Abstract

Magneto-optical Kerr effect (MOKE) spectroscopy in the -1st diffraction order with p-polarized incidence is applied to study arrays of submicron Permalloy wires at polar magnetization. A theoretical approach combining two methods, the local modes method neglecting the edge effects of wires and the rigorous coupled wave analysis, is derived to evaluate the diffraction losses due to irregularities of the wire edges. A new parameter describing the quality of the edges is defined according to their contribution in the diffracted MOKE. The quality factor, evaluated for two different samples, is successfully compared with irregularities visible on atomic force microscopy pictures.

© 2005 Optical Society of America

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References

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    [CrossRef]
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Acta Phys. Slov.

P. Klapetek, I. Ohlidal, D. Franta, A. Montaigne-Ramil, A. Bonanni, D. Stifter, and H. Sitter, �??Atomic force microscopy characterization of ZnTe epitaxial films,�?? Acta Phys. Slov. 53, 223-230 (2003).

Appl. Phys. Lett.

P. Garcia-Mochales, J. L. Costa-Kramer, G. Armelles, F. Briones, D. Jaque, J. I. Martin, and J. L. Vicent, �??Simulations and experiments on magneto-optical diffraction by an array of epitaxial Fe(001) microsquares,�?? Appl. Phys. Lett. 81, 3206-3208 (2002).
[CrossRef]

R. Antos, J. Mistrik, T. Yamaguchi, S. Visnovsky, S.O. Demokritov, and B. Hillebrands, �??Evidence of native oxides on the capping and substrate of Permalloy gratings by magneto-optical spectroscopy in the zeroth- and first-diffraction orders,�?? Appl. Phys. Lett. 86, 231101 (2005).
[CrossRef]

G. Neuber, R. Rauer, J. Kunze, T. Korn, C. Pels, G. Meier, U. Merkt, J. Backstrom, and M. Rubhausen, �??Temperature-dependent spectral generalized magneto-optical ellipsometry,�?? Appl. Phys. Lett. 83, 4509-4511 (2003).
[CrossRef]

Appl. Surf. Sci.

R. Antos, I. Ohlidal, J. Mistrik, K. Murakami, T. Yamaguchi, J. Pistora, M. Horie, and S. Visnovsky, �??Spectroscopic ellipsometry on lamellar gratings,�?? Appl. Surf. Sci. 244, 225-229 (2005).
[CrossRef]

Handbook of Optical Constants of Solids

D. F. Edwards, �??Silicon (Si),�?? in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Tokyo, 1998); H. R. Philipp, �??Silicon Dioxide (SiO2) (Glass),�?? ibid.

J. Appl. Phys.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, �??Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,�?? J. Appl. Phys. 97, 053107 (2005).
[CrossRef]

J. Magn. Magn. Mater.

Y. Suzuki, C. Chappert, P. Bruno, and P. Veillet, �??Simple model for the magneto-optical Kerr diffraction of a regular array of magnetic dots,�?? J. Magn. Magn. Mater. 165, 516-519 (1997).
[CrossRef]

R. Antos, J. Mistrik, M. Aoyama, T. Yamaguchi, S. Visnovsky, and B. Hillebrands, �??Magneto-optical spectroscopy on permalloy wires in 0th and 1st diffraction orders,�?? J. Magn. Magn. Mater. 272-276, 1670-1671 (2004).
[CrossRef]

J. I. Martin, J. Nogues, K. Liu, J. L. Vicent, and I. K. Schuller, �??Ordered magnetic nanostructures: fabrication and properties,�?? J. Magn. Magn. Mater. 256, 449-501 (2003).
[CrossRef]

Y. Souche, V. Novosad, B. Pannetier, and O. Geoffroy, �??Magneto-optical diffraction and transverse Kerr effect,�?? J. Magn. Magn. Mater. 177-181, 1277-1278 (1998).
[CrossRef]

J. Mod. Opt.

D. Franta and I. Ohlidal, �??Ellipsometric parameters and reflectances of thin films with slightly rough boundaries,�?? J. Mod. Opt. 45, 903-934 (1998).
[CrossRef]

J. Opt. Soc. Am.

J. Phys.:Condens. Matter.

M. Grimsditch and P. Vavassori, �??The diffracted magneto-optic Kerr effect: what does it tell you?�?? J. Phys.:Condens. Matter. 16, R275-R294 (2004).
[CrossRef]

Nanotechnology

J. L. Costa-Kramer, C. Guerrero, S. Melle, P. Garcia-Mochales, and F. Briones, �??Pure magneto-optic diffraction by a periodic domain structure,�?? Nanotechnology 14, 239-244 (2003).
[CrossRef]

Opt. Commun.

D. van Labeke, A. Vial, V. A. Novosad, Y. Souche, M. Schlenker, and A. D. Dos Santos, �??Diffraction of light by a corrugated magnetic grating: experimental results and calculation using a perturbation approximation to the Rayleigh method,�?? Opt. Commun. 124, 519-528 (1996).
[CrossRef]

A. Vial and D. Van Labeke, �??Diffraction hysteresis loop modelisation in transverse magneto-optical Kerr effect,�?? Opt. Commun. 153, 125-133 (1998).
[CrossRef]

Y. Pagani, D. Van Labeke, B. Guizal, A. Vial, and F. Baida, �??Diffraction hysteresis loop modeling in magneto-optical gratings,�?? Opt. Commun. 209, 237-244 (2002).
[CrossRef]

Progress in Optics

I. Ohlidal and D. Franta, �??Ellipsometry of Thin Film Systems,�?? Progress in Optics 41, 181-282 (2000).
[CrossRef]

Surf. Coat. Tech.

P. Hones, M. Diserens, and F. Levy, �??Characterization of sputter-deposited chromium oxide thin films,�?? Surf. Coat. Tech. 120-121, 277-283 (1999).
[CrossRef]

Surf. Interface Anal.

P. Klapetek, I. Ohlidal, D. Franta, and P. Pokorny, �??Analysis of the boundaries of ZrO2 and HfO2 thin films by atomic force microscopy and the combined optical method,�?? Surf. Interface Anal. 34, 559-564 (2002).
[CrossRef]

Thin Solid Films

H.-T. Huang and F. L. Terry, Jr., �??Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring,�?? Thin Solid Films 455-456, 828-836 (2004).
[CrossRef]

Trans. Magn. Soc. Japan

R. Antos, J. Mistrik, S. Visnovsky, M. Aoyama, T. Yamaguchi, and B. Hillebrands, �??Characterization of Permalloy wires by optical and magneto-optical spectroscopy,�?? Trans. Magn. Soc. Japan 4, 282-285 (2004).
[CrossRef]

Other

S. Ingvarsson, �??Magnetization dynamics in transition metal ferromagnets studied by magneto-tunneling and ferromagnetic resonance,�?? (Ph.D. thesis, Brown University, 2001).

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Figures (4)

Fig. 1.
Fig. 1.

Atomic force microscopy pictures of the analyzed sample (a) and a sample of higher quality (b). Top view of each sample is accompanied by the cross section.

Fig. 2.
Fig. 2.

Absolute values of two simulated amplitude reflectances, |rsp | (a) and |rpp | (b), in the-1st diffraction order. Simulations of the RCWA (solid curves) are compared with the LMM (dotted curves).

Fig. 3.
Fig. 3.

Polar Kerr rotation (a) and ellipticity (b) in the 1st diffraction order for p-polarized incidence. Experimental data (circles) are compared with simulations of RCWA (solid curves) and LMM (dotted curves).

Fig. 4.
Fig. 4.

Polar Kerr rotation (a) and ellipticity (b) in the -1st diffraction order for p-polarized incidence. Experimental data (circles) are compared with simulations of the combined RCWA-LMM model (solid curves).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

r α β ( n = 0 ) = fr w , α β + ( 1 f ) r b , α β + Δ r α β ( n = 0 ) ,
r α β ( n 0 ) = i 2 π n ( r w , α β r b , α β ) ( 1 e 2 π inf ) + Δ r α β ( n 0 ) ,
θ p ( 1 ) i ε p ( 1 ) = r sp ( 1 ) r pp ( 1 ) .
Δ r pp ( 1 ) ¯ = η ( λ ) Δ r pp ( 1 )

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