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The magneto-optical properties of thin cobalt films
Thin Solid Films, 67 (1980) L35-L40 © Elsevier Sequoia S.A., L a u s a n n e - - P r i n t e d in the Netherlands
L35
Letter
The magneto-optical properties of thin cobalt film£ R. CAREY AND B. W. J. THOMAS
Department of Applied Physics, Lanchester Polytechnic, Coventry•Vl 5FB (Gt. Britain) D. M. NEWMAN
School of Mathematics and Physics, University ofEast Anglia, Norwich NR4 7TJ (Gt. Britain) (Received November 6, 1979; accepted November 27, 1979)
Experimentally measured magneto-optical properties of magnetic materials are usually analysed using a phenomenological approach in which the permittivity is considered as a skew-symmetric tensor. Measurements of the real and imaginary parts of both the optical and the magneto-optical elements of this tensor in the region 1.0-2.5 eV are presented for a series of seven thin (108-13.4 nm) cobalt films. The prominent features of the results are remarkably consistent from film to film. 1. Introduction Experimental measurements of magneto-optical effects are analysed using a phenomenological approach by which they are related to the material parameters. The response of the magnetic medium to the exciting radiation is well described 1 for all magneto-optical effects by considering the permittivity to be a tensor whose symmetry is determined solely by the magnetization. When the magnetization lies in the z direction this tensor has the form
(s)=
'
s 0
00)(!° i0 00) =
so
+
s
s
0
so
where with fi = n - i k
e =- e 1 - - i e 2 ---- ~2
and e' = e l ' - i e 2' = Qe
= h2Q
with Q = Q 1 - i Q 2 I
h is the complex optical refractive index and Q is the complex magneto-optical parameter which is a function of the magnetization. The imaginary part e 2 (equal to 2nk) of the diagonal elements of the tensor describes ordinary optical absorption which is always positive. Likewise, under the convention adopted of multiplying the off-diagonal elements by i, the imaginary part of these elements s 2' (equal to ( n - k ) Q 2 - 2 n k Q l ) describes magneto-optical absorption. However, unlike its optical counterpart, s 2' can take either positive or negative values since its sign is directly related to the net spin polarization of the unpaired d states responsible for the spontaneous magnetization. We report the determination of the energy dependence in the range 1.0-2.5 eV
L36
LETTERS
of both the dispersive e2' parts of the magneto-optical permittivity for a series of seven thin cobalt films. Experimentally we evaluated firstly h and secondly Q. The off-diagonal permittivity was then computed by combining these intermediate parameters (e' = h2Q). 2. Experimental details The films we investigated were prepared by thermal evaporation from a resistively heated source in an ion-pumped vacuum system. The evaporant was deposited at rates between 1.0 and 4.0 A s- 1 onto carefully cleaned glass substrates held at 35-45 °C. The system pressure was maintained at around 1 x 10 -6 Torr during evaporation. Electron micrographs showed the films to be polycrystalline with a very small crystallite structure that showed little tendency to adopt a preferred orientation. The presence of both f.c.c, and h.c.p, crystal forms was indicated by the electron diffraction patterns. The thickness of each film was determined by multiple beam interferometry using a Varian A-scope and the range of thickness investigated was from 108.1 to 13.4 nm. Changes in the state of polarization which optical and magneto-optical effects introduce into beams reflected from or transmitted through optical interfaces can only be measured if they can be reduced to intensity changes. Therefore determination of the ellipticity and the rotation of the plane of polarization associated with such effects requires the inclusion of calibrated phase plates and analysers in the optical system. It is much simpler and therefore preferable both experimentally and theoretically if direct intensity variations alone can be related to the optical and magneto-optical parameters of interest. In the present work we avoided the complexities associated with polarimetry and ellipsometry. All measurements taken were of a simple relative photometric nature. The particular observables chosen for measurement were selected because the sensitivity of their relationship to the required parameters, namely h and Q, has been extensively investigated2' a. This allowed the optimization of the experimental configuration for each measurement so that high accuracy was maintained with a comparatively simple experimental system. The optical constants of the films were determined by way of a self-consistent procedure which has been reported in detail elsewhere 4. It is based on a modification ofAvery's 5 technique in which the reflectance ratio Rv/R s is measured to an accuracy of 0.5~o at two optimized angles of incidence and is combined with the independent measurement of film thickness. The magneto-optical constants of the film are evaluated from measurements of the transverse Kerr effect using p-polarized radiation. This effect is unique in that it manifests itself solely as a change in the reflectivity of the ferromagnetic surface as its magnetization if reversed from + M s to - M s along a direction perpendicular to the plane of incidence. The parameter actually measured is the fractional intensity modulation fi introduced into the reflected beam. Measurements of 6 at two optimized angles of incidence are combined with the predetermined optical constants and the measured film thickness to evaluate the real and imaginary parts of Q via a procedure described in detail by Newman 6. A check was maintained on the accuracy of the evaluation procedure by comparing the value of 6 measured at
LETTERS
L37
some third angle of incidence with its value computed using the evaluated optical and magneto-optical constants. Throughout the experimental work all photometric measurements were made using a phase-locked detection system operating at a frequency of 86 Hz; the accuracy of the magneto-optical measurements was a function of the film thickness but was typically 1 - 3 ~ for 6. 3. Results and discussion The values determined for the optical and magneto-optical permittivities of the seven films are presented in full in Tables I and II. Cobalt is known to be susceptible to oxidation and several workers have allowed for the effects of oxide layers when analysing their experimental data. It seems reasonable to assume that the effect of oxide formation on the optical and magneto-optical properties of films becomes more significant as their thickness is reduced. Consequently, since the thickness of the films under discussion varied by nearly an order of magnitude, strict quantitative agreement between films or with the results of other workers was not expected. However, when the structure in the curves depicting the variation of the optical and magneto-optical absorption as functions of incident energy is considered, the correspondence between films is remarkable. The curves shown in Fig. 1 can be considered typical of all the samples. It can be seen that the zero crossings of el' correlate very well with peaks or singularities in both the optical % and the magnetooptical %' absorption functions. There are two clear resonances at 1.1 and 1.6 eV and O4 0,4 03 Ot
°o4 -0"2
10
t5
20
25
(a)
(c) Fig. 1. (a) e2, (b) et' and (c) ~2' as functions of energy.
-03
(b)
2.495 2.263 2.053 1.908 1.754 1.649 1.548 1.467 1.307 1.181 1.078 0.991
Energy
-8.87 - 6.78 -8.74 -8.55 -8.77 -9.25 -8.54 - 10.00 - 10.02 -1 6 . 55 -15.86 - 15 . 57
11.32 9.24 ii . 26 12.63 13.74 15.42 17.63 18.52 22.46 28.84 29.12 24.45
-9.33 - 8.02 -8.21 -8.48 -9.21 -1 0. 43 -8.63 - 10.87 -1 0. 65 - 15.56 - 16.77 -16.38
~1
~1
~2
57.9nm
Film thickness 108.1 nm
VALUES O F T H E OPTICAL PERMITTIVITIES
TABLE 1
15.96 12.96 14.73 16.06 16.69 18.88 19.84 20.92 23.71 28.15 27.52 21.53
~2 -8.81 - 7.96 -8.56 -9.16 -10.62 -10.27 -10.32 -9.52 - 12.78 - 17.36 -20.46 -21.11
~1
45.7 nm
12.14 9.82 12.45 13.86 15.59 17.52 21.26 23.64 26.83 30.94 33.14 26.67
£2 -6.00 - 6.78 --7.54 -7.64 -8.40 -8.69 -8.40 -9.47 -8.78 - 10.98 - 14.55 -19.20
F'I
35.9 nm
15.75 10.72 12.08 13.46 14.56 15.88 20.36 22.58 24.66 30.16 31.45 25.86
£2 -13.46 - 11.32 -12.87 - 14.07 -15.77 -16.58 -18.58 -23.11 -24.23 -31.23 -32.71 -32.77
F'I
26.0 nm
14.13 11.40 12.39 13.81 15.70 17.50 19.23 22.16 23.98 31.61 32.00 24.52
£'2 -5.05 - 6.86 -7.35 -6.84 -6.91 -6.93 -7.76 -8.70 -7.92 - 12.69 -14.82 -19.11
F'I
22.4 nm
14.99 13.55 15.66 17.04 19.11 20.03 19.81 22.30 25.32 28.61 31.90 30.29
~2
nm
-5.86 - 6.85 -7.49 -8.02 - 8 .7 1 -10.67 -9.28 - 10.71 - 10.47 -14.65 - 1 8 .5 5 - 2 0 .6 5
£1
13.4
10.22 10.29 11.71 12.96 14.35 13.06 15.54 16.74 21.01 22.39 24.65 24.51
~2
t-'
t" t"rl
oo
2.495 2.263 2.053 1.908 1.754 1.649 1.548 1.467 1.307 1.181 1.078 0.991
Energy
-16.14 23.17 -13.17 20.47 - 19.46 32.04 - 17.25 36.88 -15.13 40.48 -13.36 48.45 -5.17 54.63 -5.60 62.77 +9.85 74.22 +11.08 1 2 7 . 5 0 +17.75 1 1 8 . 0 5 -11.74 1 0 9 . 4 6
82'
-17.63 42.17 -17.05 37.11 - 16.67 47.35 -14.16 51.57 - 14.66 58.77 -13.81 74.03 +0.66 67.68 -1.95 81.46 +15.12 85.72 +17.55 122.50 +10.42 120.68 -21.89 94.45
81'
£1'
82 ~
57.9 nm
Film thickness 108.1 nm
VALUES OF THE MAGNETO-OPTICAL PERMITrlVITIES
TABLE II
82 '
.
m
-17.81 24.22 -18.21 21.64 - 19.87 31.67 -20.86 37.49 -24.94 48.07 - 19.68 52.28 - 12.18 67.08 -8.43 78.65 +2.12 9 1 . 0 1 +5.01 1 1 7 . 4 7 -0.60 1 3 5 . 2 9 -43.56 1 1 0 . 1 0
£1'
45.7 nm
82'
-2.37 27.19 -10.71 25.06 - 11.57 3 0 . 5 5 -10.52 36.02 - 11.01 41.82 -9.07 47.70 +2.34 64.60 +7.14 77.63 +23.19 76.10 +42.89 97.28 +36.59 1 2 5 . 1 7 -26.59 1 1 2 . 9 0
81 '
35.9 nm
-34.99 -28.01 -37.06 -41.39 -45.78 -44.63 -48.86 -72.10 -54.16 -55.58 -59.61 -121.06
£1 t
26.0 nm
45.71 31.94 41.36 51.32 65.11 78.01 97.26 143.22 149.47 230.67 232.15 171.38
82 ~
82'
-I.00 27.32 -7.12 31.40 -5.12 40.80 +0.81 42.88 +6.09 50.49 +11.70 51.73 + 13.34 50.42 +19.13 58.34 + 35.29 54.34 +41.14 75.82 + 44.58 87.04 +5.80 109.93
£1'
22.4 nm
82'
14.38 16.37 19.49 21.94 25.90 27.97 30.08 34.49 37.54 42.61 55.14 59.70
£1'
-2.25 -5.31 -6.27 -5.68 -4.46 - 9.08 + 1.03 +1.57 + 14.81 +9.33 +5.79 - ! 1.08
13.4 nm
t"
t'rl
t"
L40
LETTERS
some indications, particularly from the thinner samples, of a third in the neighbourhood of 2.6 eV. The resonance at around 1.6 eV has been previously observed and interpreted by Krinchik7,a. However, his extensive work shows no evidence of the apparently stronger resonance we observed at 1.1 eV, although it is evident in the results of Afanas'yeva and Krillova9. In our analysis of the optical permittivity results4 we tentatively attributed the absorption peak at 1.1 eV to optical conduction resonance 1°. We consider it possible that as a result of the low evaporation rates we employed the films may have had a fairly rough surface structure which on partial oxidation became analogous to that of a metal-rich cermet. On this assumption reasonable success was achieved in modelling the absorption peak by using very high metal/metal oxide ratios (q ~ 0.9) in a modification of the Maxwell-Garnett theory. Lissberger and Saunders 1~ have demonstrated that the magneto-optical properties of Co-MgF cermets (albeit of low q values) can be described by combining the classical microscopic theory of Krinchik with a Maxwell-Garnetttype analysis in which the effect of particle or crystallite size on the electron mean free path is included when computing both the optical and the magneto-optical constants. In a similar fashion Carey and Thomas 12 have successfully modelled the experimental results of Gittleman et al.13 We thus felt justified in applying this model to the present magneto-optical results in the region of 1.1 eV. Unfortunately we have not as yet repeated the success achieved with the optical results: in its present form the model does not correctly describe the observed behaviour of e 1' and e2'. 4. Conclusion
In the past it has usually been necessary when evaluating theoretical magnetooptical work to use experimental values taken from different sources for the optical and magneto-optical constants. This practice is generally unsatisfactory but is particularly so when studying thin films. The extensive results which we have presented are accurate and demonstrably consistent across a wide range of film thicknesses. It is intended that they will provide a reliable data base for any subsequent theoretical studies into the magneto-optical behaviour of ferromagnetic films. I 2 3 4 5 6 7 8 9 I0 11 12 13
A.V. Sokolov, Optical Propertiesof Metals, Blackie,Glasgow, 1967, Chap. I0. R.F. MillerandA. J. Taylor, J. Phys. D, 4(1971) 1419. W. Hasan, R. B. Inwood and R. F. Miller,J. Phys. D, 8 (1975) 2090. R. Carey, D.M. NewmanandB. W.J. Thomas, ThinSolidFilms, 66(2)(1980)139. D.G. Avery, Proc. Phys. Soc., London, Sect. B, 65 (1952) 425. D. M. Newman, Magneto-optical properties of thin cobalt films, Ph.D. Thesis, Lanchester Polytechnic,Coventry, 1978. G.S. Krinchik, J. Appl. Phys., 35, (3, Part 2) (1964) 1089. G.S. Krinchik and V. A. Antemeyer, J. Appl. Phys., 39 (1968) 2. L.A. Afanas'yeva and M. M. Krillova,Fiz. Met. Metalloved.,23 (3) (1967) 472-476. J.P. MartonandJ. R. Lemon, Phys. Rev. B, 4(2)(1973)271. P.H. Lissberger and P. W. Saunders, 3rd Int. Conf. on Thin Films, Budapest, August 1974. R. Care), and B. W. J. Thomas, J. Phys. D, 8 (1975) 336. J.J. Gittleman, B. Goldstein and S. Bozowski, Phys. Rev. B, .5 (1974) 3609.
L35
Letter
The magneto-optical properties of thin cobalt film£ R. CAREY AND B. W. J. THOMAS
Department of Applied Physics, Lanchester Polytechnic, Coventry•Vl 5FB (Gt. Britain) D. M. NEWMAN
School of Mathematics and Physics, University ofEast Anglia, Norwich NR4 7TJ (Gt. Britain) (Received November 6, 1979; accepted November 27, 1979)
Experimentally measured magneto-optical properties of magnetic materials are usually analysed using a phenomenological approach in which the permittivity is considered as a skew-symmetric tensor. Measurements of the real and imaginary parts of both the optical and the magneto-optical elements of this tensor in the region 1.0-2.5 eV are presented for a series of seven thin (108-13.4 nm) cobalt films. The prominent features of the results are remarkably consistent from film to film. 1. Introduction Experimental measurements of magneto-optical effects are analysed using a phenomenological approach by which they are related to the material parameters. The response of the magnetic medium to the exciting radiation is well described 1 for all magneto-optical effects by considering the permittivity to be a tensor whose symmetry is determined solely by the magnetization. When the magnetization lies in the z direction this tensor has the form
(s)=
'
s 0
00)(!° i0 00) =
so
+
s
s
0
so
where with fi = n - i k
e =- e 1 - - i e 2 ---- ~2
and e' = e l ' - i e 2' = Qe
= h2Q
with Q = Q 1 - i Q 2 I
h is the complex optical refractive index and Q is the complex magneto-optical parameter which is a function of the magnetization. The imaginary part e 2 (equal to 2nk) of the diagonal elements of the tensor describes ordinary optical absorption which is always positive. Likewise, under the convention adopted of multiplying the off-diagonal elements by i, the imaginary part of these elements s 2' (equal to ( n - k ) Q 2 - 2 n k Q l ) describes magneto-optical absorption. However, unlike its optical counterpart, s 2' can take either positive or negative values since its sign is directly related to the net spin polarization of the unpaired d states responsible for the spontaneous magnetization. We report the determination of the energy dependence in the range 1.0-2.5 eV
L36
LETTERS
of both the dispersive e2' parts of the magneto-optical permittivity for a series of seven thin cobalt films. Experimentally we evaluated firstly h and secondly Q. The off-diagonal permittivity was then computed by combining these intermediate parameters (e' = h2Q). 2. Experimental details The films we investigated were prepared by thermal evaporation from a resistively heated source in an ion-pumped vacuum system. The evaporant was deposited at rates between 1.0 and 4.0 A s- 1 onto carefully cleaned glass substrates held at 35-45 °C. The system pressure was maintained at around 1 x 10 -6 Torr during evaporation. Electron micrographs showed the films to be polycrystalline with a very small crystallite structure that showed little tendency to adopt a preferred orientation. The presence of both f.c.c, and h.c.p, crystal forms was indicated by the electron diffraction patterns. The thickness of each film was determined by multiple beam interferometry using a Varian A-scope and the range of thickness investigated was from 108.1 to 13.4 nm. Changes in the state of polarization which optical and magneto-optical effects introduce into beams reflected from or transmitted through optical interfaces can only be measured if they can be reduced to intensity changes. Therefore determination of the ellipticity and the rotation of the plane of polarization associated with such effects requires the inclusion of calibrated phase plates and analysers in the optical system. It is much simpler and therefore preferable both experimentally and theoretically if direct intensity variations alone can be related to the optical and magneto-optical parameters of interest. In the present work we avoided the complexities associated with polarimetry and ellipsometry. All measurements taken were of a simple relative photometric nature. The particular observables chosen for measurement were selected because the sensitivity of their relationship to the required parameters, namely h and Q, has been extensively investigated2' a. This allowed the optimization of the experimental configuration for each measurement so that high accuracy was maintained with a comparatively simple experimental system. The optical constants of the films were determined by way of a self-consistent procedure which has been reported in detail elsewhere 4. It is based on a modification ofAvery's 5 technique in which the reflectance ratio Rv/R s is measured to an accuracy of 0.5~o at two optimized angles of incidence and is combined with the independent measurement of film thickness. The magneto-optical constants of the film are evaluated from measurements of the transverse Kerr effect using p-polarized radiation. This effect is unique in that it manifests itself solely as a change in the reflectivity of the ferromagnetic surface as its magnetization if reversed from + M s to - M s along a direction perpendicular to the plane of incidence. The parameter actually measured is the fractional intensity modulation fi introduced into the reflected beam. Measurements of 6 at two optimized angles of incidence are combined with the predetermined optical constants and the measured film thickness to evaluate the real and imaginary parts of Q via a procedure described in detail by Newman 6. A check was maintained on the accuracy of the evaluation procedure by comparing the value of 6 measured at
LETTERS
L37
some third angle of incidence with its value computed using the evaluated optical and magneto-optical constants. Throughout the experimental work all photometric measurements were made using a phase-locked detection system operating at a frequency of 86 Hz; the accuracy of the magneto-optical measurements was a function of the film thickness but was typically 1 - 3 ~ for 6. 3. Results and discussion The values determined for the optical and magneto-optical permittivities of the seven films are presented in full in Tables I and II. Cobalt is known to be susceptible to oxidation and several workers have allowed for the effects of oxide layers when analysing their experimental data. It seems reasonable to assume that the effect of oxide formation on the optical and magneto-optical properties of films becomes more significant as their thickness is reduced. Consequently, since the thickness of the films under discussion varied by nearly an order of magnitude, strict quantitative agreement between films or with the results of other workers was not expected. However, when the structure in the curves depicting the variation of the optical and magneto-optical absorption as functions of incident energy is considered, the correspondence between films is remarkable. The curves shown in Fig. 1 can be considered typical of all the samples. It can be seen that the zero crossings of el' correlate very well with peaks or singularities in both the optical % and the magnetooptical %' absorption functions. There are two clear resonances at 1.1 and 1.6 eV and O4 0,4 03 Ot
°o4 -0"2
10
t5
20
25
(a)
(c) Fig. 1. (a) e2, (b) et' and (c) ~2' as functions of energy.
-03
(b)
2.495 2.263 2.053 1.908 1.754 1.649 1.548 1.467 1.307 1.181 1.078 0.991
Energy
-8.87 - 6.78 -8.74 -8.55 -8.77 -9.25 -8.54 - 10.00 - 10.02 -1 6 . 55 -15.86 - 15 . 57
11.32 9.24 ii . 26 12.63 13.74 15.42 17.63 18.52 22.46 28.84 29.12 24.45
-9.33 - 8.02 -8.21 -8.48 -9.21 -1 0. 43 -8.63 - 10.87 -1 0. 65 - 15.56 - 16.77 -16.38
~1
~1
~2
57.9nm
Film thickness 108.1 nm
VALUES O F T H E OPTICAL PERMITTIVITIES
TABLE 1
15.96 12.96 14.73 16.06 16.69 18.88 19.84 20.92 23.71 28.15 27.52 21.53
~2 -8.81 - 7.96 -8.56 -9.16 -10.62 -10.27 -10.32 -9.52 - 12.78 - 17.36 -20.46 -21.11
~1
45.7 nm
12.14 9.82 12.45 13.86 15.59 17.52 21.26 23.64 26.83 30.94 33.14 26.67
£2 -6.00 - 6.78 --7.54 -7.64 -8.40 -8.69 -8.40 -9.47 -8.78 - 10.98 - 14.55 -19.20
F'I
35.9 nm
15.75 10.72 12.08 13.46 14.56 15.88 20.36 22.58 24.66 30.16 31.45 25.86
£2 -13.46 - 11.32 -12.87 - 14.07 -15.77 -16.58 -18.58 -23.11 -24.23 -31.23 -32.71 -32.77
F'I
26.0 nm
14.13 11.40 12.39 13.81 15.70 17.50 19.23 22.16 23.98 31.61 32.00 24.52
£'2 -5.05 - 6.86 -7.35 -6.84 -6.91 -6.93 -7.76 -8.70 -7.92 - 12.69 -14.82 -19.11
F'I
22.4 nm
14.99 13.55 15.66 17.04 19.11 20.03 19.81 22.30 25.32 28.61 31.90 30.29
~2
nm
-5.86 - 6.85 -7.49 -8.02 - 8 .7 1 -10.67 -9.28 - 10.71 - 10.47 -14.65 - 1 8 .5 5 - 2 0 .6 5
£1
13.4
10.22 10.29 11.71 12.96 14.35 13.06 15.54 16.74 21.01 22.39 24.65 24.51
~2
t-'
t" t"rl
oo
2.495 2.263 2.053 1.908 1.754 1.649 1.548 1.467 1.307 1.181 1.078 0.991
Energy
-16.14 23.17 -13.17 20.47 - 19.46 32.04 - 17.25 36.88 -15.13 40.48 -13.36 48.45 -5.17 54.63 -5.60 62.77 +9.85 74.22 +11.08 1 2 7 . 5 0 +17.75 1 1 8 . 0 5 -11.74 1 0 9 . 4 6
82'
-17.63 42.17 -17.05 37.11 - 16.67 47.35 -14.16 51.57 - 14.66 58.77 -13.81 74.03 +0.66 67.68 -1.95 81.46 +15.12 85.72 +17.55 122.50 +10.42 120.68 -21.89 94.45
81'
£1'
82 ~
57.9 nm
Film thickness 108.1 nm
VALUES OF THE MAGNETO-OPTICAL PERMITrlVITIES
TABLE II
82 '
.
m
-17.81 24.22 -18.21 21.64 - 19.87 31.67 -20.86 37.49 -24.94 48.07 - 19.68 52.28 - 12.18 67.08 -8.43 78.65 +2.12 9 1 . 0 1 +5.01 1 1 7 . 4 7 -0.60 1 3 5 . 2 9 -43.56 1 1 0 . 1 0
£1'
45.7 nm
82'
-2.37 27.19 -10.71 25.06 - 11.57 3 0 . 5 5 -10.52 36.02 - 11.01 41.82 -9.07 47.70 +2.34 64.60 +7.14 77.63 +23.19 76.10 +42.89 97.28 +36.59 1 2 5 . 1 7 -26.59 1 1 2 . 9 0
81 '
35.9 nm
-34.99 -28.01 -37.06 -41.39 -45.78 -44.63 -48.86 -72.10 -54.16 -55.58 -59.61 -121.06
£1 t
26.0 nm
45.71 31.94 41.36 51.32 65.11 78.01 97.26 143.22 149.47 230.67 232.15 171.38
82 ~
82'
-I.00 27.32 -7.12 31.40 -5.12 40.80 +0.81 42.88 +6.09 50.49 +11.70 51.73 + 13.34 50.42 +19.13 58.34 + 35.29 54.34 +41.14 75.82 + 44.58 87.04 +5.80 109.93
£1'
22.4 nm
82'
14.38 16.37 19.49 21.94 25.90 27.97 30.08 34.49 37.54 42.61 55.14 59.70
£1'
-2.25 -5.31 -6.27 -5.68 -4.46 - 9.08 + 1.03 +1.57 + 14.81 +9.33 +5.79 - ! 1.08
13.4 nm
t"
t'rl
t"
L40
LETTERS
some indications, particularly from the thinner samples, of a third in the neighbourhood of 2.6 eV. The resonance at around 1.6 eV has been previously observed and interpreted by Krinchik7,a. However, his extensive work shows no evidence of the apparently stronger resonance we observed at 1.1 eV, although it is evident in the results of Afanas'yeva and Krillova9. In our analysis of the optical permittivity results4 we tentatively attributed the absorption peak at 1.1 eV to optical conduction resonance 1°. We consider it possible that as a result of the low evaporation rates we employed the films may have had a fairly rough surface structure which on partial oxidation became analogous to that of a metal-rich cermet. On this assumption reasonable success was achieved in modelling the absorption peak by using very high metal/metal oxide ratios (q ~ 0.9) in a modification of the Maxwell-Garnett theory. Lissberger and Saunders 1~ have demonstrated that the magneto-optical properties of Co-MgF cermets (albeit of low q values) can be described by combining the classical microscopic theory of Krinchik with a Maxwell-Garnetttype analysis in which the effect of particle or crystallite size on the electron mean free path is included when computing both the optical and the magneto-optical constants. In a similar fashion Carey and Thomas 12 have successfully modelled the experimental results of Gittleman et al.13 We thus felt justified in applying this model to the present magneto-optical results in the region of 1.1 eV. Unfortunately we have not as yet repeated the success achieved with the optical results: in its present form the model does not correctly describe the observed behaviour of e 1' and e2'. 4. Conclusion
In the past it has usually been necessary when evaluating theoretical magnetooptical work to use experimental values taken from different sources for the optical and magneto-optical constants. This practice is generally unsatisfactory but is particularly so when studying thin films. The extensive results which we have presented are accurate and demonstrably consistent across a wide range of film thicknesses. It is intended that they will provide a reliable data base for any subsequent theoretical studies into the magneto-optical behaviour of ferromagnetic films. I 2 3 4 5 6 7 8 9 I0 11 12 13
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