我們研究 RuSr2RCu2O8 (R = Gd, Eu, Sm, and Nd) 多晶樣品的光譜性質。RuSr2GdCu2O8 樣品的室溫拉曼散射光譜與之前的論文 [Physica C 341, 2209 (2000)] 結果相當吻合，以離子半徑較大的稀土元素 (R = Eu, Sm, and Nd) 取代 Gd 離子時，可觀察到 A1g(5) 及 A1g(6) 振動模的頻率位置隨著置換離子半徑增大出現紅移現象且半高寬增大，印證了中心離子變大造成單位晶胞體積增加的趨勢。

其次，我們研究這些樣品的變溫全頻反射光譜。室溫時，由光譜圖中可觀察到 RuSr2RCu2O8 (R = Gd, Eu, and Sm) 三個樣品在低頻處有居德響應，表示樣品呈現金屬性。隨著溫度的降低，RuSr2GdCu2O8 樣品的 638 cm-1 振動模及 RuSr2EuCu2O8 樣品的 656 cm-1 振動模頻率位置出現藍移現象且半高寬變窄。相反地，RuSr2NdCu2O8 樣品的 346、583 及 648 cm-1 振動模隨溫度降低出現紅移現象，我們猜測這些聲子頻率的位移可能是因為電子自旋與聲子耦合的影響，或是在降溫後樣品結構上出現局部相轉變有關。在超導相變溫度以下時，我們利用偏總和定則，計算出有效電荷數的減少量，並進一步估算出 RuSr2GdCu2O8 與 RuSr2EuCu2O8 的倫敦穿透深度 (λL) 約為 9410 Å 與 23805 Å。

We study the optical properties of weak-ferromagnetic superconductor system RuSr2RCu2O8 (R = Gd, Eu, Sm, and Nd). The room-temperature Raman spectrum of RuSr2GdCu2O8 is similar to the reported results [Physica C 341, 2209 (2000)]. When replaced with larger rare earth ions (R = Eu, Sm, and Nd) on Gd, the frequencies of A1g(5) and A1g(6) Raman-active phonons show a shift of the peak position to lower frequencies and their linewidths are broadening, which is mainly due to the expansion effects of the unit cell volume.

The optical reflectance spectra of RuSr2RCu2O8 (R = Gd, Eu, Sm, and Nd) were measured between 10 and 340 K. At room temperature, the spectra of RuSr2RCu2O8 (R = Gd, Eu, and Sm) show the characteristics of metallic behavior at low frequencies with Drude response. With decreasing temperature, the phonon modes at about 638 cm-1 in RuSr2GdCu2O8 and 656 cm-1 in RuSr2EuCu2O8 harden and become narrowing. On the contrary, the frequencies of infrared-active phonon modes at about 346, 583, and 648 cm-1 in RuSr2NdCu2O8 shift toward lower frequency, which may be attributed to a strong spin-phonon interaction or a local lattice distortion. In the superconducting state, a partial sum-rule evaluation of the effective number of carriers from the optical conductivity indicates that the values of London penetration depth (λL) of RuSr2GdCu2O8 and RuSr2EuCu2O8 are about 9410 and 23805 Å, respectively.

[1] H. K. Onnes, “The Superconductivity of Mercury”, Comm. Phys. Lab. Univ. Leiden, 122 and 124 (1911).
[2] W. Meissner and R. Ochsenfeld, “Ein neuer Effekt bei Eintritt der Supraleitfähigkeit”, Naturwissenschaften 21, 787 (1933).
[3] A. W. Sleight, J. L. Gillson, and P. E. Bierstedt, “High-temperature superconductivity in the BaPb1-xBixO3 systems”, Solid State Commun. 17, 27 (1975).
[4] Ǿ. Fischer, A. Treyvaud, R. Chevrel, and M. Sergent, “Superconductivity in the RexMo6S8”, Solid State Commun. 17, 721 (1975).
[5] J. G. Bednoz and K. A. Muller, “Possible highTc superconductivity in the Ba−La−Cu−O system”, Zeitschrift für Physik B Condensed Matter 64, 189 (1986).
[6] M. K. Wu, J. R. Ashburn, C. J. Torng, P. H. Hor, R. L. Meng, L. Gao, Z. J. Huang, Y. Q. Wang, and C. W. Chu, “Superconductivity at 93 K in a new mixed-phase Yb-Ba-Cu-O compound system at ambient pressure”, Phys. Rev. Lett. 58, 908 (1987).
[7] H. Maeda, Y. Tanaka, M. Fukutomi, and T. Asano, “A new high-Tc oxide superconductor without a rare earth element”, Jpn. J. Appl. Phys. 27, L209 (1988).
[8] Z. Z. Sheng and A. M. Hermann, “Bulk superconductivity at 120 K in the Tl–Ca/Ba–Cu–O system”, Nature 332, 138 (1988).
[9] A. Schilling, M. Cantoni, J. D. Guo, and H. R. Ott, “Superconductivity above 130 K in the Hg–Ba–Ca–Cu–O system”, Nature (London) 363, 56 (1993).
[10] L. Gao, Y. Y. Xue, F. Chen, Q. Xiong, R. L. Meng, D. Ramirez, C. W. Chu, J. J. Eggert, and H. K. Mao, “Superconductivity up to 164 K in HgBa2Cam-1CumO2m+2+δ (m = 1, 2, and 3) under quasihydrostatic pressures”, Phys. Rev. B 50, 4260 (1994).
[11] J. H. Schon, Ch. Kloc, and B. Batlogg, “Superconductivity at 52 K in hole-doped C60”, Nature 408, 549 (2000).
[12] J. H. Schon, Ch. Kloc, and B. Batlogg, “High-temperature superconductivity in lattice-expanded C60”, Science 293, 2432 (2001).
[13] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, “Superconductivity at 39 K in magnesium diboride”, Nature 410, 63 (2001).
[14] K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R. A. Dilanian, and T. Sasaki, “Superconductivity in two-dimensional CoO2 layers”, Nature 422, 53 (2003).
[15] Yoichi Kamihara, Takumi Watanabe, Masahiro Hirano, and Hideo Hosono, “Iron-based layered superconductor La[O1-xFx]FeAs (x = 0.05-0.12) with Tc = 26 K”, J. Am. Chem. Soc. 130, 3296 (2008).
[16] L. N. Cooper, “Bound electron pairs in a degenerate fermi gas”, Phys. Rev 104, 1189 (1956).
[17] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, “Microscopic theory of superconductivity”, Phys. Rev. 106, 162 (1957).
[18] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, “Theory of Superconductivity”, Phys. Rev. 108, 1175 (1957).
[19] C. Bernhard, J. L. Tallon, Ch. Niedermayer, Th. Blasius, A. Golnik, E. Brucher, R. K. Kremer, D. R. Noakes, C. E. Stronach, and E. J. Ansaldo, “Coexistence of ferromagnetism and superconductivity in the hybrid ruthenate-cuprate compound RuSr2GdCu2O8 studied by muon spin rotation and dc magnetization”, Phys. Rev. B 59, 14099 (1999).
[20] L. Bauernfeind, W. Widder, and H. F. Braun, “Ruthenium-based layered cuprates RuSr2LnCu2O8 and RuSr2(Lnl+x Cel-x)Cu2O10 (Ln = Sm, Eu and Gd)”, Physica C 254, 151 (1995).
[21] J. L. Tallon, J. W. Loram, G. V. M. Williams, and C. Bernhard, “Heat capacity and transport studies of the ferromagnetic superconductor RuSr2GdCu2O8”, Phys. Rev. B 61, R6471 (2000).
[22] R. S. Liu, L. Y. Jang, H. H. Hung, and J. L. Tallon, “Determination of Ru valence from x-ray absorption near-edge structure in RuSr2GdCu2O8-type superconductors”, Phys. Rev. B 63, 212507 (2001).
[23] Y. Tokunaga, H. Kotegawa, K. Ishida, Y. Kitaoka, H. Takagiwa, and J. Akimitsu, “NMR evidence for coexistence of superconductivity and ferromagnetic component in magnetic superconductor RuSr2YCu2O8: 99,101Ru and 63Cu NMR”, Phys. Rev. Lett. 86, 5767 (2001).
[24] K. Kumagai, S. Takada, and Y. Furukawa, “Charge and spin states of Ru and Cu in magnetic superconductor RuSr2GdCu2O8 studied by NMR”, Phys. Rev. B 63, 180509 (2001).
[25] O. Chmaissem, J. D. Jorgensen, H. Shaked, P. Dollar, and J. L. Tallon, “Crystal and magnetic structure of ferromagnetic superconducting RuSr2GdCu2O8”, Phys. Rev. B 61, 6401 (2000).
[26] J. W. Lynn, B. Keimer, C. Ulrich, C. Bernhard, and J. L. Tallon, “Antiferromagnetic ordering of Ru and Gd in superconducting RuSr2GdCu2O8”, Phys. Rev. B 61, R14964 (2000).
[27] J. D. Jorgensen, O. Chmaissem, H. Shaked, S. Short, P. W. Klamut, B. Dabrowski, and J. L. Tallon, “Magnetic ordering in the superconducting weak ferromagnets RuSr2GdCu2O8 and RuSr2EuCu2O8”, Phys. Rev. B 63, 054440 (2001).
[28] H. Takagiwa, J. Akimitsu, H. Kawono-Furukawa, and H. Yoshizawa, “Coexistence of superconductivity and (anti-)ferromagnetism in RuSr2YCu2O8”, J. Phys. Soc. Jap. 70, 333 (2001).
[29] R. Weht, A. Shick, and W. E. Pickett, “High temperature superconductivity”, AIP Conf. Proc. 483, 141 (1999).
[30] K. Nakamura, K. T. Park, and A. J. Freeman, “Magnetic and electronic structures of superconducting RuSr2GdCu2O8”, Phys. Rev. B 63, 024507 (2001).
[31] P. W. Klamut, B. Dabrowski, S. M. Mini, M. Maxwell, J. Mais, I. Felner, U. Asaf, F. Ritter, A. Shengelaya, R. Khasanov, I. M. Savic, H. Keller, A. Wisniewski, R. Puzniak, I. M. Fita, C. Sulkowski, and M. Matusiak, “On the effect of heterovalent substitutions in ruthenocuprates”, Physica C 387, 33 (2003).
[32] P. W. Klamut, B. Dabrowski, S. Kolesnik, M. Maxwell, and J. Mais, “Superconductivity in Ru1-xSr2GdCu2+xO8-y compounds”, Phys. Rev. B 63, 224512 (2001).
[33] P. W. Klamut, B. Dabrowski, J. Mais, and M. Maxwell, “Effect of Ce doping on the superconducting and magnetic properties of RuSr2GdCu2O8”, Physica C 350, 24 (2001).
[34] B. Lorenz, R. L. Meng, Y. Y. Xue, and C. W. Chu, “Pressure effect on the superconducting and magnetic transitions of the superconducting ferromagnet RuSr2GdCu2O8”, Physica C 383, 337 (2003).
[35] R. Citro, G. G. N. Anginella, M. Marinaro, and R. Pucci, “Pressure dependence of superconducting and magnetic critical temperatures in the ruthenocuprates”, Phys. Rev. B 71, 134525 (2005).
[36] V. L. Ginsburg, “Ferromagnetic superconductors”, Zh. Eksp. Teor. Fiz. 31, 202 (1956) [Sov. Phys. JETP 4, 153 (1957)].
[37] W. E. Pickett, R. Weht, and A. B. Shick, “Superconductivity in ferromagnetic RuSr2GdCu2O8”, Phys. Rev. Lett. 83, 3713 (1999).
[38] P. Fulde and R. A. Ferrell, “Superconductivity in a strong spin-exchange field”, Phys. Rev. 135, A550 (1964); A. I. Larkin and Yu. N. Ovchinnikov, “Viscosity of vortices in pure superconductors”, Zh. Eksp. Teor. Fiz. 47, 1136 (1964) [Sov. Phys. JETP 20, 762 (1965)].
[39] H. S. Greenside, E. I. Blount, and C. M. Varma, “Possible coexisting superconducting and magnetic states”, Phys. Rev. Lett. 46, 49 (1981).
[40] C. Bernhard, J. L. Tallon, E. Brücher, and R. K. Kremer, “Evidence for a bulk Meissner state in the ferromagnetic superconductor RuSr2GdCu2O8 from dc magnetization”, Phys. Rev. B 61, R14960 (2000).
[41] C. Y. Yang, B. C. Chang, H. C. Ku, and Y. Y. Hsu, “Critical fields and the spontaneous vortex state in the weakly ferromagnetic superconductor RuSr2GdCu2O8”, Phys. Rev. B 72, 174508 (2005).
[42] V. G. Hadjiev, A. Fainstein, P. Etchegoin, H. J. Trodahl, C. Bernhard, M. Cardona, and J. L. Tallon, “Rapid research note Raman scattering from magnetic excitations in the ferromagnetic superconductor RuSr2GdCu2O8-δ”, Phys. Stat. Sol. (b) 211, R5 (1999).
[43] D. J. Pringle, J. L. Tallon, B. G. Walker, and H. J. Trodahl, “Oxygen isotope effects on the critical and Curie temperatures and Raman modes in the ferromagnetic superconductor RuSr2GdCu2O8”, Phys. Rev. B 59, R11679 (1999).
[44] A. Fainstein, P. Etchegoin, H. J. Trodahl, and J. L. Tallon, “Spin-order-dependent Raman scattering in RuSr2GdCu2O8”, Phys. Rev. B 61, 15468 (2000).
[45] V. G. Hadjiev, C. Bernhard, C. T. Lin, T. Ruf, M. Cardona, and J. L. Tallon, “Raman scattering from magnetic excitations in ruthenate-cuprates”, Physica C 341, 2255 (2000).
[46] M. N. Iliev, A. P. Litvinchuk, V. N. Popov, R. L. Meng, L. M. Dezaneti, and C. W. Chu, “Raman phonons in RuSr2GdCu2O8”, Physica C 341, 2209 (2000).
[47] A. Fainstein, A. E. Pantoja, H. J. Trodahl, J. E. McCrone, J. R. Cooper, G. Gibson, Z. Barber, and J. L. Tallon, “Raman spectroscopy of RuSr2GdCu2O8 thin films”, Phys. Rev. B 63, 144505 (2001).
[48] V. G. Hadjiev, J. Backstrom, V. N. Popov, M. N. Iliev, R. L. Meng, Y. Y. Xue, and C. W. Chu, “Symmetry of phonon, magnetic, and spin-phonon excitations in GdSr2RuCu2O8 single crystals”, Phys. Rev. B 64, 134304 (2001).
[49] A. P. Litvinchuk, M. N. Iliev, Y. Y. Xue, R. L. Meng, and C. W. Chu, “Optical conductivity and infrared-active phonons in RuSr2GdCu2O8”, Phys. Rev. B 62, 9709 (2000).
[50] 林美如，國立臺灣師範大學物理研究所碩士論文，96 年 6 月。
[51] 翁士民，國立臺灣師範大學物理研究所碩士論文，93 年 6 月。
[52] 國立清華大學物理系古煥球教授實驗室。
[53] 淡江大學物理系林大欽教授實驗室。
[54] B. C. Chang, C. Y. Yang, Y. Y. Hsu, and H. C. Ku, “Origin of metal–insulator transition in the weak-ferromagnetic superconductor system RuSr2RCu2O8 (R = rare earths)”, Physica C 460, 503 (2007).
[55] D. P. Hai, S. Kamisawa, I. Kakeya, M. Furuyama, T. Mochiku, and K. Kadowaki, “Ferromagnetism and superconductivity in RuSr2RCu2O8 (R = Sm, Eu, Gd)”, Physica C 357, 406 (2001).
[56] G. F. Willian, R. D. Francis, T. M. Neil, and F. B. Freeman, “Infrared and Raman selection rules for molecular and lattice vibrations-The correlation method”, Wiley-Interscience, New York (1972).
[57] F. Wooten, “Optical properties of Solids”, Academic, New York (1972).
[58] A. A. Tsvetkov, J. Schutzmann, J. I. Gorina, G. A. Kaljushnaia, and D. van der Marel, “In-plane optical response of Bi2Sr2CuO6”, Phys. Rev. B 55, 14152 (1997).
[59] A. V. Puchkov, T. Timusk, S. Doyle, and A. M. Hermann, “ab-plane optical properties of Tl2Ba2CuO6+δ”, Phys. Rev. B 51, 3312 (1995).
[60] D. N. Basov, B. Dabrowski, and T. Timusk, “Infrared probe of transition from superconductor to nonmetal in YBa2(Cu1-xZnx)4O8”, Phys. Rev. Lett. 81, 2132 (1998).
[61] 許世杰，淡江大學物理研究所碩士論文，91 年 6 月。
[62] C. C. Homes, B. P. Clayman, J. L. Peng, and R. L. Greene, “Optical properties of Nd1.85Ce0.15CuO4”, Phys. Rev. B 56, 5525 (1997).
[63] B. Lorenz, Y. Y. Xue, R. L. Meng, and C. W. Chu, “Field dependence of the intragrain superconductive transition in RuSr2EuCu2O8”, Phys. Rev. B 65, 174503 (2002).
[64] K. C. Liang, H. L. Liu, H. D. Yang, W. N. Mei, and D. C. Ling, “Structural and optical studies of high dielectric constant (Na0.5A0.5)Cu3Ti4O12 (A = La and Bi)”, J. Phys.: Condens. Matter 20, 275238 (2008).
[65] D. C. Ling, C. H. Chen, Y. Y. Chen, B. C. Chang, and H. C. Ku, “The interplay between weak ferromagnetism and superconductivity in RuSr2EuCu2O8”, Physica C 460, 518 (2007).
[66] W. Baltensperger and J. S. Helman, “Influence of magnetic order in insulators on the optical phonon frequency”, Helv. Phys. Acta 41, 668 (1968).