Abstract

A method is described for measuring the dielectric tensor of perpendicularly magnetized metal films that are overcoated with a protective transparent layer. It uses a combination of ellipsometric and polar Kerr measurements and employs a series of consistency checks to ensure the accuracy of the data analysis. As an example, the technique is applied to an amorphous terbium-iron alloy that was overcoated in situ with silicon dioxide.

© 1983 Optical Society of America

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References

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  1. L. D. Landau, E. M. Lifshitz, Statistical Physics (Pergamon, London, 1958), pp. 379–406.
  2. M. J. Freiser, IEEE Trans. Magn. MAG-4, 152 (1968).
    [CrossRef]
  3. F. J. Kahn, P. S. Pershan, Phys. Rev. 186, 891 (1969).
    [CrossRef]
  4. M. Mansuripur, G. A. N. Connell, J. W. Goodman, J. Appl. Phys. 53, 4485 (1982).
    [CrossRef]
  5. D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), pp. 811–816.
  6. N. V. Smith, Phys. Rev. 183, 634 (1969).
    [CrossRef]
  7. P. M. Grant, W. Paul, J. Appl. Phys. 37, 3110 (1966).
    [CrossRef]
  8. F. Abeles, M. L. Theye, Surf. Sci. 5, 325 (1966).
    [CrossRef]
  9. See, for example, the articles in Proceedings, Tenth International Colloquium Magnetic Films and Surfaces (Yokohama, Japan, 1982).
  10. R. Allen, G. A. N. Connell, J. Appl. Phys. 53, 2353 (1982).
    [CrossRef]
  11. F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
    [CrossRef]
  12. L. Harris, J. K. Beasley, A. L. Loeb, J. Opt. Soc. Am. 41, 604 (1951).
    [CrossRef]
  13. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1967), pp. 205–207.

1982 (2)

M. Mansuripur, G. A. N. Connell, J. W. Goodman, J. Appl. Phys. 53, 4485 (1982).
[CrossRef]

R. Allen, G. A. N. Connell, J. Appl. Phys. 53, 2353 (1982).
[CrossRef]

1969 (2)

F. J. Kahn, P. S. Pershan, Phys. Rev. 186, 891 (1969).
[CrossRef]

N. V. Smith, Phys. Rev. 183, 634 (1969).
[CrossRef]

1968 (1)

M. J. Freiser, IEEE Trans. Magn. MAG-4, 152 (1968).
[CrossRef]

1966 (2)

P. M. Grant, W. Paul, J. Appl. Phys. 37, 3110 (1966).
[CrossRef]

F. Abeles, M. L. Theye, Surf. Sci. 5, 325 (1966).
[CrossRef]

1963 (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

1951 (1)

Abeles, F.

F. Abeles, M. L. Theye, Surf. Sci. 5, 325 (1966).
[CrossRef]

Allen, R.

R. Allen, G. A. N. Connell, J. Appl. Phys. 53, 2353 (1982).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), pp. 811–816.

Beasley, J. K.

Connell, G. A. N.

R. Allen, G. A. N. Connell, J. Appl. Phys. 53, 2353 (1982).
[CrossRef]

M. Mansuripur, G. A. N. Connell, J. W. Goodman, J. Appl. Phys. 53, 4485 (1982).
[CrossRef]

Freiser, M. J.

M. J. Freiser, IEEE Trans. Magn. MAG-4, 152 (1968).
[CrossRef]

Goodman, J. W.

M. Mansuripur, G. A. N. Connell, J. W. Goodman, J. Appl. Phys. 53, 4485 (1982).
[CrossRef]

Grant, P. M.

P. M. Grant, W. Paul, J. Appl. Phys. 37, 3110 (1966).
[CrossRef]

Harris, L.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1967), pp. 205–207.

Kahn, F. J.

F. J. Kahn, P. S. Pershan, Phys. Rev. 186, 891 (1969).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Statistical Physics (Pergamon, London, 1958), pp. 379–406.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Statistical Physics (Pergamon, London, 1958), pp. 379–406.

Loeb, A. L.

Mansuripur, M.

M. Mansuripur, G. A. N. Connell, J. W. Goodman, J. Appl. Phys. 53, 4485 (1982).
[CrossRef]

McCrackin, F. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Passaglia, E.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Paul, W.

P. M. Grant, W. Paul, J. Appl. Phys. 37, 3110 (1966).
[CrossRef]

Pershan, P. S.

F. J. Kahn, P. S. Pershan, Phys. Rev. 186, 891 (1969).
[CrossRef]

Smith, N. V.

N. V. Smith, Phys. Rev. 183, 634 (1969).
[CrossRef]

Steinberg, H. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Stromberg, R. R.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Theye, M. L.

F. Abeles, M. L. Theye, Surf. Sci. 5, 325 (1966).
[CrossRef]

IEEE Trans. Magn. (1)

M. J. Freiser, IEEE Trans. Magn. MAG-4, 152 (1968).
[CrossRef]

J. Appl. Phys. (3)

M. Mansuripur, G. A. N. Connell, J. W. Goodman, J. Appl. Phys. 53, 4485 (1982).
[CrossRef]

P. M. Grant, W. Paul, J. Appl. Phys. 37, 3110 (1966).
[CrossRef]

R. Allen, G. A. N. Connell, J. Appl. Phys. 53, 2353 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Res. Natl. Bur. Stand. Sect. A (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Phys. Rev. (2)

N. V. Smith, Phys. Rev. 183, 634 (1969).
[CrossRef]

F. J. Kahn, P. S. Pershan, Phys. Rev. 186, 891 (1969).
[CrossRef]

Surf. Sci. (1)

F. Abeles, M. L. Theye, Surf. Sci. 5, 325 (1966).
[CrossRef]

Other (4)

See, for example, the articles in Proceedings, Tenth International Colloquium Magnetic Films and Surfaces (Yokohama, Japan, 1982).

L. D. Landau, E. M. Lifshitz, Statistical Physics (Pergamon, London, 1958), pp. 379–406.

D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), pp. 811–816.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1967), pp. 205–207.

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Figures (6)

Fig. 1
Fig. 1

Schematic representation of an overcoated sample on a Dove prism.

Fig. 2
Fig. 2

Ordinary optical constants of amorphous Tb20Fe80 wavelength: (a) refractive index; (b) dielectric constant.

Fig. 3
Fig. 3

Plots of the quality factor Q vs overcoat thickness for two SiO2 coated amorphous Tb20Fe80 samples. The nominal SiO2 thicknesses are (a) 20 ± 1 and (b) 110 ± 5 nm.

Fig. 4
Fig. 4

Plots vs wavelength of the measured and calculated (—) reflectances of amorphous Tb20Fe80 samples coated with 20.3 nm ● and 110.3 nm ○ of SiO2, shown (a) directly and (b) as a difference. The experimental accuracy of the reflectance measurements is ±0.005.

Fig. 5
Fig. 5

Plots vs wavelength of the measured and calculated polar Kerr rotations and ellipticities of amorphous Tb20Fe80 samples coated with 20.3 nm ● and 110.3 nm ○ of SiO2.

Fig. 6
Fig. 6

Magnetooptical constants of amorphous Tb20Fe80 vs wavelength, determined from samples coated with 20.3 nm ● and 110.3 nm ○ of SiO2.

Equations (17)

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ɛ = ( ɛ xx i ɛ xy 0 i ɛ xy ɛ xx 0 0 0 ɛ zz ) , M z .
ɛ ii ( i = x , z ) = ɛ 1 ii + i ɛ 2 ii = ( n ii + i k ii ) 2
ɛ x x = n 1 2 { sin 2 θ 1 + sin 2 θ tan 2 θ 1 [ ( 1 ρ sp ) / ( 1 + ρ sp ) ] 2 } ,
ρ sp = r p / r s = tan ψ sp exp ( i Δ sp ) .
r i ( i = s , p ) = r i , 12 + r i , 22 exp [ 4 π i ( n 2 2 sin 2 θ 1 ) 1 / 2 d / λ ] 1 + r i , 12 r i , 23 exp [ 4 π i ( n 2 2 sin 2 θ 1 ) 1 / 2 d / λ ] ,
r p , jk = n j cos θ k n k cos θ j n k cos θ j + n j cos θ k ,
r s , j k = n j cos θ j n k cos θ k n j cos θ j + n k cos θ k ,
cos θ l ( l = 2 , 3 ) = [ 1 ( sin θ l 1 n l 1 / n l ) 2 ] 1 / 2 ,
n ± = n 3 , ± = ( ɛ xx ± ɛ yy ) 1 / 2
ρ ± = r / r + = tan ψ ± exp i Δ ±
φ = Δ ± / 2 ,
tan η = ( 1 tan ψ ± ) / ( 1 + tan ψ ± ) .
ɛ 1 xy = ɛ 1 , 0 xy + [ ( φ φ 0 ) ( η ɛ 2 xy ) ( η η 0 ) ( φ ɛ 2 xy ) ] / J ,
ɛ 2 xy = ɛ 2 , 0 xy + [ ( φ φ 0 ) ( η ɛ 1 xy ) ( η η 0 ) ( φ ɛ 1 xy ) ] / J ,
J = ( η ɛ 2 xy ) ( φ ɛ 1 xy ) ( φ ɛ 2 xy ) ( η ɛ 1 xy ) ,
( Δ ɛ i xy ) 2 ( i = 1 , 2 ) = ( ɛ i xy n 2 ) 2 Δ n 2 2 + ( ɛ i xy k 2 ) 2 Δ k 2 2 + ( ɛ i xy Φ ) 2 Δ Φ + ( ɛ i xy η ) 2 Δ η 2 + ( ɛ i xy d ) 2 Δ d 2
ɛ 0 xy = i ( φ m + i η m ) ( ɛ xx 1 ) ɛ xx ;

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