Abstract

The longitudinal Kerr magneto-optic effect can be characterized by four parameters n, k, Q0, and q. The first two parameters, n and k, are the ordinary optical refractive index and index of absorption, and the last two parameters, Q0 and q, are the magneto-optic amplitude and phase. These parameters were determined for opaque, high-vacuum deposited films of iron, nickel, and Permalloy for wavelengths between 0.360 and 0.620 μ. To find n, k, Q0, and q, the rotation and the ellipticity of the light reflected from the surface of these films were measured with a photoelectric ellipsometer. This ellipsometer employed a “Faraday cell” which sinusoidally rotated the polarization of the reflected light. To find the ellipticity, a calibrated retardation plate was placed in front of the Faraday cell. From the reflection coefficients derived by Voigt, the four parameters were computed from these data. As a check, the Kerr rotation and ellipticity for angles of incidence between 16° and 65° were then calculated from Voigt’s theory. These results compared satisfactorily with the experimental measurements at these same angles of incidence.

The complex magneto-optic conductivity σ¯1 was calculated from the four optical parameters for each kind of film. The change of σ¯1real and σ¯1imag with the frequency of the incident radiation was compared with the predictions of Argyres’s theory. This comparison indicated that the predicted frequency dependence did appear in σ¯1real and σ¯1imag; however, the data extended over such a short frequency range that the results were inconclusive.

© 1963 Optical Society of America

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References

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  1. M. Faraday, Trans. Roy. Soc. (London) 5, 592 (1846).
  2. J. Kerr, Phil. Mag. 3, 339 (1877).
    [CrossRef]
  3. J. Kerr, Phil. Mag. 5, 161 (1878).
    [CrossRef]
  4. W. Schutz, Handbuch der Experimental physik (Akademische Verlagsgesellschaft, Leipzig, 1936), Vol. 16.
  5. M. Laue, reference 4, Vol. 18.
  6. R. de Mallemann and F. Suhner, “Pouvoir Rotatoire Magnétique” and “Effet Magnéto-optique de Kerr,” Tables de Constantes et Données Numériques (Hermann et Cie., Paris, 1951).
  7. International Critical Table, edited by E. W. Washburn (McGraw-Hill Book Company, Inc., New York, 1929), Vol. 6, p. 425.
  8. W. Voigt, Magneto-und Eleklrooptik (B. G. Teubner, Leipzig, 1908).
  9. C. Snow, Phys. Rev. 2, 29 (1913).
    [CrossRef]
  10. W. Dziewulski, Diss, Gottingen (1914). Information also contained in W. Shutz, reference 4, Vol. 16, p. 362.
  11. W. Voigt, Physik Z. 16, 298 (1915).
  12. H. R. Hulme, Proc. Roy. Soc. (London) A135, 237 (1932).
    [CrossRef]
  13. P. N. Argyres, Phys. Rev. 97, 334 (1955).
    [CrossRef]
  14. F. E. Wright, J. Opt. Soc. Am. 20, 529 (1930).
    [CrossRef]
  15. C. A. Skinner, J. Opt. Soc. Am. 10, 491 (1925).
    [CrossRef]
  16. Suggested by A. C. Hardy of MIT.
  17. P. J. Fopiano and M. B. Trageser, “A Null Method Photoelectric Polarimeter,” S. B. thesis, MIT (1951).
  18. L. R. Ingersoll, Astrophys. J. 32, 265 (1910).
    [CrossRef]
  19. G. S. Krinchik, Bulletin Moscow State University 87, No. 6 (1957).
  20. G. S. Krinchik and R. D. Nuralieva, Physics of Metals and Metal Research 7, 694 (1959).
  21. G. S. Krinchik and I. S. Stroganova, Physics of Metals and Metal Research 7, 460 (1959).

1959 (2)

G. S. Krinchik and R. D. Nuralieva, Physics of Metals and Metal Research 7, 694 (1959).

G. S. Krinchik and I. S. Stroganova, Physics of Metals and Metal Research 7, 460 (1959).

1957 (1)

G. S. Krinchik, Bulletin Moscow State University 87, No. 6 (1957).

1955 (1)

P. N. Argyres, Phys. Rev. 97, 334 (1955).
[CrossRef]

1932 (1)

H. R. Hulme, Proc. Roy. Soc. (London) A135, 237 (1932).
[CrossRef]

1930 (1)

1925 (1)

1915 (1)

W. Voigt, Physik Z. 16, 298 (1915).

1913 (1)

C. Snow, Phys. Rev. 2, 29 (1913).
[CrossRef]

1910 (1)

L. R. Ingersoll, Astrophys. J. 32, 265 (1910).
[CrossRef]

1878 (1)

J. Kerr, Phil. Mag. 5, 161 (1878).
[CrossRef]

1877 (1)

J. Kerr, Phil. Mag. 3, 339 (1877).
[CrossRef]

1846 (1)

M. Faraday, Trans. Roy. Soc. (London) 5, 592 (1846).

Argyres, P. N.

P. N. Argyres, Phys. Rev. 97, 334 (1955).
[CrossRef]

de Mallemann, R.

R. de Mallemann and F. Suhner, “Pouvoir Rotatoire Magnétique” and “Effet Magnéto-optique de Kerr,” Tables de Constantes et Données Numériques (Hermann et Cie., Paris, 1951).

Dziewulski, W.

W. Dziewulski, Diss, Gottingen (1914). Information also contained in W. Shutz, reference 4, Vol. 16, p. 362.

Faraday, M.

M. Faraday, Trans. Roy. Soc. (London) 5, 592 (1846).

Fopiano, P. J.

P. J. Fopiano and M. B. Trageser, “A Null Method Photoelectric Polarimeter,” S. B. thesis, MIT (1951).

Hulme, H. R.

H. R. Hulme, Proc. Roy. Soc. (London) A135, 237 (1932).
[CrossRef]

Ingersoll, L. R.

L. R. Ingersoll, Astrophys. J. 32, 265 (1910).
[CrossRef]

Kerr, J.

J. Kerr, Phil. Mag. 5, 161 (1878).
[CrossRef]

J. Kerr, Phil. Mag. 3, 339 (1877).
[CrossRef]

Krinchik, G. S.

G. S. Krinchik and I. S. Stroganova, Physics of Metals and Metal Research 7, 460 (1959).

G. S. Krinchik and R. D. Nuralieva, Physics of Metals and Metal Research 7, 694 (1959).

G. S. Krinchik, Bulletin Moscow State University 87, No. 6 (1957).

Laue, M.

M. Laue, reference 4, Vol. 18.

Nuralieva, R. D.

G. S. Krinchik and R. D. Nuralieva, Physics of Metals and Metal Research 7, 694 (1959).

Schutz, W.

W. Schutz, Handbuch der Experimental physik (Akademische Verlagsgesellschaft, Leipzig, 1936), Vol. 16.

Skinner, C. A.

Snow, C.

C. Snow, Phys. Rev. 2, 29 (1913).
[CrossRef]

Stroganova, I. S.

G. S. Krinchik and I. S. Stroganova, Physics of Metals and Metal Research 7, 460 (1959).

Suhner, F.

R. de Mallemann and F. Suhner, “Pouvoir Rotatoire Magnétique” and “Effet Magnéto-optique de Kerr,” Tables de Constantes et Données Numériques (Hermann et Cie., Paris, 1951).

Trageser, M. B.

P. J. Fopiano and M. B. Trageser, “A Null Method Photoelectric Polarimeter,” S. B. thesis, MIT (1951).

Voigt, W.

W. Voigt, Physik Z. 16, 298 (1915).

W. Voigt, Magneto-und Eleklrooptik (B. G. Teubner, Leipzig, 1908).

Wright, F. E.

Astrophys. J. (1)

L. R. Ingersoll, Astrophys. J. 32, 265 (1910).
[CrossRef]

Bulletin Moscow State University (1)

G. S. Krinchik, Bulletin Moscow State University 87, No. 6 (1957).

J. Opt. Soc. Am. (2)

Phil. Mag. (2)

J. Kerr, Phil. Mag. 3, 339 (1877).
[CrossRef]

J. Kerr, Phil. Mag. 5, 161 (1878).
[CrossRef]

Phys. Rev. (2)

C. Snow, Phys. Rev. 2, 29 (1913).
[CrossRef]

P. N. Argyres, Phys. Rev. 97, 334 (1955).
[CrossRef]

Physics of Metals and Metal Research (2)

G. S. Krinchik and R. D. Nuralieva, Physics of Metals and Metal Research 7, 694 (1959).

G. S. Krinchik and I. S. Stroganova, Physics of Metals and Metal Research 7, 460 (1959).

Physik Z. (1)

W. Voigt, Physik Z. 16, 298 (1915).

Proc. Roy. Soc. (London) (1)

H. R. Hulme, Proc. Roy. Soc. (London) A135, 237 (1932).
[CrossRef]

Trans. Roy. Soc. (London) (1)

M. Faraday, Trans. Roy. Soc. (London) 5, 592 (1846).

Other (8)

W. Dziewulski, Diss, Gottingen (1914). Information also contained in W. Shutz, reference 4, Vol. 16, p. 362.

W. Schutz, Handbuch der Experimental physik (Akademische Verlagsgesellschaft, Leipzig, 1936), Vol. 16.

M. Laue, reference 4, Vol. 18.

R. de Mallemann and F. Suhner, “Pouvoir Rotatoire Magnétique” and “Effet Magnéto-optique de Kerr,” Tables de Constantes et Données Numériques (Hermann et Cie., Paris, 1951).

International Critical Table, edited by E. W. Washburn (McGraw-Hill Book Company, Inc., New York, 1929), Vol. 6, p. 425.

W. Voigt, Magneto-und Eleklrooptik (B. G. Teubner, Leipzig, 1908).

Suggested by A. C. Hardy of MIT.

P. J. Fopiano and M. B. Trageser, “A Null Method Photoelectric Polarimeter,” S. B. thesis, MIT (1951).

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Figures (13)

Fig. 1
Fig. 1

Quantities that describe elliptic polarization.

Fig. 2
Fig. 2

Simple graphical relation between the elliptic parameters for small values of , θ, and α.

Fig. 3
Fig. 3

Photoelectric ellipsometer. CM, collimating mirrors; P, polarizer; R, retardation plate; A, analyzer; and PM, photomultiplier.

Fig. 4
Fig. 4

Light pulses transmitted by analyzer crossed with major axis.

Fig. 5
Fig. 5

Light pulses transmitted by analyzer uncrossed with the major axis.

Fig. 6
Fig. 6

Measurements θ and θ that determine the ellipticity of P.

Fig. 7
Fig. 7

Method of calibrating the retardation plate.

Fig. 8
Fig. 8

Real and imaginary parts of the complex magneto-optic conductivity σ ¯ 1 of iron.

Fig. 9
Fig. 9

Real and imaginary parts of the complex magneto-optic conductivity σ ¯ 1 of nickel.

Fig. 10
Fig. 10

Real and imaginary parts of the complex magneto-optic conductivity σ ¯ 1 of Permalloy.

Fig. 11
Fig. 11

Kerr rotation and ellipticity as a function of angle of incidence for iron.

Fig. 12
Fig. 12

Kerr rotation and ellipticity as a function of angle of incidence for nickel.

Fig. 13
Fig. 13

Kerr rotation and ellipticity as a function of angle of incidence for Permalloy.

Tables (2)

Tables Icon

Table I Optical constants of opaque iron, nickel, and Permalloy films.

Tables Icon

Table II Magneto-optical parameters of opaque iron, nickel, and Permalloy films.

Equations (25)

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tan 2 θ = ( tan 2 α ) cos δ ,
sin 2 = ( sin 2 α ) sin δ .
2 θ = 2 α cos δ ,
2 = 2 α sin δ ,
R s = r s s I s + r s p I p ,
R p = r p s I s + r p p I p ,
R s R p = θ + i = r s s r p p ( Δ γ ± γ 2 ) + r s p r p p .
θ + i = Δ R + R + K .
N = n ( 1 i k ) ,
Q = Q 0 e i q = Q r + i Q i .
r s s = ( cos ϕ i N cos ϕ t ) / ( cos ϕ i + N cos ϕ t ) ,
r p p = ( N cos ϕ i cos ϕ t ) / ( N cos ϕ i + cos ϕ t ) ,
r s p = r p s = i Q cos ϕ i sin ϕ i cos ϕ t ( N cos ϕ t + cos ϕ i ) ( N cos ϕ i + cos ϕ t ) .
N = ( 2 R γ ) sin 2 ϕ i 2 ( 2 R + γ ) cos ϕ i ± { [ 1 2 ( 2 R γ 2 R + γ ) sin 2 ϕ i cos ϕ i ] 2 + 1 } 1 2 .
Q = i K [ ( N + cos ϕ i ) ( N cos ϕ i 1 ) / sin ϕ i cos ϕ i ] .
σ ¯ = σ + i ω 0 α .
σ ¯ = | σ ¯ 0 σ ¯ 1 0 σ ¯ 1 σ ¯ 0 0 0 0 σ ¯ 0 | .
σ ¯ 1 = σ 1 + i ω 0 α 1 .
σ 1 = ( 4 e c / m ) { m > n Q m n / ( ω m n 2 ω 2 ) Av } M ,
α 1 = ( 2 π e c / m ) { ( 1 / ω 2 ) m > n δ ( ω m n ω ) Q m n Av } M .
ε ¯ = 0 | P i Q P 0 i Q P P 0 0 0 P 0 | .
σ ¯ 0 = ω 0 { 2 n 2 k + i [ n 2 ( 1 k 2 ) + 1 ] } ,
σ ¯ 1 = ω 0 n 2 { [ Q r ( k 2 1 ) 2 k Q i ] + i [ Q i ( k 2 1 ) + 2 k Q r ] } .
= θ cot β θ csc β .
β = arc cos ( D D / P P ) .