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Magneto-optical properties of discontinuous cobalt films
Journal of Magnetism North-Holland
and Magnetic
MAGNETO-OPTICAL
L.V. NIKITIN Dept. o/Physics,
and O.M.
Materials
83 (1990) 77-78
PROPERTIES
77
OF DISCONTINUOUS
COBALT
FILMS
NAKASHIDZE
Moscow State Uniuersrty, Moscow,
USSR
We have investigated the magneto-optical and optical properties of discontinuous Co films, the weight thickness d of which was within the interval 6-300 A. The experimental results are in qualitative agreement with those predicted by the Garnett theory generalized to the case of ferromagnetic medium.
1. Introduction
in the case of reversal can be written as
The tensor of effective dielectric permittivity (TEDP) of magnetized ultrafine ferromagnetic material, by analogy with the tensor for bulk ferromagnetic materials, can be represented as
ISe =
s(AQ;,,
of magnetization
of the sample,
+my,,,),
where A = EZelf(2&ff B=
(Cff
-
cgeff
cos2 ‘p - l), +
l)cos2
cp + &leff - 1
and v is the angle of light incidence. 2. Experimental where
Cff
= glleff
-
Keff
7 GOeff = &heff
-
iGeff
and
gLff
The relationship between the effective optical constants of ultrafine medium and the optical constants of material of metal particles of spherical shape is expressed, as a rule, in terms of the Gamett equations [l]. In ref. [2] an attempt was undertaken to extend the Garnett transformations to include the case of ultrafine ferromagnetic medium. The components of the TEDP of ultrafine magnetic medium subject to the condition 8’ c 8 can be written as = 2q(b-
d elf
1) +b+
b+2-q(E-1) 2q(cFo-
8 Oeff
=
2
3. Results and discussion
’
1) +CYn+2
80+2-q(Eb-1)
’
9qE’ f%\f
=
[E(l
-4)
+ 2 + q12 ’
where q is the occupancy of the volume of the ultrafine medium with metal; d and go are the diagonal components; and 8’ are the nondiagonal components of the tensor of dielectric permittivity of metal, of which particles consist. The equatorial Kerr effect (EKE) under consideration, which consists in a change in the intensity of linearly polarized light reflected from the sample 0304-8853/90/$03.50 (North-Holland)
In this work we investigate the magneto-optical properties of discontinuous cobalt films, the weight thickness d (d = m/pS, where WI - film mass, p metal density and S - film square) of which falls within the interval 6-300 .& The films were obtained by evaporation in vacuum of 10m5 Torr on glass substrates with a rate of 1 to 5 A/s. For investigating the magneto-optical properties we have chosen the equatorial Kerr effect. The optical constants were determined using the Every method.
0 Elsevier Science Publishers
B.V.
Fig. 1 presents the Aw dependences of the EKE for the discontinuous cobalt films with different weight thicknesses d. Given there also is a similar frequency dependence for polycrystalline cobalt (curve 5). Fig. 2 shows the dependences of the EKE on cp for the same films (Aw = 2 eV). It can be seen from the figures that for the films with a different weight thickness the character of the frequency and angular dependences of the EKE is significantly different from that of the similar dependences for bulk cobalt and depends on the film effective thickness. At large weight thicknesses, corresponding to large values of the occupancy q of the volume of the film with metal, the dependences of the EKE became similar in their character to the shape of
78
L. V. Nlkrrin. 0. M. Nukashrdze
/ Disconrinuous cobalt films
10
Fig. 1. Dependences of the EKE of t2w for discontinuous Co films with weight thicknesses d = 12 (1) 23 (2). 49 (3) and 300 A (4) and for polycrystalline cobalt (5) (cp = 70 o ).
the dependence of the EKE character to the shape of the dependence of the EKE for bulk cobalt. However, the value of the EKE for thick discontinuous films is greater than that for bulk cobalt. In investigating ultrafine cobalt films with a weight thickness of 9 A and less it was found that the EKE is close to zero, which seems to be due to the fact that the particles of ultrafine discontinuous films have small sizes and are largely in a superparamagnetic state. However, even for the films with a weight thickness of about - 15 ,& the value of the EKE constitutes 1-2 X 10m3 and the Aw dependence of the EKE is monotonic in character with a broad minimum in the region 3-4 eV and differs from the similar dependence for bulk cobalt both in character and in sign. From measurements of the EKE at two angles of light incidence of ‘p = 70 o and 80” and of the optical
cs
e.10 3
Fig. 3. Dependences of the EKE on hw for ultrafine cobalt, calculated within the framework of the Garnett model for q= 0.1 (1),0.3 (2). 0.5 (3). 0.7 (4) and0.9 (5)(p,= 700).
constants using the Every method, we determined the components of the TEDP for the above-mentioned discontinuous cobalt films. For the films 300 A thick the spectral dependences of the components of the TEDP are similar to those for polycrystalline Co. With decreasing weight thickness of the films the character of the Au-dependence of the tensor components changes. In this case for the Co films 49 ,& thick on the Ao dependences of the eZeff there are maxima in the region of light quantum energies Ao = 1.8 and 2.8 eV, which seem to be dimensional in character. Our calculations, made within the framework of the Garnett model generalized to the case of ferromagnetic media [2], have shown qualitative agreement of the calculated hw dependences of the EKE with the experimental data. By way of example fig. 3 presents the results of calculations, using eqs. (2) and (3) of the EKE for different values of 4. 4. Conclusions It is shown that the main regularities of the magneto-optical behaviour of discontinuous cobalt films can be described using the tensor of effective dielectric permittivity of ultrafine medium within the framework of the Garnett model generalized to the case of ferromagnetic medium. References
Fig. 2. Dependences of the EKE on q for discontinuous Co films with weight thicknesses d = 12 (1). 20 (2), 23 (3) 49 (4) and 300 A (5) and for polycrystalline cobalt (6), measured at hw = 2 eV.
[l] J.C. Maxwell Garnett, Phil. Trans. Roy. Sot. London 203 A (1904) 385, 205 A (1906) 237. [2] G.S. Krinchik, L.V. Nikitin and O.V. Kasatkina, Poverkhnost’, Fizika, Khimiya, Mekhanika 7 (1985) 140.
and Magnetic
MAGNETO-OPTICAL
L.V. NIKITIN Dept. o/Physics,
and O.M.
Materials
83 (1990) 77-78
PROPERTIES
77
OF DISCONTINUOUS
COBALT
FILMS
NAKASHIDZE
Moscow State Uniuersrty, Moscow,
USSR
We have investigated the magneto-optical and optical properties of discontinuous Co films, the weight thickness d of which was within the interval 6-300 A. The experimental results are in qualitative agreement with those predicted by the Garnett theory generalized to the case of ferromagnetic medium.
1. Introduction
in the case of reversal can be written as
The tensor of effective dielectric permittivity (TEDP) of magnetized ultrafine ferromagnetic material, by analogy with the tensor for bulk ferromagnetic materials, can be represented as
ISe =
s(AQ;,,
of magnetization
of the sample,
+my,,,),
where A = EZelf(2&ff B=
(Cff
-
cgeff
cos2 ‘p - l), +
l)cos2
cp + &leff - 1
and v is the angle of light incidence. 2. Experimental where
Cff
= glleff
-
Keff
7 GOeff = &heff
-
iGeff
and
gLff
The relationship between the effective optical constants of ultrafine medium and the optical constants of material of metal particles of spherical shape is expressed, as a rule, in terms of the Gamett equations [l]. In ref. [2] an attempt was undertaken to extend the Garnett transformations to include the case of ultrafine ferromagnetic medium. The components of the TEDP of ultrafine magnetic medium subject to the condition 8’ c 8 can be written as = 2q(b-
d elf
1) +b+
b+2-q(E-1) 2q(cFo-
8 Oeff
=
2
3. Results and discussion
’
1) +CYn+2
80+2-q(Eb-1)
’
9qE’ f%\f
=
[E(l
-4)
+ 2 + q12 ’
where q is the occupancy of the volume of the ultrafine medium with metal; d and go are the diagonal components; and 8’ are the nondiagonal components of the tensor of dielectric permittivity of metal, of which particles consist. The equatorial Kerr effect (EKE) under consideration, which consists in a change in the intensity of linearly polarized light reflected from the sample 0304-8853/90/$03.50 (North-Holland)
In this work we investigate the magneto-optical properties of discontinuous cobalt films, the weight thickness d (d = m/pS, where WI - film mass, p metal density and S - film square) of which falls within the interval 6-300 .& The films were obtained by evaporation in vacuum of 10m5 Torr on glass substrates with a rate of 1 to 5 A/s. For investigating the magneto-optical properties we have chosen the equatorial Kerr effect. The optical constants were determined using the Every method.
0 Elsevier Science Publishers
B.V.
Fig. 1 presents the Aw dependences of the EKE for the discontinuous cobalt films with different weight thicknesses d. Given there also is a similar frequency dependence for polycrystalline cobalt (curve 5). Fig. 2 shows the dependences of the EKE on cp for the same films (Aw = 2 eV). It can be seen from the figures that for the films with a different weight thickness the character of the frequency and angular dependences of the EKE is significantly different from that of the similar dependences for bulk cobalt and depends on the film effective thickness. At large weight thicknesses, corresponding to large values of the occupancy q of the volume of the film with metal, the dependences of the EKE became similar in their character to the shape of
78
L. V. Nlkrrin. 0. M. Nukashrdze
/ Disconrinuous cobalt films
10
Fig. 1. Dependences of the EKE of t2w for discontinuous Co films with weight thicknesses d = 12 (1) 23 (2). 49 (3) and 300 A (4) and for polycrystalline cobalt (5) (cp = 70 o ).
the dependence of the EKE character to the shape of the dependence of the EKE for bulk cobalt. However, the value of the EKE for thick discontinuous films is greater than that for bulk cobalt. In investigating ultrafine cobalt films with a weight thickness of 9 A and less it was found that the EKE is close to zero, which seems to be due to the fact that the particles of ultrafine discontinuous films have small sizes and are largely in a superparamagnetic state. However, even for the films with a weight thickness of about - 15 ,& the value of the EKE constitutes 1-2 X 10m3 and the Aw dependence of the EKE is monotonic in character with a broad minimum in the region 3-4 eV and differs from the similar dependence for bulk cobalt both in character and in sign. From measurements of the EKE at two angles of light incidence of ‘p = 70 o and 80” and of the optical
cs
e.10 3
Fig. 3. Dependences of the EKE on hw for ultrafine cobalt, calculated within the framework of the Garnett model for q= 0.1 (1),0.3 (2). 0.5 (3). 0.7 (4) and0.9 (5)(p,= 700).
constants using the Every method, we determined the components of the TEDP for the above-mentioned discontinuous cobalt films. For the films 300 A thick the spectral dependences of the components of the TEDP are similar to those for polycrystalline Co. With decreasing weight thickness of the films the character of the Au-dependence of the tensor components changes. In this case for the Co films 49 ,& thick on the Ao dependences of the eZeff there are maxima in the region of light quantum energies Ao = 1.8 and 2.8 eV, which seem to be dimensional in character. Our calculations, made within the framework of the Garnett model generalized to the case of ferromagnetic media [2], have shown qualitative agreement of the calculated hw dependences of the EKE with the experimental data. By way of example fig. 3 presents the results of calculations, using eqs. (2) and (3) of the EKE for different values of 4. 4. Conclusions It is shown that the main regularities of the magneto-optical behaviour of discontinuous cobalt films can be described using the tensor of effective dielectric permittivity of ultrafine medium within the framework of the Garnett model generalized to the case of ferromagnetic medium. References
Fig. 2. Dependences of the EKE on q for discontinuous Co films with weight thicknesses d = 12 (1). 20 (2), 23 (3) 49 (4) and 300 A (5) and for polycrystalline cobalt (6), measured at hw = 2 eV.
[l] J.C. Maxwell Garnett, Phil. Trans. Roy. Sot. London 203 A (1904) 385, 205 A (1906) 237. [2] G.S. Krinchik, L.V. Nikitin and O.V. Kasatkina, Poverkhnost’, Fizika, Khimiya, Mekhanika 7 (1985) 140.