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Au multilayers
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m ELSEVIER
Journal
of Magnetism
and Magnetic
Materials
130 (1994) 442-450
A
journal of magnetism and - magnetic I materials
I
Optical and magneto-optical properties of MBE grown Co/Au multilayers R. Atkinson a,*, W.R. Hendren a, I.W. Salter a, M.J. Walker b ’ Department of Pure and Applied Physics, The QueenS University of Belfast, Belfast, BT7 INN, UK b Department of Physics, University of Leeds, Leeds, LS2 9JT, UK (Received
28 April 1993)
Abstract The optical and magneto-optical properties of Co/Au multilayers, grown by molecular beam epitaxy (MBE), have been examined in the wavelength range 300 to 900 nm using ellipsometry and normal incidence Kerr polarimetry. The dispersion of fundamental optical and magneto-optical constants and the complex Kerr rotation are discussed in terms of the interaction of electromagnetic radiation with a multilayered structure. This is done on the basis of a single equivalent layer approach for dealing with multilayered media using values for the optical constants of cobalt and gold measured on single films of these materials grown by MBE. It is suggested that a restriction of the mean free path of the conduction electrons in the gold layers, of the order of the individual sub-layer thickness, accounts for some aspects of the observed optical spectra.
1. Introduction
Thin film multilayered structures have, for many years, been of considerable importance to the optics industry; mainly because of the wide variety of device properties which can be designed and fabricated [l]. The success of this field of study has relied upon the application of Maxwell’s equations to the propagation of electromagnetic radiation through planar structured media, where the medium properties are usually assumed to be linear homogeneous and independent of layer thickness and the presence of interfaces between two different media.
* Corresponding
author.
0304-8853/94/$07.00 0 1994 Elsevier SSDI 0304-8853(93)E0555-Q
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More recently, this technology has been pushed to its practical and theoretical limits by the increasing interest in multilayered media having sub-layer dimensions which are only a few atomic monolayers thick. A particularly good example of this lies with the development of soft X-ray mirrors [2]. As layer thicknesses decrease to the point, where the composite may be referred to as a superlattice new and useful properties become apparent. In the area of magneto-optic recording the fabrication of new materials such as Co/Pt with desirable magnetic and magneto-optical properties has added considerable impetus to the search for the ideal recording medium. In such situations, however, it is not immediately obvious how such media may be macroscopically characterised nor if their macroscopic optical and magneto-optic properties can be deduced
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on the basis of bulk or thick film optical data. Work in this area has already been carried out recently for iron-noble metal (Ag) multilayers with calculations being based on published optical data for bulk iron and silver [3]. In this paper we report the results of an ellipsometric and Kerr polarimetric study of the optical and magneto-optical properties of Co/Au multilayers grown by molecular beam epitaxy. The results are interpreted on the basis of a single equivalent layer approach for dealing with superlattice media, where the elements of the permittivity tensor of the composite medium are simply related to those of the individual sub-layer media [4,5]. Calculations are based upon published data for the optical and magneto-optical constants of Co and Au and also on data determined from measurements on single layers of Co and Au grown by MBE. It is suggested that a modification of the optical properties of the gold layers, through a restriction of the mean free path of conduction electrons of the order of the gold layer thickness may account for some aspects of the observed optical spectra.
2. Experimental Three samples were grown in a VG 80M MBE facility [6] having a base pressure of 3 x lo-l1 mbar. The substrate medium consisted of a 50 nm buffer layer of germanium, grown at a rate of 0.016 rim/s on top of a clean GaAs (110) substrate held at a temperature of 500°C. Prior to deposition of the multilayer system the substrate temperature was reduced to 100°C and an epitaxial layer of bee Co (110) deposited at 0.02 rim/s from an electron beam hearth to a total thickness of 1.5 nm. To ensure a surface of high equality to act as a base for the superlattice, a 1 nm thick film of Au (111) was deposited from a Knusden source at a rate of 0.005 rim/s with the substrate temperature of 100°C. Subsequent multiple layers of hcp cobalt (0001) and gold were then deposited sequentially at the above rates whilst the substrate was maintained at a temperature of 100°C. To reduce the effects of oxidation
/S.E.L-]
1-1 s-100 nm
+
NeQe Buffer
system
GaAs (110)
(a)
(b)
Fig. 1. Schematic diagram of the structure of the multilayer samples (a) and the single layer equivalent (b).
of the system the final layer was always gold. The Co/Au sub-layer thickness ratio was constant at approximately 3:2 with the Co thickness ranging from 0.8 to 3 nm and the corresponding number of bilayers varying respectively from 80 to 20. Consequently, in all cases the total thickness (= 100 nm> of the superlattice was well in excess of the optical skin depth over the spectral range of interest. The complete structure of a typical sample is illustrated Fig. l(a). Fig. 2 shows the low and high angle X-ray diffraction spectrum for a Co/Au multilayer with d, = 1.5 nm and d,, = 1.0 nm. A total of three low angle peaks are observed corresponding to the n = 1, 2 and 3 diffracted orders for a bilayer
10’
1
2
10
3
11
12
”
F
.L b.00
0.10
0.20
0.30
0.40
0.50
Sin(B)
Fig. 2. X-ray diffraction spectrum of a Co/Au (1.5/1.0 nm) multilayer showing the Bragg reflection positions related to the multilayer periodicity (- - - - - -1 and the positions where the main reflections from epitaxially grown bulk Co and Au would occur ( -_).
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periodic&y of 2.632 k 0.006 nm. At higher angles, and in the vicinity of the usual diffraction positions corresponding to the epitaxial Co and Au lattice spacings, higher order diffraction peaks are also observed. It should be noted that we do not associate the major peak with any d-spacing corresponding to Co or Au; nor do we refer to any subsidiary peaks as satellite peaks. In fact all of these large angle peaks are simply higher diffraction orders (in this case n = 10, 11 and 12) corresponding to the periodicity of the multilayer. To demonstrate this we plot the diffracted intensity against sin 19,rather than 28, and mark the positions of the peaks which would correspond to the satisfaction of the Bragg equation (2d sin 0 = nh) with lattice spacing equal to the periodicity of the multilayer. The exceptional peak in Fig. 2 is, of course, that labelled as being due to the massive underlying substrate of GaAs.
a Normalized Response
M.O.
/i’ f
CoAu
O.&O.65
nm
b Normalised
M.O.
3. Optical and magneto-optical characterisation Spectroscopic ellipsometry, carried out at an angle of incidence of 70”, was used to determine the complex refractive index N (= n + ik) over the spectral range 300 to 900 nm. In all cases the films were much thicker than the optical skin depth so that complications arising from the details of the underlying substrate and buffer layer system were unimportant. In addition, the sublayer thicknesses and optical parameters were also assumed to be such that the superlattice, as a whole, may be regarded as a homogeneous isotropic system which can be described in terms of a single equivalent layer @EL) as illustrated in Fig. l(b). This point is elaborated upon in more detail in a previous paper [4]. The magneto-optic Kerr rotation and ellipticity were measured at normal incidence by means of a rotating analyser polarimeter. Again the spectral range was 300 to 900 nm. Although the hysteresis loops of the Co/Au samples were not square, as seen in Fig. 3, the magnetisation was relatively easily saturated in a direction perpendicular to the film plane. In the worst case this required a field of approximately 1.2 T.
Applied
Field
(T)
CoAu
1.5:l.O
nm
CoAu
3.2:2.6
nm
Fig. 3. Polar Kerr hysteresis loops of three samples of Co/Au multilayers. (Sample 1, 0.8/0.65; Sample 2, 1.5,‘l.O; Sample 3, 3.2/2.6 nm).
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0.0
“““““““““““““‘~“““ii”““““““’ 400 500
300
Wavelength
Fig. 4. Optical cobalt (0001).
constants
600
700
of Magnetism and Magnetic Materials 130 (1994) 442-450
800
900
(nm)
of MBE grown epitaxial
films of hcp
By combining the ellipsometrically determined values n and k with the Kerr rotation 8, and Kerr elliptic& Ed the complex magneto-optic Voigt parameter Q was determined using the well known relationship [71. Q = i(l -N2)(8,
+ ie,)/N
(1)
for the normal incidence Kerr effect from a boundary between air and a semi-infinite magnetic medium. Eq. (1) is valid when 113,+ ie, 1-x 1. 3.1. Optical constants of cobalt and gold In order to carry out a thorough study of the Co/Au system, ellipsometric measurements were carried out on opaque samples of both cobalt and gold films, also grown, as described earlier, by the MBE method. In the case of gold, the values of n and k were virtually indistinguishable from those determined by Johnston and Christy [Sl and others [9]. These are so well documented and regarded as reliable that we do not reproduce the results here. In the case of the hcp cobalt (0001) film however, the values of n and k were noticeably different from those found in the literature [lo]. A comparison is shown in Fig. 4 were it will be seen that, although the dispersion is similar, there are systematic differences in the magnitudes of both parameters. These differences may be due to the epitaxially grown nature of the hcp cobalt
445
(0001) or may reflect the effects of oxidation of the cobalt surface. However, since the films were measured soon after their removal from the MBE facility it is assumed that these constant are, at least, closely related to those of the cobalt sublayers of the MBE grown Co/Au multilayers. This assumption is discussed in a little more detail later. It is worth noting that the optical constants of rf sputtered polycrystalline films of cobalt measured and prepared in these laboratories were in very close agreement with those reported by Johnston and Christy [lo]. Unfortunately, the magneto-optic parameter of the MBE grown cobalt layers could not easily be determined because of difficulties of saturating the magnetisation of the film perpendicular to the substrate. Consequently, Q-values for cobalt were deduced from the recent measurements of the complex polar Kerr rotation reported by Zeper [ll]. 3.2. Optical constants of Co /Au In Fig. .%a) and (b) we present the dispersion of the ellipsometrically determined complex refractive index of the Co/Au samples. In addition we also present the values of n and k calculated on the basis of the SEL approach [4], where the optical constants of the equivalent layer N, are related to those of the sub-layer components by the expression: N:d, = N:,&,
+ &&Au,
(2)
where d,=d,,+d,,.
(3)
The theoretical SEL curves shown on Fig. 5 were obtained using the thick film values of the optical constants of MBE grown layers. Moreover, because the sub-layer thickness ratio for one sample 61) was slightly different from the other two, we include two corresponding theoretical curves. However, this has little bearing on the general conclusions which may be drawn from the results. First, it will be noticed that the general shape of the dispersion curves show features resembling
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those predicted by the simple SEL model. A point of inflection for n at about A = 450 nm is clearly seen in all three samples and also in the theoretical curves. This is related to the rapid variation of the optical parameters of the gold layer at the absorption edge which occurs at about this waveIength. The variation in k is rather less dramatic and shows a monotonic increase with wavelength in all cases. The most unsatisfactory feature of these curves is the poor agreement between the measured n values at long wavelengths compared with the SEL model. It is not unreasonable that such disagreements may occur since the assumption that the optical behaviour of the ultra-thin sub-layer materials is the same as that of thick layers is expected to become inappropriate as the sub-layers become very thin. Indeed it is interesting to note that for the thickest sub-layers (3.0/1.5), sample (3), the agreement between the measured IZ and k and the SEL is rather good in comparison to the two other samples. In addition, a small point of inflection seen in the theoretical SEL curve for k (at A w 500) is quite noticeable in the measured values. 3.2.1. Modified gold constants Bearing in mind the quite severe assumptions which have been made regarding the applicability of the fundamental constants of gold and cobalt to the sublayers, the discrepancies between the measured and computed optical parameters of
the Co/Au multilayers are not unreasonable. Nevertheless, it is fruitful to speculate upon the causes of the remaining discrepancies and attempt to reduce them. In the first instance, it is clear that one approach to this problem would be to determine, by direct measurement, the optical constants of the component materials in their ultra-thin film form. This is not easy, and the result may be a function of many factors, including the optical environment in which the sublayer finds itself. Work in this area has already been attempted for certain materials, in relation to the growth of materials used in X-ray multiIayer mirror systems [12]. It is clear from Fig. 5(a) that the major area of disagreement relates to the n values at wavelengths above 600 nm. The depressed values of n for the SEL, compared to the larger measured values, can be directly related to the very low values of n (< 0.2) which occur for gold in this spectral region. Consequently, we felt it appropriate, in the first instance, to examine the possibility of modifying the optical constants of the gold sub-layers in a way which would reflect their very thin nature. It is known that the dependence of the optical constants of metallic particles on their size is attributable to the restriction of the motion of free electrons in the medium. This is most readily visualised in terms of the classical Drude model of a free electron gas. Lissberger and Nelson [13] treated gold particles embedded in a MgF, ma-
Sample
1.8
n
Exp
S.E.L.
4.0 k
1.6
3.5 3.0
1.4 2.5 1.2
1.0
2.0
'-,~',,,,',,,~',,~~'i,,,,'111'11111“~114'1~11lllllllllll 300 400 500 600 700 800
Wavelength
Fig. 5. Ellipsometrically
1.5 900
300
“““““““““““““““““““‘U”“““““l”“‘I 400
determined
500
Wavelength
(nm)
optical
constants
of Co/Au
multilayers
and comparison
600
700
(nm)
with SEL theory.
800
900
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447
of Magnetism and Magnetic Materials 130 (1994) 442-450
1.6
1.5
1.4 3.5 "
k
1.3
3.0 1.2 2.5 1.1
1.0
t 300
400
500
600
Wavelength
700
600
900
(nm)
300
400
500
600
Wavelength
700
800
900
(nm)
Fig. 6. Measured optical constants of a Co/Au (3.2/2.6 nm) multilayer compared with SEL theory using modified optical constants of Au.
trix in this manner and obtained the following expression for the modified dielectric constant (en) of the gold constituent; namely:
ln=e,+
ig( L - R)~2,f (Ro’ + Xwg )( w + ig) ’
(4)
where E, is the thick film dielectric constant, o is the angular frequency of the radiation field, g (= 3.18 X 1013 s-l> is the damping parameter in the thick film or bulk material, wP (= 1.35 X 1017 s-l> is the free electron plasma frequency and f (= 0.8) is the fraction of free electrons that is effective [13]. L (= 42.5 nm) is the effective mean free path (mfp) of electrons in the bulk material and R is the restricted mfp (R I L),which in Lissberger’s [13] case was equated with particle size. For the multilayer system, we choose to equate the restricted mfp with the dimension of the gold sub-layer thickness. Thus, we ignore the effects of possible dimensionally induced optical anisotropy resulting from the fact that a thin planar film does not have spherical symmetry. With this single and very simple idea the optical properties of the gold layer were modified through the use of Eq. (4). The complex refractive index of the gold (= 6) was determined with a value of restricted mfp equal to the corresponding gold sub-layer thickness (d, = 2.6 nm) and then the effective SEL parameters were recalculated using Eqs. (2) and (3).
The effect which this has on the computed values of the optical constants for the Co/Au multilayer is illustrated in Fig. 6(a) and (b) for sample (3). First, it is clear that the agreement is much improved. The effect of restricting L to 2.6 nm has generally shifted the SEL IZ curve to higher values particularly at the longer wavelengths. In addition, this restriction has had little effect on the calculated k-values. As the mfp is restricted even more, to correspond to samples (1) and (2) the feature of increasing IZ, particularly at long wavelengths, continues and better agreement is observed between measured and computed constants of the Co/Au multilayers. However, it should be noted that the agreement is not as good as for sample (3) and this may be for understandable reasons related to the fact that modifications to the optical properties of the cobalt layers may also become necessary. 3.3. Magneto-optical properties The Kerr rotation and ellipticity spectra measured for the three samples are illustrated in Fig. 7(a) and (b) respectively. Also included in these figures are the theoretical predictions based on the SEL approach employing thick film values of the optical and magneto-optical constants of gold and cobalt referred to earlier. It should be noted that the sign convention for magneto-optic mea-
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448
-6
Sample
Exp
S.E.L.
A0bA.A ---~ 00000 00000 -
-8
0.8/0.65 1.5/1.0 3.2/2X
of Magnetism and Magnetic Materials I30 (1994) 442-450
(4
nm nm "m
.s-IO A r-12 p g-,4 DC
500
600
Wavelength
700
600
-10
900
L----A,"""'--' 300 400
(nm)
d"""""_ 600
500
Wavelength
700
800
900
(nm)
Fig. 7. Kerr rotation and ellipticity spectra of Co/Au multilayers and comparison with SEL theory.
surements and calculations is taken to be that recommended in ref. (14). The effective magneto-optic parameter Q, for the SEL may be determined using the expression derived elsewhere [4], namely:
N,2Q,d, = N&Qcodcw
(5)
where QCO is the Voigt parameter for cobalt and it is assumed that the gold films do not contribute to the magneto-optic activity of the system. In broad terms the dispersion of the complex Kerr rotation is similar to that predicted by SEL theory, particularly in the case of the Kerr ellipticity. The signs and magnitudes of the Kerr
rotation and ellipticity are in reasonable agreement with calculations with the exception of sample (1) which has a slightly reduced Kerr rotation and may be attributable to an increased possibility of the inapplicability of the thick film constants. The SEL theory indicates a negative peak in the Kerr rotation at a wavelength about 520 nm whereas the corresponding peak in the measurements is shifted to increasingly shorter wavelengths as the sub-layer thicknesses decrease. Again, sample (3), having the thickest sub-layers, is closest to the SEL calculation. The shape of the Kerr rotation curves are also different; with
-8
12 Exp -- - - S.E.C. R=2.6
(ai
00000
nm
10
00000
----
8 z
e
Ex S. .I..R=2.6
(b)
nm
_,---_,,'
6
L4 c
a. .$
z-14
z
z n t
2 0
,a w
-2
L
-4
k Y
-6
-16
s -18
-8 -2o300
400
500
Wavelength
600
700
(nm)
800
900
-10
‘I 100
400
500
Wavelength
600
700
(nm)
Fig. 8. Kerr rotation and ellipticity of Co/Au (1.5/1.0 nm> multilayer compared with SEL theory using modified optical constants of Au.
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the SEL theory predicting a sharper peak than the measured ones which, in addition to occurring at shorter wavelengths, are broader. It is worth noting that measured Kerr rotation curves very similar in shape and peak position to those predicted by the SEL theory have been reported by the Katayama [HI for sputtered Co/Au multilayers. Consequently the broader peaks occurring at shorter wavelengths may be associated with the magneto-optical properties of the epitaxial hcp Co (0001) layers being different from that deduced from Zeper’s original measurements [ 111. For completeness we show in Fig. 8(a) and (b), the measured Kerr rotation and ellipticity for sample 3 in comparison with the SEL calculations taking into consideration the use of the optical constants of gold modified by restriction of the mfp as indicated earlier. One can see that whilst this produces a slight improvement in the agreement for the Kerr ellipticity, the Kerr rotation is not significantly better. Finally, in Fig. 9(a) and (b) we present the complex measured magneto-optic Voigt parameter and for comparison the theoretical predictions based on SEL theory. Whilst the general trends of the measured and theoretical constants are similar it is clear that the detailed wavelength dependent structure leaves a good deal to be desired. In one sense this indicates the limitations of SEL and the dangers of simply comparing measured and theoretical Kerr rotations as a
-8 r
Sample
’ >oo
Exp
400
S.E.L.
means of testing particular theoretical models of the SEL type. It is clear that there is considerable work to be done to fully understand the fundamental optical behaviour of multilayer systems with ultra-thin constituent layers.
4. Conclusions Epitaxial films of Co/Au multilayers have been grown successfully by molecular beam epitaxy on GaAs substrates using Ge as the principal buffer layer. Subsequent buffer layers of bee Co (110) [1..5 nm] and Au (111) [LO nm] were found necessary to ensure a surface of high quality for the deposition of the main multilayer structure. The optical and magneto-optical constants of the multilayer material have been determined by spectroscopic ellipsometry and normal incidence. Kerr polarimetry and the results compared with a single equivalent layer analysis based upon the use of the optical and magneto-optical constants corresponding to the pure materials, Co and Au, in their thick film form. Results indicate that whilst agreement between theory and experiment are fair it can be significantly improved by modifying the optical constants of the Au layer through a restriction of the mean free path of the conduction electrons in the gold layers. This restriction is of the order of the Au sub-layer thickness.
(al
500
600
Wavelength
Fig. 9. Real and imaginary
449
of Magnetism and Magnetic Materials 130 (1994) 442-450
700
800
900
300
400
parts of the magneto-optic
500
Wavelength
(nm)
Voigt parameter
Q of Co/Au
multilayers
600
700
800
(nm)
compared
with SEL theory.
900
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R. Atkinson et al. /Journal
of Magnetism and Magnetic Materials 130 (1994) 442-450
5. Acknowledgements
The authors are grateful to Prof. D. Greig and those at Leeds University who kindly prepared the Co/Au samples for this work.
6. References [ll H.A. Macleod, Thin Film Optical Filters, (Adam Hilger, Bristol, 1986). [21M. Yamamoto and T. Namioka, Appl. Optics 31 (1992) 1622. [31 R. Krishnan, T. Sikora and S. Visnovsky, J. Magn. Magn. Mater. 118 (1993) 52. [41 R. Atkinson, J. Magn. Magn. Mater. 95 (1991) 61. [51 R. Atkinson, J. Magn. Magn. Mater. 95 (1991) 69.
[6] D. Greig, M.J. Hall, C. Hammond, B.J. Hickey, H.P. Ho, M.A. Howson, M.J. Walker, N. Wiser and D.G. Wright, J. Magn. Magn. Mater. 110 (1992) L239. Magn. Magn. Mater. 115 (1992) 353. I71 R. Atkinson,J. I8j P.B. Johnson and R.W. Christy, Phys. Rev. B6 (1972) 4370. I.W. Salter, M. Fitzpatrick and P.L. [91 P.H. Lissberger, Taylor, J. Phys. E 10 (1977) 635. [lOI P.B. Johnson and R.W. Christy, Phys. Rev. B9 (1974) 5056. P.F. Garcia and R.R. [Ill W.B. Zeper, F.J.A.M. Greidances, Fincher, J. Appl. Phys. 65 (1989) 4971. and T. Namioka, Appl. Optics 31 (1992) I121 M. Yamamoto 1612. and R.G. Nelson, Thin Solid Films 21 1131 P.H. Lissberger (1974) 159. Appl. Optics 31 (1992) [141 R. Atkinson and P.H. Lissberger, 6076. H. Awano and Y. Nishihara, J. Phys. Sot. [151 T. Katayama, Jpn. 55 (1986) 2539.
4 111
m ELSEVIER
Journal
of Magnetism
and Magnetic
Materials
130 (1994) 442-450
A
journal of magnetism and - magnetic I materials
I
Optical and magneto-optical properties of MBE grown Co/Au multilayers R. Atkinson a,*, W.R. Hendren a, I.W. Salter a, M.J. Walker b ’ Department of Pure and Applied Physics, The QueenS University of Belfast, Belfast, BT7 INN, UK b Department of Physics, University of Leeds, Leeds, LS2 9JT, UK (Received
28 April 1993)
Abstract The optical and magneto-optical properties of Co/Au multilayers, grown by molecular beam epitaxy (MBE), have been examined in the wavelength range 300 to 900 nm using ellipsometry and normal incidence Kerr polarimetry. The dispersion of fundamental optical and magneto-optical constants and the complex Kerr rotation are discussed in terms of the interaction of electromagnetic radiation with a multilayered structure. This is done on the basis of a single equivalent layer approach for dealing with multilayered media using values for the optical constants of cobalt and gold measured on single films of these materials grown by MBE. It is suggested that a restriction of the mean free path of the conduction electrons in the gold layers, of the order of the individual sub-layer thickness, accounts for some aspects of the observed optical spectra.
1. Introduction
Thin film multilayered structures have, for many years, been of considerable importance to the optics industry; mainly because of the wide variety of device properties which can be designed and fabricated [l]. The success of this field of study has relied upon the application of Maxwell’s equations to the propagation of electromagnetic radiation through planar structured media, where the medium properties are usually assumed to be linear homogeneous and independent of layer thickness and the presence of interfaces between two different media.
* Corresponding
author.
0304-8853/94/$07.00 0 1994 Elsevier SSDI 0304-8853(93)E0555-Q
Science
More recently, this technology has been pushed to its practical and theoretical limits by the increasing interest in multilayered media having sub-layer dimensions which are only a few atomic monolayers thick. A particularly good example of this lies with the development of soft X-ray mirrors [2]. As layer thicknesses decrease to the point, where the composite may be referred to as a superlattice new and useful properties become apparent. In the area of magneto-optic recording the fabrication of new materials such as Co/Pt with desirable magnetic and magneto-optical properties has added considerable impetus to the search for the ideal recording medium. In such situations, however, it is not immediately obvious how such media may be macroscopically characterised nor if their macroscopic optical and magneto-optic properties can be deduced
B.V. All rights reserved
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of Magnetism and Magnetic Materials 130 (199-f) 442-450
on the basis of bulk or thick film optical data. Work in this area has already been carried out recently for iron-noble metal (Ag) multilayers with calculations being based on published optical data for bulk iron and silver [3]. In this paper we report the results of an ellipsometric and Kerr polarimetric study of the optical and magneto-optical properties of Co/Au multilayers grown by molecular beam epitaxy. The results are interpreted on the basis of a single equivalent layer approach for dealing with superlattice media, where the elements of the permittivity tensor of the composite medium are simply related to those of the individual sub-layer media [4,5]. Calculations are based upon published data for the optical and magneto-optical constants of Co and Au and also on data determined from measurements on single layers of Co and Au grown by MBE. It is suggested that a modification of the optical properties of the gold layers, through a restriction of the mean free path of conduction electrons of the order of the gold layer thickness may account for some aspects of the observed optical spectra.
2. Experimental Three samples were grown in a VG 80M MBE facility [6] having a base pressure of 3 x lo-l1 mbar. The substrate medium consisted of a 50 nm buffer layer of germanium, grown at a rate of 0.016 rim/s on top of a clean GaAs (110) substrate held at a temperature of 500°C. Prior to deposition of the multilayer system the substrate temperature was reduced to 100°C and an epitaxial layer of bee Co (110) deposited at 0.02 rim/s from an electron beam hearth to a total thickness of 1.5 nm. To ensure a surface of high equality to act as a base for the superlattice, a 1 nm thick film of Au (111) was deposited from a Knusden source at a rate of 0.005 rim/s with the substrate temperature of 100°C. Subsequent multiple layers of hcp cobalt (0001) and gold were then deposited sequentially at the above rates whilst the substrate was maintained at a temperature of 100°C. To reduce the effects of oxidation
/S.E.L-]
1-1 s-100 nm
+
NeQe Buffer
system
GaAs (110)
(a)
(b)
Fig. 1. Schematic diagram of the structure of the multilayer samples (a) and the single layer equivalent (b).
of the system the final layer was always gold. The Co/Au sub-layer thickness ratio was constant at approximately 3:2 with the Co thickness ranging from 0.8 to 3 nm and the corresponding number of bilayers varying respectively from 80 to 20. Consequently, in all cases the total thickness (= 100 nm> of the superlattice was well in excess of the optical skin depth over the spectral range of interest. The complete structure of a typical sample is illustrated Fig. l(a). Fig. 2 shows the low and high angle X-ray diffraction spectrum for a Co/Au multilayer with d, = 1.5 nm and d,, = 1.0 nm. A total of three low angle peaks are observed corresponding to the n = 1, 2 and 3 diffracted orders for a bilayer
10’
1
2
10
3
11
12
”
F
.L b.00
0.10
0.20
0.30
0.40
0.50
Sin(B)
Fig. 2. X-ray diffraction spectrum of a Co/Au (1.5/1.0 nm) multilayer showing the Bragg reflection positions related to the multilayer periodicity (- - - - - -1 and the positions where the main reflections from epitaxially grown bulk Co and Au would occur ( -_).
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R. Atkinson et al. /Journal of Magnetism and Magnetic Materials 130 (1994) 442-450
periodic&y of 2.632 k 0.006 nm. At higher angles, and in the vicinity of the usual diffraction positions corresponding to the epitaxial Co and Au lattice spacings, higher order diffraction peaks are also observed. It should be noted that we do not associate the major peak with any d-spacing corresponding to Co or Au; nor do we refer to any subsidiary peaks as satellite peaks. In fact all of these large angle peaks are simply higher diffraction orders (in this case n = 10, 11 and 12) corresponding to the periodicity of the multilayer. To demonstrate this we plot the diffracted intensity against sin 19,rather than 28, and mark the positions of the peaks which would correspond to the satisfaction of the Bragg equation (2d sin 0 = nh) with lattice spacing equal to the periodicity of the multilayer. The exceptional peak in Fig. 2 is, of course, that labelled as being due to the massive underlying substrate of GaAs.
a Normalized Response
M.O.
/i’ f
CoAu
O.&O.65
nm
b Normalised
M.O.
3. Optical and magneto-optical characterisation Spectroscopic ellipsometry, carried out at an angle of incidence of 70”, was used to determine the complex refractive index N (= n + ik) over the spectral range 300 to 900 nm. In all cases the films were much thicker than the optical skin depth so that complications arising from the details of the underlying substrate and buffer layer system were unimportant. In addition, the sublayer thicknesses and optical parameters were also assumed to be such that the superlattice, as a whole, may be regarded as a homogeneous isotropic system which can be described in terms of a single equivalent layer @EL) as illustrated in Fig. l(b). This point is elaborated upon in more detail in a previous paper [4]. The magneto-optic Kerr rotation and ellipticity were measured at normal incidence by means of a rotating analyser polarimeter. Again the spectral range was 300 to 900 nm. Although the hysteresis loops of the Co/Au samples were not square, as seen in Fig. 3, the magnetisation was relatively easily saturated in a direction perpendicular to the film plane. In the worst case this required a field of approximately 1.2 T.
Applied
Field
(T)
CoAu
1.5:l.O
nm
CoAu
3.2:2.6
nm
Fig. 3. Polar Kerr hysteresis loops of three samples of Co/Au multilayers. (Sample 1, 0.8/0.65; Sample 2, 1.5,‘l.O; Sample 3, 3.2/2.6 nm).
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R. Atkinson et al. /Journal
0.0
“““““““““““““‘~“““ii”““““““’ 400 500
300
Wavelength
Fig. 4. Optical cobalt (0001).
constants
600
700
of Magnetism and Magnetic Materials 130 (1994) 442-450
800
900
(nm)
of MBE grown epitaxial
films of hcp
By combining the ellipsometrically determined values n and k with the Kerr rotation 8, and Kerr elliptic& Ed the complex magneto-optic Voigt parameter Q was determined using the well known relationship [71. Q = i(l -N2)(8,
+ ie,)/N
(1)
for the normal incidence Kerr effect from a boundary between air and a semi-infinite magnetic medium. Eq. (1) is valid when 113,+ ie, 1-x 1. 3.1. Optical constants of cobalt and gold In order to carry out a thorough study of the Co/Au system, ellipsometric measurements were carried out on opaque samples of both cobalt and gold films, also grown, as described earlier, by the MBE method. In the case of gold, the values of n and k were virtually indistinguishable from those determined by Johnston and Christy [Sl and others [9]. These are so well documented and regarded as reliable that we do not reproduce the results here. In the case of the hcp cobalt (0001) film however, the values of n and k were noticeably different from those found in the literature [lo]. A comparison is shown in Fig. 4 were it will be seen that, although the dispersion is similar, there are systematic differences in the magnitudes of both parameters. These differences may be due to the epitaxially grown nature of the hcp cobalt
445
(0001) or may reflect the effects of oxidation of the cobalt surface. However, since the films were measured soon after their removal from the MBE facility it is assumed that these constant are, at least, closely related to those of the cobalt sublayers of the MBE grown Co/Au multilayers. This assumption is discussed in a little more detail later. It is worth noting that the optical constants of rf sputtered polycrystalline films of cobalt measured and prepared in these laboratories were in very close agreement with those reported by Johnston and Christy [lo]. Unfortunately, the magneto-optic parameter of the MBE grown cobalt layers could not easily be determined because of difficulties of saturating the magnetisation of the film perpendicular to the substrate. Consequently, Q-values for cobalt were deduced from the recent measurements of the complex polar Kerr rotation reported by Zeper [ll]. 3.2. Optical constants of Co /Au In Fig. .%a) and (b) we present the dispersion of the ellipsometrically determined complex refractive index of the Co/Au samples. In addition we also present the values of n and k calculated on the basis of the SEL approach [4], where the optical constants of the equivalent layer N, are related to those of the sub-layer components by the expression: N:d, = N:,&,
+ &&Au,
(2)
where d,=d,,+d,,.
(3)
The theoretical SEL curves shown on Fig. 5 were obtained using the thick film values of the optical constants of MBE grown layers. Moreover, because the sub-layer thickness ratio for one sample 61) was slightly different from the other two, we include two corresponding theoretical curves. However, this has little bearing on the general conclusions which may be drawn from the results. First, it will be noticed that the general shape of the dispersion curves show features resembling
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R. Atkinson et al. /Journal
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those predicted by the simple SEL model. A point of inflection for n at about A = 450 nm is clearly seen in all three samples and also in the theoretical curves. This is related to the rapid variation of the optical parameters of the gold layer at the absorption edge which occurs at about this waveIength. The variation in k is rather less dramatic and shows a monotonic increase with wavelength in all cases. The most unsatisfactory feature of these curves is the poor agreement between the measured n values at long wavelengths compared with the SEL model. It is not unreasonable that such disagreements may occur since the assumption that the optical behaviour of the ultra-thin sub-layer materials is the same as that of thick layers is expected to become inappropriate as the sub-layers become very thin. Indeed it is interesting to note that for the thickest sub-layers (3.0/1.5), sample (3), the agreement between the measured IZ and k and the SEL is rather good in comparison to the two other samples. In addition, a small point of inflection seen in the theoretical SEL curve for k (at A w 500) is quite noticeable in the measured values. 3.2.1. Modified gold constants Bearing in mind the quite severe assumptions which have been made regarding the applicability of the fundamental constants of gold and cobalt to the sublayers, the discrepancies between the measured and computed optical parameters of
the Co/Au multilayers are not unreasonable. Nevertheless, it is fruitful to speculate upon the causes of the remaining discrepancies and attempt to reduce them. In the first instance, it is clear that one approach to this problem would be to determine, by direct measurement, the optical constants of the component materials in their ultra-thin film form. This is not easy, and the result may be a function of many factors, including the optical environment in which the sublayer finds itself. Work in this area has already been attempted for certain materials, in relation to the growth of materials used in X-ray multiIayer mirror systems [12]. It is clear from Fig. 5(a) that the major area of disagreement relates to the n values at wavelengths above 600 nm. The depressed values of n for the SEL, compared to the larger measured values, can be directly related to the very low values of n (< 0.2) which occur for gold in this spectral region. Consequently, we felt it appropriate, in the first instance, to examine the possibility of modifying the optical constants of the gold sub-layers in a way which would reflect their very thin nature. It is known that the dependence of the optical constants of metallic particles on their size is attributable to the restriction of the motion of free electrons in the medium. This is most readily visualised in terms of the classical Drude model of a free electron gas. Lissberger and Nelson [13] treated gold particles embedded in a MgF, ma-
Sample
1.8
n
Exp
S.E.L.
4.0 k
1.6
3.5 3.0
1.4 2.5 1.2
1.0
2.0
'-,~',,,,',,,~',,~~'i,,,,'111'11111“~114'1~11lllllllllll 300 400 500 600 700 800
Wavelength
Fig. 5. Ellipsometrically
1.5 900
300
“““““““““““““““““““‘U”“““““l”“‘I 400
determined
500
Wavelength
(nm)
optical
constants
of Co/Au
multilayers
and comparison
600
700
(nm)
with SEL theory.
800
900
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447
of Magnetism and Magnetic Materials 130 (1994) 442-450
1.6
1.5
1.4 3.5 "
k
1.3
3.0 1.2 2.5 1.1
1.0
t 300
400
500
600
Wavelength
700
600
900
(nm)
300
400
500
600
Wavelength
700
800
900
(nm)
Fig. 6. Measured optical constants of a Co/Au (3.2/2.6 nm) multilayer compared with SEL theory using modified optical constants of Au.
trix in this manner and obtained the following expression for the modified dielectric constant (en) of the gold constituent; namely:
ln=e,+
ig( L - R)~2,f (Ro’ + Xwg )( w + ig) ’
(4)
where E, is the thick film dielectric constant, o is the angular frequency of the radiation field, g (= 3.18 X 1013 s-l> is the damping parameter in the thick film or bulk material, wP (= 1.35 X 1017 s-l> is the free electron plasma frequency and f (= 0.8) is the fraction of free electrons that is effective [13]. L (= 42.5 nm) is the effective mean free path (mfp) of electrons in the bulk material and R is the restricted mfp (R I L),which in Lissberger’s [13] case was equated with particle size. For the multilayer system, we choose to equate the restricted mfp with the dimension of the gold sub-layer thickness. Thus, we ignore the effects of possible dimensionally induced optical anisotropy resulting from the fact that a thin planar film does not have spherical symmetry. With this single and very simple idea the optical properties of the gold layer were modified through the use of Eq. (4). The complex refractive index of the gold (= 6) was determined with a value of restricted mfp equal to the corresponding gold sub-layer thickness (d, = 2.6 nm) and then the effective SEL parameters were recalculated using Eqs. (2) and (3).
The effect which this has on the computed values of the optical constants for the Co/Au multilayer is illustrated in Fig. 6(a) and (b) for sample (3). First, it is clear that the agreement is much improved. The effect of restricting L to 2.6 nm has generally shifted the SEL IZ curve to higher values particularly at the longer wavelengths. In addition, this restriction has had little effect on the calculated k-values. As the mfp is restricted even more, to correspond to samples (1) and (2) the feature of increasing IZ, particularly at long wavelengths, continues and better agreement is observed between measured and computed constants of the Co/Au multilayers. However, it should be noted that the agreement is not as good as for sample (3) and this may be for understandable reasons related to the fact that modifications to the optical properties of the cobalt layers may also become necessary. 3.3. Magneto-optical properties The Kerr rotation and ellipticity spectra measured for the three samples are illustrated in Fig. 7(a) and (b) respectively. Also included in these figures are the theoretical predictions based on the SEL approach employing thick film values of the optical and magneto-optical constants of gold and cobalt referred to earlier. It should be noted that the sign convention for magneto-optic mea-
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448
-6
Sample
Exp
S.E.L.
A0bA.A ---~ 00000 00000 -
-8
0.8/0.65 1.5/1.0 3.2/2X
of Magnetism and Magnetic Materials I30 (1994) 442-450
(4
nm nm "m
.s-IO A r-12 p g-,4 DC
500
600
Wavelength
700
600
-10
900
L----A,"""'--' 300 400
(nm)
d"""""_ 600
500
Wavelength
700
800
900
(nm)
Fig. 7. Kerr rotation and ellipticity spectra of Co/Au multilayers and comparison with SEL theory.
surements and calculations is taken to be that recommended in ref. (14). The effective magneto-optic parameter Q, for the SEL may be determined using the expression derived elsewhere [4], namely:
N,2Q,d, = N&Qcodcw
(5)
where QCO is the Voigt parameter for cobalt and it is assumed that the gold films do not contribute to the magneto-optic activity of the system. In broad terms the dispersion of the complex Kerr rotation is similar to that predicted by SEL theory, particularly in the case of the Kerr ellipticity. The signs and magnitudes of the Kerr
rotation and ellipticity are in reasonable agreement with calculations with the exception of sample (1) which has a slightly reduced Kerr rotation and may be attributable to an increased possibility of the inapplicability of the thick film constants. The SEL theory indicates a negative peak in the Kerr rotation at a wavelength about 520 nm whereas the corresponding peak in the measurements is shifted to increasingly shorter wavelengths as the sub-layer thicknesses decrease. Again, sample (3), having the thickest sub-layers, is closest to the SEL calculation. The shape of the Kerr rotation curves are also different; with
-8
12 Exp -- - - S.E.C. R=2.6
(ai
00000
nm
10
00000
----
8 z
e
Ex S. .I..R=2.6
(b)
nm
_,---_,,'
6
L4 c
a. .$
z-14
z
z n t
2 0
,a w
-2
L
-4
k Y
-6
-16
s -18
-8 -2o300
400
500
Wavelength
600
700
(nm)
800
900
-10
‘I 100
400
500
Wavelength
600
700
(nm)
Fig. 8. Kerr rotation and ellipticity of Co/Au (1.5/1.0 nm> multilayer compared with SEL theory using modified optical constants of Au.
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the SEL theory predicting a sharper peak than the measured ones which, in addition to occurring at shorter wavelengths, are broader. It is worth noting that measured Kerr rotation curves very similar in shape and peak position to those predicted by the SEL theory have been reported by the Katayama [HI for sputtered Co/Au multilayers. Consequently the broader peaks occurring at shorter wavelengths may be associated with the magneto-optical properties of the epitaxial hcp Co (0001) layers being different from that deduced from Zeper’s original measurements [ 111. For completeness we show in Fig. 8(a) and (b), the measured Kerr rotation and ellipticity for sample 3 in comparison with the SEL calculations taking into consideration the use of the optical constants of gold modified by restriction of the mfp as indicated earlier. One can see that whilst this produces a slight improvement in the agreement for the Kerr ellipticity, the Kerr rotation is not significantly better. Finally, in Fig. 9(a) and (b) we present the complex measured magneto-optic Voigt parameter and for comparison the theoretical predictions based on SEL theory. Whilst the general trends of the measured and theoretical constants are similar it is clear that the detailed wavelength dependent structure leaves a good deal to be desired. In one sense this indicates the limitations of SEL and the dangers of simply comparing measured and theoretical Kerr rotations as a
-8 r
Sample
’ >oo
Exp
400
S.E.L.
means of testing particular theoretical models of the SEL type. It is clear that there is considerable work to be done to fully understand the fundamental optical behaviour of multilayer systems with ultra-thin constituent layers.
4. Conclusions Epitaxial films of Co/Au multilayers have been grown successfully by molecular beam epitaxy on GaAs substrates using Ge as the principal buffer layer. Subsequent buffer layers of bee Co (110) [1..5 nm] and Au (111) [LO nm] were found necessary to ensure a surface of high quality for the deposition of the main multilayer structure. The optical and magneto-optical constants of the multilayer material have been determined by spectroscopic ellipsometry and normal incidence. Kerr polarimetry and the results compared with a single equivalent layer analysis based upon the use of the optical and magneto-optical constants corresponding to the pure materials, Co and Au, in their thick film form. Results indicate that whilst agreement between theory and experiment are fair it can be significantly improved by modifying the optical constants of the Au layer through a restriction of the mean free path of the conduction electrons in the gold layers. This restriction is of the order of the Au sub-layer thickness.
(al
500
600
Wavelength
Fig. 9. Real and imaginary
449
of Magnetism and Magnetic Materials 130 (1994) 442-450
700
800
900
300
400
parts of the magneto-optic
500
Wavelength
(nm)
Voigt parameter
Q of Co/Au
multilayers
600
700
800
(nm)
compared
with SEL theory.
900
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R. Atkinson et al. /Journal
of Magnetism and Magnetic Materials 130 (1994) 442-450
5. Acknowledgements
The authors are grateful to Prof. D. Greig and those at Leeds University who kindly prepared the Co/Au samples for this work.
6. References [ll H.A. Macleod, Thin Film Optical Filters, (Adam Hilger, Bristol, 1986). [21M. Yamamoto and T. Namioka, Appl. Optics 31 (1992) 1622. [31 R. Krishnan, T. Sikora and S. Visnovsky, J. Magn. Magn. Mater. 118 (1993) 52. [41 R. Atkinson, J. Magn. Magn. Mater. 95 (1991) 61. [51 R. Atkinson, J. Magn. Magn. Mater. 95 (1991) 69.
[6] D. Greig, M.J. Hall, C. Hammond, B.J. Hickey, H.P. Ho, M.A. Howson, M.J. Walker, N. Wiser and D.G. Wright, J. Magn. Magn. Mater. 110 (1992) L239. Magn. Magn. Mater. 115 (1992) 353. I71 R. Atkinson,J. I8j P.B. Johnson and R.W. Christy, Phys. Rev. B6 (1972) 4370. I.W. Salter, M. Fitzpatrick and P.L. [91 P.H. Lissberger, Taylor, J. Phys. E 10 (1977) 635. [lOI P.B. Johnson and R.W. Christy, Phys. Rev. B9 (1974) 5056. P.F. Garcia and R.R. [Ill W.B. Zeper, F.J.A.M. Greidances, Fincher, J. Appl. Phys. 65 (1989) 4971. and T. Namioka, Appl. Optics 31 (1992) I121 M. Yamamoto 1612. and R.G. Nelson, Thin Solid Films 21 1131 P.H. Lissberger (1974) 159. Appl. Optics 31 (1992) [141 R. Atkinson and P.H. Lissberger, 6076. H. Awano and Y. Nishihara, J. Phys. Sot. [151 T. Katayama, Jpn. 55 (1986) 2539.