Abstract

The second-harmonic spectrum from pyroelectric and ferrimagnetic GaFeO3 has been observed under several configurations of polarized light and has been theoretically analyzed based on the microscopic model of ligand field theory for the Fe3+ ion. The linear Kerr rotation spectrum has been observed and used to supplement the microscopic model.

© 2005 Optical Society of America

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  2. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevski, Electrodynamics of Continuous Media (Pergamon, Oxford, UK, 1984).
  3. Y. Ogawa, Y. Kaneko, J. P. He, X. Z. Yu, T. Arima, and Y. Tokura, "Magnetization-induced second harmonic generation in a polar ferromagnet," Phys. Rev. Lett. 92, 047401-1-047401-4 (2004).
    [CrossRef]
  4. G. T. Rado, "Observation and possible mechanisms of magnetoelectric effects in a ferromagnet," Phys. Rev. Lett. 13, 335-337 (1964).
    [CrossRef]
  5. G. T. Rado, "Linear magnetoelectric effects in gallium iron oxide at low temperatures and in high magnetic fields," J. Appl. Phys. 37, 1403 (1966).
    [CrossRef]
  6. Yu. F. Popov, A. M. Kasomtseva, G. P. Vorob'ev, V. A. Timofeeva, D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi, "Magnetoelectric effect and toroidal ordering in Ga2−xFexO3," JETP 87, 146-151 (1998).
    [CrossRef]
  7. M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, "Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3," Phys. Rev. Lett. 73, 2127-2130 (1994).
    [CrossRef] [PubMed]
  8. M. Muto, Y. Tanabe, T. Iizuka-Sakano, and E. Hanamura, "Magnetoelectric and second-harmonic spectra in antiferromagnetic Cr2O3," Phys. Rev. B 57, 9586-9607 (1998).
    [CrossRef]
  9. A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
    [CrossRef]
  10. M. Fiebig, S. Leute, V. V. Pavlov, and R. V. Pizarev, "Nonlinear optical spectroscopy of the two-order-parameter compound YMnO3," Phys. Rev. Lett. 81, 3239-3242 (1998).
    [CrossRef]
  11. I. Iizuka-Sakano, E. Hanamura, and Y. Tanabe, "Second-harmonic-generation spectra of the hexagonal manganites RMnO3," J. Phys.: Condens. Matter 13, 3031-3055 (2001).
  12. J. P. Remeika, "GaFeO3: a ferromagnetic-piezoelectric compound," J. Appl. Phys. 31, 263S-264S (1960).
    [CrossRef]
  13. T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
    [CrossRef]
  14. S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, "Crystal structure of piezoelectric gallium iron oxide," J. Chem. Phys. 42, 3957-3968 (1965).
    [CrossRef]
  15. R. R. Briss, Symmetry and Magnetism (North-Holland, Amsterdam, 1964).
  16. M. Fiebig, Th. Lottermoser, D. Fröhlich, A. V. Goltsev, and R. V. Pisarev, "Observation of coupled magnetic and electric domains," Nature 419, 818-820 (2002).
    [CrossRef] [PubMed]
  17. E. Hanamura and Y. Tanabe, "Magnetoelectric interaction in crystals observed by nonlinear magneto-optics," in Magnetoelectric Interaction Phenomena in Crystals , M. Fiebig, V. Eremenko, and I. Chupis, eds. (Kluwer, Dordrecht, The Netherlands, 2004), pp. 151-162.
  18. F. J. Kahn, P. S. Pershan, and J. P. Remeika, "Ultraviolet magneto-optical properties of single-crystal orthoferrites, garnets, and other ferric oxide compounds," Phys. Rev. 186, 891-918 (1961).
    [CrossRef]
  19. A. S. Moskvin, "One-center charge transfer transitions in manganites," Phys. Rev. B 65, 205113-1-205113-9 (2002).
    [CrossRef]
  20. K. Shinagawa and Y. Tanabe, "Intensity of magnon sidebands," J. Phys. Soc. Jpn. 30, 1280-1971 (1971).
    [CrossRef]
  21. T. Fujiwara and Y. Tanabe, "Temperature dependence of magnon sideband," J. Phys. Soc. Jpn. 32, 912-926 (1972).
    [CrossRef]
  22. See, e.g., H. Kamimura, S. Sugano, and Y. Tanabe, Multiplets of Transition-Metal Ions in Crystals (Academic, New York, 1970).

2004

Y. Ogawa, Y. Kaneko, J. P. He, X. Z. Yu, T. Arima, and Y. Tokura, "Magnetization-induced second harmonic generation in a polar ferromagnet," Phys. Rev. Lett. 92, 047401-1-047401-4 (2004).
[CrossRef]

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

2002

M. Fiebig, Th. Lottermoser, D. Fröhlich, A. V. Goltsev, and R. V. Pisarev, "Observation of coupled magnetic and electric domains," Nature 419, 818-820 (2002).
[CrossRef] [PubMed]

A. S. Moskvin, "One-center charge transfer transitions in manganites," Phys. Rev. B 65, 205113-1-205113-9 (2002).
[CrossRef]

2001

I. Iizuka-Sakano, E. Hanamura, and Y. Tanabe, "Second-harmonic-generation spectra of the hexagonal manganites RMnO3," J. Phys.: Condens. Matter 13, 3031-3055 (2001).

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

1998

M. Fiebig, S. Leute, V. V. Pavlov, and R. V. Pizarev, "Nonlinear optical spectroscopy of the two-order-parameter compound YMnO3," Phys. Rev. Lett. 81, 3239-3242 (1998).
[CrossRef]

M. Muto, Y. Tanabe, T. Iizuka-Sakano, and E. Hanamura, "Magnetoelectric and second-harmonic spectra in antiferromagnetic Cr2O3," Phys. Rev. B 57, 9586-9607 (1998).
[CrossRef]

Yu. F. Popov, A. M. Kasomtseva, G. P. Vorob'ev, V. A. Timofeeva, D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi, "Magnetoelectric effect and toroidal ordering in Ga2−xFexO3," JETP 87, 146-151 (1998).
[CrossRef]

1994

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, "Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3," Phys. Rev. Lett. 73, 2127-2130 (1994).
[CrossRef] [PubMed]

1972

T. Fujiwara and Y. Tanabe, "Temperature dependence of magnon sideband," J. Phys. Soc. Jpn. 32, 912-926 (1972).
[CrossRef]

1971

K. Shinagawa and Y. Tanabe, "Intensity of magnon sidebands," J. Phys. Soc. Jpn. 30, 1280-1971 (1971).
[CrossRef]

1966

G. T. Rado, "Linear magnetoelectric effects in gallium iron oxide at low temperatures and in high magnetic fields," J. Appl. Phys. 37, 1403 (1966).
[CrossRef]

1965

S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, "Crystal structure of piezoelectric gallium iron oxide," J. Chem. Phys. 42, 3957-3968 (1965).
[CrossRef]

1964

G. T. Rado, "Observation and possible mechanisms of magnetoelectric effects in a ferromagnet," Phys. Rev. Lett. 13, 335-337 (1964).
[CrossRef]

1961

F. J. Kahn, P. S. Pershan, and J. P. Remeika, "Ultraviolet magneto-optical properties of single-crystal orthoferrites, garnets, and other ferric oxide compounds," Phys. Rev. 186, 891-918 (1961).
[CrossRef]

1960

J. P. Remeika, "GaFeO3: a ferromagnetic-piezoelectric compound," J. Appl. Phys. 31, 263S-264S (1960).
[CrossRef]

Abrahams, S. C.

S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, "Crystal structure of piezoelectric gallium iron oxide," J. Chem. Phys. 42, 3957-3968 (1965).
[CrossRef]

Arima, T.

Y. Ogawa, Y. Kaneko, J. P. He, X. Z. Yu, T. Arima, and Y. Tokura, "Magnetization-induced second harmonic generation in a polar ferromagnet," Phys. Rev. Lett. 92, 047401-1-047401-4 (2004).
[CrossRef]

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Bernstein, J. L.

S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, "Crystal structure of piezoelectric gallium iron oxide," J. Chem. Phys. 42, 3957-3968 (1965).
[CrossRef]

Blonche, P.-A.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

Dan, N. T.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

Fiebig, M.

M. Fiebig, Th. Lottermoser, D. Fröhlich, A. V. Goltsev, and R. V. Pisarev, "Observation of coupled magnetic and electric domains," Nature 419, 818-820 (2002).
[CrossRef] [PubMed]

M. Fiebig, S. Leute, V. V. Pavlov, and R. V. Pizarev, "Nonlinear optical spectroscopy of the two-order-parameter compound YMnO3," Phys. Rev. Lett. 81, 3239-3242 (1998).
[CrossRef]

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, "Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3," Phys. Rev. Lett. 73, 2127-2130 (1994).
[CrossRef] [PubMed]

Fröhlich, D.

M. Fiebig, Th. Lottermoser, D. Fröhlich, A. V. Goltsev, and R. V. Pisarev, "Observation of coupled magnetic and electric domains," Nature 419, 818-820 (2002).
[CrossRef] [PubMed]

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, "Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3," Phys. Rev. Lett. 73, 2127-2130 (1994).
[CrossRef] [PubMed]

Fujiwara , T.

T. Fujiwara and Y. Tanabe, "Temperature dependence of magnon sideband," J. Phys. Soc. Jpn. 32, 912-926 (1972).
[CrossRef]

Goltsev, A. V.

M. Fiebig, Th. Lottermoser, D. Fröhlich, A. V. Goltsev, and R. V. Pisarev, "Observation of coupled magnetic and electric domains," Nature 419, 818-820 (2002).
[CrossRef] [PubMed]

Goto, T.

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Hanamura, E.

I. Iizuka-Sakano, E. Hanamura, and Y. Tanabe, "Second-harmonic-generation spectra of the hexagonal manganites RMnO3," J. Phys.: Condens. Matter 13, 3031-3055 (2001).

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

M. Muto, Y. Tanabe, T. Iizuka-Sakano, and E. Hanamura, "Magnetoelectric and second-harmonic spectra in antiferromagnetic Cr2O3," Phys. Rev. B 57, 9586-9607 (1998).
[CrossRef]

He, J. P.

Y. Ogawa, Y. Kaneko, J. P. He, X. Z. Yu, T. Arima, and Y. Tokura, "Magnetization-induced second harmonic generation in a polar ferromagnet," Phys. Rev. Lett. 92, 047401-1-047401-4 (2004).
[CrossRef]

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Higashiyama, D.

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Iizuka-Sakano, I.

I. Iizuka-Sakano, E. Hanamura, and Y. Tanabe, "Second-harmonic-generation spectra of the hexagonal manganites RMnO3," J. Phys.: Condens. Matter 13, 3031-3055 (2001).

Iizuka-Sakano, T.

M. Muto, Y. Tanabe, T. Iizuka-Sakano, and E. Hanamura, "Magnetoelectric and second-harmonic spectra in antiferromagnetic Cr2O3," Phys. Rev. B 57, 9586-9607 (1998).
[CrossRef]

Kahn, F. J.

F. J. Kahn, P. S. Pershan, and J. P. Remeika, "Ultraviolet magneto-optical properties of single-crystal orthoferrites, garnets, and other ferric oxide compounds," Phys. Rev. 186, 891-918 (1961).
[CrossRef]

Kamiyama, T.

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Kaneko, Y.

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Y. Ogawa, Y. Kaneko, J. P. He, X. Z. Yu, T. Arima, and Y. Tokura, "Magnetization-induced second harmonic generation in a polar ferromagnet," Phys. Rev. Lett. 92, 047401-1-047401-4 (2004).
[CrossRef]

Kasomtseva, A. M.

Yu. F. Popov, A. M. Kasomtseva, G. P. Vorob'ev, V. A. Timofeeva, D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi, "Magnetoelectric effect and toroidal ordering in Ga2−xFexO3," JETP 87, 146-151 (1998).
[CrossRef]

Kawabe, Y.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

Kimura, T.

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Krichevtsov, B. B.

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, "Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3," Phys. Rev. Lett. 73, 2127-2130 (1994).
[CrossRef] [PubMed]

Kumai, R.

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Lee, J.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

Leute, S.

M. Fiebig, S. Leute, V. V. Pavlov, and R. V. Pizarev, "Nonlinear optical spectroscopy of the two-order-parameter compound YMnO3," Phys. Rev. Lett. 81, 3239-3242 (1998).
[CrossRef]

Lottermoser, Th.

M. Fiebig, Th. Lottermoser, D. Fröhlich, A. V. Goltsev, and R. V. Pisarev, "Observation of coupled magnetic and electric domains," Nature 419, 818-820 (2002).
[CrossRef] [PubMed]

Miyasaka, S.

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Moskvin, A. S.

A. S. Moskvin, "One-center charge transfer transitions in manganites," Phys. Rev. B 65, 205113-1-205113-9 (2002).
[CrossRef]

Muto, M.

M. Muto, Y. Tanabe, T. Iizuka-Sakano, and E. Hanamura, "Magnetoelectric and second-harmonic spectra in antiferromagnetic Cr2O3," Phys. Rev. B 57, 9586-9607 (1998).
[CrossRef]

Naito, M.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

Ogawa, Y.

Y. Ogawa, Y. Kaneko, J. P. He, X. Z. Yu, T. Arima, and Y. Tokura, "Magnetization-induced second harmonic generation in a polar ferromagnet," Phys. Rev. Lett. 92, 047401-1-047401-4 (2004).
[CrossRef]

Oikawa, K.

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Pavlov, V. V.

M. Fiebig, S. Leute, V. V. Pavlov, and R. V. Pizarev, "Nonlinear optical spectroscopy of the two-order-parameter compound YMnO3," Phys. Rev. Lett. 81, 3239-3242 (1998).
[CrossRef]

Pershan, P. S.

F. J. Kahn, P. S. Pershan, and J. P. Remeika, "Ultraviolet magneto-optical properties of single-crystal orthoferrites, garnets, and other ferric oxide compounds," Phys. Rev. 186, 891-918 (1961).
[CrossRef]

Peyghambarian, N.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

Pisarev, R. V.

M. Fiebig, Th. Lottermoser, D. Fröhlich, A. V. Goltsev, and R. V. Pisarev, "Observation of coupled magnetic and electric domains," Nature 419, 818-820 (2002).
[CrossRef] [PubMed]

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, "Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3," Phys. Rev. Lett. 73, 2127-2130 (1994).
[CrossRef] [PubMed]

Pizarev, R. V.

M. Fiebig, S. Leute, V. V. Pavlov, and R. V. Pizarev, "Nonlinear optical spectroscopy of the two-order-parameter compound YMnO3," Phys. Rev. Lett. 81, 3239-3242 (1998).
[CrossRef]

Popov, Yu. F.

Yu. F. Popov, A. M. Kasomtseva, G. P. Vorob'ev, V. A. Timofeeva, D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi, "Magnetoelectric effect and toroidal ordering in Ga2−xFexO3," JETP 87, 146-151 (1998).
[CrossRef]

Rado, G. T.

G. T. Rado, "Linear magnetoelectric effects in gallium iron oxide at low temperatures and in high magnetic fields," J. Appl. Phys. 37, 1403 (1966).
[CrossRef]

G. T. Rado, "Observation and possible mechanisms of magnetoelectric effects in a ferromagnet," Phys. Rev. Lett. 13, 335-337 (1964).
[CrossRef]

Reddy, J. M.

S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, "Crystal structure of piezoelectric gallium iron oxide," J. Chem. Phys. 42, 3957-3968 (1965).
[CrossRef]

Remeika, J. P.

F. J. Kahn, P. S. Pershan, and J. P. Remeika, "Ultraviolet magneto-optical properties of single-crystal orthoferrites, garnets, and other ferric oxide compounds," Phys. Rev. 186, 891-918 (1961).
[CrossRef]

J. P. Remeika, "GaFeO3: a ferromagnetic-piezoelectric compound," J. Appl. Phys. 31, 263S-264S (1960).
[CrossRef]

Sato, H.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

Schülzgen, A.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

Shinagawa , K.

K. Shinagawa and Y. Tanabe, "Intensity of magnon sidebands," J. Phys. Soc. Jpn. 30, 1280-1971 (1971).
[CrossRef]

Tanabe, Y.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

I. Iizuka-Sakano, E. Hanamura, and Y. Tanabe, "Second-harmonic-generation spectra of the hexagonal manganites RMnO3," J. Phys.: Condens. Matter 13, 3031-3055 (2001).

M. Muto, Y. Tanabe, T. Iizuka-Sakano, and E. Hanamura, "Magnetoelectric and second-harmonic spectra in antiferromagnetic Cr2O3," Phys. Rev. B 57, 9586-9607 (1998).
[CrossRef]

T. Fujiwara and Y. Tanabe, "Temperature dependence of magnon sideband," J. Phys. Soc. Jpn. 32, 912-926 (1972).
[CrossRef]

K. Shinagawa and Y. Tanabe, "Intensity of magnon sidebands," J. Phys. Soc. Jpn. 30, 1280-1971 (1971).
[CrossRef]

Tegeranchi, M. M.

Yu. F. Popov, A. M. Kasomtseva, G. P. Vorob'ev, V. A. Timofeeva, D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi, "Magnetoelectric effect and toroidal ordering in Ga2−xFexO3," JETP 87, 146-151 (1998).
[CrossRef]

Timofeeva, V. A.

Yu. F. Popov, A. M. Kasomtseva, G. P. Vorob'ev, V. A. Timofeeva, D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi, "Magnetoelectric effect and toroidal ordering in Ga2−xFexO3," JETP 87, 146-151 (1998).
[CrossRef]

Tokura, Y.

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

Y. Ogawa, Y. Kaneko, J. P. He, X. Z. Yu, T. Arima, and Y. Tokura, "Magnetization-induced second harmonic generation in a polar ferromagnet," Phys. Rev. Lett. 92, 047401-1-047401-4 (2004).
[CrossRef]

Uchida, S.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

Ustinin, D. M.

Yu. F. Popov, A. M. Kasomtseva, G. P. Vorob'ev, V. A. Timofeeva, D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi, "Magnetoelectric effect and toroidal ordering in Ga2−xFexO3," JETP 87, 146-151 (1998).
[CrossRef]

Vorob'ev, G. P.

Yu. F. Popov, A. M. Kasomtseva, G. P. Vorob'ev, V. A. Timofeeva, D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi, "Magnetoelectric effect and toroidal ordering in Ga2−xFexO3," JETP 87, 146-151 (1998).
[CrossRef]

Yamanaka, A.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

Yu, X. Z.

Y. Ogawa, Y. Kaneko, J. P. He, X. Z. Yu, T. Arima, and Y. Tokura, "Magnetization-induced second harmonic generation in a polar ferromagnet," Phys. Rev. Lett. 92, 047401-1-047401-4 (2004).
[CrossRef]

Zvezdin, A. K.

Yu. F. Popov, A. M. Kasomtseva, G. P. Vorob'ev, V. A. Timofeeva, D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi, "Magnetoelectric effect and toroidal ordering in Ga2−xFexO3," JETP 87, 146-151 (1998).
[CrossRef]

J. Appl. Phys.

G. T. Rado, "Linear magnetoelectric effects in gallium iron oxide at low temperatures and in high magnetic fields," J. Appl. Phys. 37, 1403 (1966).
[CrossRef]

J. P. Remeika, "GaFeO3: a ferromagnetic-piezoelectric compound," J. Appl. Phys. 31, 263S-264S (1960).
[CrossRef]

J. Chem. Phys.

S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, "Crystal structure of piezoelectric gallium iron oxide," J. Chem. Phys. 42, 3957-3968 (1965).
[CrossRef]

J. Phys. Soc. Jpn.

K. Shinagawa and Y. Tanabe, "Intensity of magnon sidebands," J. Phys. Soc. Jpn. 30, 1280-1971 (1971).
[CrossRef]

T. Fujiwara and Y. Tanabe, "Temperature dependence of magnon sideband," J. Phys. Soc. Jpn. 32, 912-926 (1972).
[CrossRef]

J. Phys.: Condens. Matter

I. Iizuka-Sakano, E. Hanamura, and Y. Tanabe, "Second-harmonic-generation spectra of the hexagonal manganites RMnO3," J. Phys.: Condens. Matter 13, 3031-3055 (2001).

JETP

Yu. F. Popov, A. M. Kasomtseva, G. P. Vorob'ev, V. A. Timofeeva, D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi, "Magnetoelectric effect and toroidal ordering in Ga2−xFexO3," JETP 87, 146-151 (1998).
[CrossRef]

Nature

M. Fiebig, Th. Lottermoser, D. Fröhlich, A. V. Goltsev, and R. V. Pisarev, "Observation of coupled magnetic and electric domains," Nature 419, 818-820 (2002).
[CrossRef] [PubMed]

Phys. Rev.

F. J. Kahn, P. S. Pershan, and J. P. Remeika, "Ultraviolet magneto-optical properties of single-crystal orthoferrites, garnets, and other ferric oxide compounds," Phys. Rev. 186, 891-918 (1961).
[CrossRef]

Phys. Rev. B

A. S. Moskvin, "One-center charge transfer transitions in manganites," Phys. Rev. B 65, 205113-1-205113-9 (2002).
[CrossRef]

T. Arima, D. Higashiyama, Y. Kaneko, J. P. He, T. Goto, S. Miyasaka, T. Kimura, K. Oikawa, T. Kamiyama, R. Kumai, and Y. Tokura, "Structural and magnetoelectric properties of Ga2−xFexO3 single crystals grown by a floating-zone method," Phys. Rev. B 70, 064426-1-064426-8 (2004).
[CrossRef]

M. Muto, Y. Tanabe, T. Iizuka-Sakano, and E. Hanamura, "Magnetoelectric and second-harmonic spectra in antiferromagnetic Cr2O3," Phys. Rev. B 57, 9586-9607 (1998).
[CrossRef]

Phys. Rev. Lett.

A. Schülzgen, Y. Kawabe, E. Hanamura, A. Yamanaka, P.-A. Blonche, J. Lee, N. T. Dan, H. Sato, M. Naito, S. Uchida, Y. Tanabe, and N. Peyghambarian, "Two-photon resonant third-harmonic generation in La2CuO4," Phys. Rev. Lett. 86, 3164-3167 (2001).
[CrossRef]

M. Fiebig, S. Leute, V. V. Pavlov, and R. V. Pizarev, "Nonlinear optical spectroscopy of the two-order-parameter compound YMnO3," Phys. Rev. Lett. 81, 3239-3242 (1998).
[CrossRef]

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, "Second harmonic generation and magnetic-dipole-electric-dipole interference in antiferromagnetic Cr2O3," Phys. Rev. Lett. 73, 2127-2130 (1994).
[CrossRef] [PubMed]

Y. Ogawa, Y. Kaneko, J. P. He, X. Z. Yu, T. Arima, and Y. Tokura, "Magnetization-induced second harmonic generation in a polar ferromagnet," Phys. Rev. Lett. 92, 047401-1-047401-4 (2004).
[CrossRef]

G. T. Rado, "Observation and possible mechanisms of magnetoelectric effects in a ferromagnet," Phys. Rev. Lett. 13, 335-337 (1964).
[CrossRef]

Other

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevski, Electrodynamics of Continuous Media (Pergamon, Oxford, UK, 1984).

R. R. Briss, Symmetry and Magnetism (North-Holland, Amsterdam, 1964).

E. Hanamura and Y. Tanabe, "Magnetoelectric interaction in crystals observed by nonlinear magneto-optics," in Magnetoelectric Interaction Phenomena in Crystals , M. Fiebig, V. Eremenko, and I. Chupis, eds. (Kluwer, Dordrecht, The Netherlands, 2004), pp. 151-162.

See, e.g., H. Kamimura, S. Sugano, and Y. Tanabe, Multiplets of Transition-Metal Ions in Crystals (Academic, New York, 1970).

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Figures (7)

Fig. 1
Fig. 1

Crystal structure of GaFeO3 with space group Pc21n. Large bright, large dark, and small dark spheres correspond to Ga, Fe, and O ions, respectively.

Fig. 2
Fig. 2

Finite elements of third-rank tensors describing the second-harmonic generation in GaFeO3.

Fig. 3
Fig. 3

Absorption spectrum (α cm-1) and the second-harmonic spectrum due to (a) χbaa(i)p(2ω) at 100 and 300 K and (b) χbbb(i)p(2ω) at room temperature.

Fig. 4
Fig. 4

Temperature dependence of the second-harmonic intensity at 800 nm due to (a) χbaa(i)p(2ω) and (b) χbbb(i)p(2ω).

Fig. 5
Fig. 5

Matrix elements appearing in q,q(-)qσqσ-q4T1aq|P¯z|m (m|PX2|4T1aq or m|PY2|4T1aq). The upper (lower) sign corresponds to PX2(PY2).

Fig. 6
Fig. 6

Matrix elements appearing in q,q(-)qσqσ-q4T1aq|P¯Z|mm|PZ2|4T1aq.

Fig. 7
Fig. 7

Polar Kerr ellipticity spectrum shown with (a) a parameter of lattice temperature at magnetic field 12 kOe and (b) a parameter of magnetic field at 9.6 K. The magnetization is perpendicular to the ab plane, and the magnetic field is applied in this direction. (c) The hysteresis of polar Kerr ellipticity against the applied magnetic field by use of the incident light with λ=336 nm.

Equations (71)

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X=(2z-x-y)/6,
Y=(x-y)/2,
Z=(x+y+z)/3.
χbqq(i)p=4N0χbqq(i)p(1),
χbqq(i)p(1)=i,m,kρi (PZ)im(Pq)mk(Pq)ki(ΔE(mi)-2ω)(ΔE(ki)-ω),
(PZ)ipert.m=i|Hso|q/ΔE(iq)(PZ)qm,
(PX)kipert.=(PX)kqq|Hso|i/ΔE(iq).
q|P¯Z|m=-j q|PZ|jj|Vodd|mΔE(jm)-j q|Vodd|jj|PZ|mΔE(jq),
P¯Z=-(PZVodd+VoddPZ)/ΔEo.
k PX|kk|PXΔE(ki)-ω=PX2ΔEo.
χbcc(i)p(1)=i,q,q,mρi i|Hso|qΔE(iq) (P¯Z)qm(PX)mq2[ΔE(mi)-2ω]ΔEo×q|Hso|iΔE(iq),
τq|A1=i|αT1aq,
A1|(-)q(τ)-q=-iαT1aq|,
i|Hso|q=ζ(iq)SMs|σq|S-1Ms×A1|(-)qτ-q|αT1aq,
q|Hso|i=ζ(iq)S-1Ms|(-)qσ-q|SMs×αT1αq|τq|A1,
|i=|6A1,|q=|α 4T1,
ζ(iq)=6A1g|Hso|α 4T1S|σ|S-1A1g|τ|T1.
q,q(-)qσqσ-q4T1aq|P¯Z|mm|PX2|4T1aq
P±1=12(PX±iPY),P0=PZ.
PX2=(P+12+P-12)/2-(P+1P-1+P-1P+1)/2,
PY2=-(P+12+P-12)/2-(P+1P-1+P-1P+1)/2.
P¯z=i=15(p¯i)z,
P±2=i=15(pi)±2,
PP=i=15{(pi)+1(pi)-1+(pi)-1(pi)+1}
-σ±1σ±1=12(S±)2/2S(2S-1),
-σ0σ±1=12(SS±SzS±)/2S(2S-1),
σ±1σ0=12(SS±±S±Sz)/2S(2S-1),
-σ1σ±1=12[S2-S+Sz2(2S-1)Sz)]/2S(2S-1),
σ0σ0=(S2-Sz2)/2S(2S-1).
χbcc(i)p(1)=mqq(-)qσqσ-qλ*(iq)λ(iq)×4T1aq|P¯z|mm|PX2|4T1aqΔE(iq)ΔE(iq)ΔE0[ΔE(mi)-2ω].
χbaa(i)p(1)=cA(4T1a+)ΔE(4T1a+)-2ω+A(4T1a-)ΔE(4T1a-)-2ω+A(4T1a0)ΔE(4T1a0)-2ω+B(4T2x+)ΔE(4T2x+)-2ω+B(4T2x-)ΔE(4T2x-)-2ω,
c=λ*λCe2r22ΔE(4T1a-)ΔE(4T1a+)ΔE0,
A(4T1a±1)=-6949σ±1σ±1,
A(4T1a0)=6649σ0σ0,
B(4T2x±)=1196σ±1σ1.
σ±1σ±1=-14S(2S-1)[S(S-1)±m(2S-1)+m2],
σ0σ0=S2-m22S(2S-1),
χbbb(i)p(1)=cA(4T1a+)ΔE(4T1a+)-2ω+A(4T1a-)ΔE(4T1a-)-2ω+A(4T1a0)ΔE(4T1a0)-2ω+B(4T2x+)ΔE(4T2x+)-2ω+B(4T2x-)ΔE(4T2x-)-2ω,
A(4T1a±)=-3649σ±1σ±1,
A(4T1a0)=121196σ0σ0,
B(4T2x±)=-1196σ±1σ±1.
-σ+1σ-1-σ-1σ+1+σ0σ0=σ·σ=1/2.
Ψ[t24(3T1)e 4T1M=3/2, aq]=Ψ1(aq):
Ψ1(a+)=i2(|x+x-x0x¯0u+|-|x+x-x0x¯-u-|),
Ψ1(a-)=i2(|x+x-x0x¯0u-|+|x+x-x0x¯+u+|),
Ψ1(a0)=-i2(|x+x-x0x¯-u+|+|x+x-x0x¯+u-|).
Ψ2(a+)=i2(-|x+x-x¯+u+u-|+|x+x0x¯0u+u-|),
Ψ2(a-)=i2(|x+x-x¯-u+u-|+|x-x0x¯0u+u-|),
Ψ2(a0)=i2(|x+x0x¯-u+u-|+|x-x0x¯+u+u-|).
Ψ3(a+)=-i2(-|x+x-u+u-u¯+|+|x-x0u+u-u¯-|),
Ψ3(a-)=-i2(|x+x-u+u-u¯-|-|x+x0u+u-u¯+|),
Ψ3(a0)=+i2(|x-x0u+u-u¯+|+|x+x0u+u-u¯-|).
Ψ1(x+)=-12(|x+x-x0x¯0u+|+|x+x-x0x¯-u-|),
Ψ1(x-)=12(|x+x-x0x¯0u-|-|x+x-x0x¯+u+|),
Ψ1(x0)=12(|x+x-x0x¯-u+|-|x+x-x0x¯+u-|).
Ψ2(x+)=16(|x+x-x¯+u+u-|+|x+x0x¯0u+u-|-2|x-x0x¯-u+u-|),
Ψ2(x-)=16(|x+x-x¯-u+u-|-|x-x0x¯0u+u-|-2|x+x0x¯+u+u-|),
Ψ2(x0)=16(-|x+x0x¯-u+u-|+|x-x0x¯+u+u-|-2|x+x-x¯0u+u-|).
Ψ3(x+)=-12(|x+x-u+u-u¯+|+|x-x0u+u-u¯-|),
Ψ3(x-)=-12(|x+x-u+u-u¯-|+|x+x0u+u-u¯+|),
Ψ3(x0)=-12(|x-x0u+u-u¯+|-|x+x0u+u-u¯-|).
a+1|P¯Z|a+1=q=±,0xq|p¯Z|xq+12 q=±uq|p¯Z|uq+12(x0|p¯Z|x0+x-|p¯Z|x-)=67cr2,
a0|P¯Z|a0=q=±,0xq|p¯Z|xq+12 q=±uq|p¯Z|uq+12(x-|p¯Z|x-+x+|p¯Z|x+)=1114cr2,
a+1|P+12|a-1=12(x0|p+12|x++u+|p+12|u--x-|p+12|x0)=221e2r2,
a-1|P+12|a0=-12(x0|p+12|x++u+|p+12|u-+x+|p+12|x-)=121e2r2,
a+1|PP|a+1=q=±,0xq|pp|xq+12 q=±uq|pp|uq+12(x0|pp|x0+x-|pp|x-)=-237e2r2,
a0|PP|a0=q=±,0xq|pp|xq+12 q=±uq|pp|uq+12(x-|pp|x-+x+|pp|x+)=-247e2r2.
a+1|P¯Z|x+1=i2(x0|p¯Z|x0-x-|p¯Z|x-)=i 114cr2,
x+1|P+12|a-1=-i2(x0|p+12|x++u+|p+12|u-+x-|p+12|x0)=i 221e2r2,
x-1|P+12|a0=-i2(x0|p+12|x+-u+|p+12|u--x+|p+12|x-)=-i 521e2r2,
x+1|PP|a+1=-i2(x0|pp|x0-x-|pp|x-)=-i 17e2r2.

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