Resonant X-ray Scattering and Orbital Degree of Freedom in Correlated Electron Systems

Chapter
First Online:
Part of the Springer Tracts in Modern Physics book series (STMP, volume 269)

Abstract

The resonant X-ray scattering (RXS) and the resonant inelastic X-ray scattering (RIXS) in correlated electron systems with the orbital degree of freedom are reviewed from the theoretical view points. In the first part, the orbital order and RXS as an experimental tool to detect the orbital order are reviewed. We introduce characteristic interacting-orbital models and orbital orders, in which a unique orbital frustration effect emerges. As a case study, the theoretical and experimental studies in an impurity effect on the orbital order are presented. In the second part, the RIXS studies for observation of the orbital excitation are reviewed. In particular, we focus on the polarization dependence of RIXS which is crucial to identify the scattering from the orbital excitation. We introduce the recent progresses of the collective orbital excitations coupled with the lattice vibration. The non-resonant inelastic X-ray scattering as a tool to detect the orbital excitations is also reviewed.

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Notes

Acknowledgements

We thank T. Arima, A.R. Baron, Y. Endoh, K. Hirota, D.J. Huang, T. Inami, K. Ishii, T. Matsumura, S. Maekawa, J. Mizuki, Y. Murakami, H. Nakao, J. Nasu, H. Sawa and Y. Wakabayashi for their collaborations and helpful discussions. This work was supported by MEXT KAKENHI Grant Nos. 26287070 and 15H02100. Some of the numerical calculations were performed using the facilities of the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo.

References

  1. 1.
    Y. Murakami, H. Kawada, H. Kawata, M. Tanaka, T. Arima, H. Moritomo, Y. Tokura, Phys. Rev. Lett. 80, 1932 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    Y. Murakami, J.P. Hill, D. Gibbs, M. Blume, I. Koyama, M. Tanaka, H. Kawata, T. Arima, Y. Tokura, K. Hirota, Y. Endoh, Phys. Rev. Lett. 81, 582 (1998)ADSCrossRefGoogle Scholar
  3. 3.
    S. Ishihara, S. Maekawa, Rep. Prog. Phys. 65, 561 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    S. Maekawa, T. Tohyama, S.E. Barnes, S. Ishihara, W. Koshibae, G. Khaliullin, Physics of Transition Metal Oxides (Springer, Berlin, 2004)CrossRefGoogle Scholar
  5. 5.
    S. Ishihara, Y. Murakami, T. Inami, K. Ishii, J. Mizuki, K. Hirota, S. Maekawa, Y. Endoh, New J. Phys. 7, 119 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    T. Matsumura, H. Nakao, Y. Murakami, J. Phys. Soc. Jpn. 82, 021007 (2013)ADSCrossRefGoogle Scholar
  7. 7.
    L.M. Roth, Phys. Rev. 149, 306 (1966)ADSCrossRefGoogle Scholar
  8. 8.
    K.I. Kugel, D.I. Khomskii, Sov. Phys. JETP Lett. 15, 446 (1972)ADSGoogle Scholar
  9. 9.
    M. Cyrot, C. Lyon-Caen, J. Phys. 36, 253 (1975)CrossRefGoogle Scholar
  10. 10.
    S. Inagaki, J. Phys. Soc. Jpn. 39, 596 (1975)ADSCrossRefGoogle Scholar
  11. 11.
    D.I. Khomskii, Transition Metal Compounds (Cambridge University Press, Cambridge, 2014)CrossRefGoogle Scholar
  12. 12.
    L.I. Korovin, E.K. Kudinov, Sov. Phys. Solid State 16, 1666 (1975)Google Scholar
  13. 13.
    J.D. Dunitz, L.E. Orgel, J. Phys. Chem. Solids 3, 12S (1957)ADSGoogle Scholar
  14. 14.
    J. Kanamori, J. Appl. Phys. 31, S14 (1960)ADSCrossRefGoogle Scholar
  15. 15.
    M.D. Kaplan, B.G. Vekhter, Cooperative Phenomena in Jahn-Teller Crystals (Plenum, NewYork, 1995)CrossRefGoogle Scholar
  16. 16.
    P.M. Levy, Sol. Stat. Comm. 7, 1813 (1969)ADSCrossRefGoogle Scholar
  17. 17.
    S. Ishihara, J. Inoue, S. Maekawa, Phys. Rev. B 55, 8280 (1997)ADSCrossRefGoogle Scholar
  18. 18.
    L.F. Feiner, A.M. Oleś, J. Zaanen Phys. Rev. 78, 2799 (1997)ADSGoogle Scholar
  19. 19.
    R. Shiina, T. Nishitani, H. Shiba, J. Phys. Soc. Jpn. 66, 3159 (1997)ADSCrossRefGoogle Scholar
  20. 20.
    Y. Yamashita, N. Nishitani, K. Ueda, Phys. Rev. B 58, 9114 (1998)ADSCrossRefGoogle Scholar
  21. 21.
    Y.Q. Li, M. Ma, D.N. Shi, F.C. Zhang, Phys. Rev. B 60, 12781 (1999)ADSCrossRefGoogle Scholar
  22. 22.
    I. Affleck, Nucl. Phys. B 265, 409 (1986)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    M. Kataoka, J. Kanamori, J. Phys. Soc. Jpn. 32, 113 (1972)ADSCrossRefGoogle Scholar
  24. 24.
    A.J. Millis, Phys. Rev. B 53, 8434 (1996)ADSCrossRefGoogle Scholar
  25. 25.
    S. Okamoto, S. Ishihara, S. Maekawa, Phys. Rev. B 65, 144403 (2002)ADSCrossRefGoogle Scholar
  26. 26.
    S. Ishihara, M. Yamanaka, N. Nagaosa, Phys. Rev. B 56, 686 (1997)ADSCrossRefGoogle Scholar
  27. 27.
    G. Khaliullin, V. Oudovenko, Phys. Rev. B 56, R14243 (1997)ADSCrossRefGoogle Scholar
  28. 28.
    L.F. Feiner, A.M. Oleś, Phys. Rev. B 59, 3295 (1999)ADSCrossRefGoogle Scholar
  29. 29.
    Z. Nussinov, M. Biskup, L. Chayes, J. van den Brink, Europhys. Lett. 67, 990 (2004)ADSCrossRefGoogle Scholar
  30. 30.
    T. Tanaka, S. Ishihara, Phys. Rev. B 79, 035109 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52, R5467(R) (1995)ADSCrossRefGoogle Scholar
  32. 32.
    I. Leonov, N. Binggeli, D. Korotin, V.I. Anisimov, N. Stojić, D. Vollhardt, Phys. Rev. Lett. 101, 096405 (2008)ADSCrossRefGoogle Scholar
  33. 33.
    E. Pavarini, E. Koch, A.I. Lichtenstein, Phys. Rev. Lett. 101, 266405 (2008)ADSCrossRefGoogle Scholar
  34. 34.
    Y. Ito, J. Akimitsu, J. Phys. Soc. Jpn. 40, 1333 (1976)ADSCrossRefGoogle Scholar
  35. 35.
    J. Akimitsu, H. Ichikawa, N. Eguchi, T. Miyano, M. Nishi, K. Kakurai, J. Phys. Soc. Jpn. 70, 3475 (2001)ADSCrossRefGoogle Scholar
  36. 36.
    H. Ichikawa, L. Kano, M. Saitoh, S. Miyahara, N. Furukawa, J. Akimitsu, T. Yokoo, T. Matsumura, M. Takeda, K. Hirota, J. Phys. Soc. Jpn. 74, 1020 (2005)ADSCrossRefGoogle Scholar
  37. 37.
    M. Takata, E. Nishibori, K. Kato, M. Sakata, Y. Moritomo, J. Phys. Soc. Jpn. 68, 2190 (1999)ADSCrossRefGoogle Scholar
  38. 38.
    T. Itakura, T. Nakao, H. Kimura, Y. Noda, Y. Ishikawa, Y. Tokura, S. Miyasaka, Meeting abstracts of the Phys. Soc. Jpn. 67, 592 (2012)Google Scholar
  39. 39.
    T. Fujii, T. Sugawara, T. Higuchi, N. Katayama, H. Sawa, T. Shishido, K. Sugimoto, M. Takada, T. Arima, N. Taguchi, Y. Tokura, Meeting abstracts of the Phys. Soc. Jpn. 70, 2422 (2015)Google Scholar
  40. 40.
    A.N. Mariano, R.E. Hanneman, J. Appl. Phys. 34, 384 (1963)ADSCrossRefGoogle Scholar
  41. 41.
    R.J. Wakelin, E.L. Yates, Proc. Phys. Soc. B 66, 221 (1953)ADSCrossRefGoogle Scholar
  42. 42.
    Y. Waseda, S. Tamaki, Phil. Mag. 32, 951 (1975)ADSCrossRefGoogle Scholar
  43. 43.
    D.H. Templeton, L.K. Templeton, Acta. Cryst. A 36, 237 (1980)CrossRefGoogle Scholar
  44. 44.
    D.H. Templeton, L.K. Templeton, Acta. Cryst. A 38, 62 (1982)CrossRefGoogle Scholar
  45. 45.
    V.E. Dmitrienko, Acta. Cryst. A 39, 29 (1983)CrossRefGoogle Scholar
  46. 46.
    S. Ishihara, S. Maekawa, Phys. Rev. B 58, 13442 (1998)ADSCrossRefGoogle Scholar
  47. 47.
    L. Paolasini, C. Vettier, F. de Bergevin, F. Yakhou, D. Mannix, A. Stunault, W. Neubeck, Phys. Rev. Lett. 82, 4719 (1999)ADSCrossRefGoogle Scholar
  48. 48.
    M. Fabrizio, M. Altarelli, M. Benfatto, Phys. Rev. Lett. 80, 3400 (1998)ADSCrossRefGoogle Scholar
  49. 49.
    Y. Endoh, K. Hirota, S. Ishihara, S. Okamoto, Y. Murakami, A. Nishizawa, T. Fukuda, H. Kimura, H. Nojiri, K. Kaneko, S. Maekawa, Phys. Rev. Lett. 82, 4328 (1999)ADSCrossRefGoogle Scholar
  50. 50.
    M.V. Zimmermann, J.P. Hill, D. Gibbs, M. Blume, D. Casa, B. Keimer, Y. Murakami, Y. Tomioka, Y. Tokura, Phys. Rev. Lett. 83, 4872 (1999)ADSCrossRefGoogle Scholar
  51. 51.
    Y. Wakabayashi, Y. Murakami, I. Koyama, T. Kimura, Y. Tokura, Y.A. Moritomo, K. Hirota, Y. Endoh, J. Phys. Soc. Jpn. 69, 2731 (2000)ADSCrossRefGoogle Scholar
  52. 52.
    J. García, M.C. Sanchez, J. Blasco, G. Subias, M.G. Proietti, J. Phys. Condens. Matter 13, 3243 (2001)ADSCrossRefGoogle Scholar
  53. 53.
    M.V. Zimmermann, C.S. Nelson, J.P. Hill, D. Gibbs, M. Blume, D. Casa, B. Keimer, Y. Murakami, C.-C. Kao, C. Venkataraman, T. Gog, Y. Tomioka, Y. Tokura, Phys. Rev. B 64, 195133 (2001)ADSCrossRefGoogle Scholar
  54. 54.
    Y. Wakabayashi, Y. Murakami, I. Koyama, T. Kimura, Y. Tokura, Y. Moritomo, Y. Endoh, K. Hirota, J. Phys. Soc. Jpn. 72, 618 (2003)ADSCrossRefGoogle Scholar
  55. 55.
    S.B. Wilkins, P.D. Spencer, T.A.W. Beale, P.D. Hatton, M.V. Zimmermann, S.D. Brown, D. Prabhakaran, A.T. Boothroyd, Phys. Rev. B 67, 205110 (2003)ADSCrossRefGoogle Scholar
  56. 56.
    H. Ohsumi, Y. Murakami, T. Kiyama, H. Nakao, M. Kubota, Y. Wakabayashi, Y. Konishi, M. Izumi, M. Kawasaki, Y. Tokura, J. Phys. Soc. Jpn. 72, 1006 (2003)ADSCrossRefGoogle Scholar
  57. 57.
    S. Di Matteo, T. Chatterji, Y. Joly, A. Stunault, J.A. Paixao, R. Suryanarayanan, G. Dhalenne, A. Revcolevschi, Phys. Rev. B 68, 024414 (2003)ADSCrossRefGoogle Scholar
  58. 58.
    Y. Sua, K. Istomina, D. Wermeilleb, A. Fattaha, P. Foucarta, P. Meuffelsa, D. Hupfelda, T. Brueckela, J. Mag. Mag. Mat. 272–276, E291 (2004)CrossRefGoogle Scholar
  59. 59.
    S. Grenier, J.P. Hill, D. Gibbs, K.J. Thomas, M.V. Zimmermann, C.S. Nelson, V. Kiryukhin, Y. Tokura, Y. Tomioka, D. Casa, T. Gog, C. Venkataraman, Phys. Rev. B 69, 134419 (2004)ADSCrossRefGoogle Scholar
  60. 60.
    J.H. Martín, J. Garcia, G. Subías, J. Blasco, M.C. Sanchez, Phys. Rev. B 70, 024408 (2004)ADSCrossRefGoogle Scholar
  61. 61.
    S.S. Dhesi, A. Mirone, C. De, Nada\({\ddot{\rm i}}\) P. Ohresser, P. Bencok, N.B. Brookes, P. Reutler, A. Revcolevschi, A. Tagliaferri, O. Toulemonde, G. van der Laan. Phys. Rev. Lett. 92, 056403 (2004)Google Scholar
  62. 62.
    H. Nakao, Y. Wakabayashi, T. Kiyama, Y. Murakami, M.V. Zimmermann, J.P. Hill, D. Gibbs, S. Ishihara, Y. Taguchi, Y. Tokura, Phys. Rev. B 66, 184419 (2002)ADSCrossRefGoogle Scholar
  63. 63.
    H. Nakao, M. Tsubota, F. Iga, K. Uchihira, T. Nakano, T. Takabatake, K. Kato, Y. Murakami, J. Phys. Soc. Jpn. 73, 2620 (2004)ADSCrossRefGoogle Scholar
  64. 64.
    M. Kubota, H. Nakao, Y. Murakami, Y. Taguchi, M. Iwama, Y. Tokura, Phys. Rev. B 70, 245125 (2004)ADSCrossRefGoogle Scholar
  65. 65.
    M. Tsubota, F. Iga, K. Uchihira, T. Nakano, S. Kura, T. Takabatake, S. Kodama, H. Nakao, Y. Murakami, J. Phys. Soc. Jpn. 74, 3259 (2005)ADSCrossRefGoogle Scholar
  66. 66.
    H. Nakao, S. Kodama, K. Kiyoto, Y. Murakami, M. Tsubota, F. Iga, K. Uchihira, T. Takabatake, H. Ohsumi, M. Mizumaki, N. Ikeda, J. Phys. Soc. Jpn. 75, 094706 (2006)ADSCrossRefGoogle Scholar
  67. 67.
    M. Noguchi, A. Nakazawa, S. Oka, T. Arima, Y. Wakabayashi, H. Nakao, Y. Murakami, Phys. Rev. B 62, R9271(R) (2000)ADSCrossRefGoogle Scholar
  68. 68.
    D. Bizen, N. Shirane, T. Murata, H. Nakao, Y. Murakami, J. Fujioka, T. Yasue, S. Miyasaka, Y. Tokura, J. Phys. Conf. Ser. 150, 042010 (2009)ADSCrossRefGoogle Scholar
  69. 69.
    T.A.W. Beale, R.D. Johnson, Y. Joly, S.R. Bland, P.D. Hatton, L. Bouchenoire, C. Mazzoli, D. Prabhakaran, Phys. Rev. B 82, 024105 (2010)ADSCrossRefGoogle Scholar
  70. 70.
    H. Nakao, T. Murata, D. Bizen, Y. Murakami, K. Ohoyama, K. Yamada, S. Ishiwata, W. Kobayashi, I. Terasaki, J. Phys. Soc. Jpn. 80, 023711 (2011)ADSCrossRefGoogle Scholar
  71. 71.
    J. Fujioka, Y. Yamasaki, H. Nakao, R. Kumai, Y. Murakami, M. Nakamura, M. Kawasaki, Y. Tokura, Phys. Rev. Lett. 111, 027206 (2013)ADSCrossRefGoogle Scholar
  72. 72.
    U. Staub, G.I. Meijer, F. Fauth, R. Allenspach, J.G. Bednorz, J. Karpinski, S.M. Kazakov, L. Paolasini, F. d’Acapito, Phys. Rev. Lett. 88, 126402 (2002)ADSCrossRefGoogle Scholar
  73. 73.
    V. Scagnoli, U. Staub, A.M. Mulders, M. Janousch, G.I. Meijer, G. Hammerl, J.M. Tonnerre, N. Stojic, Phys. Rev. B 73, 100409(R) (2006)ADSCrossRefGoogle Scholar
  74. 74.
    R. Caciuffo, L. Paolasini, A. Sollier, P. Ghigna, E. Pavarini, J. van den Brink, M. Altarelli, Phys. Rev. B 65, 174425 (2002)ADSCrossRefGoogle Scholar
  75. 75.
    C. Mazzoli, L. Paolasini, F. de Bergevin, P. Ghigna, R. Caciuffo, Phys. B Condens. Matter 378–380, 563 (2006)CrossRefGoogle Scholar
  76. 76.
    J.C.T. Lee, S. Yuan, S. Lal, Y.I. Joe, Y. Gan, S. Smadici, K. Finkelstein, Y. Feng, A. Rusydi, P.M. Goldbart, S.L. Cooper, P. Abbamonte, Nat. Phys. 8, 63 (2012)CrossRefGoogle Scholar
  77. 77.
    J. García, G. Subias, M.G. Proietti, H. Renevier, Y. Joly, J.L. Hodeau, J. Blasco, M.C. Sanchez, J.F. Berar, Phys. Rev. Lett. 85, 578 (2000)ADSCrossRefGoogle Scholar
  78. 78.
    D.J. Huang, H.-J. Lin, J. Okamoto, K.S. Chao, H.-T. Jeng, G.Y. Guo, C.-H. Hsu, C.-M. Huang, D.C. Ling, W.B. Wu, C.S. Yang, C.T. Chen, Phys. Rev. Lett. 96, 096401 (2006)ADSCrossRefGoogle Scholar
  79. 79.
    S. Ishihara, S. Maekawa, Phys. Rev. Lett. 80, 3799 (1998)ADSCrossRefGoogle Scholar
  80. 80.
    I.S. Elfimov, V.I. Anisimov, G.A. Sawatzky, Phys. Rev. Lett. 82, 4264 (1999)ADSCrossRefGoogle Scholar
  81. 81.
    M. Takahashi, J. Igarashi, P. Fulde, J. Phys. Soc. Jpn. 68, 2530 (1999)ADSCrossRefGoogle Scholar
  82. 82.
    M. Benfatto, Y. Joly, C.R. Natoli, Phys. Rev. Lett. 83, 636 (1999)ADSCrossRefGoogle Scholar
  83. 83.
    S. Ishihara, S. Maekawa, Phys. Rev. B 62, 5690 (2000)ADSCrossRefGoogle Scholar
  84. 84.
    S. Ishihara, S. Maekawa, Phys. Rev. B 62, R9252 (2000)ADSCrossRefGoogle Scholar
  85. 85.
    C. Castleton, M. Altarelli, Phys. Rev. B 62, 1033 (2000)ADSCrossRefGoogle Scholar
  86. 86.
    P. Benedetti, J. van den Brink, E. Pavarini, A. Vigliante, P. Wochner, Phys. Rev. B 63, 060408 (2001)ADSCrossRefGoogle Scholar
  87. 87.
    M. Takahashi, J. Igarashi, Phys. Rev. B 64, 075110 (2001)ADSCrossRefGoogle Scholar
  88. 88.
    I. Elfimov, N. Skorikov, V. Anisimov, G. Sawatzky, Phys. Rev. Lett. 88, 015504 (2001)ADSCrossRefGoogle Scholar
  89. 89.
    S.W. Lovesey, K.S. Knight, D.S. Sivia, Phys. Rev. B 65, 224402 (2002)ADSCrossRefGoogle Scholar
  90. 90.
    Y. Tanaka, T. Inami, T. Nakamura, H. Yamauchi, H. Onodera, K. Ohoyama, Y. Yamaguchi, J. Phys. Condens. Matter 11, L505 (1999)ADSCrossRefGoogle Scholar
  91. 91.
    K. Hirota, N. Oumi, T. Matsumura, H. Nakao, Y. Wakabayashi, Y. Murakami, Y. Endoh, Phys. Rev. Lett. 84, 2706 (2000)ADSCrossRefGoogle Scholar
  92. 92.
    H. Nakao, K. Magishi, Y. Wakabayashi, Y. Murakami, K. Koyama, K. Hirota, Y. Endoh, S. Kunii, J. Phys. Soc. Jpn. 70, 1857 (2001)ADSCrossRefGoogle Scholar
  93. 93.
    D. McMorrow, K. McEwen, U. Steigenberger, H. Ronnow, F. Yakhou, Phys. Rev. Lett. 87, 057201 (2001)ADSCrossRefGoogle Scholar
  94. 94.
    T. Matsumura, N. Oumi, K. Hirota, H. Nakao, Y. Wakabayashi, Y. Murakami, J. Phys. Soc. Jpn. 71, 91 (2002)ADSCrossRefGoogle Scholar
  95. 95.
    T. Matsumura, N. Oumi, K. Hirota, H. Nakao, Y. Murakami, Y. Wakabayashi, T. Arima, S. Ishihara, Y. Endoh, Phys. Rev. B 65, 094420 (2002)ADSCrossRefGoogle Scholar
  96. 96.
    J. Paixao, C. Detlefs, M. Longfield, R. Caciuffo, P. Santini, N. Bernhoeft, J. Rebizant, G. Lander, Phys. Rev. Lett. 89, 187202 (2002)ADSCrossRefGoogle Scholar
  97. 97.
    D. Mannix, Y. Tanaka, D. Carbone, N. Bernhoeft, S. Kunii, Phys. Rev. Lett. 95, 117206 (2005)ADSCrossRefGoogle Scholar
  98. 98.
    T. Nagao, J. Igarashi, J. Phys. Soc. Jpn. 70, 2892 (2001)ADSCrossRefGoogle Scholar
  99. 99.
    H. Kusunose, Y. Kuramoto, J. Phys. Soc. Jpn. 74, 3139 (2005)ADSCrossRefGoogle Scholar
  100. 100.
    T. Nagao, J. Igarashi, J. Phys. Soc. Jpn. 75, 247 (2006)ADSCrossRefGoogle Scholar
  101. 101.
    T. Kiyama, Y. Wakabayashi, H. Nakao, H. Ohsumi, Y. Murakami, M. Izumi, M. Kawasaki, Y. Tokura, J. Phys. Soc. Jpn. 72, 785 (2003)ADSCrossRefGoogle Scholar
  102. 102.
    H. Nakao, J. Nishimura, Y. Murakami, A. Ohtomo, T. Fukumura, M. Kawasaki, T. Koida, Y. Wakabayashi, H. Sawa, J. Phys. Soc. Jpn. 78, 024602 (2009)ADSCrossRefGoogle Scholar
  103. 103.
    H. Nakao, T. Sudayama, M. Kubota, J. Okamoto, Y. Yamasaki, Y. Murakami, H. Yamada, A. Sawa, K. Iwasa, Phys. Rev. B 92, 245104 (2015)ADSCrossRefGoogle Scholar
  104. 104.
    S.B. Wilkins, P.D. Spencer, P.D. Hatton, S.P. Collins, M.D. Roper, D. Prabhakaran, A.T. Boothroyd, Phys. Rev. Lett. 91, 167205 (2003)ADSCrossRefGoogle Scholar
  105. 105.
    K.J. Thomas, J.P. Hill, S. Grenier, Y.-J. Kim, P. Abbamonte, L. Venema, A. Rusydi, Y. Tomioka, Y. Tokura, D.F. McMorrow, G. Sawatzky, M. van Veenendaal, Phys. Rev. Lett. 92, 237204 (2004)ADSCrossRefGoogle Scholar
  106. 106.
    J.H. Martín, J. García, G. Subías, J. Blasco, M.C. Sánchez, S. Stanescu, Phys. Rev. B 73, 224407 (2006)ADSCrossRefGoogle Scholar
  107. 107.
    S.B. Wilkins, N. Stoji, T.A.W. Beale, N. Binggeli, C.W.M. Castleton, P. Bencok, D. Prabhakaran, A.T. Boothroyd, P.D. Hatton, M. Altarelli, Phys. Rev. B 71, 245102 (2005)ADSCrossRefGoogle Scholar
  108. 108.
    H. Wadati, J. Geck, E. Schierle, R. Sutarto, F. He, D.G. Hawthorn, M. Nakamura, M. Kawasaki, Y. Tokura, G.A. Sawatzky, New J. Phys. 16, 033006 (2014)ADSCrossRefGoogle Scholar
  109. 109.
    B.J. Kim, H. Ohsumi, T. Komesu, S. Sakai, T. Morita, H. Takagi, T. Arima, Science 323, 1329 (2009)ADSCrossRefGoogle Scholar
  110. 110.
    K. Ohgushi, J. Yamaura, H. Ohsumi, K. Sugimoto, S. Takeshita, A. Tokuda, H. Takagi, M. Takata, T. Arima, Phys. Rev. Lett. 110, 217212 (2013)ADSCrossRefGoogle Scholar
  111. 111.
    M.M. Sala, M. Rossi, S. Boseggia, J. Akimitsu, N.B. Brookes, M. Isobe, M. Minola, H. Okabe, H.M. R\({\rm{ }}\)nnow, L. Simonelli, D.F. McMorrow, G. Monaco. Phys. Rev. B 89, 121101(R) (2014)ADSCrossRefGoogle Scholar
  112. 112.
    T. Inami, T. Fukuda, J. Mizuki, S. Ishihara, H. Kondo, H. Nakao, T. Matsumura, K. Hirota, Y. Murakami, S. Maekawa, Y. Endoh, Phys. Rev. B 67, 045108 (2003)ADSCrossRefGoogle Scholar
  113. 113.
    K. Ishii, T. Inami, K. Ohwada, K. Kuzushita, J. Mizuki, Y. Murakami, S. Ishihara, Y. Endoh, S. Maekawa, K. Hirota, Y. Moritomo, Phys. Rev. B 70, 224437 (2004)ADSCrossRefGoogle Scholar
  114. 114.
    Y. Kim, J.P. Hill, F.C. Chou, D. Casa, T. Gog, C.T. Venkataraman, Phys. Rev. B 69, 155105 (2004)ADSCrossRefGoogle Scholar
  115. 115.
    S. Grenier, J. Hill, V. Kiryukhin, W. Ku, Y.-J. Kim, K. Thomas, S.-W. Cheong, Y. Tokura, Y. Tomioka, D. Casa, T. Gog, Phys. Rev. Lett. 94, 047203 (2005)ADSCrossRefGoogle Scholar
  116. 116.
    J. Kim, D.S. Ellis, T. Gog, D. Casa, Y.-J. Kim, Phys. Rev. B 81, 073109 (2010)ADSCrossRefGoogle Scholar
  117. 117.
    F. Weber, S. Rosenkranz, J.-P. Castellan, R. Osborn, J.F. Mitchell, H. Zheng, D. Casa, J.H. Kim, T. Gog, Phys. Rev. B 82, 085105 (2010)ADSCrossRefGoogle Scholar
  118. 118.
    K. Ishii, S. Ishihara, Y. Murakami, K. Ikeuchi, K. Kuzushita, T. Inami, K. Ohwada, M. Yoshida, I. Jarrige, N. Tatami, S. Niioka, D. Bizen, Y. Ando, J. Mizuki, S. Maekawa, Y. Endoh, Phys. Rev. B 83, 241101(R) (2011)ADSCrossRefGoogle Scholar
  119. 119.
    X. Liu, T.F. Seman, K.H. Ahn, M. van Veenendaal, D. Casa, D. Prabhakaran, A.T. Boothroyd, H. Ding, J.P. Hill, Phys. Rev. B 87, 201103 (2013)ADSCrossRefGoogle Scholar
  120. 120.
    C.S. Nelson, J.P. Hill, D. Gibbs, F. Yakhou, F. Livet, Y. Tomioka, T. Kimura, Y. Tokura, Phys. Rev. B 66, 134412 (2002)ADSCrossRefGoogle Scholar
  121. 121.
    J.J. Turner, K.J. Thomas, J.P. Hill, M.A. Pfeifer, K. Chesnel, Y. Tomioka, Y. Tokura, S.D. Kevan, New J. Phys. 10, 053023 (2008)CrossRefGoogle Scholar
  122. 122.
    H. Ehrke, R.I. Tobey, S. Wall, S.A. Cavill, M. Forst, V. Khanna, N. Th Garl, D. Stojanovic, A.T. Prabhakaran, M. Boothroyd, A. Gensch, P. Mirone, A. Reutler, S.S. Revcolevschi, A.Cavalleri Dhesi, Phys. Rev. Lett. 106, 217401 (2011)ADSCrossRefGoogle Scholar
  123. 123.
    P. Beaud, A. Caviezel, S.O. Mariager, L. Rettig, G. Ingold, C. Dornes, S.-W. Huang, J.A. Johnson, M. Radovic, T. Huber, T. Kubacka, A. Ferrer, H.T. Lemke, M. Chollet, D. Zhu, J.M. Glownia, M. Sikorski, A. Robert, H. Wadati, M. Nakamura, M. Kawasaki, Y. Tokura, S.L. Johnson, U. Staub, Nat. Mater. 13, 923 (2014)ADSCrossRefGoogle Scholar
  124. 124.
    M. Blume, in Resonant Anomalous X-ray Scattering, ed. by G. Materlik, C.J. Sparks, K. Fischer (Elsevier Science, Amsterdam, 1994)Google Scholar
  125. 125.
    S.W. Lovesey, S.P. Collins, X-ray Scattering and Absorption by Magnetic Materials (Oxford University Press, Oxford, 1995)Google Scholar
  126. 126.
    J.J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Massachusetts, 1967)Google Scholar
  127. 127.
    M. Azuma, Y. Fujishiro, M. Takano, M. Nohara, H. Takagi, Phys. Rev. B 55, R8658 (1997)ADSCrossRefGoogle Scholar
  128. 128.
    M. Sigrist, A. Furusaki, J. Phys. Soc. Jpn. 65, 2385 (1996)ADSCrossRefGoogle Scholar
  129. 129.
    S.B. Oseroff, S.-W. Cheong, B. Aktas, M.F. Hundley, Z. Fisk, L.W. Rupp Jr., Phys. Rev. Lett. 74, 1450 (1995)ADSCrossRefGoogle Scholar
  130. 130.
    M. Hase, K. Uchinokura, R.J. Birgeneau, K. Hirota, G. Shirane, J. Phys. Soc. Jpn. 65, 1392 (1996)ADSCrossRefGoogle Scholar
  131. 131.
    N. Tatami, Y. Ando, S. Niioka, H. Kira, M. Onodera, H. Nakao, K. Iwasa, Y. Murakami, T. Kakiuchi, Y. Wakabayashi, H. Sawa, S. Itoh, J. Mag. Mag. Mater. 310, 787 (2007)ADSCrossRefGoogle Scholar
  132. 132.
    N. Tatami: Master thesis, Tohoku University, 2004Google Scholar
  133. 133.
    S. Ohtani, Y. Watanabe, M. Saito, N. Abe, K. Taniguchi, H. Sagayama, T. Arima, M. Watanabe, Y. Noda, J. Phys. Condens. Matter 22, 176003 (2010)ADSCrossRefGoogle Scholar
  134. 134.
    R.B. Stinchcombe, in Phase Transition in Critical Phenomena, vol. 7, ed. by C. Domb, J.L. Lebowitz (Academic Press, London, 1983)Google Scholar
  135. 135.
    D.J. Breed, K. Gilijamse, J.W.E. Sterkenburg, A.R. Miedema, J. Appl. Phys. 41, 1267 (1970)ADSCrossRefGoogle Scholar
  136. 136.
    T. Tanaka, M. Matsumoto, S. Ishihara, Phys. Rev. Lett. 98, 256402 (2007)ADSCrossRefGoogle Scholar
  137. 137.
    T. Tanaka, S. Ishihara, Phys. Rev. B 78, 153106 (2008)ADSCrossRefGoogle Scholar
  138. 138.
    A.G. Komarov, L.I. Korovin, E.K. Kudinov, Sov Phys. Solid State 17, 1531 (1975)Google Scholar
  139. 139.
    S. Ishihara, J. Inoue, S. Maekawa, Phys. C 263, 130 (1996)ADSCrossRefGoogle Scholar
  140. 140.
    S. Ishihara, S. Maekawa, Phys. Rev. B 62, 2338 (2000)ADSCrossRefGoogle Scholar
  141. 141.
    J. van den Brink, Phys. Rev. Lett. 87, 217202 (2001)ADSCrossRefGoogle Scholar
  142. 142.
    P.B. Allen, V. Perebeinos, Phys. Rev. Lett. 83, 4828 (1999)ADSCrossRefGoogle Scholar
  143. 143.
    V. Perebeinos, P.B. Allen, Phys. Rev. B 64, 085118 (2001)ADSCrossRefGoogle Scholar
  144. 144.
    J.H. Jung, K.H. Kim, D.J. Eom, T.W. Noh, E.J. Choi, J. Yu, Y.S. Kwon, Y. Chung, Phys. Rev. B 55, 15 489 (1997)Google Scholar
  145. 145.
    J. Nasu, S. Ishihara, Phys. Rev. B 88, 205110 (2013)ADSCrossRefGoogle Scholar
  146. 146.
    J. Inoue, S. Okamoto, S. Ishihara, W. Koshibae, Y. Kawamura, S. Maekawa, Phys. B 237–238, 51 (1997)CrossRefGoogle Scholar
  147. 147.
    E. Saitoh, K.T. Okamoto, K. Tobe, K. Yamamoto, T. Kimura, S. Ishihara, S. Maekawa, Y. Tokura, Nature 418, 40 (2001)ADSCrossRefGoogle Scholar
  148. 148.
    S. Okamoto, S. Ishihara, S. Maekawa, Phys. Rev. B 66, 014435 (2002)ADSCrossRefGoogle Scholar
  149. 149.
    M. Gruninger, R. Ruckamp, M. Windt, P. Reutler, C. Zobel, T. Lorenz, A. Freimuth, A. Revcolevshi, Nature 418, 39 (2002)ADSCrossRefGoogle Scholar
  150. 150.
    R. Kruger, B. Schulz, S. Naler, R. Rauer, D. Budelmann, J. Backstrom, K.H. Kim, S.-W. Cheong, V. Pereveinos, M. Rubhausen, Phys. Rev. Lett. 92, 097203 (2004)ADSCrossRefGoogle Scholar
  151. 151.
    S. Ishihara, Phys. Rev. B 69, 075118 (2004)ADSCrossRefGoogle Scholar
  152. 152.
    S. Miyasaka, S. Onoda, Y. Okimoto, J. Fujioka, M. Iwama, N. Nagaosa, Y. Tokura, Phys. Rev. Lett. 94, 076405 (2005)ADSCrossRefGoogle Scholar
  153. 153.
    C. Ulrich, A. Gossling, M. Gruninger, M. Guennou, H. Roth, M. Cwik, T. Lorenz, G. Khaliullin, B. Keimer, Phys. Rev. Lett. 97, 157401 (2006)ADSCrossRefGoogle Scholar
  154. 154.
    G. Khaliullin, S. Okamoto, Phys. Rev. Lett. 89, 167201 (2002)ADSCrossRefGoogle Scholar
  155. 155.
    D. Kawana, Y. Murakami, T. Yokoo, S. lto, A.T. Savich, G.E. Granrth, K. lkeuchi, H. Nakao, K. lwasa, R. Fukuta, S. Miyasaka, S. Taiima, S. lshihara, Y. Tokura, Meeting Abstract of Japanese Physical Society Meeting 67, 675 (2012)Google Scholar
  156. 156.
    Y. Tanaka, A.Q. Baron, Y.-J. Kim, K.J. Thomas, J.P. Hill, Z. Honda, F. Iga, S. Tsutui, D. Ishihkawa, C.S. Nelson, New J. Phys. 6, 161 (2004)ADSCrossRefGoogle Scholar
  157. 157.
    B.C. Larson, W. Ku, J.Z. Tischler, C.-C. Lee, O.D. Restrepo, A.G. Eguiluz, P. Zschack, K.D. Finkelstein, Phys. Rev. Lett. 99, 026401 (2007)ADSCrossRefGoogle Scholar
  158. 158.
    M. van Veenendaal, M.W. Haverkort, Phys. Rev. B 77, 224107 (2008)ADSCrossRefGoogle Scholar
  159. 159.
    W. Haverkort, A. Tanaka, L.H. Tjeng, G.A. Sawatzky, Phys. Rev. Lett. 99, 257401 (2007)ADSCrossRefGoogle Scholar
  160. 160.
    W. Haverkort, A. Tanaka, L.H. Tjeng, G.A. Sawatzky, Phys. Rev. B 77, 224107 (2008)CrossRefGoogle Scholar
  161. 161.
    K. Tsutsui, E. Kaneshita, T. Tohyama, Phys. Rev. B 92, 195103 (2015)ADSCrossRefGoogle Scholar
  162. 162.
    S. Ishihara: (unpublished)Google Scholar
  163. 163.
    L.J.P. Ament, M. van Veenendaal, T.P. Devereaux, J.P. Hill, J. van den Brink, Rev. Mod. Phys. 83, 705 (2011)ADSCrossRefGoogle Scholar
  164. 164.
    C. Jia, K. Wohlfeld, Y. Wang, B. Moritz, T.P. Devereaux, Phys. Rev. X 6, 021020 (2016)Google Scholar
  165. 165.
    K. Ishii, T. Tohyama, J. Mizuki, J. Phys. Soc. Jpn. 82, 021015 (2013)ADSCrossRefGoogle Scholar
  166. 166.
    J. van den Brink, M. van Veenendaal, Europhys. Lett. 73, 121 (2006)ADSCrossRefGoogle Scholar
  167. 167.
    L.J.P. Ament, F. Forte, J. van den Brink, Phys. Rev. B 75, 115118 (2007)ADSCrossRefGoogle Scholar
  168. 168.
    H. Kondo, S. Ishihara, S. Maekawa, Phys. Rev. B 64, 014414 (2001); Erratum. Phys. Rev. B 64, 179904 (2001)ADSCrossRefGoogle Scholar
  169. 169.
    T. Semba, M. Takahashi, J. Igarashi, Phys. Rev. B 78, 155111 (2008)ADSCrossRefGoogle Scholar
  170. 170.
    J.P. Hill, C.C. Kao, W.A.L. Caliebe, M. Matsubara, A. Kotani, J.L. Peng, R.L. Greene, Phys. Rev. Lett. 80, 4967 (1998)ADSCrossRefGoogle Scholar
  171. 171.
    K. Hamalainen, J.P. Hill, S. Huotari, C.-C. Kao, L.E. Berman, A. Kotani, T. Ide, J.L. Peng, R.L. Greene, Phys. Rev. B 61, 1836 (2000)ADSCrossRefGoogle Scholar
  172. 172.
    L. Lu, J.N. Hancock, G. Chabot-Couture, K. Ishii, O.P. Vajk, G. Yu, J. Mizuki, D. Casa, T. Gog, M. Greven, Phys. Rev. B 74, 224509 (2006)ADSCrossRefGoogle Scholar
  173. 173.
    G. Chabot-Couture, J.N. Hancock, P.K. Mang, D.M. Casa, T. Gog, M. Greven, Phys. Rev. B 82, 035113 (2010)ADSCrossRefGoogle Scholar
  174. 174.
    M. van Veenendaal, X. Liu, M.H. Carpenter, S.P. Cramer, Phys. Rev. B 83, 045101 (2011)ADSCrossRefGoogle Scholar
  175. 175.
    M. van Veenendaal, Phys. Rev. Lett. 96, 117404 (2006)ADSCrossRefGoogle Scholar
  176. 176.
    L.J.P. Ament, G. Ghiringhelli, M.M. Sala, L. Braicovich, J. van den Brink, Phys. Rev. Lett. 103, 117003 (2009)ADSCrossRefGoogle Scholar
  177. 177.
    C. Ulrich, L.J.P. Ament, G. Ghiringhelli, L. Braicovich, M. Moretti, Sala, N. Pezzotta, T. Schmitt, G. Khaliullin, J. van den Brink, H. Roth, T. Lorenz, B. Keimer. Phys. Rev. Lett. 103, 107205 (2009)ADSCrossRefGoogle Scholar
  178. 178.
    L.J.P. Ament, G. Khaliullin, Phys. Rev. B 81, 125118 (2010)ADSCrossRefGoogle Scholar
  179. 179.
    J. Schlappa, K. Wohlfeld, K.J. Zhou, M. Mourigal, M.W. Haverkort, V.N. Strocov, L. Hozoi, C. Monney, S. Nishimoto, S. Singh, A. Revcolevschi, J.-S. Caux, L. Patthey, H.M. Ronnow, J. van den Brink, T. Schmitt, Nature 485, 82 (2012)ADSCrossRefGoogle Scholar
  180. 180.
    V. Bisogni, K. Wohlfeld, S. Nishimoto, C. Monney, J. Trinckauf, K. Zhou, R. Kraus, K. Koepernik, C. Sekar, V. Strocov, B. Buchner, T. Schmitt, J. van den Brink, J. Geck, Phys. Rev. Lett. 114, 096402 (2015)ADSCrossRefGoogle Scholar
  181. 181.
    K. Wohlfeld, M. Daghofer, S. Nishimoto, G. Khaliullin, J. van den Brink, Phys. Rev. Lett. 107, 147201 (2011)ADSCrossRefGoogle Scholar
  182. 182.
    K. Wohlfeld, S. Nishimoto, M.W. Haverkort, J. van den Brink, Phys. Rev. B 88, 195138 (2013)ADSCrossRefGoogle Scholar
  183. 183.
    S. Ishihara, S. Ihara, J. Phys. Chem. Sol. 69, 3184 (2008)ADSCrossRefGoogle Scholar
  184. 184.
    T. Nomura, J. Phys. Soc. Jpn. 83, 064707 (2014)ADSCrossRefGoogle Scholar
  185. 185.
    P. Abbamonte, C.A. Burns, E.D. Isaacs, P.M. Platzman, L.L. Miller, M.V. Klein, Phys. Rev. Lett. 83, 860 (1999) ibid.preprintGoogle Scholar
  186. 186.
    M. Naka, S. Ishihara, J. Phys. Soc. Jpn. 79, 063707 (2010)ADSCrossRefGoogle Scholar
  187. 187.
    C. Hotta, Phys. Rev. B 82, R31044 (2010)CrossRefGoogle Scholar
  188. 188.
    M. Naka, S. Ishihara, J. Phys. Soc. Jpn. 82, 023701 (2013)ADSCrossRefGoogle Scholar
  189. 189.
    K. Itoh, H. Itoh, M. Naka, S. Saito, I. Hosako, N. Yoneyama, S. Ishihara, T. Sasaki, S. Iwai, Phys. Rev. Lett. 110, 106401 (2013)ADSCrossRefGoogle Scholar
  190. 190.
    J. Nasu, T. Watanabe, M. Naka, S. Ishihara, Phys. Rev. B 93, 205136 (2016)ADSCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of PhysicsTohoku UniversitySendaiJapan

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