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Faraday rotation in thin discontinuous iron films and thin iron magnetic fluid layers
Journal of Magnetism and Magnetic Materials 148 (1995) 279-280
Journal of magnetism
j~
and magnetic materials
ELSEVIER
Faraday rotation in thin discontinuous iron films and thin iron magnetic fluid layers L.V. Nikitin a, * L.G. Kalandadze a, M.Z. Akhmedov a, S.2~k. Nepijko b, A.P. Ostranitsa b a Department o f Physics, Moscow State University, 119899 Moscow, Russi~ b Institute of Physics o f the Ukrainian Academy o f Sciences, Prospect Nauki 46, 252650 Keeu-22, Ukraine
Abstract We investigated the Faraday rotation in thin discontinuous iron films and in thin layers of magnetic fluids, based on iron particles. The experimental results are in qualitative agreement with those predicted by tlae Maxweil-Garnett theory generalized to the case of ferromagnetic medium.
particles with average size approximately 50 ,~ in different liquid silicon-organic compounds.
1. Introduction
In the framework of the theoretical Maxwelt-Garnett model generalized to the ease of a magnellc ultra~ne medium [1] Faraday rotation ot F can be written as
-F -~ Re(~'.,,/~:d~), =
O)
where 2q(6-So) + 8+ 26 o e'eft = G° E(1 -- q) + E0(2 + q ) ' 9qe2~ ' 8"n=
[ ,~(1 -- q ) + . o ( 2 + q)]2
(E and ~' are diagonal and nondiagonal components of the tensor of dielectric permittivity of the metal, 8a is the dielectric permittivity of the medium, surrounding metal particles and q is the occupancy of the volume of the ultrafine medium with metal).
3. Results and discussion
For example, Fig. 1 presents the experimental dependences of Faraday rotation con the quantum energy of incident light, h to, for diseor, tinuous films with different weight thicknesses. We can see from the figure that dependences of Faraday rotation on h to for discontinuous films differ essentially from analogous dependence received in Ref. [2] for relatively thick iron film. Obtained experimental results were compared with calculations in the framework o f the theoretical Max~ell-Garnett model. Fig. 2 gives the dependences of Faraday rotation on h oJ, calculated for ultra.fine iron medium as given in Eq. (1) for different q and Go = 1. In this and following calculations the dielectric permittivity tens~r components for bulk iron were used. In this figure an analogous dependence for bulk iron (curve 4) is also presented.
2. E x p e r i m e n t a l
It
,tp 4
The results of experimental investigation of ]Faraday rotation in the two ultrafine structures such as thin discontinuous metal films and thin layers of magnetic fluids based on iron particles are presented in this work. Discontinuous films were obtained by evaporation in vacuum of 10 - s Torr on glass substrates with a rate of 1 to 5 A / s . The magnetic fluids were prepared on the base of iron
* Corresponding author. Fax: +7-095-932 8820.
2 1 0
,o/NT ,to
-1 -2
Fig. 1. Dependences of the Faradaty rotatioa on /i to for discontinuous iron films with weight thickness d = 50 A (1), 100/~ (2), 150 A (3) and for thick iron film (4).
0304-8853/95/$09.50 © 1995 Elsevier Science BN. All rights reserved SSD! 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 2 3 6 - 7
o,.o
280
L.V. Nikitin et al. ~Journal of Magnetism and Magnetic kfaterials 148 (1995) 279-280
_j,llO_3)de~fem/
~ y / K ' l O -3, d e 6 / ~
6
4
4 2
0
4
4
O -2
0 "4
-2
0.~ •
1.0 ?
~
1.5 "
! ;~.O
1 I~ 1;.0. e v
2,5 !
Fig. 2. Dependences of the Faraday rotation on h ¢o, calculated in the framework of the IClaxwell-Garnett model for ultrafine iron medium with q = 0.I (I); 0.2 (2); 0.4 (3) and for bulk iron (4). Coefficient K is involved to change the scale of ot~. For curves 1 and 2 K = 1, for the curve 3 K = 10 and for the curve 4 K = 100.
Fig. 4. Dependences of Faraday rotation on h o,, calculated in the framework of the Maxwell-Garaett model (60 = 2,05) for ultrafine iron medium with q = 0.01 (1), 0.02 (2), 0.03 (3), 0.04 (4), 0.05 (5) and 0.08 (6).
Experimental frequency dependences o f Faraday rotation in thin layers o f iron magnetic fluids with q --- 0.012, 0.017 and 0.027 are presented in Fig. 3. These dependences have a similar character and differ between each other only b y the effective value. Experimental results obtained for magnetic fluids conform with results received for the thin discontinuous films. In Fig. 4 the freq~uency dependences o f Faraday rotation are presented for ultrafine iron m e d i u m with different q, calculated in the framework o f the M a x w e i l - G a m e t t m o d e l for s o = 2.05.
Analysis o f obtained results shows that the theoretical M a x w e l l - G a m e t t m;)del satisfactorily describes the experimental results. In the present work w e consider the influence o f m a g netic particle aggregation in magnetic fluids on the character o f Faraday rotation frequency dependences. Experimental studies showed that the character o f the frequency dependences of Faraday rotation is not changed, though the intensive growth o f aggregates takes place in an increasing magnetic field.
4. Conclusions 3
~ * 1 0 "3) aeg/~a
2
'
1
0
~,.5
1,.0
1)5 a ~ 2 . 0
1 2.~,
It is shown that the m a i n appropriateness o f the Faraday rotation in discontinuous iron films and in thin layers o f magnetic fluids based on iron particles can be discribed using the tensor o f effective dielectric permittivity o f ultrafine medium within the framework o f the M a x w e l l Garnett model generalized to the case o f ferromagnetic medium.
-1
References Fig. 3. Dependences o f the Faraday rotation on h o~ in thin laycrs of iron magnetic fluids with q = 0.012 (1), 0.017 (2) and 0.027 (3).
[1] G.S. Krinchik, L.V. Nikitin and O.V. Kasatkina, Poverkhnost Fizika Khimiya Mekhanika 7 (1985) 140. [2] K.H. Clemens and I. Iaumann, Z. Physik 173 (1963) 135.
Journal of magnetism
j~
and magnetic materials
ELSEVIER
Faraday rotation in thin discontinuous iron films and thin iron magnetic fluid layers L.V. Nikitin a, * L.G. Kalandadze a, M.Z. Akhmedov a, S.2~k. Nepijko b, A.P. Ostranitsa b a Department o f Physics, Moscow State University, 119899 Moscow, Russi~ b Institute of Physics o f the Ukrainian Academy o f Sciences, Prospect Nauki 46, 252650 Keeu-22, Ukraine
Abstract We investigated the Faraday rotation in thin discontinuous iron films and in thin layers of magnetic fluids, based on iron particles. The experimental results are in qualitative agreement with those predicted by tlae Maxweil-Garnett theory generalized to the case of ferromagnetic medium.
particles with average size approximately 50 ,~ in different liquid silicon-organic compounds.
1. Introduction
In the framework of the theoretical Maxwelt-Garnett model generalized to the ease of a magnellc ultra~ne medium [1] Faraday rotation ot F can be written as
-F -~ Re(~'.,,/~:d~), =
O)
where 2q(6-So) + 8+ 26 o e'eft = G° E(1 -- q) + E0(2 + q ) ' 9qe2~ ' 8"n=
[ ,~(1 -- q ) + . o ( 2 + q)]2
(E and ~' are diagonal and nondiagonal components of the tensor of dielectric permittivity of the metal, 8a is the dielectric permittivity of the medium, surrounding metal particles and q is the occupancy of the volume of the ultrafine medium with metal).
3. Results and discussion
For example, Fig. 1 presents the experimental dependences of Faraday rotation con the quantum energy of incident light, h to, for diseor, tinuous films with different weight thicknesses. We can see from the figure that dependences of Faraday rotation on h to for discontinuous films differ essentially from analogous dependence received in Ref. [2] for relatively thick iron film. Obtained experimental results were compared with calculations in the framework o f the theoretical Max~ell-Garnett model. Fig. 2 gives the dependences of Faraday rotation on h oJ, calculated for ultra.fine iron medium as given in Eq. (1) for different q and Go = 1. In this and following calculations the dielectric permittivity tens~r components for bulk iron were used. In this figure an analogous dependence for bulk iron (curve 4) is also presented.
2. E x p e r i m e n t a l
It
,tp 4
The results of experimental investigation of ]Faraday rotation in the two ultrafine structures such as thin discontinuous metal films and thin layers of magnetic fluids based on iron particles are presented in this work. Discontinuous films were obtained by evaporation in vacuum of 10 - s Torr on glass substrates with a rate of 1 to 5 A / s . The magnetic fluids were prepared on the base of iron
* Corresponding author. Fax: +7-095-932 8820.
2 1 0
,o/NT ,to
-1 -2
Fig. 1. Dependences of the Faradaty rotatioa on /i to for discontinuous iron films with weight thickness d = 50 A (1), 100/~ (2), 150 A (3) and for thick iron film (4).
0304-8853/95/$09.50 © 1995 Elsevier Science BN. All rights reserved SSD! 0 3 0 4 - 8 8 5 3 ( 9 5 ) 0 0 2 3 6 - 7
o,.o
280
L.V. Nikitin et al. ~Journal of Magnetism and Magnetic kfaterials 148 (1995) 279-280
_j,llO_3)de~fem/
~ y / K ' l O -3, d e 6 / ~
6
4
4 2
0
4
4
O -2
0 "4
-2
0.~ •
1.0 ?
~
1.5 "
! ;~.O
1 I~ 1;.0. e v
2,5 !
Fig. 2. Dependences of the Faraday rotation on h ¢o, calculated in the framework of the IClaxwell-Garnett model for ultrafine iron medium with q = 0.I (I); 0.2 (2); 0.4 (3) and for bulk iron (4). Coefficient K is involved to change the scale of ot~. For curves 1 and 2 K = 1, for the curve 3 K = 10 and for the curve 4 K = 100.
Fig. 4. Dependences of Faraday rotation on h o,, calculated in the framework of the Maxwell-Garaett model (60 = 2,05) for ultrafine iron medium with q = 0.01 (1), 0.02 (2), 0.03 (3), 0.04 (4), 0.05 (5) and 0.08 (6).
Experimental frequency dependences o f Faraday rotation in thin layers o f iron magnetic fluids with q --- 0.012, 0.017 and 0.027 are presented in Fig. 3. These dependences have a similar character and differ between each other only b y the effective value. Experimental results obtained for magnetic fluids conform with results received for the thin discontinuous films. In Fig. 4 the freq~uency dependences o f Faraday rotation are presented for ultrafine iron m e d i u m with different q, calculated in the framework o f the M a x w e i l - G a m e t t m o d e l for s o = 2.05.
Analysis o f obtained results shows that the theoretical M a x w e l l - G a m e t t m;)del satisfactorily describes the experimental results. In the present work w e consider the influence o f m a g netic particle aggregation in magnetic fluids on the character o f Faraday rotation frequency dependences. Experimental studies showed that the character o f the frequency dependences of Faraday rotation is not changed, though the intensive growth o f aggregates takes place in an increasing magnetic field.
4. Conclusions 3
~ * 1 0 "3) aeg/~a
2
'
1
0
~,.5
1,.0
1)5 a ~ 2 . 0
1 2.~,
It is shown that the m a i n appropriateness o f the Faraday rotation in discontinuous iron films and in thin layers o f magnetic fluids based on iron particles can be discribed using the tensor o f effective dielectric permittivity o f ultrafine medium within the framework o f the M a x w e l l Garnett model generalized to the case o f ferromagnetic medium.
-1
References Fig. 3. Dependences o f the Faraday rotation on h o~ in thin laycrs of iron magnetic fluids with q = 0.012 (1), 0.017 (2) and 0.027 (3).
[1] G.S. Krinchik, L.V. Nikitin and O.V. Kasatkina, Poverkhnost Fizika Khimiya Mekhanika 7 (1985) 140. [2] K.H. Clemens and I. Iaumann, Z. Physik 173 (1963) 135.