Effect of magnetic alloying on magnetic anisotropy in ultrathin fcc Ni-like films
C.C. Kuo
a,b, W.C. Lin
a, S.F. Chuang
a, Minn-Tsong Lin
a,c,*aDepartment of Physics, National Taiwan University, 1. Sec. 4, Roosevelt Rd., Taipei 106, Taiwan
bDepartment of Physics, National Sun Yet-Sen University, Kaohsiung 804, Taiwan
cInstitute of Atomic and Molecular Sciences, Academia Sinica, Taipei 115, Taiwan Received 22 October 2004; accepted for publication 6 December 2004
Available online 20 December 2004
Abstract
For identifying the magnetic alloying effect on the magnetic anisotropy in the magnetic ultrathin films, the spin- reorientation transition was studied by preparing the ultrathin FexNi1x and CoxNi1xalloy films on Cu(1 0 0) with variations of coverage and alloy concentration x. The comparison between FexNi1x/Cu(1 0 0) and CoxNi1x/ Cu(1 0 0) shows that the modification of the critical thickness for the spin-reorientation transition by the alloy concen- tration x for Fe is 1.35 times larger than modification by Co. The evolution of spin-reorientation transition in this Ni-dominant films could be mainly traced back into the local behavior of d-electrons in impurities and host element, corrected with the charge transfer of d-electrons between them.
Ó 2004 Elsevier B.V. All rights reserved.
Keywords: Magnetic ultrathin alloy film; Magnetic anisotropy; Spin-reorientation transition
1. Introduction
The magnetic properties of the 3d-transition metal ultrathin films are strongly dependent on the d-band characteristics of the films, such as
band filling, band dispersion, and exchange split- ting. This is not only because of the complicated 3d-band structures around Fermi energy with sub- stantial density of states, but also because of the critical evolution of the band filling difference be- tween the majority (n") and minority (n#) bands.
In alloy films, there exits an interplay between local behavior and itinerant properties of d-elec- trons, such as charge transfer between various ele- ments due to different electronegativities. Thus, it is more difficult to clarify how the band shape
0039-6028/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2004.12.003
*Corresponding author. Address: Department of Physics, National Taiwan University, 1. Sec. 4, Roosevelt Rd., Taipei 106, Taiwan, ROC. Tel.: +886 233665173; fax: +886 223639984.
E-mail address:[email protected](M.-T. Lin).
www.elsevier.com/locate/susc
and band filling influence the magnetic properties in alloy films. Theoretically, the band filling was often treated as a parameter with continuous var- iation of electron numbers. Many efforts were made on the study of the correlation between band structures and magnetic properties, such as the magnetic moment and anisotropy, as a function of d-electron number (nd) by the first-principle cal- culation [1–7]. Different from the magnetic mo- ment which follows the Slater–Pauling curve with nearly linear dependence on nd, the magnetic anisotropy, however, exhibits more complicated behavior as a function of nd. Either rapid oscilla- tions [1,3] or slow variation [2,7] showed a non- monotonic nddependence of anisotropy.
In an alloy film, the added magnetic element, however, should not only result in change of the d-band filling, but also affect the band width or dispersion. The question arises herein is how the magnetic alloying manipulates the electronic structure in the alloy system. One could either consider it as an artificial system with a band structure overall determined by the averaged elec- tron numbers from the alloy composition, or must go into the details of the alloying effect on the electronic states of each element involved, such as local density state, band shape, and exchange splitting. A strong effect, which is relevant to mag- netotransport properties, of magnetic impurities from Fe and Cr on valence band of the Ni host has been observed by means of angle-resolved photoemission [8]. The strong variation of these effects suggest the concept of the magnetic alloy- ing rather than an averaging band behavior or band filling determined by the corresponding elec- tron number.
In this article, we report on a detailed measure- ment of the alloying effect on spin-reorientation transition (SRT) as well as magnetic anisotropy in fcc Ni-like films. Comparing the results from different magnetic impurities (Fe and Co), the evo- lution of the magnetic anisotropy at variation of alloy concentration can be well understood by merely considering a Ni-like band shape and a local exchange splitting determined by the mag- netic moment of added element, entangled with the interplay of the local density of states and charge transfer from added and host elements.
2. Experiment
The magnetic alloy ultrathin films were pre- pared and investigated in situ in an ultrahigh vac- uum (UHV) chamber[9]. To deposit the films with desired and subtle-varied alloy composition is rel- evant to the study on the drastic variation of crit- ical thickness for SRT. The coverage and alloy composition of the alloy films in our experiments can be precisely controlled in the co-deposition technique to an accuracy of 0.05 ML and ±0.5%, respectively [10,11]. Furthermore, Auger electron spectroscopy (AES) was employed for studying the chemical structure and for double check of alloy composition of the alloy films [10,12]. The medium energy electron diffraction (MEED) was taken for calibration of the film coverage as well as for providing an information of the morphology of the film surface [13,14]. To identify the struc- tural properties of the films, the crystalline struc- ture and interlayer distance of the alloy films were performed via the low energy electron diffrac- tion (LEED) and LEED I(E) in the kinematic approximation [15–18]. In addition, the study of the magnetic hysteresis loops was carried out by means of magneto-optical Kerr effect (MOKE) in polar and longitudinal configurations quasi-simul- taneously with benefit of the lock-in technique to investigate the evolution of SRT with variation of alloy concentration of the films.
3. Results
Several characteristics could be altered while changing alloy composition of the films: crystalline structure, morphology, and electronic structure.
Each of them will influence the magnetic behavior.
It becomes crucial to confirm the structural invari- ance on the variation of the alloy composition. In the previous study, we found that the crystalline structure, lattice constant, as well as morphology of CoxNi1x/Cu(1 0 0) and FexNi1x/Cu(1 0 0) are invariant with alloy composition[10,11,9]. In addi- tion, all these alloy films behave like the Ni/
Cu(1 0 0) film. It implies that these alloy films are the Ni/Cu(1 0 0)-like systems at least within the composition range of x 6 8%, indicating that the
structure of these alloy films are Ni-dominant and varied insignificantly within the alloy composition in our study. These structural evidences allow us to attribute the change in the magnetic properties to the effect of electronic structures mentioned above.
To observe how SRT evolves with alloy concen- tration is crucial to characterize the alloy-induced magnetic behavior of the film. The critical thick- ness (dc) of SRT, which was identified as the thick- ness where the magnetic easy axis transfers from in-plane to out-of-plane orientation, is a good characteristic to describe the evolution of SRT.
The magnetic easy axis was identified by taking the hysteresis loops at 110 K with the applied field perpendicular and parallel to the film surface. As illustrated in Fig. 1(open and solid circles), dc of SRT for FexNi1x/Cu(1 0 0) varies from 7.5 ML for x = 0% [pure Ni/Cu(1 0 0)] to 16 ML for x = 5%. No SRT was found for x > 6% with the cover- age up to 20 ML. In comparison with CoxNi1x/ Cu(1 0 0) [10] (open and solid triangles inFig. 1), dcof the FexNi1x/Cu(1 0 0) alloy film is more sen-
sitive to the content of Fe. That is, the less Fe is needed to achieve the same dc when alloys with Ni, as shown inFig. 1.
The critical thickness in CoxNi1x/Cu(1 0 0) can be well evaluated by fitting magnetic moments and anisotropies of Co/Cu(1 0 0) and Ni/Cu(1 0 0) as [10]
dc¼ 2½xKCos þ ð1 xÞKNis
½xKCov þ ð1 xÞKNiv 2p½xMCoþ ð1 xÞMNi 2 ð1Þ by assuming linear variation of the magnetic mo- ments and anisotropies between Co/Cu(1 0 0) and Ni/Cu(1 0 0). However, the estimation of dcsimilar to Eq. (1) by linearly superposing the magnetic moments and anisotropies of Fe/Cu(1 0 0) and Ni/Cu(1 0 0) (listed inTable 1) makes large discrep- ancy from our experiments, as depicted by dotted line in Fig. 1. The failure of the linear model may result from the fact that FexNi1x/Cu(1 0 0) reveals ‘‘compressed’’ distortion along the surface normal while Fe/Cu(1 0 0) is tetragonal ‘‘ex- panded’’. It may result in different signs between them. Therefore, Kvadopted for Fe/Cu(1 0 0) could fail to describe Fe in FexNi1x/Cu(1 0 0). On the other hand, it is possible that Kv of Fe in FexNi1x/Cu(1 0 0) is still positive but the linear model does not work any more. Since Kv of Ni and Fe is positive a linear model will also yield a positive value for all concentrations. But due to the different structure (expanded versus com- pressed) of the Fe and Ni this linear model is flawed. However, many problems may be encoun- tered for the argument of Kvfor Fe/Cu(1 0 0). This debate remains unsolved till now. Moreover, it would be also a good point to include further data of Fe/Cu(1 0 0)[19]. Adopting Kv= 77.7 leV/atom 5
10 15 20
0 2 4 6 8 10
// (FeNi) ⊥ (FeNi) dc (FeNi) // (CoNi) ⊥ (CoNi) dc (CoNi)
Coverage (ML)
Concentration x (%)
Fig. 1. Comparison of the magnetic phase diagrams of mag- netic easy axis for FexNi1x/Cu(1 0 0) and CoxNi1x/Cu(1 0 0).
The dotted curve represents the evaluation of dcfor FexNi1x/ Cu(1 0 0) similar to Eq.(1)by linear superposition of magnetic moments and anisotropies of Fe/Cu(1 0 0) and Ni/Cu(1 0 0). The solid and dashed curves show the evaluation of dcfor FexNi1x/ Cu(1 0 0) and CoxNi1x/Cu(1 0 0), respectively, in terms of Eq.
(3)by considering the magnetostriction coefficient as a function of alloy concentration x in Ni.
Table 1
Magnetic moments and anisotropies of Fe and Ni
Element M (lB) Ks(leV/atom) Kv(leV/atom)
Fe 2.5a 115.8b 103.6b
Ni 0.57c 77d 29d
a Ref.[6].
bRef.[26].
cRef.[25].
dRef.[21].
and Ks= 120 leV/atom for Fe/Cu(1 0 0) by Platow et al.[19], we got another descending curve similar to the dotted line in Fig. 3 but with different slope.
For example, dcvaries from 6.6 ML to 7.0 ML for x = 5%. It still fails for the description of Fe–Ni alloy.
One may doubt whether the magnetic aniso- tropy for Fe/Cu(1 0 0) is temperature-dependent variable and affect the tricky fitting of phase dia- gram for FeNi alloy. Another detailed study[20]
on more reliable temperature-dependent aniso- tropy for Fe/Cu(1 0 0) provides a good opportunity to clarify this point. For the anisotropy of Fe/
Cu(1 0 0) taken at about 110 K, the measurement temperature in our experiments, the fitting of phase diagram is a little closer to the experimental one than the other fitting. However, the value of critical thickness is still decreasing with variation of Fe composition x. This descending tendency will be even enhanced if one adopts the anisotropy of Fe/Cu(1 0 0) at higher temperature. Obviously, although taking the temperature-dependent aniso- tropy constants for fcc Fe/Cu(1 0 0) from the previous study (Ref.[20]) can give a temperature- dependence of the critical thickness, it still failed to describe the experimental results of evolution of the critical thickness at variation of the alloy composition. Thus, the FeNi alloy ultrathin films in our experiments can not be just simply treated as a linear combination of fcc Fe and Ni films on Cu(1 0 0) substrate even taking the temperature- dependence of the anisotropy for fcc Fe into account.
The previous study indicated that the SRT for Ni/Cu(1 0 0) is mainly attributed to the volume- type magnetoelastic anisotropy (KNiv ) [21]. It can be expressed as
KNiv ¼ 3
2ðc11 c12Þk100ðe1 e2Þ; ð2Þ where c11 and c12 are elastic stiffness constants, e1
and e2represent the strain and the tetragonal dis- tortion, respectively; k1 0 0 denotes the magneto- striction coefficient along the [1 0 0] direction.
Apparently KNiv depends on the strain of the film and magnetostriction coefficient k1 0 0. As men- tioned in our previous study [9], the strain of FexNi1x/Cu(1 0 0) keeps almost invariant for dif-
ferent compositions x. By contrast, the magneto- striction coefficient (k1 0 0) is greatly sensitive to the alloy composition x. It has been shown, by first principle calculation [7], to be strongly dependent on the minority band filling nd, which is propor- tional to the alloy concentration x in Ni. Therefore the magnetoelastic anisotropy varies dramatically upon variation of alloy concentration. The evalua- tion of dccan thus be implemented as
dcðndÞ ¼ 2KNis
KNiv ðndÞ 2pM2NiðndÞ ð3Þ by approximation of linear dependence of mag- netoelastic anisotropy (KNiv ) as well as magnetic moment (MNi) on 3d-band filling nd (Ref. [7]) and, in turn, on the alloy concentration x in FexNi1x/Cu(1 0 0). Noted that the surface mag- netic anisotropy KNis in Eq. (3) was assumed to be invariant with alloy concentration, which is compatible with the previous study [22]. The solid curve illustrated inFig. 1represents the evaluated dcas a function of alloy concentration x from Eq.
(3), where MNi(nd) is taken by superposition of magnetic moments for Fe and Ni listed in Table 1. Apparently, the trend of dc evaluated by this method agrees very well with the experimental re- sults. It should be emphasized that within the low Fe content limit (x 6 8%), the magnetic anisotro- pies of FexNi1x/Cu(1 0 0) can not be oversimpli- fied as a linear combination of those of Fe/
Cu(1 0 0) and Ni/Cu(1 0 0). Iron in the FexNi1x/ Cu(1 0 0) films behaves like an electron regulator to modify the band characteristics of the Ni/
Cu(1 0 0) films. Besides, our simulation of phase boundary is very similar to that by Thamankar et al. [22] where the magneto-elastic properties of bulk Fe–Ni was taken into account to derive the value of dc. This is mainly because that both sim- ulations was based on the same tendency for mag- netostriction coefficient k1 0 0 of Ni while alloying with Fe.
4. Discussion
It is reasonable to expect the stronger modifica- tion of SRT by Fe than that by cobalt when these two elements are alloyed into Ni films since the
difference of d-electron numbers between Fe and Ni is twice of that between Co and Ni. It agrees with our result, as shown in Fig. 1. Furthermore, for the same critical thickness dc, the concentration of Co (xCo) is about 1.35 times of the concentra- tion of Fe (xFe), as shown inFig. 1. It means that modification of dcfor SRT by the alloy concentra- tion x for Fe is 1.35 times larger than modification by Co. On the other hand, according to Eq. (3) there exists a pole in the dc(x) curve for Kv 2pM2= 0. This pole describes the transition from Ni-type SRT to Fe-type SRT or Co-type films (no SRT). By comparing the pole positions be- tween FexNi1x/Cu(1 0 0) and CoxNi1x/Cu(1 0 0), a factor of 1.32 between the concentration of Co and Fe in alloy can be obtained. This is very close to 1.35 in the above evaluation. Not that magnetic moment could only affect the pole position a min- or shift and change the factor from 1.32 to 1.37 if we take the magnetic moment of Fe from 2.5lBto 3.0lB. The factor of about 1.35 can mainly be attributed to the facts as follows: First, the distri- butions of electrons in metals iron, cobalt, and nickel are different from those in free atoms. For example, there are five spin-up and one spin-down d-electrons for a free iron atom such that there is no spin-up hole in the d-orbit of iron atom. How- ever, there exists an incompletely filled majority- spin band for the metal iron. Second, what affects dc of SRT in CoxNi1x/Cu(1 0 0) and FexNi1x/ Cu(1 0 0) is likely to be the difference of filling num- bers Dndbetween the majority and minority bands, rather than the total number of d-electrons nd. The magnetic anisotropies which influence dc of SRT originate from the interplay between magnetic mo- ment and spin–orbit interaction. Each of them is correlated to the Dnd in the films. The average Dnd of nickel with iron composition will then be suppressed due to the vacancy of majority band in iron[23]. A simple estimation of dcmodification by alloy concentration of iron (xFe) and cobalt (xCo) can therefore be made by considering the dif- ferences of the filling numbers for majority and minority bands in iron, cobalt, and nickel. For the same dc, the relation of the concentration xFe
in Fe–Ni alloy and xCo in Co-Ni alloy was ex- pressed, by considering the averaged d-band asym- metry Dnalloyd , as
Dnalloyd ¼ DnFed xFeþ DnNid ð1 xFeÞ
¼ DnCod xCoþ DnNid ð1 xCoÞ; ð4Þ where DnFed , DnCod , and DnNid represent the difference of majority and minority bands for iron, cobalt, and nickel, respectively. Note that Dnd is similar to the ‘‘magnetic moment’’ if the orbital moment is not taken into consideration. For the transition metals, the orbital moment is insignificant although it should be enhanced at the surface.
Thus, Dndcould be analogous to the magnetic mo- ment for a rough estimate. The ratio of the alloy concentration xCo/xFe, which is equivalent to the relative contribution of the alloy concentration F e on dcin comparison with Co, can be simplified as
xCo
xFe ¼DnFed DnNid
DnCod DnNid : ð5Þ
In order to estimate the xCo/xFeratio in terms of DnFed , DnCod , and DnNid , we adopted the filling num- bers for majority and minority bands of Co and Fe by modifying the spin-dependent density of states for fcc Ni (Ref.[24]) with the spin splitting (equiv- alent to Dnd) proportional to magnetic moment in accordance with the Stoner theory[23]. Meanwhile the band shapes for added Fe and Co were kept invariant with that for host element Ni, as illus- trated in Fig. 2. This assumption is reasonable since the band shape with tiny alloy concentration is mainly determined by periodically neighboring
Fig. 2. Density of states for majority and minority bands in Fe, Co, and Ni. The densities of states for iron and cobalt were evaluated by taking the band shape of fcc nickel[24]modified with the spin splitting proportional to magnetic moment in accordance with the Stoner theory[23].
host elements. Table 2 listed the spin-dependent band filling numbers (DndÕs) as well as the densities of states at Fermi level (DNd(EF)Õs) for Fe, Co, and Ni. Using the estimated values inTable 2, xCo/xFe
can be evaluated as 1.61 which is much less than two, the expected value from the d-electrons of free atoms. That is, 1.61 times of Co content is need as compared with Fe for achieving the same dc under our d-band asymmetry consideration. It means that Dndrather than ndshould be the prin- cipal factor to modify the magnetic anisotropies and, in turn, to affect dcin the films. Furthermore, if the charge transfer d between nickel and iron or cobalt is taken into consideration[23], the effect of alloy content for iron and cobalt on dcexpressed in Eq.(5) can be modified as
xCo
xFe ¼½DnFed DNFed ðEFÞd ½DnNid þ DNNid ðEFÞd
½DnCod DNCod ðEFÞd ½DnNid þ DNNid ðEFÞd ; ð6Þ where DNFeðCo;NiÞd ðEFÞ represents the difference of spin density of states at Fermi energy for Fe(Co, Ni), as listed in Table 2. Due to almost the same electronegativity of iron (1.83), cobalt (1.88), and nickel (1.89), the charge transfer between the two elements alloyed in films is insignificant for CoxNi1x/Cu(1 0 0) and FexNi1x/Cu(1 0 0). How- ever, the densities of states at Fermi energy could be significantly different for iron, cobalt, and nickel. Therefore, even a little charge transfer will strongly alter the spin asymmetry Dndand result in significant modification of xCo/xFeratio. By adopt- ing the values listed in Table 2, xCo/xFe was approximated as 1.61 2.1d. If there exists, for example, a charge transfer of about 0.1 electron [23], xCo/xFe could be modified as 1.40 which is closer to our experimental result.
It is noted that the averaged d-band asymmetry Dnd considered to evaluate dc should be traced back to the effect of local behavior of d-electrons in each element of alloy. Nevertheless, the consid- eration of charge transfer in Eq. (6) reflects the itinerant behavior of d-electrons just like the over- all d-band filling effect in alloy films. In addition, there could be no universal behavior for the dcvar- iation on d-band filling for overall alloy composi- tions since there could be more complicated evolution including not only electronic but also structural variations with x. Furthermore, the physical origin of the magnetic anisotropy should be the spin–orbit coupling in the materials. In the non-relativistic limit, the spin–orbit coupling is proportional to the spin moment S and orbital moment L, with some spin–orbit coefficient which is structural dependent. If the structures are kept invariant, the orbital moment as well as spin–orbit coefficient should be also unchange. Therefore, the evolution of magnetic anisotropy could be con- ducted in a good approximation with the magnetic moment under this situation, which is described by Dndin our analysis. This could be hold, in partic- ular for the very low concentration x in our exper- iments. In stead of dealing with the anisotropy directly, the band filling asymmetry, Dndwas eval- uated in our analysis.
5. Summary
As well known, the magnetic anisotropy is really difficult to quantitatively study for both theoreti- cally and experimentally approach due to its several order of magnitude less than magnetic moment.
However, by observing the evolution of the critical
Table 2
3d-Band filling numbers (nd) and densities of states at Fermi level [Nd(EF)] for transition metal Fe, Co, and Ni. The ndÕs as well as Nd(EF)Õs of iron and cobalt were evaluated by modifying the spin-dependent density of states of fcc nickel[24]with the spin splitting proportional to magnetic moment in accordance with the Stoner theory[23], as illustrated inFig. 2
Majority (") Minority (#) Asymmetry (" #)
nd Nd(EF) nd Nd(EF) Dnd DNd(EF)
Fe 4.614 1.020 2.109 1.290 2.505 0.270
Co 4.756 0.131 2.951 1.110 1.805 0.979
Ni 4.756 0.131 4.105 1.977 0.651 1.846
thickness for spin-reorientation transition, it is pos- sible to analyze the evolution of magnetic aniso- tropy quantitatively. Also, by means of the successfully theoretical approach[7], the rigid band approximation could be checked in comparison with the experimental data. The spin-reorientation transition for ultrathin films FexNi1x/Cu(1 0 0) was investigated to study how the magnetic behav- iors are modified by the alloy composition. The composition-driven spin-reorientation transitions for both FexNi1x/Cu(1 0 0) and CoxNi1x/ Cu(1 0 0) are shown to be attributed to the effect of alloy concentration on the magnetostriction coefficient and, in turn, on the magnetoelastic anisotropy of the Ni/Cu(1 0 0)-dominant films.
Based on the experimental results, the asymmetry of the 3d electron numbers between the majority and minority bands was also successfully applied to evaluate the contribution of iron on the critical thickness of spin-reorientation transition in the FexNi1x/Cu(1 0 0) films as compared with that of cobalt in the CoxNi1x/Cu(1 0 0) films. It reveals that the band asymmetry is the key factor to affect the magnetic anisotropies of the films. Addition- ally, a small charge transfer between the magnetic impurities and host element Ni was also taken into consideration as the further correction to evaluate the contribution of different impurities on the criti- cal thickness of spin-reorientation transition in Ni- like films. These evaluations might help us to clarify the interplay between local and itinerant behaviors of d-electrons in alloy films under ultrathin limit.
Acknowledgment
The authors thank Prof. D.-S. Wang, Prof.
G.Y. Guo and Dr. H.T. Tseng for helpful discus- sions. This research was supported by the grant from the National Science Council of Taiwan through the contract No. NSC-91-2112-M-002- 016, MOEA Program (92-EC-17-A-08-S1-0006) and by MOE Program for Promoting Academic Excellence of Universities.
References
[1] G.H.O. Daalderop, P.J. Kelly, M.F.H. Schuurmans, Phys.
Rev. B 41 (1990) 11919.
[2] D.-S. Wang, R. Wu, A.J. Freeman, Phys. Rev. Lett. 70 (1993) 869.
[3] A. Lessard, T.H. Moos, W. Hu¨ber, Phys. Rev. B 56 (1997) 2594.
[4] J. Zabloudil, L. Szunyogh, U. Pustogowa, C. Uiberacker, P. Weinberger, Phys. Rev. B 58 (1998) 6316.
[5] E.A. Smirnova, I.A. Abrikosov, B. Johansson, Y.K.
Vekilov, A.N. Baranov, V.S. Stepanyuk, W. Hergert, P.H. Dederichs, Phys. Rev. B 59 (1999) 14417.
[6] P. James, O. Eriksson, B. Johansson, I.A. Abrikosov, Phys. Rev. B 59 (1999) 419.
[7] P. James, O. Eriksson, O. Hjortstam, B. Johansson, L. Nordstro¨m, Appl. Phys. Lett. 76 (2000) 915.
[8] K.N. Altmann, N. Gilman, J. Hayoz, R.F. Willis, F.J.
Himpsel, Phys. Rev. Lett. 87 (2001) 137201.
[9] C.C. Kuo, S.F. Chuang, W. Pan, W.C. Lin, M.-T. Lin, J. Appl. Phys. 91 (2002) 7185.
[10] M.-T. Lin, W.C. Lin, C.C. Kuo, C.L. Chiu, Phys. Rev. B 62 (2000) 14268.
[11] W.C. Lin, C.C. Kuo, C.L. Chiu, M.-T. Lin, Surf. Sci. 478 (2001) 9.
[12] W.C. Lin, C.C. Kuo, C.L. Chiu, M.-T. Lin, J. Appl. Phys.
89 (2001) 7139.
[13] J.A. Stroscio, D.T. Pierce, R.A. Dragoset, Phys. Rev. Lett.
70 (1993) 3615.
[14] C.C. Kuo, W.C. Lin, C.L. Chiu, H.L. Huang, M.-T. Lin, J. Appl. Phys. 89 (2001) 7153.
[15] M. Zharnikov, A. Dittschar, W. Kuch, C.M. Schneider, J. Kirschner, Phys. Rev. Lett. 76 (1996) 4620.
[16] M.-T. Lin, J. Shen, W. Kuch, H. Jenniches, M. Klaua, C.M. Schneider, J. Kirschner, Phys. Rev. B 55 (1997) 5886.
[17] M.-T. Lin, J. Shen, W. Kuch, H. Jenniches, M. Klaua, C.M. Schneider, J. Kirschner, Surf. Sci. 410 (1998) 290.
[18] C.C. Kuo, C.L. Chiu, W.C. Lin, M.-T. Lin, Surf. Sci. 520 (2002) 121.
[19] W. Platow, M. Farle, K. Baberschke, Europhys. Lett. 43 (1998) 713.
[20] J.P. Pierce, M.A. Torija, J. Shen, E.W. Plummer, Phys.
Rev. B 64 (2001) 224409.
[21] B. Schulz, K. Baberschke, Phys. Rev. B 50 (1994) 13467.
[22] R. Thamankar, A. Ostroukhova, F.O. Schumann, Phys.
Rev. B 66 (2002) 134414.
[23] R. Richter, H. Eschrig, J. Phys. F18 (1988) 1813.
[24] D.A. Papaconstantopoulos, Handbook of the Bandstruc- ture of Elemental Solids, Plenum Press, New York, 1986.
[25] R.M. Bozorth, Ferromagnetism, IEEE Press, New York, 1993.
[26] D.E. Fowler, J.V. Barth, Phys. Rev. B 53 (1996) 5563.
