磁自旋與晶格、磁自旋與墊偶極交互作用力在強關連電子材料系統被廣泛研究。單晶的樣品Bi2Sr2CoO6+delta與LiCu2O2可以藉由光學聚焦式熔化液體懸浮區方式成長。在低維度強關連材料Bi2Sr2CoO6+delta與LiCu2O2分別發現了磁自旋與聲子交互作用力與無磁性粒子參雜誘發新的短程磁有序排列。
在Bi2Sr2CoO6+delta的樣品中，可以藉由變溫的遠紅外光譜與x光粉末繞射研究，在反鐵磁有序相轉變溫度下可以發現磁自旋與聲子有交互作用。而此交互作用令聲子在溫度低於反鐵磁相轉變溫度下有頻率位置紅移的現象。
在Zn參雜的LiCu2O2樣品中，低濃度(Zn < 5%)的參雜使得樣品的磁有序溫度降至18 K，但是高濃度(Zn > 5 %)的樣品中，配合磁性、電性、晶格與比熱的量測，一個新的磁有序性被發現，並且與理論預測吻合。

The spin-lattice and spin-electric dipole interactions have been the focus on the study of strongly correlated electron materials. Herein, spin-phonon coupling constant and non-magnetic ion substitution effects in the strong correlated low dimensional materials Bi2Sr2CoO6+delta and LiCu2O2 have been studied. For low-dimensional and spin 1/2 system, the impact of quantum fluctuations becomes important for the ground state of the system. The quantum fluctuations is even more pronounced if the system under consideration exhibits strongly frustrated interactions. Single crystal samples were grown by using traveling solvent floating zone method and physical properties have been studied thoroughly.
Bi2Sr2CoO6+delta shows the antiferromagnetic (AFM) transition (T_N) from 100 K to 280 K depending on the ratio of Co2+ and Co3+. In a Co3+ rich region, where delta ~ 0.5, T_N is around 280 K. While delta ~ 0.25, where crystal has the equal number of Co2+ and Co3+, except T_N reduces to around 100 K and also exhibits ferromagnetic (FM) behavior. For 0.25 < delta < 0.5, both ferromagnetism and antiferromagnetism coexist in the system. The ab-plane infrared and optical reflectance of Bi2Sr2CoO6+delta (delta ~ 0.3 and 0.4 < delta < 0.5) single crystals has been measured over a wide frequency range (50-55000 cm^-1) and at temperatures between 20 and 330 K. The room-temperature infrared spectrum displays an insulating character. The optical gap determined from the infrared conductivity (~ 0.53 eV) is consistent with thermal activation energy from dc transport measurements. Upon passing through the 150 and 265 K antiferromagnetic ordering transition, a softening of the phonon mode near 205 cm^-1 correlates well with the temperature dependent normalized square of the sublattice magnetization. Furthermore, the magnetic-ordering induced splitting of the phonon modes at about 238 and 386 cm^-1 is observed. Additionally, the phonon mode at about 588 cm^-1 exhibits a Fano-like line shape. Since no appreciable structural change was detected at low temperatures in x-ray diffraction studies, all of these observations support the suggestion of a complex nature of spin-phonon coupling in these materials. Floating-zone growth of untwinned single crystal of LixCu2-zZnzO2 is reported. Li content of Zn free LixCu2O2 has been determined accurately through combined iodometric titration and thermogravimetric methods, which also ruled out the speculation of chemical disorder between Li and Cu ions. The morphology and physical properties of single crystals obtained from slowing-cooling (SL) and floating-zone (FZ) methods are compared. The floating-zone growth under Ar/O2=7:1 gas mixture at 0.64 MPa produces large area of untwinned crystal with highest Li content of x ~ 0.99 , which has the lowest helimagnetic ordering temperature ~ 19 K in the LixCu2O2 system. Helical ordering transition temperature (T_h) of the original LiCu2O2 follows nite size scaling for less than ~ 5.5% Zn substitution, which implies that the existence of finite helimagnetic domains with domain boundaries formed with nearly isolated spins. Higher Zn substitution > 5.5% quenches the long range helical ordering and introduces an intriguing Zn level dependent magnetic phase transition with slight thermal hysteresis and a universal quadratic eld dependence for Tc(Zn > 0.055,H). The magnetic coupling constants of nearest-neighbor (nn) J1 and next-nearest-neighbor (nnn) J2 (alpha=J2/J1) are extracted from high temperature series expansion (HTSE) fitting and N=16 finite chain exact diagnolization simulation. We have provided evidence of direct correlation between long range helical spin ordering and the magnitude of electric polarization in this spin driven multiferroic material also.

[1] S. Jin, T. H. Tiefel, M. McCormack, R. A. Fastnacht, R. Ramesh, and L. H. Chen, "Thousandfold change in resistivity in magnetoresistive La-Ca-Mn-O films". Science 264, 413 (1994).
[2] I. Terasaki, Y. Sasago, and K. Uchinokura, "Large thermoelectric power in NaCo2O4 single crystals". Phys. Rev. B 56, R12685 (1997).
[3] 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 YBa-Cu-O compound system at ambient pressure". Phys. Rev. Lett. 58, 908 (1987).
[4] A. A. Tsvetkov, D. Dulic, D. van der Marel, A. Damascelli, G. A. Kaljushnaia, J. I. Gorina, N. N. Senturina, N. N. Kolesnikov, Z. F. Ren, J. H. Wang, A. A. Menovsky, and T. T. M. Palstra, "Systematics of c-axis phonons in the thallium- and bismuthbased cuprate superconductors", Phys. Rev. B 60, 13196 (1999).
[5] C. C. Lee, J. M. Wu, and C. P. Huang, "Studies on forming gas annealing treated BiFeO3 thin films and capacitors", Appl. Phys. Lett. 91, 202902 (2007).
[6] J.T. Jeng, H.C. Yang, and H.E. Horng, "Application of high-Tc SQUID to nondestructive evaluation", Sing. J. Phys., 18, 7 (2002).
[7] Y. Nakaya and H. Mori, "Magnetocardiography", Clin. Phys. Physiol. Meas., 13, 191 (1992).
[8] A. K. Zvezdin, A. S. Logginov, G. A. Meshkov, and A. P. Pyatakov, "Multiferroics: promising materials for microelectronics, spintronics, and sensor techinique", Bulletin of the Russian Academy of Sciences: Physics 71, 1604 (2007).
[9] J. M. Tarascon, P. F. Miceli, P. Barboux, D. M. Hwang, G. W. Hull, M. Giroud, L. H. Greene, Yvon LePage, W. R. McKinnon, E. Tselepis, G. Pleizier, M. Eibschutz, D. A. Neumann, and J. J. Rhyne, "Structure and magnetic properties of nonsuperconducting doped Co and Fe Bi2Sr2Cu1-xMxOy phases", Phys. Rev. B 39, 11587 (1989).
[10] K. J. Thomas, Y. S. Lee, F. C. Chou, B. Khaykovich, P. A. Lee, M. A. Kastner, R. J. Cava, and J. W. Lynn, "Antiferromagnetism, ferromagnetism, and magnetic phase separation in Bi2Sr2CoO6+delta", Phys. Rev. B 66, 054415 (2002).
[11] Y. Nagao, I. Terasaki, and T. Nakano, "Dielectric constant and ac conductivity of the layered cobalt oxide Bi2Sr2CoO6+delta: A possible metal-dielectric composite made by self-organization of Co2+ and Co2+ ions", Phys. Rev. B 76, 144203 (2007).
[12] E. Dagotto, T. Hotta, and A. Moreo, "Colossal magnetoresistant materials: the key role of phase separation", Phys. Rep. 344, 1 (2001).
[13] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, "Magnetic control of ferroelectric polarization", Nature (London) 426, 55 (2003).
[14] S.-W. Cheong and M. Mostovoy, "Multiferroics: a magnetic twist for ferroelectricity", Nature Mater. 6, 13 (2007).
[15] R. Seshadri, and N. A. Hill, "Visualizing the role of Bi 6s "Lone Pairs" in the off-center distortion in ferromagnetic BiMnO3", Chem. Mater. 13, 2892 (2001).
[16] B. B. V. Aken, T. T. M. Palstra, A. Filippetti, and N. A. Spaldin, "The origin of ferroelectricity in magnetoelectric YMnO3", Nature Mater. 3, 164 (2004).
[17] N. Ikeda, H. Ohsumi, K. Ohwada, K. Ishii, T. Inami, K. Kakurai, Y. Murakami, K. Yoshii, S. Mori, Y. Horibe, and H. Kito, "Ferroelectricity from iron valence ordering in the charge-frustrated system LuFe2O4", Nature (London) 436, 1136 (2005).
[18] Y. Tokunaga, T. Lottermoser, Y. Lee, R. Kumai, M. Uchida, T. Arima, and Y. Tokura, "Rotation of orbital stripes and the consequent charge-polarized state in bilayer manganites", Natura. Mater. 5, 937 (2006).
[19] T. Kimura, G. Lawes, T. Goto, Y. Tokura, and A. P. Ramirez, "Magnetoelectric phase diagrams of orthorhombic RMnO3 (R=Gd, Tb, and Dy)", Phys. Rev. B 71, 224425 (2005).
[20] T. Masuda, A. Zheludev, A. Bush, M. Markina, and A. Vasiliev, "Competition between helimagnetism and commensurate quantum spin correlations in LiCu2O2", Phys. Rev. Lett. 92, 177201 (2004).
[21] S. Park, Y. J. Choi, C. L. Zhang, and S.-W. Cheong, "Ferroelectricity in an S = 1/2 chain cuprate", Phys. Rev. Lett. 98, 057601 (2007).
[22] S. Seki, Y. Yamasaki, M. Soda, M. Matsuura, K. Hirota, and Y. Tokura, "Correlation between spin helicity and electric polarization vector in quantum-spin chain magnet LiCu2O2", Phys. Rev. Lett. 100, 127201 (2008).
[23] Y. Naito, K. Sato, Y. Yasui, Y. Kobayashi, Y. Kobayashi, and M. Sato, "Ferroelectric transition induced by the incommensurate magnetic ordering in LiCuVO4", J. Phys. Soc. Jpn. 76, 023708 (2007).
[24] C.-W. Liu, S. Liu, Y.-J. Kao, A. L. Chemyshev and A. W. Sandvik, "Impurityinduced frustration in correlated oxides", Phys. Rev. Lett. 102, 167201 (2009).
[25] S. B. Oseroff, S-W. Cheong, B. Aktas, M. F. Hundley, Z. Fisk, and L. W. Rupp, Jr., "Spin-Peierls state versus Neel state in doped CuGeO3", Phys. Rev. Lett. 74, 1450 (1995).
[26] M. Hase, K. Uchinokura, R. J. Birgeneau, K. Hirota, and G. Shirane, "Neutron scattering study of magnetism in single crystal Cu1-xZnxGeO3", J. Phys. Soc. Jpn. 65, 1392 (1996).
[27] H. Fukuyama, T. Tanimoto, and M. Saito, "Antiferromagnet long range order in disordered spin-Peierls systems", J. Phys. Soc. Jpn. 65, 1182 (1996).
[28] K. M. Kojima, Y. Fudamoto, M. Larkin, G. M. Luke, J. Merrin, B. Nachumi, Y. J. Uemura, M. Hase, Y. Sasago, K. Uchinokura, Y. Ajiro, A. Revcolevschi, and J.- P. Renard, "Antiferromagnetic order with spatially inhomogeneous ordered moment size of Zn- and Si-doped CuGeO3", Phys. Rev. Lett. 79, 503 (1997).
[29] W. Eerenstein, N. D. Nathur, and J. F. Scott. "Multiferroic and magnetoelectric materials", Nature 442, 759 (2006).
[30] M. Onoda and M. Sato, "Superlattice structure of superconducting Bi-Sr-Cu-O system", Solid State Commun. 67, 799 (1988).
[31] Y. Le Page, W. R. McKinnon, J. -M. Tarascon, and P. Barboux, "Origin of the incommensurate modulation of the 80 K superconductor Bi2Sr2CaCu2O8.21 derived from isostructural commensurate Bi10Sr15Fe10O46", Phys. Rev. B 40, 6810 (1989).
[32] Y. Watanabe, D. C. Tsui, J. T. Birmingham, N. P. Ong, and J. M. Tarascon, "Infrared reflectivity of single crystal Bi2Mm+1ComOy (M = Ca, Sr, Ba; m =1,2), Bi2Sr3Fe2O9.2, and Bi2Sr2MnO6.25, isomorphic to Bi-Cu-based high-Tc oxides", Phys. Rev. B 43, 3026 (1991).
[33] J. M. Tarascon, W. R. McKinnon, L. H. Greene, G. W. Hull, and E. M. Vogel, "Oxygen and rare-earth doping of the 90 K superconducting perovskite YBa2Cu3O7-x", Phys. Rev. B 36, 226 (1987).
[34] P. W. Anderson, "Antiferromagnetism. Theory of superexchange interaction", Phys. Rev. 79, 350 (1950).
[35] J. Kanamori, "Superexchange interaction and symmetry properties of electron orbitals", J. Phys. Chem. Solids 10, 87 (1959).
[36] J. B. Goodenough, "Theory of the role of covalence in the perovskite-type manganites [La, M(II)]MnO3", Phys. Rev. 100, 564 (1955).
[37] C. Zener, "Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure", Phys. Rev. 81, 440 (1951).
[38] P. W. Anderson and H. Hasegawa, "Considerations on double exchange", Phys. Rev. 100, 675 (1955).
[39] P. -G. de Gennes, "Effects of double exchange in magnetic crystals", Phys. Rev. 118, 141 (1960).
[40] J. B. Shi, J. C. Ho, T. J. Lee, B. S. Chiou, and H. C. Ku, "Cobalt ordering in layered Bi2Sr2CoO6+delta single crystal", Physica C 205, 129 (1993).
[41] W. Kobayashi, A. Satake, and I. Terasaki, "Thermoelectric properties of the brownmillerite oxide Ca2-yLayCo2-xAlxO5", Jpn. J. Appl. Phys., Part 1 41, 3025 (2002).
[42] C. N. R. Rao, D. J. Buttrey, N. Otsuka, P. Ganguly, H. R. Harrison, C. J. Sandberg, and J. M. Honig, "Crystal structure and semiconductor-metal transition of the quasi-two-dimensional transition metal oxide, La2NiO4", J. Solid State Chem. 51, 266
(1984).
[43] T. T. M. Palstra, A. P. Ramirez, S.-W. Cheong, B. R. Zegarski, P. Schiffer, and J. Zaanen, "Transport mechanisms in doped LaMnO3: Evidence for polaron formation", Phys. Rev. B 56, 5104 (1997).
[44] G. Chern, L. R. Song, and J. B. Shi, "Observation of high dielectric permittivity in single-crystal Bi2Sr2CoO6+delta", Physica C 253, 97 (1995).
[45] T. Takayanagi, M. Kogure, and I. Terasaki, "Out-of-plane dielectric constant and insulator-superconductor transition in Bi2Sr2Dy1-xErxCu2O8 single crystals", J. Phys.: Condens. Matter 14, 1361 (2002).
[46] C. Y. Chen, N. W. Preyer, P. J. Picone, M. A. Kastner, H. P. Jenssen, D. R. Gabbe, A. Cassanho, and R. J. Birgeneau, "Frequency dependence of the conductivity and dielectric Constant of La2CuO4+y near the insulator-metal transition", Phys. Rev. Lett. 63, 2307 (1989).
[47] S. Yamada, T. Arima, and K. Takita, "Dielectric spectra in charge ordering state of Pr1-xCaxMnO3", J. Phys. Soc. Jpn. 68, 3701 (1999).
[48] A. B. Pakhomov, S. K. Wong, X. Yan, and X. X. Zhang, "Low-frequency divergence of the dielectric constant in metal-insulator nanocomposites with tunneling", Phys. Rev. B 58, R13375 (1998).
[49] P. Lunkenheimer and A. Loidl, "Origin of apparent colossal dielectric constants", Phys. Rev. Lett. 91, 207601 (2003).
[50] J. C. Dyre and T. B. Schroer, "Universality of ac conduction in disordered solids", Rev. Mod. Phys. 72, 873 (2000), and references therein.
[51] D. L. Sidebottom, "Universal approach for scaling the ac conductivity in ionic glasses", Phys. Rev. Lett. 82, 3653 (1999).
[52] J. C. Dyre, "Universal low-temperature ac conductivity of macroscopically disordered nonmetals", Phys. Rev. B 48, 12511 (1993).
[53] S. J. Hibble, J. Kohler, A. Simon, and S. Paider, "LiCu2O2 and LiCu3O3: New mixed valent copper oxides", J. Solid State Chem. 88, 534 (1990).
[54] R. Berger, A. Meetsma, S. v. Smaalen and M. Sundberg, "The structure of LiCu2O2 with mixed-valence copper from twin-crystal data", J. LessCommon Met. 175, 119 (1991).
[55] R. Berger, P. Onnerud, and R. Tellgren, "Structure refinements of LiCu2O2 and LiCu3O3 from neutron powder diffraction data", J. Alloys Compd. 184, 315 (1992).
[56] B. Roessli, U. Staub, A. Amato, D. Herlach, P. Pattison, K. Sablina, and G. A. Petrakovskii, "Magnetic phase transitions in the double spin-chains compound LiCu2O2", Physica B 296, 306 (2001).
[57] R. A. Erickson, "Neutron diffraction studies of antiferromagnetism in manganous fluoride and some isomorphous compounds", Phys. Rev. 90, 779 (1953).
[58] M. Schmitt, J. Malek, S.-L. Drechsler, and H. Rosner, "Electronic structure and magnetic properties of Li2ZrCuO4: A spin - 1/2 Heisenberg system close to a quantum critical point", Phys. Rev. B 80, 205111 (2009).
[59] F. D. M. Haldane, "Spontaneous dimerization in the S = 1/2 Heisenberg antiferromagnetic chain with competing interactions", Phys. Rev. B. 25, 4925 (1982).
[60] F. C. Fritschij, H. B. Brom, and R. Berger, "NMR and susceptibility characterization of two oxocuprates with antiferromagnetic Cu-chains: LiCuO2 and LiCu2O2", Solid State Commun. 107, 719 (1998).
[61] A. M. Vorotynov, A. I. Pankrats, G. A. Petrakovkii, K. A. Sablina, W. Paszkowicz, and H. Szymczak, "Magnetic and resonance properties of LiCu2O2 single crystals", JETP 86, 1020 (1998).
[62] A. Buhler, N. Elstner, and G. S. Uhrig, "High temperature expansion for frustrated and unfrustrated S = 1/2 spin chains", Eur. Phys. J. B 16, 475 (2000).
[63] S. Zvyagin, G. Cao, Y. Xin, S. McCall, T. Caldwell, W. Moulton, L.-C. Brunel, A. Angerhofer, and J. E. Crow, "Dimer liquid state in the quantum antiferromagnet compound LiCu2O2", Phys. Rev. B 66, 064424 (2002).
[64] T. Masuda, A. Zheludev, B. Roessli, A. Bush, M. Markina, and A. Vasiliev, "Spin waves and magnetic interactions in LiCu2O2", Phys. Rev. B 72, 014405 (2005).
[65] A. A. Gippius, E. N. Morozova, A. S. Moskvin, A. V. Zalessky, A. A. Bush, M. Baenitz, H. Rosner, and S.-L. Drechsler, "NMR and local-density-approximation evidence for spiral magnetic order in the chain cuprate LiCu2O2", Phys. Rev. B 70, R020406 (2004).
[66] Y. Mizuno, T. Toyama, S. Maekawa, T. Osafune, N. Motoyama, H. Eisaki, and S. Uchida, "Electronic states and magnetic properties of edge-sharing Cu-O chains", Phys. Rev. B 57, 5326 (1998).
[67] T. Kimura, Y. Sekio, H. Nakamura, T. Siegrist, and A. P. Ramirez, "Cupric oxide as an induced-multiferroic with high-Tc", Nature Mater. 7, 291 (2008).
[68] S.-L. Drechsler, J. Malek, J. Richter, A. S. Moskvin, A. A. Gippius, and H. Rosner, "Comment on "Competition between helimagnetism and commensurate quantum spin correlations in LiCu2O2", Phys. Rev. Lett. 94, 039705 (2005).
[69] V. V. Mazurenko, S. L. Skornyakov, A. V. Kozhevnikov, F. Mila, and V. I. Anisimov, "Wannier functions and exchange integrals: The example of LiCu2O2", Phys. Rev. B 75, 224408 (2007).
[70] S. W. Huang, D. J. Huang, J. Okamoto, C. Y. Mou, W. B. Wu, K. W. Yeh, C. L. Chen, M. K. Wu, H. C. Hsu, F. C. Chou, and C. T. Chen, "Magnetic ground state and transition of a quantum multiferroic LiCu2O2", Phys. Rev. Lett. 101, 077205 (2008).
[71] H. Bethe, "On the theory of metals. Eigenvalues and eigenfunctions of the linear atom chain", Z. Phys. 71, 205 (1931).
[72] M. Enderle, C. Mukherjee, B. Fak, R. K. Kremer, J.-M. Broto, H. Rosner, S.-L. Drechsler, J. Richter, J. Malek, A. Prokofiev, W. Assmus, S. Pujol, J.-L. Raggazzoni, H. Rakoto, M. Rheinstadter, and H. M. Ronnow, "Quantum helimagnetism of the frustrated spin - 1/2 chain LiCuVO4", Europhys. Lett. 70, 237 (2005).
[73] S.-L. Drechsler, O. Volkova, A. N. Vasiliev, N. Tristan, J. Richter, M. Schmitt, H. Rosner, J. Malek, R. Klingeler, A. A. Zvyagin, and B. Buchner, "Frustrated cuprate route from antiferromagnetic to ferromagnetic spin - 1/2 Heisenberg chains: Li2ZrCuO4 as a missing link near the quantum critical point", Phys. Rev. Lett. 98, 077202 (2007).
[74] R. Bursill, G. A. Gehring, D. J. J. Farnell, J. B. Parkinson, T. Xiang, and C. Zeng, "Numerical and approximate analytical results for the frustrated spin - 1/2 quantum spin chain", J. Phys.: Condens. Matter 7, 8605 (1995).
[75] K. Okamoto and K. Nomura, "Fluid-dimer critical point in spin - 1/2 antiferromagnetic Heisenberg chain with next nearest neighbor interactions", Phys. Lett. A 169, 433 (1992).
[76] H. Katsura, N. Nagaosa, and A. V. Balatsky, "Spin current and magnetoelectric effect in noncollinear magnets", Phys. Rev. Lett. 95, 057205 (2005).
[77] I. A. Sergienko and E. Dagotto, "Role of the Dzyaloshinskii-Moriya interaction in multiferroic perovskites", Phys. Rev. B 73, 094434 (2006).
[78] A. S. Moskvin, Yu. D. Panov, and S.-L. Drechsler, "Nonrelativistic multiferroicity in the nonstoichiometric spin S = 1/2 spiral chain cuprate LiCu2O2", Phys. Rev. B 79, 104112 (2009).
[79] R. Chitra, S. Pati, H. R. Krishnamurthy, D. Sen, and S. Ramasesha, "Density-matrix renormalization-group studies of the spin - 1/2 Heisenberg system with dimerization and frustration", Phys. Rev. B. 52, 6581 (1995).
[80] B. S. Shastry, and B. Sutherland, "Exact ground state of a quantum mechanical antiferromagnet", Physica B+C. 108, 1069 (1981).
[81] W. Ku, H. Rosner, W. E. Pickett, and R. T. Scalettar, "Insulating ferromagnetism in La4Ba2Cu2O10: An Ab Initio Wannier function analysis", Phys. Rev. Lett. 89, 167204 (2002).
[82] A. A. Bush and K. E. Kamentsev, "Crystal growth, thermal stability, and electrical properties of LiCu2O2", Phys. Solid State. 46, 445 (2004).
[83] L. Mihaly, B. Dora, A. Vanyolos, H. Berger, and L. Forro, "Spin-lattice interaction in the quasi-one-dimensional helimagnet LiCu2O2", Phys. Rev. Lett. 97, 067206 (2006).
[84] L. Capogna, M. Mayr, P. Horsch, M. Raichle, R. K. Kremer, M. Son A. Maljuk, M. Jansen, and B. Keimer, "Helicoidal magnetic order in the spin-chain compound NaCu2O2", Phys. Rev. B 71, 140402(R) (2005).
[85] M. Hase, I. Terasaki, Y. Sasago, K. Uchinokura, and H. Obara, "Effects of substitution of Zn for Cu in the spin-Peierls cuprate, CuGeO3: the suppression of the spin-Peierls transition and the occurrence of a new spin glass state", Phys. Rev. Lett. 71, 4059 (1993).
[86] J. C. Bonner, and M. E. Fisher, "Linear magnetic chains with anisotropic coupling", Phys. Rev. 135, A640 (1964).
[87] W. E. Hateld, "New magnetic and structural results for uniformly spaced, alternatingly spaced, and ladder-like copper (II) linear chain compounds", J. Appl. Phys. 52, 1985 (1981).
[88] K. Watanabe, Y. Watanabe, S. Awaji, M. Fujiwara, N. Kobayashi, and T. Hasebe, Adv. Cryo. Eng. 44, 747 (1998).
[89] D. Andreone, E. Arri, V. Lacquaniti, and G. Marullo, "The reproduction of the asmaintained unit of voltage at IEN by means of 2eh ", IEEE Trans. Instrum. Meas., 32, 272 (1983).
[90] R. A. Cowley, "The lattice dynamics of an anharmonic crystal", Adv. Phys. 12, 421 (1963).
[91] 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).
[92] I. A. Nekrasov, S. V. Streltsov, M. A. Korotin, and V. I. Anisimov, "Influence of rare-earth ion radii on the low-spin to intermediate-spin state transition in lanthanide cobaltite perovskites: LaCoO3 versus HoCoO3", Phys. Rev. B 68, 235113 (2003).
[93] J. Zhou, P. Zheng, and N. L. Wang, "Optical properties of Pr0.5Ca0.5CoO3 single crystal", J. Phys.: Condens. Matter 20, 055222 (2008).
[94] G. Burns, G. V. Chandrashekhar, F. H. Dacol, M. W. Shafer, and P. Strobel, "Phonon in the high temperature Bi2Can-1Sr2CunO4+2n superconductors", Solid State Commun. 67, 603 (1988).
[95] J. Prade, A. D. Kulkarni, F. W. de Wette, U. Schroder, and W. Kress, "Calculation of Raman- and infrared-active modes of Bi2CaSr2Cu2O8", Phys. Rev. B 39, 2771 (1989).
[96] 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).
[97] W. Baltensperger and J. S. Helman, "Influence of magnetic order in insulators on the optical phonon frequency", Helv. Phys. Acta 41, 668 (1968).
[98] W. Baltensperger, "Influence of magnetic order on conduction electrons and phonons in magnetic semiconductors", J. Appl. Phys. 41, 1052 (1970).
[99] K. H. Kim, J. Y. Gu, H. S. Choi, G. W. Park, and T. W. Noh, "Frequency shifts of the internal phonon modes in La0.7Ca0.3MnO3", Phys. Rev. Lett. 77, 1877 (1996).
[100] M. N. Iliev, A. P. Litvinchuk, H.-G. Lee, C. L. Chen, M. L. Dezaneti, C. W. Chu, V. G. Ivanov, M. V. Abrashev, and V. N. Popov, "Raman spectroscopy of SrRuO3 near the paramagnetic-to-ferromagnetic phase transition", Phys. Rev. B 59, 364 (1999).
[101] E. Granado, A. Garcia, J. A. Sanjurjo, C. Rettori, I. Torriani, F. Prado, R. D. Sanchez, A. Caneiro, and S. B. Oseroff, "Magnetic ordering effects in the Raman spectra of La1-xMn1-xO3", Phys. Rev. B 60, 11879 (1999).
[102] J. Laverdiere, S. Jandl, A. A. Mukhin, V. Yu. Ivanov, V. G. Ivanov, and M. N. Iliev, "Spin-phonon coupling in orthorhombic RMnO3 (R=Pr,Nd,Sm,Eu,Gd,Tb,Dy,Ho,Y): A Raman study", Phys. Rev. B 73, 214301 (2006).
[103] S. Massidda, M. Posternak, A. Baldereschi, and R. Resta, "Noncubic behavior of antiferromagnetic transition-metal monoxides with the rocksalt structure", Phys. Rev. Lett. 82, 430 (1999).
[104] W. Luo, P. Zhang, and M. L. Cohen, "Splitting of the zone-center phonon in MnO and NiO", Solid State Commun. 142, 504 (2007).
[105] T. Rudolf, Ch. Kant, F. Mayr, and A. Loidl, "Magnetic-order induced phonon splitting in MnO from far-infrared spectroscopy", Phys. Rev. B 77, 024421 (2008).
[106] U. Fano, "Effects of conguration interaction on intensities and phase shifts", Phys. Rev. 124, 1866 (1961).
[107] Smekal, "Zur Quantentheorie der Dispersion", Naturwiss. 11, 873 (1923).
[108] C. V. Raman, "A new radiation", Ind. J. Phys. 2, 387 (1928).
[109] G. Burns, P. Strobel, G. V. Chandrashekhar, F. H. Dacol, F. Holtzberg, and M. W. Shafer, "Raman-active phonons in the high-temperature superconductors and results in Bi2Sr2CuO6", Phys. Rev. B 39, 2245 (1989).
[110] M. Karppinen, M. Matvejeff, K. Salomaki, and H. Yamauchi, "Oxygen content analysis of functional perovskite-derived cobalt oxides", J. Mater. Chem., 12, 1761 (2002).
[111] P. R. Slater, and D. S. Wragg, "Synthesis and thermal stability of the new copper oxide carbonate Ba4ScCu2O7-xCO3 and other members of the series Ba4ScxCu2Oy(CO3)2-x", J. Mater. Chem., 9, 545 (1999).
[112] M. Goiran, M. Costes, J. M. Broto, F. C. Chou, R. Klingeler, E. Arushanov, S.-L. Drechsler, B. Buchner, and V. Kataev, "High-field ESR studies of the quantum spin magnet CaCu2O3", New J. Phys. 8, 74 (2006).
[113] O. Prokhnenko, R. Feyerherm, E. Dudzik, S. Landsgesell, N. Aliouane, L. C. Chapon, and D. N. Argyriou, "Enhanced ferroelectric polarization by induced Dy spin order in multiferroic DyMnO3", Phys. Rev. Lett. 98, 057206 (2007).
[114] H. C. Hsu, H. L. Liu, and F. C. Chou, "Li nonstoichiometry and crystal growth of an untwinned one-dimensional quantum spin system LixCu2O2", Phys. Rev. B. 78, 212401 (2008).
[115] R. D. Shannon, "Revised eective ionic radii and systematic studies of interatomie distances in halides and chaleogenides", Acta Cryst. A32, 751 (1976).
[116] J. Bobroff, N. Laflorencie, L. K. Alexander, A. V. Mahajan, B. Koteswararao, and P. Mendels, "Impurity-induced magnetic order in low dimensional spin gapped materials", Phys. Rev. Lett. 103, 047201 (2009).
[117] L. N. Bulaevskii, A. I. Buzdin, and D. I. Khomskii, "Spin-Peierls transition in magnetic field", Solid State Commun. 27, 5 (1978).
[118] M. E. Fisher and M. N. Barber, "Scaling theory for finite-size effects in the critical region", Phys. Rev. Lett. 28, 1516 (1972).
[119] J. H. Cho, F. C. Chou, and D. C. Johnston, "Phase separation and finite size scaling in La2-xSrxCuO4+delta [0 < (x,delta) < 0.03]", Phys. Rev. Lett. 70, 222 (1993).
[120] J. W. Johnson, D. C. Johnston, A. J. Jacobson, and J. F. Brody, "Preparation and characterization of VO(HPO4)0.5H2O and its topotactic transformation to (VO)2P2O7", J. Am. Chem. Soc. 106, 8123 (1984).
[121] N. Laflorencie and D. Poilblanc, "Confinement and critical regime in doped frustrated quasi-one dimensional magnets", J. Phys. Soc. Jpn. Suppl. 74, 277 (2005).
[122] N. Laflorencie and D. Poilblanc, "Doped coupled frustrated spin - 1/2 chains with four-spin exchange", Phys. Rev. Lett. 90, 157202 (2003).
[123] S. Furukawa, M. Sato, Y. Saiga, and S. Onoda, "Quantum fluctuations of chirality in one-dimensional spin - 1/2 multiferroics: gapless dielectric response from phasons and chiral solitons", J. Phys. Soc. Jpn 77, 123712 (2008).
[124] C. K. Majumdar and D. K. Ghosh, "On next-nearest-neighbor interaction in linear chain. I", J. Math. Phys. 10, 1388 (1969).
[125] E. Dagotto, "Complexity in strongly correlated electronic systems", Science 309, 257 (2005).
[126] S. Furukawa, M. Sato and S. Onoda, "Chiral spin order and electromagnetic dynamics in one-dimensional multiferroic cuprates", arXiv:1003.3940 (2010).
[127] T. Hamada, J. Kane, S. Nakagawa and Y. Natsume, "Exact solution of the ground state for uniformly distributed RVB in one-dimensional spin - 1/2 Heisenberg systems with frustration", J. Phys. Soc. Jpn. 57, 1891 (1988).