Abstract

Magneto-optic (MO) response in nanostructures with ultrathin Fe considered for the MO mapping of current pulses with a two-dimensional diffraction limited resolution is investigated in detail. The structures consist of an ultrathin Fe layer sandwiched with dielectric layers, deposited on a reflector and covered by a noble metal protecting layer. The structures are modeled as five-layer systems with abrupt interfaces. Analytical expressions are provided that are useful in the search for the maximum of MO reflected wave amplitude polarized perpendicular to the incident linearly polarized wave, |ryx(05)|. The procedure of finding the maximal |ryx(05)| is illustrated on the structures with ultrathin Fe at the laser wavelength of 632.8 nm. The maximal |ryx(05)| of 0.018347 was achieved in the structure AlN(52 nm)/Fe(15 nm)/AlN(26 nm)/Au. The deposition of a 5 nm protecting Au layer reduced |ryx(05)| by 6 per cent.

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2012 (1)

J. A. Arregi, J. B. Gonzales-Diaz, E. Bergaretxe, O. Idigoras, T. Unsal, and A. Berger, “Study of generalized magneto-optical ellipsometry measurement reliability,” J. Appl. Phys.111(10), 103912 (2012).
[CrossRef]

2010 (3)

M. Moradi and M. Ghanaatshoar, “Cavity enhancement of the magneto-optic Kerr effect in glass/Al/SnO2/PtMnSb/SnO2 structure,” Opt. Commun.283(24), 5053–5057 (2010).
[CrossRef]

J. Y. Hwang, M. Ferrera, L. Razzari, A. Pignolet, and R. Morandotti, “The role of Bi3+ ions in magneto-optic Ce and Bi comodified epitaxial iron garnet films,” Appl. Phys. Lett.97(16), 161901 (2010).
[CrossRef]

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

2009 (1)

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

2008 (1)

E. Liskova, S. Visnovsky, R. Lopusnik, I. Harward, M. Wenger, T. Christensen, and Z. Celinski, “Magneto-optical AlN/Fe/AlN structures optimized for operation in the violet spectral region,” J. Phys. D Appl. Phys.41(15), 155007 (2008).
[CrossRef]

2007 (1)

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

2005 (1)

W. R. Hendren, R. Atkinson, R. J. Pollard, I. W. Salter, C. D. Wright, W. W. Clegg, and D. F. L. Jenkins, “The design and optimization of disk structures for MAMMOS/MSR magneto-optic recording,” J. Phys. D Appl. Phys.38(14), 2310–2320 (2005).
[CrossRef]

2004 (1)

N. Qureshi, H. Schmidt, and A. R. Hawkins, “Cavity enhancement of the magneto-optic Kerr effect for optical studies of magnetic nanostructures,” Appl. Phys. Lett.85(3), 431–433 (2004).
[CrossRef]

2002 (1)

2000 (1)

M. R. Pufall and A. Berger, “Studying the reversal mode of the magnetization vector versus applied field angle using generalized magneto-optical ellipsometry,” J. Appl. Phys.87(9), 5834–5836 (2000).
[CrossRef]

1999 (1)

A. Berger and M. R. Pufall, “Quantitative vector magnetometry using generalized magneto-optical ellipsometry,” J. Appl. Phys.85(8), 4583–4585 (1999).
[CrossRef]

1997 (1)

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys.82(10), 5090–5096 (1997).
[CrossRef]

1996 (3)

R. Pittini, J. Schoenes, O. Vogt, and P. Wachter, “Discovery of 90 degree magneto-optical polar Kerr rotation in CeSb,” Phys. Rev. Lett.77(5), 944–947 (1996).
[CrossRef] [PubMed]

A. Y. Elezzabi and M. R. Freeman, “Ultrafast magneto-optic sampling of picosecond current pulses,” Appl. Phys. Lett.68(25), 3546–3548 (1996).
[CrossRef]

S. Visnovsky, R. Krishnan, M. Nyvlt, and V. Prosser, “Optical behaviour of Fe in magnetic multilayers,” J. Magn. Soc. Jpn.20, Supplement No. S1, 41–46 (1996).

1992 (1)

1986 (2)

Š. Višňovský, “Magneto-optical ellipsometry,” Czech. J. Phys. B36(5), 625–650 (1986).
[CrossRef]

M. Mansuripur, “Figure of merit for magneto-optical media based on the dielectric tensor,” Appl. Phys. Lett.49(1), 19–21 (1986).
[CrossRef]

1984 (1)

1979 (1)

1975 (1)

S. Wittekoek, T. J. A. Popma, J. M. Robertson, and P. F. Bongers, “Magneto-optic spectra and the dielectric tensor elements of bismuth-substituted iron garnets at photon energies between 2.2-5.2 eV,” Phys. Rev. B12(7), 2777–2788 (1975).
[CrossRef]

1974 (1)

P. B. Johnson and R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,” Phys. Rev. B9(12), 5056–5070 (1974).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

1969 (1)

C. F. Buhrer, “Faraday rotation and dichroism of bismuth calcium vanadium iron garnet,” J. Appl. Phys.40(11), 4500–4502 (1969).
[CrossRef]

1968 (1)

G. S. Krinchik and V. A. Artem’ev, “Magneto-optical properties of Ni, Co and Fe in ultraviolet visible and infrared parts of spectrum,” Sov. Phys. JETP26, 1080–1085 (1968).

1958 (1)

H. Suhl, “Origin and use of instabilities in ferromagnetic resonance,” J. Appl. Phys.29(3), 416–421 (1958).
[CrossRef]

1950 (1)

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris)5, 596–640, 706–782 (1950).

1948 (1)

C. Kittel, “On the theory of ferromagnetic resonance absorption,” Phys. Rev.73(2), 155–161 (1948).
[CrossRef]

Abelès, F.

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris)5, 596–640, 706–782 (1950).

Ambacher, O.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys.82(10), 5090–5096 (1997).
[CrossRef]

Angerer, H.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys.82(10), 5090–5096 (1997).
[CrossRef]

Arregi, J. A.

J. A. Arregi, J. B. Gonzales-Diaz, E. Bergaretxe, O. Idigoras, T. Unsal, and A. Berger, “Study of generalized magneto-optical ellipsometry measurement reliability,” J. Appl. Phys.111(10), 103912 (2012).
[CrossRef]

Artem’ev, V. A.

G. S. Krinchik and V. A. Artem’ev, “Magneto-optical properties of Ni, Co and Fe in ultraviolet visible and infrared parts of spectrum,” Sov. Phys. JETP26, 1080–1085 (1968).

Atkinson, R.

W. R. Hendren, R. Atkinson, R. J. Pollard, I. W. Salter, C. D. Wright, W. W. Clegg, and D. F. L. Jenkins, “The design and optimization of disk structures for MAMMOS/MSR magneto-optic recording,” J. Phys. D Appl. Phys.38(14), 2310–2320 (2005).
[CrossRef]

R. Atkinson, I. W. Salter, and J. Xu, “Design, fabrication, and performance of enhanced magneto-optic quadrilayers with controllable ellipticity,” Appl. Opt.31(23), 4847–4852 (1992).
[CrossRef] [PubMed]

Balin, K.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

Bergaretxe, E.

J. A. Arregi, J. B. Gonzales-Diaz, E. Bergaretxe, O. Idigoras, T. Unsal, and A. Berger, “Study of generalized magneto-optical ellipsometry measurement reliability,” J. Appl. Phys.111(10), 103912 (2012).
[CrossRef]

Berger, A.

J. A. Arregi, J. B. Gonzales-Diaz, E. Bergaretxe, O. Idigoras, T. Unsal, and A. Berger, “Study of generalized magneto-optical ellipsometry measurement reliability,” J. Appl. Phys.111(10), 103912 (2012).
[CrossRef]

M. R. Pufall and A. Berger, “Studying the reversal mode of the magnetization vector versus applied field angle using generalized magneto-optical ellipsometry,” J. Appl. Phys.87(9), 5834–5836 (2000).
[CrossRef]

A. Berger and M. R. Pufall, “Quantitative vector magnetometry using generalized magneto-optical ellipsometry,” J. Appl. Phys.85(8), 4583–4585 (1999).
[CrossRef]

Bongers, P. F.

S. Wittekoek, T. J. A. Popma, J. M. Robertson, and P. F. Bongers, “Magneto-optic spectra and the dielectric tensor elements of bismuth-substituted iron garnets at photon energies between 2.2-5.2 eV,” Phys. Rev. B12(7), 2777–2788 (1975).
[CrossRef]

Brunner, D.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys.82(10), 5090–5096 (1997).
[CrossRef]

Buhrer, C. F.

C. F. Buhrer, “Faraday rotation and dichroism of bismuth calcium vanadium iron garnet,” J. Appl. Phys.40(11), 4500–4502 (1969).
[CrossRef]

Bustarret, E.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys.82(10), 5090–5096 (1997).
[CrossRef]

Celinski, Z.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

E. Liskova, S. Visnovsky, R. Lopusnik, I. Harward, M. Wenger, T. Christensen, and Z. Celinski, “Magneto-optical AlN/Fe/AlN structures optimized for operation in the violet spectral region,” J. Phys. D Appl. Phys.41(15), 155007 (2008).
[CrossRef]

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

Christensen, T.

E. Liskova, S. Visnovsky, R. Lopusnik, I. Harward, M. Wenger, T. Christensen, and Z. Celinski, “Magneto-optical AlN/Fe/AlN structures optimized for operation in the violet spectral region,” J. Phys. D Appl. Phys.41(15), 155007 (2008).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,” Phys. Rev. B9(12), 5056–5070 (1974).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Clegg, W. W.

W. R. Hendren, R. Atkinson, R. J. Pollard, I. W. Salter, C. D. Wright, W. W. Clegg, and D. F. L. Jenkins, “The design and optimization of disk structures for MAMMOS/MSR magneto-optic recording,” J. Phys. D Appl. Phys.38(14), 2310–2320 (2005).
[CrossRef]

Correu, J.

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

Demirtas, S.

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

Dimitrov, R.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys.82(10), 5090–5096 (1997).
[CrossRef]

Elezzabi, A. Y.

A. Y. Elezzabi and M. R. Freeman, “Ultrafast magneto-optic sampling of picosecond current pulses,” Appl. Phys. Lett.68(25), 3546–3548 (1996).
[CrossRef]

Ferrera, M.

J. Y. Hwang, M. Ferrera, L. Razzari, A. Pignolet, and R. Morandotti, “The role of Bi3+ ions in magneto-optic Ce and Bi comodified epitaxial iron garnet films,” Appl. Phys. Lett.97(16), 161901 (2010).
[CrossRef]

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Freeman, M. R.

A. Y. Elezzabi and M. R. Freeman, “Ultrafast magneto-optic sampling of picosecond current pulses,” Appl. Phys. Lett.68(25), 3546–3548 (1996).
[CrossRef]

Freudenberg, F.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys.82(10), 5090–5096 (1997).
[CrossRef]

Ghanaatshoar, M.

M. Moradi and M. Ghanaatshoar, “Cavity enhancement of the magneto-optic Kerr effect in glass/Al/SnO2/PtMnSb/SnO2 structure,” Opt. Commun.283(24), 5053–5057 (2010).
[CrossRef]

Gonzales-Diaz, J. B.

J. A. Arregi, J. B. Gonzales-Diaz, E. Bergaretxe, O. Idigoras, T. Unsal, and A. Berger, “Study of generalized magneto-optical ellipsometry measurement reliability,” J. Appl. Phys.111(10), 103912 (2012).
[CrossRef]

Harnagea, C.

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Harward, I.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

E. Liskova, S. Visnovsky, R. Lopusnik, I. Harward, M. Wenger, T. Christensen, and Z. Celinski, “Magneto-optical AlN/Fe/AlN structures optimized for operation in the violet spectral region,” J. Phys. D Appl. Phys.41(15), 155007 (2008).
[CrossRef]

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

Hawkins, A. R.

N. Qureshi, H. Schmidt, and A. R. Hawkins, “Cavity enhancement of the magneto-optic Kerr effect for optical studies of magnetic nanostructures,” Appl. Phys. Lett.85(3), 431–433 (2004).
[CrossRef]

Hendren, W. R.

W. R. Hendren, R. Atkinson, R. J. Pollard, I. W. Salter, C. D. Wright, W. W. Clegg, and D. F. L. Jenkins, “The design and optimization of disk structures for MAMMOS/MSR magneto-optic recording,” J. Phys. D Appl. Phys.38(14), 2310–2320 (2005).
[CrossRef]

Höpler, R.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys.82(10), 5090–5096 (1997).
[CrossRef]

Hwang, J. Y.

J. Y. Hwang, M. Ferrera, L. Razzari, A. Pignolet, and R. Morandotti, “The role of Bi3+ ions in magneto-optic Ce and Bi comodified epitaxial iron garnet films,” Appl. Phys. Lett.97(16), 161901 (2010).
[CrossRef]

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Idigoras, O.

J. A. Arregi, J. B. Gonzales-Diaz, E. Bergaretxe, O. Idigoras, T. Unsal, and A. Berger, “Study of generalized magneto-optical ellipsometry measurement reliability,” J. Appl. Phys.111(10), 103912 (2012).
[CrossRef]

Jenkins, D. F. L.

W. R. Hendren, R. Atkinson, R. J. Pollard, I. W. Salter, C. D. Wright, W. W. Clegg, and D. F. L. Jenkins, “The design and optimization of disk structures for MAMMOS/MSR magneto-optic recording,” J. Phys. D Appl. Phys.38(14), 2310–2320 (2005).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,” Phys. Rev. B9(12), 5056–5070 (1974).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Kittel, C.

C. Kittel, “On the theory of ferromagnetic resonance absorption,” Phys. Rev.73(2), 155–161 (1948).
[CrossRef]

Krinchik, G. S.

G. S. Krinchik and V. A. Artem’ev, “Magneto-optical properties of Ni, Co and Fe in ultraviolet visible and infrared parts of spectrum,” Sov. Phys. JETP26, 1080–1085 (1968).

Krishnan, R.

S. Visnovsky, R. Krishnan, M. Nyvlt, and V. Prosser, “Optical behaviour of Fe in magnetic multilayers,” J. Magn. Soc. Jpn.20, Supplement No. S1, 41–46 (1996).

Lesnák, M.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

Linzon, Y.

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Liskova, E.

E. Liskova, S. Visnovsky, R. Lopusnik, I. Harward, M. Wenger, T. Christensen, and Z. Celinski, “Magneto-optical AlN/Fe/AlN structures optimized for operation in the violet spectral region,” J. Phys. D Appl. Phys.41(15), 155007 (2008).
[CrossRef]

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

Lišková, E.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

Lopusnik, R.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

E. Liskova, S. Visnovsky, R. Lopusnik, I. Harward, M. Wenger, T. Christensen, and Z. Celinski, “Magneto-optical AlN/Fe/AlN structures optimized for operation in the violet spectral region,” J. Phys. D Appl. Phys.41(15), 155007 (2008).
[CrossRef]

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

Lopusník, R.

Mansuripur, M.

M. Mansuripur, “Figure of merit for magneto-optical media based on the dielectric tensor,” Appl. Phys. Lett.49(1), 19–21 (1986).
[CrossRef]

Maslankiewicz, P.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

Mistrík, J.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

Moradi, M.

M. Moradi and M. Ghanaatshoar, “Cavity enhancement of the magneto-optic Kerr effect in glass/Al/SnO2/PtMnSb/SnO2 structure,” Opt. Commun.283(24), 5053–5057 (2010).
[CrossRef]

Morandotti, R.

J. Y. Hwang, M. Ferrera, L. Razzari, A. Pignolet, and R. Morandotti, “The role of Bi3+ ions in magneto-optic Ce and Bi comodified epitaxial iron garnet films,” Appl. Phys. Lett.97(16), 161901 (2010).
[CrossRef]

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Nyvlt, M.

S. Visnovsky, R. Krishnan, M. Nyvlt, and V. Prosser, “Optical behaviour of Fe in magnetic multilayers,” J. Magn. Soc. Jpn.20, Supplement No. S1, 41–46 (1996).

Pignolet, A.

J. Y. Hwang, M. Ferrera, L. Razzari, A. Pignolet, and R. Morandotti, “The role of Bi3+ ions in magneto-optic Ce and Bi comodified epitaxial iron garnet films,” Appl. Phys. Lett.97(16), 161901 (2010).
[CrossRef]

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Pištora, J.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

Pittini, R.

R. Pittini, J. Schoenes, O. Vogt, and P. Wachter, “Discovery of 90 degree magneto-optical polar Kerr rotation in CeSb,” Phys. Rev. Lett.77(5), 944–947 (1996).
[CrossRef] [PubMed]

Pollard, R. J.

W. R. Hendren, R. Atkinson, R. J. Pollard, I. W. Salter, C. D. Wright, W. W. Clegg, and D. F. L. Jenkins, “The design and optimization of disk structures for MAMMOS/MSR magneto-optic recording,” J. Phys. D Appl. Phys.38(14), 2310–2320 (2005).
[CrossRef]

Popma, T. J. A.

S. Wittekoek, T. J. A. Popma, J. M. Robertson, and P. F. Bongers, “Magneto-optic spectra and the dielectric tensor elements of bismuth-substituted iron garnets at photon energies between 2.2-5.2 eV,” Phys. Rev. B12(7), 2777–2788 (1975).
[CrossRef]

Postava, K.

Prosser, V.

S. Visnovsky, R. Krishnan, M. Nyvlt, and V. Prosser, “Optical behaviour of Fe in magnetic multilayers,” J. Magn. Soc. Jpn.20, Supplement No. S1, 41–46 (1996).

Pufall, M. R.

M. R. Pufall and A. Berger, “Studying the reversal mode of the magnetization vector versus applied field angle using generalized magneto-optical ellipsometry,” J. Appl. Phys.87(9), 5834–5836 (2000).
[CrossRef]

A. Berger and M. R. Pufall, “Quantitative vector magnetometry using generalized magneto-optical ellipsometry,” J. Appl. Phys.85(8), 4583–4585 (1999).
[CrossRef]

Qureshi, N.

N. Qureshi, H. Schmidt, and A. R. Hawkins, “Cavity enhancement of the magneto-optic Kerr effect for optical studies of magnetic nanostructures,” Appl. Phys. Lett.85(3), 431–433 (2004).
[CrossRef]

Razzari, L.

J. Y. Hwang, M. Ferrera, L. Razzari, A. Pignolet, and R. Morandotti, “The role of Bi3+ ions in magneto-optic Ce and Bi comodified epitaxial iron garnet films,” Appl. Phys. Lett.97(16), 161901 (2010).
[CrossRef]

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Robertson, J. M.

S. Wittekoek, T. J. A. Popma, J. M. Robertson, and P. F. Bongers, “Magneto-optic spectra and the dielectric tensor elements of bismuth-substituted iron garnets at photon energies between 2.2-5.2 eV,” Phys. Rev. B12(7), 2777–2788 (1975).
[CrossRef]

Salter, I. W.

W. R. Hendren, R. Atkinson, R. J. Pollard, I. W. Salter, C. D. Wright, W. W. Clegg, and D. F. L. Jenkins, “The design and optimization of disk structures for MAMMOS/MSR magneto-optic recording,” J. Phys. D Appl. Phys.38(14), 2310–2320 (2005).
[CrossRef]

R. Atkinson, I. W. Salter, and J. Xu, “Design, fabrication, and performance of enhanced magneto-optic quadrilayers with controllable ellipticity,” Appl. Opt.31(23), 4847–4852 (1992).
[CrossRef] [PubMed]

Schmidt, H.

N. Qureshi, H. Schmidt, and A. R. Hawkins, “Cavity enhancement of the magneto-optic Kerr effect for optical studies of magnetic nanostructures,” Appl. Phys. Lett.85(3), 431–433 (2004).
[CrossRef]

Schoenes, J.

R. Pittini, J. Schoenes, O. Vogt, and P. Wachter, “Discovery of 90 degree magneto-optical polar Kerr rotation in CeSb,” Phys. Rev. Lett.77(5), 944–947 (1996).
[CrossRef] [PubMed]

Sekhar, M. C.

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Stutzmann, M.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys.82(10), 5090–5096 (1997).
[CrossRef]

Suhl, H.

H. Suhl, “Origin and use of instabilities in ferromagnetic resonance,” J. Appl. Phys.29(3), 416–421 (1958).
[CrossRef]

Tomita, Y.

Unsal, T.

J. A. Arregi, J. B. Gonzales-Diaz, E. Bergaretxe, O. Idigoras, T. Unsal, and A. Berger, “Study of generalized magneto-optical ellipsometry measurement reliability,” J. Appl. Phys.111(10), 103912 (2012).
[CrossRef]

Veis, M.

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

Visnovsky, S.

E. Liskova, S. Visnovsky, R. Lopusnik, I. Harward, M. Wenger, T. Christensen, and Z. Celinski, “Magneto-optical AlN/Fe/AlN structures optimized for operation in the violet spectral region,” J. Phys. D Appl. Phys.41(15), 155007 (2008).
[CrossRef]

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

S. Visnovsky, R. Krishnan, M. Nyvlt, and V. Prosser, “Optical behaviour of Fe in magnetic multilayers,” J. Magn. Soc. Jpn.20, Supplement No. S1, 41–46 (1996).

Visnovský, Š.

Višnovský, Š.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

Š. Višňovský, “Magneto-optical ellipsometry,” Czech. J. Phys. B36(5), 625–650 (1986).
[CrossRef]

Vlcek, J.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

Vogt, O.

R. Pittini, J. Schoenes, O. Vogt, and P. Wachter, “Discovery of 90 degree magneto-optical polar Kerr rotation in CeSb,” Phys. Rev. Lett.77(5), 944–947 (1996).
[CrossRef] [PubMed]

Wachter, P.

R. Pittini, J. Schoenes, O. Vogt, and P. Wachter, “Discovery of 90 degree magneto-optical polar Kerr rotation in CeSb,” Phys. Rev. Lett.77(5), 944–947 (1996).
[CrossRef] [PubMed]

Wenger, M.

E. Liskova, S. Visnovsky, R. Lopusnik, I. Harward, M. Wenger, T. Christensen, and Z. Celinski, “Magneto-optical AlN/Fe/AlN structures optimized for operation in the violet spectral region,” J. Phys. D Appl. Phys.41(15), 155007 (2008).
[CrossRef]

Widuch, S.

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

Wittekoek, S.

S. Wittekoek, T. J. A. Popma, J. M. Robertson, and P. F. Bongers, “Magneto-optic spectra and the dielectric tensor elements of bismuth-substituted iron garnets at photon energies between 2.2-5.2 eV,” Phys. Rev. B12(7), 2777–2788 (1975).
[CrossRef]

Wright, C. D.

W. R. Hendren, R. Atkinson, R. J. Pollard, I. W. Salter, C. D. Wright, W. W. Clegg, and D. F. L. Jenkins, “The design and optimization of disk structures for MAMMOS/MSR magneto-optic recording,” J. Phys. D Appl. Phys.38(14), 2310–2320 (2005).
[CrossRef]

Xu, J.

Yamaguchi, T.

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

Š. Visnovský, K. Postava, T. Yamaguchi, and R. Lopusník, “Magneto-optic ellipsometry in exchange-coupled films,” Appl. Opt.41(19), 3950–3960 (2002).
[CrossRef] [PubMed]

Yeh, P.

Yoshino, T.

Zaezjev, M.

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

Ann. Phys. (Paris) (1)

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés. Application aux couches minces,” Ann. Phys. (Paris)5, 596–640, 706–782 (1950).

Appl. Opt. (2)

Appl. Phys. Lett. (5)

A. Y. Elezzabi and M. R. Freeman, “Ultrafast magneto-optic sampling of picosecond current pulses,” Appl. Phys. Lett.68(25), 3546–3548 (1996).
[CrossRef]

M. C. Sekhar, J. Y. Hwang, M. Ferrera, Y. Linzon, L. Razzari, C. Harnagea, M. Zaezjev, A. Pignolet, and R. Morandotti, “Strong enhancement of the Faraday rotation in Ce and Bi comodified epitaxial iron garnet thin films,” Appl. Phys. Lett.94(18), 181916 (2009).
[CrossRef]

J. Y. Hwang, M. Ferrera, L. Razzari, A. Pignolet, and R. Morandotti, “The role of Bi3+ ions in magneto-optic Ce and Bi comodified epitaxial iron garnet films,” Appl. Phys. Lett.97(16), 161901 (2010).
[CrossRef]

N. Qureshi, H. Schmidt, and A. R. Hawkins, “Cavity enhancement of the magneto-optic Kerr effect for optical studies of magnetic nanostructures,” Appl. Phys. Lett.85(3), 431–433 (2004).
[CrossRef]

M. Mansuripur, “Figure of merit for magneto-optical media based on the dielectric tensor,” Appl. Phys. Lett.49(1), 19–21 (1986).
[CrossRef]

Czech. J. Phys. B (1)

Š. Višňovský, “Magneto-optical ellipsometry,” Czech. J. Phys. B36(5), 625–650 (1986).
[CrossRef]

J. Appl. Phys. (7)

H. Suhl, “Origin and use of instabilities in ferromagnetic resonance,” J. Appl. Phys.29(3), 416–421 (1958).
[CrossRef]

R. Lopusnik, J. Correu, I. Harward, S. Widuch, P. Maslankiewicz, S. Demirtas, Z. Celinski, E. Liskova, M. Veis, and S. Visnovsky, “Optimization of magneto-optical response of FeF2/Fe/ FeF2 sandwiches for microwave field detection,” J. Appl. Phys.101(9), 09C516 (2007).
[CrossRef]

C. F. Buhrer, “Faraday rotation and dichroism of bismuth calcium vanadium iron garnet,” J. Appl. Phys.40(11), 4500–4502 (1969).
[CrossRef]

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Höpler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys.82(10), 5090–5096 (1997).
[CrossRef]

A. Berger and M. R. Pufall, “Quantitative vector magnetometry using generalized magneto-optical ellipsometry,” J. Appl. Phys.85(8), 4583–4585 (1999).
[CrossRef]

M. R. Pufall and A. Berger, “Studying the reversal mode of the magnetization vector versus applied field angle using generalized magneto-optical ellipsometry,” J. Appl. Phys.87(9), 5834–5836 (2000).
[CrossRef]

J. A. Arregi, J. B. Gonzales-Diaz, E. Bergaretxe, O. Idigoras, T. Unsal, and A. Berger, “Study of generalized magneto-optical ellipsometry measurement reliability,” J. Appl. Phys.111(10), 103912 (2012).
[CrossRef]

J. Magn. Soc. Jpn. (1)

S. Visnovsky, R. Krishnan, M. Nyvlt, and V. Prosser, “Optical behaviour of Fe in magnetic multilayers,” J. Magn. Soc. Jpn.20, Supplement No. S1, 41–46 (1996).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. D Appl. Phys. (3)

W. R. Hendren, R. Atkinson, R. J. Pollard, I. W. Salter, C. D. Wright, W. W. Clegg, and D. F. L. Jenkins, “The design and optimization of disk structures for MAMMOS/MSR magneto-optic recording,” J. Phys. D Appl. Phys.38(14), 2310–2320 (2005).
[CrossRef]

J. Pištora, M. Lesňák, E. Lišková, Š. Višňovský, I. Harward, P. Maslankiewicz, K. Balin, Z. Celinski, J. Mistrík, T. Yamaguchi, R. Lopusnik, and J. Vlček, “The effect of FeF2 on the magneto-optic response in FeF2/Fe/FeF2 sandwiches,” J. Phys. D Appl. Phys.43(15), 155301 (2010).
[CrossRef]

E. Liskova, S. Visnovsky, R. Lopusnik, I. Harward, M. Wenger, T. Christensen, and Z. Celinski, “Magneto-optical AlN/Fe/AlN structures optimized for operation in the violet spectral region,” J. Phys. D Appl. Phys.41(15), 155007 (2008).
[CrossRef]

Opt. Commun. (1)

M. Moradi and M. Ghanaatshoar, “Cavity enhancement of the magneto-optic Kerr effect in glass/Al/SnO2/PtMnSb/SnO2 structure,” Opt. Commun.283(24), 5053–5057 (2010).
[CrossRef]

Phys. Rev. (1)

C. Kittel, “On the theory of ferromagnetic resonance absorption,” Phys. Rev.73(2), 155–161 (1948).
[CrossRef]

Phys. Rev. B (3)

S. Wittekoek, T. J. A. Popma, J. M. Robertson, and P. F. Bongers, “Magneto-optic spectra and the dielectric tensor elements of bismuth-substituted iron garnets at photon energies between 2.2-5.2 eV,” Phys. Rev. B12(7), 2777–2788 (1975).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd,” Phys. Rev. B9(12), 5056–5070 (1974).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

R. Pittini, J. Schoenes, O. Vogt, and P. Wachter, “Discovery of 90 degree magneto-optical polar Kerr rotation in CeSb,” Phys. Rev. Lett.77(5), 944–947 (1996).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

G. S. Krinchik and V. A. Artem’ev, “Magneto-optical properties of Ni, Co and Fe in ultraviolet visible and infrared parts of spectrum,” Sov. Phys. JETP26, 1080–1085 (1968).

Other (5)

S. Chikazumi, Physics of Magnetism (Oxford Science Publications, Clarendon Press, 1997).

M. Mansuripur, Physical Principles of Magneto-optical Recording (Cambridge University Press, 1996).

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1997), pp.51–70.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, 1987).

Š. Višňovský, Optics in Magnetic Multilayers and Nanostructures (CRC Taylor & Francis, 2006), Chapter 4, pp. 198–211.

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Figures (8)

Fig. 1
Fig. 1

Ferromagnetic resonance frequency, f, vs. magnetic flux density field, Bappl, applied in-plane on the plates with the saturation magnetizations µ0Ms = 0.0160 Tesla (gallium substituted yttrium iron garnet, GaYIG) and µ0Ms = 2.158 Tesla (Fe).

Fig. 2
Fig. 2

Diagram of the multilayer system operating as a magneto-optic probe.

Fig. 3
Fig. 3

Effect of the thickness of the Fe layer, d(3), on the parameters of the structure AlN(50 nm)/Fe(d(3))/AlN(26 nm)/Au(1000 nm): (a) power reflection (R), transmission (T), and absorption (A) coefficients, (b) off-diagonal amplitude reflection coefficient r yx (05) =| r yx (05) |exp[ j arg( r yx (05) ) ] , (c) diagonal amplitude reflection coefficient r xx (05) =| r xx (05) |exp[ j arg( r xx (05) ) ] , and (d) magneto-optic azimuth rotation, θ r (05) , and ellipticity, ε r (05) at 10% magnetic saturation.

Fig. 4
Fig. 4

Effect of the thickness of the upper AlN layer, d(2), on the parameters of the structure AlN(d(2))/Fe(14 nm)/AlN(26)/Au(1000 nm): (a) power reflection (R), transmission (T), and absorption (A) coefficients, (b) off-diagonal amplitude reflection coefficient r yx (05) =| r yx (05) |exp[ j arg( r yx (05) ) ] , (c) diagonal amplitude reflection coefficient r xx (05) =| r xx (05) |exp[ j arg( r xx (05) ) ] , and (d) magneto-optic azimuth rotation, θ r (05) , and ellipticity, ε r (05) at 10% magnetic saturation.

Fig. 5
Fig. 5

Effect of the thickness of the lower AlN layer, d(4), on the parameters of the structure AlN(50 nm)/Fe(14 nm)/AlN(d(4))/Au(1000 nm): (a) power reflection (R), transmission (T), and absorption (A) coefficients, (b) off-diagonal amplitude reflection coefficient r yx (05) =| r yx (05) |exp[ j arg( r yx (05) ) ] , (c) diagonal amplitude reflection coefficient r xx (05) =| r xx (05) |exp[ j arg( r xx (05) ) ] , and (d) magneto-optic azimuth rotation, θ r (05) , and ellipticity, ε r (05) at 10% magnetic saturation.

Fig. 6
Fig. 6

Effect of the thickness of the Fe layer, d(3), on the parameters of the structure Au(5 nm)/AlN(73 nm)/Fe(d(3))/AlN(20 nm)/Au(1000 nm): (a) power reflection (R), transmission (T), and absorption (A) coefficients, (b) off-diagonal amplitude reflection coefficient r yx (05) =| r yx (05) |exp[ j arg( r yx (05) ) ] , (c) diagonal amplitude reflection coefficient r xx (05) =| r xx (05) |exp[ j arg( r xx (05) ) ] , and (d) magneto-optic azimuth rotation, θ r (05) , and ellipticity, ε r (05) at 10% magnetic saturation.

Fig. 7
Fig. 7

Effect of the thickness of the Fe layer, d(3), on the parameters of the structure Au(5 nm)/AlN(d(2))/Fe(15 nm)/AlN(20 nm)/Au(1000 nm): (a) power reflection (R), transmission (T), and absorption (A) coefficients, (b) off-diagonal amplitude reflection coefficient r yx (05) =| r yx (05) |exp[ j arg( r yx (05) ) ] , (c) diagonal amplitude reflection coefficient r xx (05) =| r xx (05) |exp[ j arg( r xx (05) ) ] , and (d) magneto-optic azimuth rotation, θ r (05) , and ellipticity, ε r (05) at 10% magnetic saturation.

Fig. 8
Fig. 8

Effect of the thickness of the Fe layer, d(3), on the parameters of the structure Au(5 nm)/AlN(73 nm)/Fe(15 nm)/AlN(d(4))/Au(1000 nm): (a) power reflection (R), transmission (T), and absorption (A) coefficients, (b) off-diagonal amplitude reflection coefficient r yx (05) =| r yx (05) |exp[ j arg( r yx (05) ) ] , (c) diagonal amplitude reflection coefficient r xx (05) =| r xx (05) |exp[ j arg( r xx (05) ) ] , and (d) magneto-optic azimuth rotation, θ r (05) , and ellipticity, ε r (05) at 10% magnetic saturation.

Tables (4)

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Table 1 Optical and magneto-optical parameters of Fe

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Table 2 Optical parameters of Au

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Table 3 Structures AlN/Fe/AlN/Au with d(1) = 0

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Table 4 Structures Au/AlN/Fe/AlN/Au with d(1) = 5 nm

Equations (24)

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f= γ 2π [ B appl ( B appl + μ 0 M s ) ] 1/2 ,
[ E x (r) E y (r) ]=[ r xx r yx r yx r xx ][ E x (i) E y (i) ],
[ E x (t) E y (t) ]=[ t xx t yx t yx t xx ][ E x (i) E y (i) ].
| r yx ( ω ) | max =| ε xy (m) ( ω,M ) 2Im[ ε xx (m) ( ω )] |.
2 E( .E )+ ω 2 c 2 ε (m) E=0
ε (m) =[ ε xx (m) ε xy (m) 0 ε xy (m) ε xx (m) 0 0 0 ε zz (m) ],
( N z 2 E x ε xx (m) E x ε xy (m) E y ) x ^ +( N z 2 E y + ε xy (m) E x ε xx (m) E y ) y ^ ε zz (m) E z z ^ =0
E 1,2 (m) = 2 1/2 ( x ^ +j y ^ ) E 1,2 (m) exp[ jω( τ N + (m) z/c ) ], E 3,4 (m) = 2 1/2 ( x ^ j y ^ ) E 3,4 (m) exp[ jω( τ N (m) z/c ) ].
r ± (i,i+1) = N ± (i) N ± (i+1) N ± (i) + N ± (i+1) = r ± (i+1,i) , t ± (i,i+1) = 2 N ± (i) N ± (i) + N ± (i+1) , t ± (i+1,i) = 2 N ± (i+1) N ± (i) + N ± (i+1) ,
r ± (05) = r (01) + e 2j β (1) r (12) + r ± (25) e 2j β (2) 1+ r (12) r ± (25) e 2j β (2) 1+ r (01) e 2j β (1) r (12) + r ± (25) e 2j β (2) 1+ r (12) r ± (25) e 2j β (2) ,
t ± (05) = t (01) e j β (1) t (12) t ± (25) e j β (2) 1+ r (12) r ± (25) e 2j β (2) 1+ r (01) e 2j β (1) r (12) + r ± (25) e 2j β (2) 1+ r (12) r ± (25) e 2j β (2) .
r ± (25) = r ± (23) + e 2j β ± (3) r ± (34) + r (45) e 2j β (4) 1+ r ± (34) r (45) e 2j β (4) 1+ r ± (23) e 2j β ± (3) r ± (34) + r (45) e 2j β (4) 1+ r ± (34) r (45) e 2j β (4) ,
t ± (25) = t ± (23) e j β ± (3) t ± (34) t (45) e j β (4) 1+ r ± (34) r (45) e 2j β (4) 1+ r ± (23) e 2j β ± (3) r ± (34) + r (45) e 2j β (4) 1+ r ± (34) r (45) e 2j β (4) .
t ± (50) = t (10) e j β (1) t (21) t ± (52) e j β (2) 1+ r (12) r ± (25) e 2j β (2) 1+ r (01) e 2j β (1) r (12) + r ± (25) e 2j β (2) 1+ r (12) r ± (25) e 2j β (2) ,
t ± (52) = t ± (32) e j β ± (3) t ± (43) t (54) e j β (4) 1+ r ± (34) r (45) e 2j β (4) 1+ r ± (23) e 2j β ± (3) r ± (34) + r (45) e 2j β (4) 1+ r ± (34) r (45) e 2j β (4) .
r xx (05) = 1 2 ( r + (05) + r (05) ), r yx (05) = 1 2 j( r + (05) r (05) ), t xx (05) = 1 2 ( t + (05) + t (05) ), t yx (05) = 1 2 j( t + (05) t (05) ), t xx (50) = 1 2 ( t + (50) + t (50) ), t yx (50) = 1 2 j( t + (50) t (50) ).
r yx (05) ε yx (3) 4 ε xx (3) t (03) t (30) [ 4j β (3) e 2j β (3) r (35) +( 1 e 2j β (3) )( 1+ r (35)2 e 2j β (3) ) ] ( 1+ r (30) r (35) e 2j β (3) ) 2 ,
t (03) t (30) = ( 1 r (01)2 )( 1 r (12)2 )( 1 r (23)2 ) e 2j β (1) e 2j β (2) [ ( 1+ r (01) r (12) e 2j β (1) )+ r (23) e 2j β (2) ( r (01) e 2j β (1) + r (12) ) ] 2 ,
r (30) = r (23) + r (01) e 2j β (1) + r (12) 1+ r (01) r (12) e 2j β (1) e 2j β (2) 1+ r (01) e 2j β (1) + r (12) 1+ r (01) r (12) e 2j β (1) r (23) e 2j β (2) ,
r (35) = r (34) + r (45) e 2j β (4) 1+ r (34) r (45) e 2j β (4)
t yx (05) t (01) t (12) e j β (1) ( 1+ r (01) r (12) e 2j β (1) ) t (34) t (45) e j β (4) ( 1+ r (34) r (45) e 2j β (4) ) × t (23) e j( β (2) + β (3) ) ( 1+ r (30) r (35) e 2j β (3) ) 2 ( 1+ r (20) r (23) e 2j β (2) ) × ε yx (3) 4 ε xx (3) [ 2j β (3) ( 1 r (30) r (35) e 2j β (3) )( 1 e 2j β (3) )( r (30) r (35) ) ],
r (20) = r (01) e 2j β (1) + r (12) 1+ r (01) r (12) e 2j β (1) .
θ r (05) = 1 2 arctan 2{ χ r (05) } 1 | χ r (05) | 2 ,
ε r (05) = 1 2 arcsin 2Im{ χ r (05) } 1+ | χ r (05) | 2 ,

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