KKR Green’s Function Method in Reciprocal and Real Space

  • Ján Minár
  • Ondřej Šipr
  • Jürgen Braun
  • Hubert Ebert
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 204)

Abstract

The Korringa–Kohn–Rostoker (KKR) method is a very flexible band structure technique which is based on the multiple scattering formalism. In contrast to many other band structure methods, which are based on a representation of the electronic structure in terms of Bloch wave functions, the KKR method represents the properties of solids in terms of Green’s functions. In this chapter we demonstrate the flexibility of the KKR method as a tool to describe spectroscopic aspects such as x-ray absorption spectra theory and one-step model of photoemission.

Notes

Acknowledgements

We thank the DFG for financial support via Ebe154/32-1, BMBF (05K16WMA) and to the COST action MP1306 EUSpec for travel grants. JM was supported by the CEDAMNF project (CZ.02.1.01/0.0/0.0/15_003/0000358), co-funded by the ERDF as part of the OP RDE program of the Ministry of Education, Youth and Sports (Czech Republic). OS would like to acknowledge support by the GACR (project 17-14840S).

References

  1. 1.
    H. Ebert, D. Ködderitzsch, J. Minár, Rep. Prog. Phys. 74, 096501 (2011)ADSCrossRefGoogle Scholar
  2. 2.
    O.K. Andersen, Phys. Rev. B 12, 3060 (1975)ADSCrossRefGoogle Scholar
  3. 3.
    J. Korringa, Physica 13, 392 (1947)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    W. Kohn, N. Rostoker, Phys. Rev. 94, 1111 (1954)ADSCrossRefGoogle Scholar
  5. 5.
    J.S. Faulkner, J. Phys. C Solid State Phys. 10, 4661 (1977)ADSCrossRefGoogle Scholar
  6. 6.
    J.L. Beeby, Proc. R. Soc. Lond. A 302, 113 (1977)ADSCrossRefGoogle Scholar
  7. 7.
    J.S. Faulkner, Phys. Rev. B 19, 6186 (1979)ADSCrossRefGoogle Scholar
  8. 8.
    J.S. Faulkner, G.M. Stocks, Phys. Rev. B 21, 3222 (1980)ADSCrossRefGoogle Scholar
  9. 9.
    B.L. Gyorffy, G.M. Stocks, in Electrons in Finite and Infinite Structures, ed. by P. Phariseau, E. Sheire (Plenum, New York, 1976), 144 pGoogle Scholar
  10. 10.
    Y. Onodera, M. Okazaki, J. Phys. Soc. Jpn. 21, 1273 (1966)ADSCrossRefGoogle Scholar
  11. 11.
    P. Strange, H. Ebert, J.B. Staunton, B.L. Gyorffy, J. Phys. Condens. Matter 1, 2959 (1989)Google Scholar
  12. 12.
    P. Weinberger, Electron Scattering Theory for Ordered and Disordered Matter (Oxford University Press, Oxford, 1990)Google Scholar
  13. 13.
    P. Strange, Relativistic Quantum Mechanics (Cambridge University Press, Cambridge, 1998)CrossRefGoogle Scholar
  14. 14.
    H. Ebert, in Electronic Structure and Physical Properties of Solids, ed. by H. Dreyssé (Springer, Berlin, 2000), 191 pGoogle Scholar
  15. 15.
    R. Zeller, P.H. Dederichs, Phys. Rev. Lett. 42, 1713 (1979)ADSCrossRefGoogle Scholar
  16. 16.
    I. Turek, V. Drchal, J. Kudrnovský, M. Šob, P. Weinberger, Electronic Structure of Disordered Alloys, Surfaces and Interfaces (Kluwer Academic Publishers, Boston, 1997)CrossRefGoogle Scholar
  17. 17.
    P. Soven, Phys. Rev. 156, 809 (1967)ADSCrossRefGoogle Scholar
  18. 18.
    P.J. Durham, B.L. Gyorffy, A.J. Pindor, J. Phys. F Met. Phys. 10, 661 (1980)ADSCrossRefGoogle Scholar
  19. 19.
    H. Ebert, Rep. Prog. Phys. 59, 1665 (1996)ADSCrossRefGoogle Scholar
  20. 20.
    M.E. Rose, Relativistic Electron Theory (Wiley, New York, 1961)MATHGoogle Scholar
  21. 21.
    H. Ebert, G.Y. Guo, Solid State Commun. 91, 85 (1994)ADSCrossRefGoogle Scholar
  22. 22.
    W.L. Schaich, Phys. Rev. B 29, 6513 (1984)ADSCrossRefGoogle Scholar
  23. 23.
    H. Ebert, in Spin-orbit Influenced Spectroscopies of Magnetic Solids, ed. by H. Ebert, G. Schütz (Springer, Berlin, 1996), 159 pGoogle Scholar
  24. 24.
    R. Feder, F. Rosicky, B. Ackermann, Z. Physik B 52, 31 (1983)ADSCrossRefGoogle Scholar
  25. 25.
    P. Strange, J. Staunton, B.L. Gyorffy, J. Phys. C Solid State Phys. 17, 3355 (1984)ADSCrossRefGoogle Scholar
  26. 26.
    H. Ebert, J. Phys. Condens. Matter 1, 9111 (1989)Google Scholar
  27. 27.
    F. Reinert, S. Hüfner, (Springer, Berlin, 2007), pp. 13–53Google Scholar
  28. 28.
    A. Damascelli, Z. Hussain, Z.X. Shen, Rev. Mod. Phys. 75, 473 (2003)ADSCrossRefGoogle Scholar
  29. 29.
    I. Adawi, Phys. Rev. 134, A788 (1964)ADSCrossRefGoogle Scholar
  30. 30.
    G.D. Mahan, Phys. Rev. B 2, 4334 (1970)ADSCrossRefGoogle Scholar
  31. 31.
    W. Schaich, N. Ashcroft, Solid State Commun. 8, 1959 (1970)ADSCrossRefGoogle Scholar
  32. 32.
    C. Caroli, D. Lederer-Rozenblatt, B. Roulet, D. Saint-James, Phys. Rev. B 8, 4552 (1973)ADSCrossRefGoogle Scholar
  33. 33.
    P.J. Feibelman, D.E. Eastman, Phys. Rev. B 10, 4932 (1974)ADSCrossRefGoogle Scholar
  34. 34.
    C.N. Berglund, W.E. Spicer, Phys. Rev. 136, A1030 (1964)ADSCrossRefGoogle Scholar
  35. 35.
    A. Liebsch, Phys. Rev. Lett. 32, 1203 (1974)ADSCrossRefGoogle Scholar
  36. 36.
    D.J. Spanjaard, D.W. Jepsen, P.M. Marcus, Phys. Rev. B 15, 1728 (1977)ADSCrossRefGoogle Scholar
  37. 37.
    J.B. Pendry, Surf. Sci. 57, 679 (1976)ADSCrossRefGoogle Scholar
  38. 38.
    J.F.L. Hopkinson, J.B. Pendry, D.J. Titterington, Comput. Phys. Commun. 19, 69 (1980)ADSCrossRefGoogle Scholar
  39. 39.
    J.B. Pendry, Low Energy Electron Diffraction (Academic Press, London, 1974)Google Scholar
  40. 40.
    P. Hohenberg, W. Kohn, Phys. Rev. 136, B 864 (1964)Google Scholar
  41. 41.
    W. Kohn, L.J. Sham, Phys. Rev. 140, A 1133 (1965)Google Scholar
  42. 42.
    L.J. Sham, W. Kohn, Phys. Rev. 145, 561 (1966)ADSCrossRefGoogle Scholar
  43. 43.
    J. Braun, Rep. Prog. Phys. 59, 1267 (1996)ADSCrossRefGoogle Scholar
  44. 44.
    B. Ackermann, R. Feder, J. Phys. C Solid State Phys. 18, 1093 (1985)ADSCrossRefGoogle Scholar
  45. 45.
    J. Braun, G. Thrner, G. Borstel, Phys. Stat. Sol. (b) 130, 643 (1985)Google Scholar
  46. 46.
    B. Ginatempo, P.J. Durham, B.I. Gyorffy, J. Phys. Condens. Matter 1, 6483 (1989)Google Scholar
  47. 47.
    S.V. Halilov, E. Tamura, D. Meinert, H. Gollisch, R. Feder, J. Phys. Condens. Matter 5, 3859 (1993)Google Scholar
  48. 48.
    J. Braun, G. Borstel, Phys. Rev. B 48, 14373 (1993)ADSCrossRefGoogle Scholar
  49. 49.
    M. Fluchtmann, M. Grass, J. Braun, G. Borstel, Phys. Rev. B 52, 9564 (1995)ADSCrossRefGoogle Scholar
  50. 50.
    J. Henk, T. Scheunemann, S.V. Halilov, R. Feder, J. Phys. Condens. Matter 8, 47 (1996)Google Scholar
  51. 51.
    M. Grass, J. Braun, G. Borstel, Prog. Surf. Sci. 46, 107 (1994)ADSCrossRefGoogle Scholar
  52. 52.
    P.J. Durham, J. Phys. F Met. Phys. 11, 2475 (1981)ADSCrossRefGoogle Scholar
  53. 53.
    A.X. Gray, C. Papp, S. Ueda, B. Balke, Y. Yamashita, L. Plucinski, J. Minár, J. Braun, E.R. Ylvisaker, C.M. Schneider, W.E. Pickett, H. Ebert, K. Kobayashi, C.S. Fadley, Nat. Mater. 10, 759 (2011)ADSCrossRefGoogle Scholar
  54. 54.
    C. Papp, L. Plucinski, J. Minár, J. Braun, H. Ebert, C.M. Schneider, C.S. Fadley, Phys. Rev. B 84, 045433 (2011)ADSCrossRefGoogle Scholar
  55. 55.
    A.X. Gray, J. Minár, S. Ueda, P.R. Stone, Y. Yamashita, J. Fujii, J. Braun, L. Plucinski, C.M. Schneider, G. Panaccione, H. Ebert, O.D. Dubon, K. Kobayashi, C.S. Fadley, Nat. Mater. 11, 957 (2012)ADSCrossRefGoogle Scholar
  56. 56.
    J. Fujii, B.R. Salles, M. Sperl, S. Ueda, M. Kobata, K. Kobayashi, Y. Yamashita, P. Torelli, M. Utz, C.S. Fadley, A.X. Gray, J. Braun, H. Ebert, I. Di Marco, O. Eriksson, P. Thunström, G.H. Fecher, H. Stryhanyuk, E. Ikenaga, J. Minár, C.H. Back, G. van der Laan, G. Panaccione, Phys. Rev. Lett. 111, 097201 (2013)ADSCrossRefGoogle Scholar
  57. 57.
    J. Minár, J. Braun, H. Ebert, J. Electron. Spectrosc. Relat. Phenom. 189, 129 (2013)CrossRefGoogle Scholar
  58. 58.
    J. Minár, J. Braun, H. Ebert, J. Electron. Spectrosc. Relat. Phenom. 190 (Part B), 159 (2013)Google Scholar
  59. 59.
    A.X. Gray, J. Minár, L. Plucinski, M. Huijben, A. Bostwick, E. Rotenberg, S. Yang, J. Braun, A. Winkelmann, G. Conti, D. Eiteneer, A. Rattanachata, A.A. Greer, J. Ciston, C. Ophus, G. Rijnders, D.H.A. Blank, D. Doennig, R. Pentcheva, J.B. Kortright, C.M. Schneider, H. Ebert, C.S. Fadley, Europhys. Lett. 104, 17004 (2013)ADSCrossRefGoogle Scholar
  60. 60.
    J. Braun, K. Miyamoto, A. Kimura, T. Okuda, M. Donath, H. Ebert, J. Minár, New J. Phys. 16, 015005 (2014)CrossRefGoogle Scholar
  61. 61.
    J. Braun, J. Minár, S. Mankovsky, V.N. Strocov, N.B. Brookes, L. Plucinski, C.M. Schneider, C.S. Fadley, H. Ebert, Phys. Rev. B 88, 205409 (2013)ADSCrossRefGoogle Scholar
  62. 62.
    J. Braun, J. Minár, F. Matthes, C.M. Schneider, H. Ebert, Phys. Rev. B 82, 024411 (2010)ADSCrossRefGoogle Scholar
  63. 63.
    J. Minár, L. Chioncel, A. Perlov, H. Ebert, M.I. Katsnelson, A.I. Lichtenstein, Phys. Rev. B 72, 045125 (2005)ADSCrossRefGoogle Scholar
  64. 64.
    J. Braun, J. Minár, H. Ebert, M.I. Katsnelson, A.I. Lichtenstein, Phys. Rev. Lett. 97, 227601 (2006)ADSCrossRefGoogle Scholar
  65. 65.
    M. Pickel, A.B. Schmidt, F. Giesen, J. Braun, J. Minár, H. Ebert, M. Donath, M. Weinelt, Phys. Rev. Lett. 101, 066402 (2008)ADSCrossRefGoogle Scholar
  66. 66.
    J. Sánchez-Barriga, J. Fink, V. Boni, I. Di Marco, J. Braun, J. Minár, A. Varykhalov, O. Rader, V. Bellini, F. Manghi, H. Ebert, M.I. Katsnelson, A.I. Lichtenstein, O. Eriksson, W. Eberhardt, H.A. Dürr, Phys. Rev. Lett. 103, 267203 (2009)ADSCrossRefGoogle Scholar
  67. 67.
    J. Braun, J. Minár, H. Ebert, A. Chainani, J. Miyawaki, Y. Takata, M. Taguchi, M. Oura, S. Shin, Phys. Rev. B 85, 165105 (2012)ADSCrossRefGoogle Scholar
  68. 68.
    J. Sánchez-Barriga, J. Braun, J. Minár, I. Di Marco, A. Varykhalov, O. Rader, V. Boni, V. Bellini, F. Manghi, H. Ebert, M.I. Katsnelson, A.I. Lichtenstein, O. Eriksson, W. Eberhardt, H.A. Dürr, J. Fink, Phys. Rev. B 85, 205109 (2012)ADSCrossRefGoogle Scholar
  69. 69.
    K. Kambe, Z. Naturf, 22a, 322 (1967)Google Scholar
  70. 70.
    J.M. MacLaren, S. Crampin, D.D. Vvedensky, J.B. Pendry, Phys. Rev. B 40, 12164 (1989)ADSCrossRefGoogle Scholar
  71. 71.
    G. Borstel, Appl. Phys. A 38, 193 (1985)ADSCrossRefGoogle Scholar
  72. 72.
    J.S. Faulkner, Prog. Mater. Sci. 27, 1 (1982)CrossRefGoogle Scholar
  73. 73.
    R.O. Jones, O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989)ADSCrossRefGoogle Scholar
  74. 74.
    S.Y. Savrasov, G. Kotliar, Phys. Rev. B 69, 245101 (2004)ADSCrossRefGoogle Scholar
  75. 75.
    A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)ADSCrossRefGoogle Scholar
  76. 76.
    G. Kotliar, S.Y. Savrasov, K. Haule, V.S. Oudovenko, O. Parcollet, C.A. Marianetti, Rev. Mod. Phys. 78, 865 (2006)ADSCrossRefGoogle Scholar
  77. 77.
    K. Held, Adv. Phys. 56, 829 (2007)ADSCrossRefGoogle Scholar
  78. 78.
    J. Minár, J. Phys. Condens. Matter 23, 253201 (2011)Google Scholar
  79. 79.
    A.H. MacDonald, S.H. Vosko, J. Phys. C Solid State Phys. 12, 2977 (1979)ADSCrossRefGoogle Scholar
  80. 80.
    R.M. Dreizler, E.K.U. Gross, Density Functional Theory (Springer, Heidelberg, 1990)MATHCrossRefGoogle Scholar
  81. 81.
    H. Ebert, S. Bornemann, J. Braun, D. Ködderitzsch, S. Lowitzer, S. Mankovskyy, J. Minár, M. Offenberger, S. Polesya, V. Popescu, Recent Developments in KKR Theory, Newsletter of the \(\varPsi _{k}\) Network (Scientific highlight of the month) 97, 79 (2010)Google Scholar
  82. 82.
    A. Gonis, W.H. Butler, Multiple Scattering in Solids (Springer, Berlin, 1999)MATHGoogle Scholar
  83. 83.
    E.N. Economou, Green Functions in Quantum Physics (Springer, Berlin, 1990)Google Scholar
  84. 84.
    R. Zeller, J. Deutz, P.H. Dederichs, Solid State Commun. 44, 993 (1982)ADSCrossRefGoogle Scholar
  85. 85.
    E. Tamura, Phys. Rev. B 45, 3271 (1992)ADSCrossRefGoogle Scholar
  86. 86.
    L.V. Pourovskii, M.I. Katsnelson, A.I. Lichtenstein, Phys. Rev. B 72, 115106 (2005)ADSCrossRefGoogle Scholar
  87. 87.
    S. Chadov, Application of Many-body Perturbation Theory to the Description of Correlated Metals (Universität München, Doktorarbeit, 2007)Google Scholar
  88. 88.
    S. Chadov, J. Minár, M.I. Katsnelson, H. Ebert, D. Ködderitzsch, A.I. Lichtenstein, Europhys. Lett. 82, 37001 (2008)ADSCrossRefGoogle Scholar
  89. 89.
    J. Sánchez-Barriga, J. Minár, J. Braun, A. Varykhalov, V. Boni, I. Di Marco, O. Rader, V. Bellini, F. Manghi, H. Ebert, M.I. Katsnelson, A.I. Lichtenstein, O. Eriksson, W. Eberhardt, H.A. Dürr, J. Fink, Phys. Rev. B 82, 104414 (2010)ADSCrossRefGoogle Scholar
  90. 90.
    S. Biermann, F. Aryasetiawan, A. Georges, Phys. Rev. Lett. 90, 086402 (2003)ADSCrossRefGoogle Scholar
  91. 91.
    O. Šipr, J. Minár, S. Mankovsky, H. Ebert, Phys. Rev. B 78, 144403 (2008)ADSCrossRefGoogle Scholar
  92. 92.
    V. Drchal, V. Janiš, J. Kudrnovský, Phys. Rev. B 60, 15664 (1999)ADSCrossRefGoogle Scholar
  93. 93.
    O. Šipr, H. Ebert, Phys. Rev. B 72, 134406 (2005)ADSCrossRefGoogle Scholar
  94. 94.
    O. Šipr, M. Košuth, H. Ebert, J. Magn. Magn. Mater. 272–276, 713 (2004)CrossRefGoogle Scholar
  95. 95.
    S. Bouarab, A. Vega, J.A. Alonso, M.P. Iñiguez, Phys. Rev. B 54, 3003 (1996)ADSCrossRefGoogle Scholar
  96. 96.
    O. Šipr, H. Ebert, Czech. J. Phys. 53, 55 (2003)ADSCrossRefGoogle Scholar
  97. 97.
    R. Wienke, G. Schütz, H. Ebert, J. Appl. Phys. 69, 6147 (1991)ADSCrossRefGoogle Scholar
  98. 98.
    G. Schütz, M. Knülle, H. Ebert, Physica Scripta T49, 302 (1993)ADSCrossRefGoogle Scholar
  99. 99.
    P. Carra, B.T. Thole, M. Altarelli, X. Wang, Phys. Rev. Lett. 70, 694 (1993)ADSCrossRefGoogle Scholar
  100. 100.
    K. Hirsch, V. Zamudio-Bayer, J. Rittmann, A. Langenberg, M. Vogel, T. Möller, B.v Issendorff, J.T. Lau, Phys. Rev. B 86, 165402 (2012)Google Scholar
  101. 101.
    M. Niemeyer, K. Hirsch, V. Zamudio-Bayer, A. Langenberg, M. Vogel, M. Kossick, C. Ebrecht, K. Egashira, A. Terasaki, T. Möller, B.v Issendorff, J.T. Lau, Phys. Rev. Lett. 108, 057201 (2012)Google Scholar
  102. 102.
    G.A. Mulhollan, R.L. Fink, J.L. Erskine, Phys. Rev. B 44, 2393 (1991)Google Scholar
  103. 103.
    C. Liu, S.D. Bader, Phys. Rev. B 44, 12062 (1991)Google Scholar
  104. 104.
    A.J. Cox, J.G. Louderback, S.E. Apsel, L.A. Bloomfield, Phys. Rev. B 49, 12295 (1994)ADSCrossRefGoogle Scholar
  105. 105.
    J. Honolka, K. Kuhnke, L. Vitali, A. Enders, K. Kern, S. Gardonio, C. Carbone, S.R. Krishnakumar, P. Bencok, S. Stepanow, P. Gambardella, Phys. Rev. B 76, 144412 (2007)ADSCrossRefGoogle Scholar
  106. 106.
    V. Sessi, K. Kuhnke, J. Zhang, J. Honolka, K. Kern, C. Tieg, O. Šipr, J. Minár, H. Ebert, Phys. Rev. B 82, 184413 (2010)ADSCrossRefGoogle Scholar
  107. 107.
    Y. Jinlong, F. Toigo, W. Kelin, Phys. Rev. B 50, 7915 (1994)ADSCrossRefGoogle Scholar
  108. 108.
    K. Lee, Z. Phys. D 40, 164 (1997)Google Scholar
  109. 109.
    V. Kumar, Y. Kawazoe, Eur. Phys. J. D 24, 81 (2003)ADSCrossRefGoogle Scholar
  110. 110.
    T. Futschek, M. Marsman, J. Hafner, J. Phys. Condens. Matter 17, 5927 (2005)Google Scholar
  111. 111.
    O. Šipr, H. Ebert, J. Minár, J. Phys. Condens. Matter 27, 056004 (2015)Google Scholar
  112. 112.
    M. Benfatto, C.R. Natoli, A. Filipponi, Phys. Rev. B 40, 9626 (1989)ADSCrossRefGoogle Scholar
  113. 113.
    K. Hayakawa, T. Fujikawa, K. Nakagawa, I. Shimoyama, R. Tittsworth, P. Schilling, V. Saile, Chem. Phys. 289, 281 (2003)ADSCrossRefGoogle Scholar
  114. 114.
    O. Šipr, J. Vackář, A. Kuzmin, J. Synchr. Rad. 23, 1433 (2016)CrossRefGoogle Scholar
  115. 115.
    G. Calas, L. Cormier, L. Galoisy, P. Jollivet, Comptes Rendus Chimie 5, 831 (2002)CrossRefGoogle Scholar
  116. 116.
    F. Rocca, G. Dalba, P. Fornasini, F. Monti, in Borate Glasses, Crystals and Melts, ed. by A.C. Wright, S.A. Feller, A.C. Hannon (The Society of Glass Technology, Sheffield, 1997), 295 pGoogle Scholar
  117. 117.
    G. Dalba, P. Fornasini, F. Rocca, F. Monti, J. Non-Cryst, Solids 293, 93 (2001)Google Scholar
  118. 118.
    J. Swenson, L. Börjesson, W. Howells, J. Phys. Condens. Matter 11, 9275 (1999)Google Scholar
  119. 119.
    O. Šipr, F. Rocca, G. Dalba, J. Synchr. Rad. 6, 770 (1999)CrossRefGoogle Scholar
  120. 120.
    O. Šipr, G. Dalba, F. Rocca, Phys. Rev. B 69, 134201 (2004)ADSCrossRefGoogle Scholar
  121. 121.
    A. Kuzmin, G. Dalba, P. Fornasini, F. Rocca, O. Šipr, Phys. Rev. B 73, 174110 (2006)ADSCrossRefGoogle Scholar
  122. 122.
    A. Kuzmin, Phys. B Condens. Matter 208, 175 (1995)ADSCrossRefGoogle Scholar
  123. 123.
    P.J. Bray, in Borate Glasses, Crystals and Melts, ed. by A.C. Wright, S.A. Feller, A.C. Hannon (The Society of Glass Technology, Sheffield, 1992), 1 pGoogle Scholar
  124. 124.
    O. Šipr, F. Rocca, J. Synchr. Rad. 17, 367 (2010)CrossRefGoogle Scholar
  125. 125.
    O. Šipr, P. Machek, A. Šimůnek, J. Vackář. J. Horák Phys. Rev. B 56, 13151 (1997)Google Scholar
  126. 126.
    L.A.J. Garvie, A.J. Craven, R. Brydson, Am. Mineral. 80, 1132 (1995)ADSCrossRefGoogle Scholar
  127. 127.
    M. Kasrai, M.E. Fleet, S. Muthupari, D. Li, G.M. Bancroft, Phys. Chem. Miner. 25, 268 (1998)ADSCrossRefGoogle Scholar
  128. 128.
    O. Šipr, A. Šimůnek, J. Vackář, G. Dalba, F. Rocca, Phys. Chem. Glasses Eur. J. Glass Sci. Technol. B 47, 412 (2006)Google Scholar
  129. 129.
    F. Wilhelm, M. Angelakeris, N. Jaouen, P. Poulopoulos, E.T. Papaioannou, C. Mueller, P. Fumagalli, A. Rogalev, N.K. Flevaris, Phys. Rev. B 69, 220404(R) (2004)ADSCrossRefGoogle Scholar
  130. 130.
    O. Šipr, J. Minár, J. Vackář, H. Ebert, Phys. Rev. B 75, 134422 (2007)ADSCrossRefGoogle Scholar
  131. 131.
    F.J.A. den Broeder, D. Kuiper, A.P. van de Mosselaer, W. Hoving, Phys. Rev. Lett. 60, 2769 (1988)ADSCrossRefGoogle Scholar
  132. 132.
    K. Spörl, D. Weller, J. Magn. Magn. Mater. 101, 217 (1991)ADSCrossRefGoogle Scholar
  133. 133.
    G. Gubbiotti, G. Carlotti, F. Albertini, F. Casoli, E. Bontempi, L.E. Depero, H. Koo, R.D. Gomez, Thin Solid Films 428, 102 (2003)ADSCrossRefGoogle Scholar
  134. 134.
    A. Zunger, S. Lany, H. Raebiger, Physics 3, 53 (2010)CrossRefGoogle Scholar
  135. 135.
    M. Snure, D. Kumar, A. Tiwari, Appl. Phys. Lett. 94, 012510 (2009)ADSCrossRefGoogle Scholar
  136. 136.
    A. Ney, V. Ney, S. Ye, K. Ollefs, T. Kammermeier, T.C. Kaspar, S.A. Chambers, F. Wilhelm, A. Rogalev, Phys. Rev. B 82, 041202 (2010)ADSCrossRefGoogle Scholar
  137. 137.
    G. Ciatto, A. Di Trolio, E. Fonda, P. Alippi, A.M. Testa, A.A. Bonapasta, Phys. Rev. Lett. 107, 127206 (2011)ADSCrossRefGoogle Scholar
  138. 138.
    Q. Ma, J.T. Prater, C. Sudakar, R.A. Rosenberg, J. Narayan, J. Phys. Condens. Matter 24, 306002 (2012)CrossRefGoogle Scholar
  139. 139.
    M. Sawicki, E. Guziewicz, M.I. łukasiewicz, O. Proselkov, I.A. Kowalik, W. Lisowski, P. Dluzewski, A. Wittlin, M. Jaworski, A. Wolska, W. Paszkowicz, R. Jakiela, B.S. Witkowski, L. Wachnicki, M.T. Klepka, F.J. Luque, D. Arvanitis, J.W. Sobczak, M. Krawczyk, A. Jablonski, W. Stefanowicz, D. Sztenkiel, M. Godlewski, T. Dietl, Phys. Rev. B 88, 085204 (2013)Google Scholar
  140. 140.
    A. Ney, V. Ney, M. Kieschnick, F. Wilhelm, K. Ollefs, A. Rogalev, Appl. Phys. Lett. 115, 172603 (2014)Google Scholar
  141. 141.
    P. Vachhani, O. Šipr, A. Bhatnagar, R. Ramamoorthy, R. Choudhary, D. Phase, G. Dalba, A. Kuzmin, F. Rocca, J. Alloys Comput. 678, 304 (2016)CrossRefGoogle Scholar
  142. 142.
    A. Ney, K. Ollefs, S. Ye, T. Kammermeier, V. Ney, T. Kasper, S.A. Chambers, F. Wilhelm, A. Rogalev, Phys. Rev. Lett. 100, 157201 (2008)ADSCrossRefGoogle Scholar
  143. 143.
    P.S. Vachhani, G. Dalba, R.K. Ramamoorthy, F. Rocca, O. ipr, A.K. Bhatnagar, J. Phys. Condens. Matter 24, 506001 (2012)Google Scholar
  144. 144.
    O. Šipr, J. Vackář, P.S. Vachhani, R.K. Ramamoorthy, G. Dalba, A.K. Bhatnagar, F. Rocca, J. Phys. Conf. Ser. 430, 012128 (2013)CrossRefGoogle Scholar
  145. 145.
    F. Manghi, V. Bellini, J. Osterwalder, T.J. Kreutz, P. Aebi, C. Arcangeli, Phys. Rev. B 59, R10409 (1999)ADSCrossRefGoogle Scholar
  146. 146.
    S. Hüfner, G.K. Wertheim, Phys. Lett. A 51A, 299 (1975)ADSCrossRefGoogle Scholar
  147. 147.
    C. Guillot, Y. Ballu, J. Paigné, J. Lecante, K.P. Jain, P. Thiry, R. Pinchaux, Y. Pétroff, L.M. Falicov, Phys. Rev. Lett. 39, 1632 (1977)ADSCrossRefGoogle Scholar
  148. 148.
    A. Kakizaki, K. Ono, K. Tanaka, K. Shimada, T. Sendohda, Phys. Rev. B 55, 6678 (1997)ADSCrossRefGoogle Scholar
  149. 149.
    K.N. Altmann, D.Y. Petrovykh, G.J. Mankey, N. Shannon, N. Gilman, M. Hochstrasser, R.F. Willis, F.J. Himpsel, Phys. Rev. B 61, 15661 (2000)ADSCrossRefGoogle Scholar
  150. 150.
    J. Osterwalder, J. Elec. Spec. Rel. Phenom. 117–118, 71 (2001)CrossRefGoogle Scholar
  151. 151.
    N. Kamakura, Y. Takata, T. Tokushima, Y. Harada, A. Chainani, K. Kobayashi, S. Shin, Phys. Rev. B 74, 045127 (2006)ADSCrossRefGoogle Scholar
  152. 152.
    O. Karis, S. Svensson, J. Rusz, J. Oppeneer, M. Gorgoi, F. Schäfers, W. Braun, W. Eberhardt, M. Mårtensson, Phys. Rev. B 78, 233105 (2008)ADSCrossRefGoogle Scholar
  153. 153.
    A. Liebsch, Phys. Rev. Lett. 43, 1431 (1979)ADSCrossRefGoogle Scholar
  154. 154.
    A. Liebsch, Phys. Rev. B 23, 5203 (1981)ADSCrossRefGoogle Scholar
  155. 155.
    O. Miura, T. Fujiwara, Phys. Rev. B 77, 195124 (2008)ADSCrossRefGoogle Scholar
  156. 156.
    D.E. Eastman, F.J. Himpsel, J.A. Knapp, Phys. Rev. Lett. 40, 1514 (1978)ADSCrossRefGoogle Scholar
  157. 157.
    F.J. Himpsel, J.A. Knapp, D.E. Eastman, Phys. Rev. B 19, 2919 (1979)ADSCrossRefGoogle Scholar
  158. 158.
    W. Eberhardt, E.W. Plummer, Phys. Rev. B 21, 3245 (1980)ADSCrossRefGoogle Scholar
  159. 159.
    C.S. Wand, J. Callaway, Phys. Rev. B 15, 298 (1977)ADSCrossRefGoogle Scholar
  160. 160.
    J. Kanski, P.O. Nilsson, C.G. Larsson, Solid State Commun. 35, 397 (1980)ADSCrossRefGoogle Scholar
  161. 161.
    Y. Sakisaka, T. Kommeda, M. Onchi, H. Kato, S. Masuda, K. Yagi, Phys. Rev. B 36, 6383 (1987)ADSCrossRefGoogle Scholar
  162. 162.
    T. Kinoshita, T. Ikoma, A. Kakizaki, T. Ishii, J. Fujii, H. Fukutani, K. Shimada, A. Fujimori, T. Okane, S. Sato, Phys. Rev. B 47, 6787 (1993)ADSCrossRefGoogle Scholar
  163. 163.
    N. Nakajima, S. Hatta, J. Odagiri, H. Kato, Y. Sakisaka, Phys. Rev. B 70, 233103 (2004)ADSCrossRefGoogle Scholar
  164. 164.
    A.I. Lichtenstein, M.I. Katsnelson, G. Kotliar, Phys. Rev. Lett. 87, 067205 (2001)ADSCrossRefGoogle Scholar
  165. 165.
    W. Eberhardt, E.W. Plummer, K. Horn, J. Erskine, Phys. Rev. Lett. 45, 273 (1980)ADSCrossRefGoogle Scholar
  166. 166.
    C. Calandra, F. Manghi, Phys. Rev. B 50, 2061 (1994)ADSCrossRefGoogle Scholar
  167. 167.
    M.M. Steiner, R.C. Albers, L.J. Sham, Phys. Rev. B 45, 13272 (1992)ADSCrossRefGoogle Scholar
  168. 168.
    M. Cococcioni, S. de Gironcoli, Phys. Rev. B 71, 035105 (2005)ADSCrossRefGoogle Scholar
  169. 169.
    T. Allmers, M. Donath, J. Braun, J. Minár, H. Ebert, Phys. Rev. B 84, 245426 (2011)ADSCrossRefGoogle Scholar
  170. 170.
    G. Derondeau, J. Braun, H. Ebert, J. Minár, Phys. Rev. B 93, 144513 (2016)ADSCrossRefGoogle Scholar
  171. 171.
    P.M. Echenique, J.B. Pendry, J. Phys. C Solid State Phys. 11, 2065 (1978)ADSCrossRefGoogle Scholar
  172. 172.
    E.G. McRae, Rev. Mod. Phys. 51, 541 (1979)ADSCrossRefGoogle Scholar
  173. 173.
    J. Braun, M. Donath, Europhys. Lett. 59, 592 (2002)ADSCrossRefGoogle Scholar
  174. 174.
    M. Yi, D. Lu, J.H. Chu, J.G. Analytis, A.P. Sorini, A.F. Kemper, B. Moritz, S.K. Mo, R.G. Moore, M. Hashimoto, W.S. Lee, Z. Hussain, T.P. Devereaux, I.R. Fisher, Z.X. Shen, Proc. Nat. Ac. Sci. US. 108, 6878 (2011)ADSCrossRefGoogle Scholar
  175. 175.
    J.E. Hoffman, Rep. Prog. Phys. 74, 124513 (2011)ADSCrossRefGoogle Scholar
  176. 176.
    G. Profeta, C. Franchini, K.A.I.L.W. Gamalath, A. Continenza, Phys. Rev. B 82, 195407 (2010)Google Scholar
  177. 177.
    F. Massee, S. de Jong, Y. Huang, J. Kaas, E. van Heumen, J.B. Goedkoop, M.S. Golden, Phys. Rev. B 80, 140507 (2009)ADSCrossRefGoogle Scholar
  178. 178.
    V.B. Nascimento, A. Li, D.R. Jayasundara, Y. Xuan, J. O’Neal, S. Pan, T.Y. Chien, B. Hu, X.B. He, G. Li, A.S. Sefat, M.A. McGuire, B.C. Sales, D. Mandrus, M.H. Pan, J. Zhang, R. Jin, E.W. Plummer, Phys. Rev. Lett. 103, 076104 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ján Minár
    • 1
  • Ondřej Šipr
    • 2
  • Jürgen Braun
    • 3
  • Hubert Ebert
    • 3
  1. 1.New Technologies-Research CenterUniversity of West BohemiaPlzeňCzech Republic
  2. 2.Institute of Physics, Czech Academy of SciencesPraha 6Czech Republic
  3. 3.Department ChemieLudwig-Maximilians-Universität MünchenMunich, BavariaGermany

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