long range coupling between these layers via nonmagnetic spacer is studied [7]. Authors studied Mls, prepared by sputtering, where after each Fe or Tb layer the Au layer was placed. It was concluded that in contrast to the theory the sign of exchange interaction does not change with interlayer thickness. In this paper we investigate the carefully prepared Fe/ ( bi- and trilayers, grown in the x Au/Tb (x ¼ 0 35 A) MBE system. We will show that oscillations of the net *Corresponding author. Tel.: +380-44-444-9593; fax: +38044-444-1020. E-mail address: [email protected] (E. Shypil).
magnetic moment are well observed in magnetic, magneto-optical and magneto-transport methods and ( We will also demonstrate their periods are 8 and 26 A. for the first time, that the indirect coupling changes the sign with interlayer thickness in the Fe/Au/Tb system. Two sets of Fe/Au/Tb trilayers on quartz and silicon substrates were prepared by electron-beam evaporation in MBE system with a background pressure of 1–5 1010 Torr and maintaining a pressure of 1–3 109 Torr during the film growth. To minimize interdiffusion of layers, the substrate temperature during evaporation was kept no higher than 01C. The rates of ( and were indepenevaporation did not exceed 0.4 A/s dently controlled with quartz crystal monitors. Samples ( thick layer on quartz substrate were protected with 30 A of Al2O3, whereas on Si substrate they were capped ( Au layer. SQUID magnetometer and polar with 30 A magneto-optical Kerr effect (PMOKE), were used to characterize the films magnetically. Extraordinary Hall Effect (EHE) and magneto-resistance (MR) of trilayers were measured using standard techniques. The details of these experiments are published in Ref. [8]. The thickness of the individual layers, dFe and dTb ; were 3 monolayers (ML), which were chosen on the basis of the previous experiments [8], where the ferrimagnetic ordering of Fe/Tb multilayer has been shown; dFe and dTb ( (3 ML) and 12 A ( (3 ML), were maintained at 8 A respectively, while dAu was increased. Theoretical works for noble-metal spacers based on the RKKY model have predicted two oscillations of the
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 1 1 3 6 - 2
E. Shypil et al. / Journal of Magnetism and Magnetic Materials 242–245 (2002) 532–534
interlayer coupling with the spacer thickness reflecting the topological properties of the Fermi surface [9] 1 2pd Jinter ðdÞ ¼ 2 A1 sin þ F1 d L1 2pd ; ð1Þ þ F2 þA2 sin L2
Tb
-6
Au
15
EHE, 10
Fe
Fe /3Å Au/ Tb
0.03
Tb Au Fe Tb Au Fe
(a)
0.00
Tb Fe -0.03
0 0.8
5
10
15
20
25
30
10
15
20
25
30
35
(b)
8Å Fe
MR, %
Q, min.
PMOKE angle, Θ (min.)
6
measured for the Fe/Au/Fe system [11] and also with values of 2.51 and 8.6 ML, extracted [12] from measurements of the Au Fermi surface. The facts that the second oscillation period appears and also the high amplitude ratio, A1max =A1min ; show that the growth conditions for the trilayers were good and the quality of interface was 0 0 high. The amplitude ratio, A1max =A1min ; of PMOKE angle seen in our work, which is proportional to the net magnetic moment, is evaluated as 1.26–1.33 for trilayers on quartz substrate and 1.64 for the silicon substrate. Magneto-transport data plotted in Fig. 2 for trilayers show oscillations of Hall resistivity and MR with dAu : We observed alternate (‘right and left’) loops for EHE for different dAu ; showing the sign change of magnetic interaction (inset at Fig. 2b). MR increase is observed at the periods of EHE-resistivity modulations, where the antiparallel coupling of Fe and Tb magnetic moments occurs. In Fig. 3, we show the magnetization loops measured by SQUID with magnetic field applied parallel to the film plane. The sharp change of susceptibility seen ( can be attributed to for the trilayer with dAu ¼ 9 A remagnetization of one of the magnetic sublattices from the antiparallel state. The sign of EHE loop is observed on antiferromagnetic coupling (AF) of Fe and Tb magnetic moments for this trilayer. M2H loop, that shows AF coupling, can be useful for extracting the exchange coupling constants. In the case of AF coupling, there are three possible phases when H increases, namely, (1) AF, (2) 901, where the angle between external magnetic field, H; and one of the magnetic moments (the smaller) is 901 and (3) saturated, when both magnetic moments are parallel to H: The coupling constant for the trilayer with a spacer between
Ohm cm
where Jinter ðdÞ is the interlayer exchange coupling as a function of the spacer thickness d; A1 ; A2 are amplitudes and L1 ; L2 are periods of energy oscillations. The phases and the amplitude ratio A1 =A2 have been found to depend critically on the sample quality and ferromagnetic layer thickness. It is only for a few trilayers that two periods of oscillations and antiferromagnetic coupling have been observed for spacers thinner than 3–4 ML, e.g., for Fe/Au/Fe [10]. In Fig. 1, oscillations of PMOKE angle in Fe/Au/Tb trilayers (top inset) are shown. PMOKE angle was measured at a kink of the loop (bottom inset). Starting with 1 ML of spacer in ( PMOKE loops showed that magtrilayer (dAu ¼ 3 A), netic moments of Fe and Tb layers are no more perpendicular to the film plane. Instead of a rectangular loop we observed loops with a kink, which connected two regions. The origin of one of them is the rotation of magnetic moments of the layers from the film plane at H ¼ 0; following the increasing perpendicular magnetic field. Position of the kink (values of PMOKE angle and magnetic field) changes the oscillation while dAu increases. The difference of the loops for the control Fe ( and for trilayers shows that an film with dFe ¼ 8 A interaction between Fe and Tb layers still exists. The periods we observed for the Fe/Au/Tb system was about ( that is 2.75 and 8.9 ML, correlate well with 8 and 26 A, the oscillation periods 2.5 and 8.6 ML, which were
533
0
4 -15 -2
0.0 -1
0
1
2
50
55
H, T
0
5
10
15
20
25
30
35
40
45
Au interlayer thickness, Å. Fig. 1. Oscillation of PMOKE angle for Fe/x Au/Tb trilayers as a function of dAu : The top inset: scheme of trilayer, studied in this work. The bottom inset: PMOKE loop for the trilayers, ( Fe film. Arrows show the kink at compared with the control 8 A a critical field.
0
5
35
Au interlayer thickness, Å.
Fig. 2. (a) EHE resistivity and (b) MR (perpendicularF‘white’ and transverseF‘black triangles’) as a function of dAu : Insets: schemes of the antiparallel and parallel orientations of Fe and Tb magnetic moments as a result of coupling via Au spacer (a) the change of sign in EHE loops (b).
E. Shypil et al. / Journal of Magnetism and Magnetic Materials 242–245 (2002) 532–534
534 800 600
Fe/6Å Au/Tb
400 200
Magnetic moment, emu/cm 3
0 -200 -400 -600 -2
-1
0
800
1
2
o
90 phase
Fe/9Å Au/Tb
600 400 200 0 -200 -400 -600 -2
-1
0
1
compensation composition. The vectors of Fe and Tb magnetic moments are antiparallel to one another directed perpendicular to the film plane. Only 1 ML of Au interposed between Fe and Tb layers is sufficient to shield the short-range magnetic interactions. The vectors of Fe and Tb magnetic moments are no more perpendicular to the film plane. It is supported with the change of the loop shape in PMOKE and SQUID data [8]. At a further increase of dAu ; the vectors of magnetic moments change their inter-orientation in keeping with the film plane (EHE data). Further, up to 12 Au MLs this process is shown to be periodical. At the negative periods of modulations the sharp increase of MR is observed, that shows the sign change of the long-range exchange interaction. In conclusion, it is experimentally shown for the first time with different methods, characterization tools, that Fe and Tb layers, separated by thin Au layer, couple their magnetic moments parallel–antiparallel for different Au thicknesses, i.e., the sign of exchange interaction oscillates. The exchange coupling constant is evaluated. Presented results correlate well with the existing experimental and theoretical data. No change in sign [7] could be observed in sputtered multilayers because of the interfacial mixing.
2
H, T. Fig. 3. SQUID loops measured in the parallel magnetic field ( ( ( and Fe (8 A)/Au ( for two trilayers. Fe (8 A)/Au (6 A)/Tb (12 A) ( ( at T ¼ 300 K. For the second sample the point, (9 A)/Tb (12 A) where sharp change of susceptibility is observed, is marked as 901 phase.
two different ferromagnetic layers, one of which is Fe and the second is Tb with induced magnetization is described [7]: 1 m1 m2 A¼ HCR : ð2Þ 2 mðHCR Þ To evaluate it we used the data extracted from the ( Au/Tb trilayer (Fig. 3): M2H loop for Fe/9 A m1 ¼ 457 emu/cm3 and m2 ¼ 42 emu/cm3 are magnetizations of Fe and Tb layers, mðHCR Þ ¼ 634 emu/cm3 and HCR ¼ 0:6 T is a field, at which 901 phase is observed. Accounting the layer thickness, dFe and dTb ; we obtain A ¼ 4 103 erg/cm2. This value is almost one order less than what was observed for the Fe/Au/Fe trilayers (2 102 erg/cm2) [3]. By analysing the data, obtained with different methods, we can reconstruct the change dynamics of Fe and Tb magnetic moments with the increase of dAu : Without Au layer PMA was observed in Fe/Tb interface, similar to amorphous Fe–Tb films closer to
The work was supported by CRDF UP2-2117 and NSF International Collaborative Grant No. 9940368.
References [1] P. Grunberg, . R. Schreiber, Y. Pang, M.B. Brodski, H. Sowers, Phys. Rev. Lett. 57 (1986) 2442. [2] M. Baibich, J.U. Bruto, A. Fert, F. Ngnyen van Dan, F. Petroff, P. Etienne, G. Creuzot, J. Chazeles, Phys. Rev. Lett. 61 (1988) 2472. [3] B. Heinrich, J.F. Cochran, Adv. Phys. 42 (1993) 523. [4] S.S.P. Parkin, Annu. Rev. Mater. Sci. 25 (1995) 357. [5] B. Scholz, R.A. Brand, W. Keune, Phys. Rev. B 50 (1994) 2537. [6] W.S. Kim, W. Kleeman, J. Tappert, W. Keune, J. Appl. Phys. 84 (1) (1998) 4384. [7] H. Hoffmann, R. Scherschlicht, in: R. Helbig (Ed.), . Festkorperprobleme, Vieweg, Braunschweig/Wiesbaden, 1998, p. 275. [8] E. Shypil, A. Pogorilyy, D. Podyalovski, Ye. Pogoryelov, Low Temp. Phys. 27 (8) (2001) 650. [9] A. Ney, F. Wilhelm, M. Farle, P. Poulopoulos, P. Srivastava, K. Baberschke, Phys. Rev. B 59 (1999) R3938. [10] J. Unguris, R.J. Celotta, D.T. Pierce, Phys. Rev. Lett. 79 (1997) 2734. [11] J. Unguris, R.J. Celotta, D.T. Pierce, J. Appl. Phys. 75 (1994) 6437. [12] P. Bruno, L. Chappert, Phys. Rev. Lett. 67 (1991) 1602.