Abstract

We have analyzed the effects of polarizer and analyzer imperfections in a phase-modulated magneto-optical Kerr spectrometer, using Jones matrices, and found that these imperfections do not seriously affect measurements of magneto-optical effects, to a first-order approximation. The analysis was experimentally proved in a magneto-optical Kerr spectrometer with a dichroic polarizer and analyzer with an extinction ratio of 10-2.

© 2000 Optical Society of America

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References

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  1. S. Hashimoto, Y. Ochiai, and K. Aso, “Light wavelength dependence of magneto-optical properties in ultrathin Co/Pt and Co/Pd multilayered films,” Jpn. J. Appl. Phys. 28, L1824–L1826 (1989).
    [CrossRef]
  2. Y. J. Cheo, S. Tsunashima, T. Katakyama, and S. Uchiyama, “Magneto-optical spectra of amorphous RE-Co thin films,” J. Magn. Soc. Jpn. Suppl. 11, 273–276 (1987).
  3. K. H. J. Buschow, “Magneto-optical properties of alloys and intermetallic compounds,” in Ferromagnetic Materials, E. P. Wohlfarth and K. H. J. Buschow, eds. (North-Holland, Amsterdam, 1988), Vol. 4, Chap. 5, p. 538.
  4. K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Wagonage, K. Takanashi, and H. Fujimori, “Magneto-optical Kerr spectrometer for 1.2–5.9 eV region and its application to FePt/Pt multilayers,” Jpn. J. Appl. Phys. 32, 989–995 (1993).
    [CrossRef]
  5. G. E. Jellison, Jr. and F. A. Modine, “Optical constants for silicon at 300 and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
    [CrossRef]
  6. V. M. Bermudez and V. H. Ritz, “Wavelength-scanning polarization-modulation ellipsometry: some practical considerations,” Appl. Opt. 17, 542–552 (1978).
    [CrossRef] [PubMed]
  7. F. A. Modine, G. E. Jellison, Jr., and G. R. Gruzalski, “Errors in ellipsometry measurements made with a photoelastic modulator,” J. Opt. Soc. Am. 73, 892–900 (1983).
    [CrossRef]
  8. C.-Y. You and S.-C. Shin, “Zone-averaged method to minimize polarizer and analyzer imperfections in a phase-modulated spectroscopic ellipsometer,” Rev. Sci. Instrum. 68, 3519–3522 (1997).
    [CrossRef]
  9. C.-Y. You and S.-C. Shin, “A highly sensitive magneto-optical Kerr spectrometer using a sheet-type polarizer,” presented at the International Magnetism Conference, New Orleans, La., April 1–4, 1997.
  10. R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).
  11. G. Srinivas and S.-C. Shin, “Novel (Pt/Co/Pt/Ni) multilayers for magneto-optical recording media,” Appl. Phys. Lett. 69, 3086–3088 (1996).
    [CrossRef]

1997 (1)

C.-Y. You and S.-C. Shin, “Zone-averaged method to minimize polarizer and analyzer imperfections in a phase-modulated spectroscopic ellipsometer,” Rev. Sci. Instrum. 68, 3519–3522 (1997).
[CrossRef]

1996 (1)

G. Srinivas and S.-C. Shin, “Novel (Pt/Co/Pt/Ni) multilayers for magneto-optical recording media,” Appl. Phys. Lett. 69, 3086–3088 (1996).
[CrossRef]

1993 (1)

K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Wagonage, K. Takanashi, and H. Fujimori, “Magneto-optical Kerr spectrometer for 1.2–5.9 eV region and its application to FePt/Pt multilayers,” Jpn. J. Appl. Phys. 32, 989–995 (1993).
[CrossRef]

1989 (1)

S. Hashimoto, Y. Ochiai, and K. Aso, “Light wavelength dependence of magneto-optical properties in ultrathin Co/Pt and Co/Pd multilayered films,” Jpn. J. Appl. Phys. 28, L1824–L1826 (1989).
[CrossRef]

1987 (1)

Y. J. Cheo, S. Tsunashima, T. Katakyama, and S. Uchiyama, “Magneto-optical spectra of amorphous RE-Co thin films,” J. Magn. Soc. Jpn. Suppl. 11, 273–276 (1987).

1983 (1)

1982 (1)

G. E. Jellison, Jr. and F. A. Modine, “Optical constants for silicon at 300 and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

1978 (1)

Aso, K.

S. Hashimoto, Y. Ochiai, and K. Aso, “Light wavelength dependence of magneto-optical properties in ultrathin Co/Pt and Co/Pd multilayered films,” Jpn. J. Appl. Phys. 28, L1824–L1826 (1989).
[CrossRef]

Bermudez, V. M.

Cheo, Y. J.

Y. J. Cheo, S. Tsunashima, T. Katakyama, and S. Uchiyama, “Magneto-optical spectra of amorphous RE-Co thin films,” J. Magn. Soc. Jpn. Suppl. 11, 273–276 (1987).

Fujimori, H.

K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Wagonage, K. Takanashi, and H. Fujimori, “Magneto-optical Kerr spectrometer for 1.2–5.9 eV region and its application to FePt/Pt multilayers,” Jpn. J. Appl. Phys. 32, 989–995 (1993).
[CrossRef]

Gruzalski, G. R.

Hashimoto, S.

S. Hashimoto, Y. Ochiai, and K. Aso, “Light wavelength dependence of magneto-optical properties in ultrathin Co/Pt and Co/Pd multilayered films,” Jpn. J. Appl. Phys. 28, L1824–L1826 (1989).
[CrossRef]

Hongu, H.

K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Wagonage, K. Takanashi, and H. Fujimori, “Magneto-optical Kerr spectrometer for 1.2–5.9 eV region and its application to FePt/Pt multilayers,” Jpn. J. Appl. Phys. 32, 989–995 (1993).
[CrossRef]

Ikekame, H.

K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Wagonage, K. Takanashi, and H. Fujimori, “Magneto-optical Kerr spectrometer for 1.2–5.9 eV region and its application to FePt/Pt multilayers,” Jpn. J. Appl. Phys. 32, 989–995 (1993).
[CrossRef]

Jellison Jr., G. E.

F. A. Modine, G. E. Jellison, Jr., and G. R. Gruzalski, “Errors in ellipsometry measurements made with a photoelastic modulator,” J. Opt. Soc. Am. 73, 892–900 (1983).
[CrossRef]

G. E. Jellison, Jr. and F. A. Modine, “Optical constants for silicon at 300 and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

Katakyama, T.

Y. J. Cheo, S. Tsunashima, T. Katakyama, and S. Uchiyama, “Magneto-optical spectra of amorphous RE-Co thin films,” J. Magn. Soc. Jpn. Suppl. 11, 273–276 (1987).

Modine, F. A.

F. A. Modine, G. E. Jellison, Jr., and G. R. Gruzalski, “Errors in ellipsometry measurements made with a photoelastic modulator,” J. Opt. Soc. Am. 73, 892–900 (1983).
[CrossRef]

G. E. Jellison, Jr. and F. A. Modine, “Optical constants for silicon at 300 and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

Ochiai, Y.

S. Hashimoto, Y. Ochiai, and K. Aso, “Light wavelength dependence of magneto-optical properties in ultrathin Co/Pt and Co/Pd multilayered films,” Jpn. J. Appl. Phys. 28, L1824–L1826 (1989).
[CrossRef]

Ritz, V. H.

Sato, K.

K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Wagonage, K. Takanashi, and H. Fujimori, “Magneto-optical Kerr spectrometer for 1.2–5.9 eV region and its application to FePt/Pt multilayers,” Jpn. J. Appl. Phys. 32, 989–995 (1993).
[CrossRef]

Shin, S.-C.

C.-Y. You and S.-C. Shin, “Zone-averaged method to minimize polarizer and analyzer imperfections in a phase-modulated spectroscopic ellipsometer,” Rev. Sci. Instrum. 68, 3519–3522 (1997).
[CrossRef]

G. Srinivas and S.-C. Shin, “Novel (Pt/Co/Pt/Ni) multilayers for magneto-optical recording media,” Appl. Phys. Lett. 69, 3086–3088 (1996).
[CrossRef]

Srinivas, G.

G. Srinivas and S.-C. Shin, “Novel (Pt/Co/Pt/Ni) multilayers for magneto-optical recording media,” Appl. Phys. Lett. 69, 3086–3088 (1996).
[CrossRef]

Takanashi, K.

K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Wagonage, K. Takanashi, and H. Fujimori, “Magneto-optical Kerr spectrometer for 1.2–5.9 eV region and its application to FePt/Pt multilayers,” Jpn. J. Appl. Phys. 32, 989–995 (1993).
[CrossRef]

Tosaka, Y.

K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Wagonage, K. Takanashi, and H. Fujimori, “Magneto-optical Kerr spectrometer for 1.2–5.9 eV region and its application to FePt/Pt multilayers,” Jpn. J. Appl. Phys. 32, 989–995 (1993).
[CrossRef]

Tsunashima, S.

Y. J. Cheo, S. Tsunashima, T. Katakyama, and S. Uchiyama, “Magneto-optical spectra of amorphous RE-Co thin films,” J. Magn. Soc. Jpn. Suppl. 11, 273–276 (1987).

Uchiyama, S.

Y. J. Cheo, S. Tsunashima, T. Katakyama, and S. Uchiyama, “Magneto-optical spectra of amorphous RE-Co thin films,” J. Magn. Soc. Jpn. Suppl. 11, 273–276 (1987).

Wagonage, M.

K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Wagonage, K. Takanashi, and H. Fujimori, “Magneto-optical Kerr spectrometer for 1.2–5.9 eV region and its application to FePt/Pt multilayers,” Jpn. J. Appl. Phys. 32, 989–995 (1993).
[CrossRef]

You, C.-Y.

C.-Y. You and S.-C. Shin, “Zone-averaged method to minimize polarizer and analyzer imperfections in a phase-modulated spectroscopic ellipsometer,” Rev. Sci. Instrum. 68, 3519–3522 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. Srinivas and S.-C. Shin, “Novel (Pt/Co/Pt/Ni) multilayers for magneto-optical recording media,” Appl. Phys. Lett. 69, 3086–3088 (1996).
[CrossRef]

J. Appl. Phys. (1)

G. E. Jellison, Jr. and F. A. Modine, “Optical constants for silicon at 300 and 10 K determined from 1.64 to 4.73 eV by ellipsometry,” J. Appl. Phys. 53, 3745–3753 (1982).
[CrossRef]

J. Magn. Soc. Jpn. Suppl. (1)

Y. J. Cheo, S. Tsunashima, T. Katakyama, and S. Uchiyama, “Magneto-optical spectra of amorphous RE-Co thin films,” J. Magn. Soc. Jpn. Suppl. 11, 273–276 (1987).

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (2)

S. Hashimoto, Y. Ochiai, and K. Aso, “Light wavelength dependence of magneto-optical properties in ultrathin Co/Pt and Co/Pd multilayered films,” Jpn. J. Appl. Phys. 28, L1824–L1826 (1989).
[CrossRef]

K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Wagonage, K. Takanashi, and H. Fujimori, “Magneto-optical Kerr spectrometer for 1.2–5.9 eV region and its application to FePt/Pt multilayers,” Jpn. J. Appl. Phys. 32, 989–995 (1993).
[CrossRef]

Rev. Sci. Instrum. (1)

C.-Y. You and S.-C. Shin, “Zone-averaged method to minimize polarizer and analyzer imperfections in a phase-modulated spectroscopic ellipsometer,” Rev. Sci. Instrum. 68, 3519–3522 (1997).
[CrossRef]

Other (3)

C.-Y. You and S.-C. Shin, “A highly sensitive magneto-optical Kerr spectrometer using a sheet-type polarizer,” presented at the International Magnetism Conference, New Orleans, La., April 1–4, 1997.

R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).

K. H. J. Buschow, “Magneto-optical properties of alloys and intermetallic compounds,” in Ferromagnetic Materials, E. P. Wohlfarth and K. H. J. Buschow, eds. (North-Holland, Amsterdam, 1988), Vol. 4, Chap. 5, p. 538.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of a MO Kerr spectrometric system: L, Xe lamp; M1, ellipsoidal mirror 1; M2, ellipsoidal mirror 2; P, polarizer; A, analyzer; L1, lock-in amplifier 1; L2, lock-in amplifier 2; D, double monochromator; PM, photomultiplier tube; E, electromagnet; G, gaussmeter; C, PEM controller; FS, feedback system; PS, power supply; PC, computer system (GPIB, analog-to-digital, digital-to-analog, serial, parallel).

Fig. 2
Fig. 2

Ellipticity measured at polarizer angles p=±1°. Any discrepancy in the ellipticity between the two polarizer angles reflects the contribution of an imperfect analyzer.

Fig. 3
Fig. 3

Dependence of the I(2ω)/I(0) signal on polarizer angle p. Open circles, experimental data; solid curve, a fitting curve.

Fig. 4
Fig. 4

Kerr hysteresis loop of a 20× (4.6-Å Pt–5 Å Co–4.6 Å Pt–5 Å Ni) film measured at a wavelength of 300 nm. Inset, detail of the middle part of the hysteresis loop, where the Kerr rotation angles are very small.

Equations (22)

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P, A=1000,S=r˜+00r˜-,M=100eiδ.
I=|Ef |2=|AR(-a)MF-1SFR(p)PEi|2,
F=121i1-i.
I=I0R1-ΔR2Rsin δ-sin(2p+Δθ)cos δ.
II(0)+I(ω)sin(ωt)+I(2ω)cos(2ωt)+ ,
I(0)=I0R[1+J0(δ0)sin(2θK)],
I(ω)=-4AI0RKJ1(δ0),
I(2ω)=4BI0RθKJ2(δ0),
P=1α˜1α˜2α˜3,A=1β˜1β˜2β˜3,
α=α˜2-α˜31+α˜12.
I(0)=I0(R)(1+2α1r)-2(α2i+α3i) ΔR2R-2β1r cos(2p+Δθ)+J0(δ0)×-sin(2p+Δθ)-2(α2r+α3r)×cos(2p+Δθ)-2β1i ΔR2R,
I(ω)=2J1(δ0)I0R-(1+2α1r) ΔR2R-2(α2i+α3i)+2β1i sin(2p+Δθ),
I(2ω)=2J2(δ0)I0R×-(1+α1r)sin(2p+Δθ)+2(α2r+α3r)cos(2p+Δθ)-2β1i ΔR2R.
I(0)I0R(1+2α1r),
I(ω)-2AJ1(δ0)I0R×(1+2α1r) ΔR2R-2β1i sin(2p+Δθ),
I(2ω)-2BJ2(δ0)I0R(1+2α1r)×sin(2p+Δθ)+2β1iΔR2R.
I(2ω)-4J2(δ0)I0Rsin(2p-ϕ0)+2β1iΔR2R,
I0=I0[(1+2α1r)2+4(α2r+α3r)2]1/2,
ϕ0=arctan2(α2r+α3r)(1+2α1r),
β1i=β1i[(1+2α1r)2+4(α2r+α3r)2]1/2.
I(ω)I(0)-4AJ1(δ0)K,
I(2ω)I(0)4BJ2(δ0)θK.

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