Lattice-Mediated Magnetic Order Melting in Multiferroic Mott Insulators

  • Edoardo Baldini
Part of the Springer Theses book series (Springer Theses)


One fascinating topic in the field of nonequilibrium dynamics concerns the manipulation and control of magnetic order using ultrashort laser pulses. This subject has rapidly improved in the last decade, due to its relevance for modern data storage and processing technology by Kirilyuk et al. (Rev Mod Phys 82(3):2731, 2010 [1]). The ultimate success of this research field is intimately related to the comprehension of the response that a specific magnetic material will exhibit upon the interaction with a tailored light pulse. Being able to predict the pathway followed by the energy and the angular momentum from the initial photons to the spin degrees of freedom can pave the route to the development of novel materials with superior functionalities.


  1. 1.
    A. Kirilyuk, A.V. Kimel, T. Rasing, Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82(3), 2731 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    E. Beaurepaire, J.-C. Merle, A. Daunois, J.-Y. Bigot, Ultrafast spin dynamics in ferromagnetic nickel. Phys. Rev. Lett. 76(22), 4250 (1996)ADSCrossRefGoogle Scholar
  3. 3.
    J. Hohlfeld, E. Matthias, R. Knorren, K.H. Bennemann, Nonequilibrium magnetization dynamics of nickel. Phys. Rev. Lett. 78(25), 4861 (1997)ADSCrossRefGoogle Scholar
  4. 4.
    A. Scholl, L. Baumgarten, R. Jacquemin, W. Eberhardt, Ultrafast spin dynamics of ferromagnetic thin films observed by fs spin-resolved two-photon photoemission. Phys. Rev. Lett. 79(25), 5146 (1997)Google Scholar
  5. 5.
    J. Güdde, U. Conrad, V. Jähnke, J. Hohlfeld, E. Matthias, Magnetization dynamics of Ni and Co films on Cu(001) and of bulk nickel surfaces. Phys. Rev. B 59(10), R6608 (1999)ADSCrossRefGoogle Scholar
  6. 6.
    G. Ju, A.V. Nurmikko, R.F.C. Farrow, R.F. Marks, M.J. Carey, B.A. Gurney, Ultrafast time resolved photoinduced magnetization rotation in a ferromagnetic/antiferromagnetic exchange coupled system. Phys. Rev. Lett. 82(18), 3705 (1999)ADSCrossRefGoogle Scholar
  7. 7.
    M. Van Kampen, C. Jozsa, J.T. Kohlhepp, P. LeClair, L. Lagae, W.J.M. De Jonge, B. Koopmans, All-optical probe of coherent spin waves. Phys. Rev. Lett. 88(22), 227201 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    A.V. Kimel, A. Kirilyuk, A. Tsvetkov, R.V. Pisarev, T. Rasing, Laser-induced ultrafast spin reorientation in the antiferromagnet TmFeO\(_3\). Nature 429(6994), 850–853 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    J.-Y. Bigot, M. Vomir, L.H.F. Andrade, E. Beaurepaire, Ultrafast magnetization dynamics in ferromagnetic cobalt: the role of the anisotropy. Chem. Phys. 318(1), 137–146 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    G. Ju, J. Hohlfeld, B. Bergman, R.J.M. van de Veerdonk, O.N. Mryasov, J.-Y. Kim, X. Wu, D. Weller, B. Koopmans, Ultrafast generation of ferromagnetic order via a laser-induced phase transformation in FeRh thin films. Phys. Rev. Lett. 93, 197403 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    J.-U. Thiele, M.s Buess, C.H. Back, Spin dynamics of the antiferromagnetic-to-ferromagnetic phase transition in FeRh on a sub-picosecond time scale. Appl. Phys. Lett. 85(14) (2004)Google Scholar
  12. 12.
    M. Först, R.I. Tobey, S. Wall, H. Bromberger, V. Khanna, A.L. Cavalieri, Y.-D. Chuang, W.S. Lee, R. Moore, W.F. Schlotter, J.J. Turner, O. Krupin, M. Trigo, H. Zheng, J.F. Mitchell, S.S. Dhesi, J.P. Hill, A. Cavalleri, Driving magnetic order in a manganite by ultrafast lattice excitation. Phys. Rev. B 84, 241104 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    S.L. Johnson, R.A. De Souza, U. Staub, P. Beaud, E. Möhr-Vorobeva, G. Ingold, A. Caviezel, V. Scagnoli, W.F. Schlotter, J.J. Turner et al., Femtosecond dynamics of the collinear-to-spiral antiferromagnetic phase transition in CuO. Phys. Rev. Lett. 108(3), 037203 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    J.A. Johnson, T. Kubacka, M.C. Hoffmann, C. Vicario, S. de Jong, P. Beaud, S. Grübel, S.-W. Huang, L. Huber, Y.W. Windsor, E.M. Bothschafter, L. Rettig, M. Ramakrishnan, A. Alberca, L. Patthey, Y.-D. Chuang, J.J. Turner, G.L. Dakovski, W.-S. Lee, M.P. Minitti, W. Schlotter, R.G. Moore, C.P. Hauri, S.M. Koohpayeh, V. Scagnoli, G. Ingold, S.L. Johnson, U. Staub, Magnetic order dynamics in optically excited multiferroic \({\rm TbMnO}_{3}\). Phys. Rev. B 92, 184429 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    E.M. Bothschafter, E. Abreu, L. Rettig, T. Kubacka, S. Parchenko, M. Porer, C. Dornes, Y.W. Windsor, M. Ramakrishnan, A. Alberca, S. Manz, J. Saari, S.M. Koohpayeh, M. Fiebig, T. Forrest, P. Werner, S.S. Dhesi, S.L. Johnson, U Staub, Dynamic pathway of the photoinduced phase transition of \({\rm TbMnO}_{3}\). Phys. Rev. B 96, 184414 (2017)Google Scholar
  16. 16.
    N.N. Kovaleva, A.V. Boris, C. Bernhard, A. Kulakov, A. Pimenov, A.M. Balbashov, G. Khaliullin, B. Keimer, Spin-controlled Mott-Hubbard bands in LaMnO\(_3\) probed by optical ellipsometry. Phys. Rev. Lett. 93(14), 147204 (2004)ADSCrossRefGoogle Scholar
  17. 17.
    T. Kimura, S. Ishihara, H. Shintani, T. Arima, K.T. Takahashi, K. Ishizaka, Y. Tokura, Distorted perovskite with e\(_g^1\) configuration as a frustrated spin system. Phys. Rev. B 68(6), 060403 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    J.-S. Zhou, J.B. Goodenough, Unusual evolution of the magnetic interactions versus structural distortions in RMnO\(_3\) perovskites. Phys. Rev. Lett. 96(24), 247202 (2006)Google Scholar
  19. 19.
    D. Khomskii, Transition Metal Compounds (Cambridge University Press, Cambridge, 2014)Google Scholar
  20. 20.
    P.W. Anderson, Antiferromagnetism. Theory of superexchange interaction. Phys. Rev. 79(2), 350 (1950)ADSCrossRefzbMATHGoogle Scholar
  21. 21.
    J.B. Goodenough, Theory of the role of covalence in the perovskite-type manganites [La, M (II)] MnO\(_3\). Phys. Rev. 100(2), 564 (1955)ADSCrossRefGoogle Scholar
  22. 22.
    J.B. Goodenough, An interpretation of the magnetic properties of the perovskite-type mixed crystals La\(_{1-x}\)Sr\(_x\)CoO\(_{3-\lambda }\). J. Phys. Chem. Solids 6(2–3), 287–297 (1958)ADSCrossRefGoogle Scholar
  23. 23.
    J. Kanamori, Superexchange interaction and symmetry properties of electron orbitals. J. Phys. Chem. Solids. 10(2–3), 87–98 (1959)ADSCrossRefGoogle Scholar
  24. 24.
    S. Quezel, F. Tcheou, J. Rossat-Mignod, G. Quezel, E. Roudaut, Magnetic structure of the perovskite-like compound TbMnO\(_3\). Phys. B+ C 86, 916–918 (1977)Google Scholar
  25. 25.
    M. Kenzelmann, A.B. Harris, S. Jonas, C. Broholm, J. Schefer, S.B. Kim, C.L. Zhang, S.-W. Cheong, O.P. Vajk, J.W. Lynn, Magnetic inversion symmetry breaking and ferroelectricity in TbMnO\(_3\). Phys. Rev. Lett. 95(8), 087206 (2005)ADSCrossRefGoogle Scholar
  26. 26.
    D. Senff, P. Link, K. Hradil, A. Hiess, L.P. Regnault, Y. Sidis, N. Aliouane, D.N. Argyriou, M. Braden, Magnetic excitations in multiferroic TbMnO\(_3\): evidence for a hybridized soft mode. Phys. Rev. Lett. 98(13), 137206 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    S.B. Wilkins, T.R. Forrest, T.A.W. Beale, S.R. Bland, H.C. Walker, D. Mannix, F. Yakhou, D. Prabhakaran, A.T. Boothroyd, J.P. Hill et al., Nature of the magnetic order and origin of induced ferroelectricity in TbMnO\(_3\). Phys. Rev. Lett. 103(20), 207602 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    H.C. Walker, F. Fabrizi, L. Paolasini, F. de Bergevin, D. Prabhakaran, A.T. Boothroyd, D.F. McMorrow, Circularly polarized x-ray scattering investigation of spin-lattice coupling in TbMnO\(_3\) in crossed electric and magnetic fields. Phys. Rev. B 88(21), 214415 (2013)ADSCrossRefGoogle Scholar
  29. 29.
    S.W. Lovesey, V. Scagnoli, M. Garganourakis, S.M. Koohpayeh, C. Detlefs, U. Staub, Melting of chiral order in terbium manganate (TbMnO\(_3\)) observed with resonant x-ray Bragg diffraction. J. Phys-Condens. Mat. 25(36), 362202 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, Y. Tokura, Magnetic control of ferroelectric polarization. Nature 426(6962), 55–58 (2003)ADSCrossRefGoogle Scholar
  31. 31.
    I.A. Sergienko, E. Dagotto, Role of the Dzyaloshinskii-Moriya interaction in multiferroic perovskites. Phys. Rev. B 73(9), 094434 (2006)ADSCrossRefGoogle Scholar
  32. 32.
    N.S. Fedorova, C. Ederer, N.A. Spaldin, A. Scaramucci, Biquadratic and ring exchange interactions in orthorhombic perovskite manganites. Phys. Rev. B 91(16), 165122 (2015)ADSCrossRefGoogle Scholar
  33. 33.
    T. Goto, T. Kimura, G. Lawes, A.P. Ramirez, Y. Tokura, Ferroelectricity and giant magnetocapacitance in perovskite rare-earth manganites. Phys. Rev. Lett. 92(25), 257201 (2004)ADSCrossRefGoogle Scholar
  34. 34.
    N.N. Kovaleva, A.M. Oleś, A.M. Balbashov, A. Maljuk, D.N. Argyriou, G. Khaliullin, B. Keimer, Low-energy Mott-Hubbard excitations in LaMnO\(_3\) probed by optical ellipsometry. Phys. Rev. B 81(23), 235130 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    A.S. Moskvin, A.A. Makhnev, L.V. Nomerovannaya, N.N. Loshkareva, A.M. Balbashov, Interplay of p-d and d-d charge transfer transitions in rare-earth perovskite manganites. Phys. Rev. B 82(3), 035106 (2010)ADSCrossRefGoogle Scholar
  36. 36.
    J.F. Lawler, J.G. Lunney, J.M.D. Coey, Magneto-optic Faraday effect in (La\(_{1-x}\)Ca\(_x\))MnO\(_3\) films. Appl. Phys. Lett. 65(23), 3017–3018 (1994)ADSCrossRefGoogle Scholar
  37. 37.
    N.N. Kovaleva, K.I. Kugel, Z. Pot\({\mathring{\rm u}}\)ček, O.E. Kusmartseva, N.S. Goryachev, Z. Bryknar, E.I. Demikhov, V.A. Trepakov, A. Dejneka, F.V. Kusmartsev, A.M. Stoneham, Optical evidence of quantum rotor orbital excitations in orthorhombic manganites. J. Exp. Theor. Phys. 122(5), 890–901 (2016)Google Scholar
  38. 38.
    K.H. Ahn, A.J. Millis, Effects of magnetic ordering on the anisotropy and temperature dependence of the optical conductivity in LaMnO\(_3\): a tight-binding approach. Phys. Rev. B 61(20), 13545 (2000)ADSCrossRefGoogle Scholar
  39. 39.
    P. Ravindran, A. Kjekshus, H. Fjellvåg, A. Delin, O. Eriksson, Ground-state and excited-state properties of LaMnO\(_3\) from full-potential calculations. Phys. Rev. B 65(6), 064445 (2002)ADSCrossRefGoogle Scholar
  40. 40.
    M. Bastjan, S.G. Singer, G. Neuber, S. Eller, N. Aliouane, D.N. Argyriou, S.L. Cooper, M. Rübhausen, Magneto-optical study of the spin-polarized electronic states in multiferroic TbMnO\(_3\). Phys. Rev. B 77(19), 193105 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    Y. Okimoto, T. Katsufuji, T. Ishikawa, T. Arima, Y. Tokura, Variation of electronic structure in La\(_{1-x}\)Sr\(_x\)MnO\(_3\) f (0 \(\le \) x \(\le \) 0.3) as investigated by optical conductivity spectra. Phys. Rev. B 55(7), 4206 (1997)Google Scholar
  42. 42.
    K. Takenaka, K. Iida, Y. Sawaki, S. Sugai, Y. Moritomo, A. Nakamura, Optical reflectivity spectra measured on cleaved surfaces of La\(_{1-x}\)Sr\(_x\)MnO\(_3\): evidence against extremely small Drude weight. J. Phys. Soc. Jpn. 68(6), 1828–1831 (1999)Google Scholar
  43. 43.
    K. Tobe, T. Kimura, Y. Okimoto, Y. Tokura, Anisotropic optical spectra in a detwinned LaMnO\(_3\) crystal. Phys. Rev. B 64(18), 184421 (2001)ADSCrossRefGoogle Scholar
  44. 44.
    M.A. Quijada, J.R. Simpson, L. Vasiliu-Doloc, J.W. Lynn, H.D. Drew, Y.M. Mukovskii, S.G. Karabashev, Temperature dependence of low-lying electronic excitations of LaMnO\(_3\). Phys. Rev. B 64(22), 224426 (2001)ADSCrossRefGoogle Scholar
  45. 45.
    A. Nucara, F.M. Granozio, M. Radovic, F.M. Vitucci, P. Maselli, R. Fittipaldi, A. Vecchione, P. Calvani, Optical investigation of LaMnO\(_3\) thin films: a study of the 2-eV band. Eur. Phys. J. B 79(4), 435–441 (2011)ADSCrossRefGoogle Scholar
  46. 46.
    M.W. Kim, S.J. Moon, J.H. Jung, J. Yu, S. Parashar, P. Murugavel, J.H. Lee, T.W. Noh, Effect of orbital rotation and mixing on the optical properties of orthorhombic RMnO\(_3\) (R= La, Pr, Nd, Gd, and Tb). Phys. Rev. Lett. 96(24), 247205 (2006)ADSCrossRefGoogle Scholar
  47. 47.
    J. Zaanen, G.A. Sawatzky, J.W. Allen, Band gaps and electronic structure of transition-metal compounds. Phys. Rev. Lett. 55(4), 418 (1985)ADSCrossRefGoogle Scholar
  48. 48.
    P.B. Allen, V. Perebeinos, Self-trapped exciton and Franck-Condon spectra predicted in LaMnO\(_3\). Phys. Rev. Lett. 83(23), 4828 (1999)ADSCrossRefGoogle Scholar
  49. 49.
    J.S. Lee, M.W. Kim, T.W. Noh, Optical excitations of transition-metal oxides under the orbital multiplicity effects. New J. Phys. 7(1), 147 (2005)ADSCrossRefGoogle Scholar
  50. 50.
    R. Krüger, B. Schulz, S. Naler, R. Rauer, D. Budelmann, J. Bäckström, K.H. Kim, S.W. Cheong, V. Perebeinos, M. Rübhausen, Orbital ordering in LaMnO\(_3\) investigated by resonance Raman spectroscopy. Phys. Rev. Lett. 92(9), 097203 (2004)ADSCrossRefGoogle Scholar
  51. 51.
    H.J. Zeiger, J. Vidal, T.K. Cheng, E.P. Ippen, G. Dresselhaus, M.S. Dresselhaus, Theory for displacive excitation of coherent phonons. Phys. Rev. B 45(2), 768 (1992)ADSCrossRefGoogle Scholar
  52. 52.
    R. Merlin, Generating coherent THz phonons with light pulses. Sol. State Comm. 102(2), 207–220 (1997)ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    P. Rovillain, J. Liu, M. Cazayous, Y. Gallais, M.-A. Measson, H. Sakata, A. Sacuto, Electromagnon and phonon excitations in multiferroic TbMnO\(_3\). Phys. Rev. B 86, 014437 (2012)ADSCrossRefGoogle Scholar
  54. 54.
    G.A. Smolenskiĭ, I.E. Chupis, Ferroelectromagnets. Sov. Phys. Uspekhi 25(7), 475 (1982)ADSCrossRefGoogle Scholar
  55. 55.
    A.B. Sushkov, R. Valdés Aguilar, S. Park, S.-W. Cheong, H.D. Drew, Electromagnons in multiferroic \({\rm YMn}_{2}{\rm O}_{5}\) and \({\rm TbMn}_{2}{\rm O}_{5}\). Phys. Rev. Lett. 98, 027202 (2007)ADSCrossRefGoogle Scholar
  56. 56.
    Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, Y. Tokura, Evidence for an electric-dipole active continuum band of spin excitations in multiferroic \({\rm TbMnO}_{3}\). Phys. Rev. Lett. 101, 187201 (2008)ADSCrossRefGoogle Scholar
  57. 57.
    A. Pimenov, A.A. Mukhin, V.Y. Ivanov, V.D. Travkin, A.M. Balbashov, A. Loidl, Possible evidence for electromagnons in multiferroic manganites. Nat. Phys. 2(2), 97–100 (2006)CrossRefGoogle Scholar
  58. 58.
    P. Rovillain, M. Cazayous, Y. Gallais, A. Sacuto, M.-A. Measson, H. Sakata, Magnetoelectric excitations in multiferroic TbMnO\(_3\) by Raman scattering. Phys. Rev. B 81, 054428 (2010)ADSCrossRefGoogle Scholar
  59. 59.
    L. Martín-Carrón, A. de Andrés, M.J. Martínez-Lope, M.T. Casais, J.A. Alonso, Raman phonons as a probe of disorder, fluctuations, and local structure in doped and undoped orthorhombic and rhombohedral manganites. Phys. Rev. B 66, 174303 (2002)ADSCrossRefGoogle Scholar
  60. 60.
    M.N. Iliev, M.V. Abrashev, J. Laverdiere, S. Jandl, M.M. Gospodinov, Y.-Q. Wang, Y.-Y. Sun, Distortion-dependent Raman spectra and mode mixing in RMnO\(_3\) perovskites (R = La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Y). Phys. Rev. B 73(6), 064302 (2006)ADSCrossRefGoogle Scholar
  61. 61.
    J. Laverdiere, S. Jandl, A.A. Mukhin, V.Y. Ivanov, V.G. Ivanov, M.N. Iliev, Spin-phonon coupling in orthorhombic RMnO\(_3\) (R = Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Y): a Raman study. Phys. Rev. B 73(21), 214301 (2006)ADSCrossRefGoogle Scholar
  62. 62.
    P. Kumar, S. Saha, D.V.S. Muthu, J.R. Sahu, A.K. Sood, C.N.R. Rao, Raman evidence for orbiton-mediated multiphonon scattering in multiferroic TbMnO\(_3\). J. Phys.-Condens. Mat. 22(11), 115403 (2010)ADSCrossRefGoogle Scholar
  63. 63.
    W. Hayes, R. Loudon, Scattering of Light by Crystals. Courier Corporation (2012)Google Scholar
  64. 64.
    M.N. Iliev, M.V. Abrashev, H.-G. Lee, V.N. Popov, Y.Y. Sun, C. Thomsen, R.L. Meng, C.W. Chu, Raman spectroscopy of orthorhombic perovskitelike \({\rm YMnO}_{3}\) and \({\rm LaMnO}_{3}\). Phys. Rev. B 57, 2872–2877 (1998)ADSCrossRefGoogle Scholar
  65. 65.
    S. Venugopalan, M. Dutta, A.K. Ramdas, J.P. Remeika, Magnetic and vibrational excitations in rare-earth orthoferrites: a Raman scattering study. Phys. Rev. B 31, 1490–1497 (1985)ADSCrossRefGoogle Scholar
  66. 66.
    H.C. Walker, F. Fabrizi, L. Paolasini, F. de Bergevin, J. Herrero-Martin, A.T. Boothroyd, D. Prabhakaran, D.F. McMorrow, Femtoscale magnetically induced lattice distortions in multiferroic TbMnO\(_3\). Science 333(6047), 1273–1276 (2011)ADSCrossRefGoogle Scholar
  67. 67.
    T.E. Stevens, J. Kuhl, R. Merlin, Coherent phonon generation and the two stimulated Raman tensors. Phys. Rev. B 65(14), 144304 (2002)ADSCrossRefGoogle Scholar
  68. 68.
    I.P. Handayani, R.I. Tobey, J. Janusonis, D.A. Mazurenko, N. Mufti, A.A. Nugroho, M.O. Tjia, T.T.M. Palstra, P.H.M. van Loosdrecht, Dynamics of photo-excited electrons in magnetically ordered TbMnO\(_3\). J. Phys.-Condens. Mat. 25(11), 116007 (2013)ADSCrossRefGoogle Scholar
  69. 69.
    S. Wall, D. Prabhakaran, A.T. Boothroyd, A. Cavalleri, Ultrafast coupling between light, coherent lattice vibrations, and the magnetic structure of semicovalent LaMnO\(_3\). Phys. Rev. Lett. 103(9), 097402 (2009)ADSCrossRefGoogle Scholar
  70. 70.
    Y. Yamada, O. Hino, S. Nohdo, R. Kanao, T. Inami, S. Katano, Polaron ordering in low-doping La\(_{1- x}\)Sr\(_x\)MnO\(_3\). Phys. Rev. Lett. 77(5), 904 (1996)ADSCrossRefGoogle Scholar
  71. 71.
    S. Shimomura, N. Wakabayashi, H. Kuwahara, Y. Tokura, X-ray diffuse scattering due to polarons in a colossal magnetoresistive manganite. Phys. Rev. Lett. 83(21), 4389 (1999)ADSCrossRefGoogle Scholar
  72. 72.
    A. Daoud-Aladine, J. Rodriguez-Carvajal, L. Pinsard-Gaudart, M.T. Fernandez-Diaz, A. Revcolevschi, Zener polaron ordering in half-doped manganites. Phys. Rev. Lett. 89(9), 097205 (2002)ADSCrossRefGoogle Scholar
  73. 73.
    S. Mildner, J. Hoffmann, P.E. Blöchl, S. Techert, C. Jooss, Temperature-and doping-dependent optical absorption in the small-polaron system Pr\(_{1-x}\)Ca\(_x\)MnO\(_3\). Phys. Rev. B 92(3), 035145 (2015)ADSCrossRefGoogle Scholar
  74. 74.
    P.B. Allen, V. Perebeinos, Anti-Jahn-Teller polaron in LaMnO\(_3\). Phys. Rev. B 60(15), 10747 (1999)ADSCrossRefGoogle Scholar
  75. 75.
    T. Mertelj, D. Kuščer, M. Kosec, D. Mihailovic, Photoinduced infrared absorption in (La\(_{1-x}\)Sr\(_x\)Mn)\(_{1-\delta }\)O\(_3\): changes of the small polaron binding energy with doping. Phys. Rev. B 61(22), 15102 (2000)ADSCrossRefGoogle Scholar
  76. 76.
    T. Holstein, Studies of polaron motion: part I. The molecular-crystal model. Ann. Phys. 8(3), 325–342 (1959)ADSCrossRefzbMATHGoogle Scholar
  77. 77.
    T. Holstein, Studies of polaron motion: part II. The “small” polaron. Ann. Phys. 8(3), 343–389 (1959)Google Scholar
  78. 78.
    T.P. Dougherty, G.P. Wiederrecht, K.A. Nelson, M.H. Garrett, H.P. Jensen, C. Warde, Femtosecond resolution of soft mode dynamics in structural phase transitions. Science 258(5083), 770–774 (1992)ADSCrossRefGoogle Scholar
  79. 79.
    T.P. Dougherty, G.P. Wiederrecht, K.A. Nelson, M.H. Garrett, H.P. Jenssen, C. Warde, Femtosecond time-resolved spectroscopy of soft modes in structural phase transitions of perovskites. Phys. Rev. B 50(13), 8996 (1994)ADSCrossRefGoogle Scholar
  80. 80.
    T. Kohmoto, K. Tada, T. Moriyasu, Y. Fukuda, Observation of coherent phonons in strontium titanate: structural phase transition and ultrafast dynamics of the soft modes. Phys. Rev. B 74(6), 064303 (2006)ADSCrossRefGoogle Scholar
  81. 81.
    M. Hase, M. Kitajima, S. Nakashima, K. Mizoguchi, Forcibly driven coherent soft phonons in GeTe with intense THz-rate pump fields. Appl. Phys. Lett. 83(24), 4921–4923 (2003)ADSCrossRefGoogle Scholar
  82. 82.
    R.C. Rai, J. Cao, J.L. Musfeldt, S.B. Kim, S.-W. Cheong, X. Wei, Spin-charge coupling and the high-energy magnetodielectric effect in hexagonal HoMnO\(_3\). Phys. Rev. B 75(18), 184414 (2007)ADSCrossRefGoogle Scholar
  83. 83.
    A.B. Souchkov, J.R. Simpson, M. Quijada, H. Ishibashi, N. Hur, J.S. Ahn, S.W. Cheong, A.J. Millis, H.D. Drew, Exchange interaction effects on the optical properties of LuMnO\(_3\). Phys. Rev. Lett. 91(2), 027203 (2003)ADSCrossRefGoogle Scholar
  84. 84.
    P. Bowlan, S.A. Trugman, J. Bowlan, J.-X. Zhu, N.J. Hur, A.J. Taylor, D.A. Yarotski, R.P. Prasankumar, Probing ultrafast spin dynamics through a magnon resonance in the antiferromagnetic multiferroic \({\text{ HoMnO }}_{3}\). Phys. Rev. B 94, 100404 (2016)ADSCrossRefGoogle Scholar
  85. 85.
    R. Mankowsky, A. von Hoegen, M. Först, A. Cavalleri, Ultrafast reversal of the ferroelectric polarization. Phys. Rev. Lett. 118, 197601 (2017)Google Scholar
  86. 86.
    M. Matsubara, S. Manz, M. Mochizuki, T. Kubacka, A. Iyama, N. Aliouane, T. Kimura, S.L. Johnson, D. Meier, M. Fiebig, Magnetoelectric domain control in multiferroic TbMnO\(_3\). Science 348(6239), 1112–1115 (2015)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations