摘要
本论文选取了准一维的自旋-Peierls化合物α'-NaV_2O_5,准二维的梯形结构化合物CaV_2O_5和三维多铁化合物PbVO_3作为研究对象,采用基于密度泛函理论(DFT)的超软赝势平面波方法和自旋极化的广义梯度近似研究了电子的自旋自由度对材料微观电子结构与宏观物理性质的影响。
通过对准一维自旋-Peierls化合物α'-NaV_2O_5的室温(RT)相的研究,揭示了磁性交换作用导致其绝缘带隙的本质,首次提出RT相α'-NaV_2O_5是Slater绝缘体的观点。成功解释了RT磁化率和角分辨光电子谱(ARPES)的实验结果,解决了一直存在争议的RT相的绝缘性起源、光谱实验中的吸收峰以及共振非弹性X射线散射实验中的能量损失峰的本质等问题。
首次在理论计算过程中考虑了电子的自旋自由度及不同自旋构型对CaV_2O_5的电子结构的影响,并联合周期性DFT电子结构计算与Noodleman-对称性破缺方法,定量拟合出微观自旋交换作用参数。结果表明CaV_2O_5中磁性耦合作用存在显著的各向异性。梯阶上的自旋形成反铁磁二聚体,并对CaV_2O_5的性质起决定性的作用,在温度降低时,形成自旋单重态,使体系进入非磁基态。梯子之间的弱铁磁作用导致基态与第一激发态之间的自旋隙明显减小。
在单电子能带理论的框架下,研究了多铁化合物PbVO_3的四方铁电相的二维C-型反铁磁绝缘基态的电子结构和铁电性起源。通过模拟四方铁电相在静水压作用下的行为,发现1.25GPa时,四方铁电相向立方顺电相转变,这个一级相变伴随晶胞体积的坍塌和晶格参数的突变。立方相PbVO_3具有半金属性铁磁体的典型特征,理论预测这一材料可能被应用到自旋电子学领域。
The competition and cooperation of the lattice, charge, spin and orbital degrees of freedom (DOF) in transition metal oxides (TMO) have gave rise to profuse physical properties and fascinating physical phenomena. They are significant not only for theoretical investigation but also for potentially practical application. Recently, the extensive technology-applications of the Giant Magnetoresistance (GMR) materials and the flourish of spintronics (or spin electronics) as well as quantum calculation have attracted considerable attention and interest. The theoretical investigations on spin DOF and the interplay with other DOF in correlated electron system have been one of the hottest topics for condensed-matter physics.
Motivated by the development of the computer technology and the advancement of theoretical methods, the first-principles (or ab initio) methods based on density functional theory (DFT) have become effective supplement to the experimental means. The theoretical calculations not only can help us to analyze the experimental results and explain the experimentally observed phenomena, but also can explore unknown materials characteristics by absolutely theoretical prediction independent of experiment.
In this thesis, we study some typical vanadate materials of the correlated electron system, including the quasi one-dimensional spin chain, quasi two-dimensional spin ladder and three-dimensional multiferroic materials. The ultrasoft pseudopotential plane-wave methods and the spin-polarized generalized gradient approximation (GGA) are employed to perform first-principles investigations. We pay our attention principally to the impacts of spin DOF on the macroscopically physical characters by electronic structure calculations. The available experimental results and phenomena are analyzed, discussed and interpreted. We also predict unknown materials properties by carrying out absolutely theoretical calculations and computer simulations independent of experiment.
First of all, we study the electronic structure of the room-temperature (RT) phase of the quasi one-dimensional spin-Peierls compoundα'-NaV_2O_5. The band structure of the crystallographic unit cell shows nonmagnetic (NM) metallic characteristics by non-spin-polarized GGA calculations. The NM metallic solution is consistent with other theoretically reported results, but can not explain the experimentally observed insulating behavior. Adopting the spin-polarized GGA method and considering the spin DOF, we can obtain an insulating ferromagnetic (FM) band structure for the unit cell, but can not explain the experimental results of the RT magnetic susceptibility and angle resolved photoemission spectroscopy (ARPES). We enlarge the crystallographic unit cell along the b axis to construct a 1×2×1 supercell, the system relaxes to the antiferromagnetic (AFM) ground state with insulating band structure. Total energies calculations indicate that the NM metallic state is instable with respect to the magnetic ordering states, and the AFM insulating state is the most stable. The dxy orbital is separated from other V 3d orbitals by the VO5 square-pyramidal crystal field, and has the lowest energy. The V 3d electron occupy the dxy orbital and is shared by two V ions, which is hopping on the same rung and forming H2+-type V-O-V molecular orbital. The magnetic S = ? effective electrons align anti-parallel with each other along the chain with AFM magnetic coupling interactions, which explains well the magnetic behavior of one-dimensional Heisenberg linear AFM chain observed in the RT magnetic susceptibility experiment. The intra-rung vanadium dxy orbitals form the bonding-antibonding orbitals splitted by inter-orbital interactions. It is not the on-site Coulomb repulsion interaction, but the AFM spin exchange couplings that lead to the half-filled bonding orbitals splitting and form a magnetic insulating gap. The essence of the insulating behavior has given rise to much controversy. The present spin-polarized DFT calculations unambiguously reveal that RT phase ofα'-NaV_2O_5 is a Slater insulator, rather than Mott-Hubbard insulator or charge-transfer insulator. Calculated electronic structure explains the controversial topics of absorption peak in the optical spectra and energy loss peak in resonant inelastic X-ray scattering (RIXS) well.
Second, the electronic structure, magnetic exchange interactions and spin gap of the ladder structural vanadate CaV_2O_5 have been studied by spin-polarized GGA method for the first time. Geometry optimization and electronic structure calculations are performed for four possible spin-ordered states. The crystal structure is independent of the magnetic ordering states. The calculated results are in line with the experimental data. The four spin ordering states have been successfully simulated, which are proved by the Mulliken population analysis. The experimentally observed insulating behavior has been reproduced successfully in the framework of the band theory by introducing the magnetic ordering. The insulating band gap has increased further provided that the spin DOF has been took into account, which is derived from the spin exchange coupling but not the Coulomb repulsion interactions. Calculated results reveal that the true magnetic ground state of CaV_2O_5 is the AFM state with AFM exchange interactions both inside the rungs and along the ladder legs. Differentiate from previous theoretical methods using in the reported literature, we calculated exchange parameters by a combination of DFT calculations and Noodleman’s broken symmetry method. The spin exchange parameters are fit quantitatively by mapping the energy differences of the four possible spin-ordered states to Heisenberg model. The calculated results are in good agreement with other theoretical results and experimental data. The magnetic coupling interactions in CaV_2O_5 show prominent anisotropic characteristic. The intra-rung AFM interaction is much stronger than that along the legs, which leads to spin-dimer on the same rung. The spin-dimer are weakly coupled along the leg with AFM interaction, whereas the inter-ladder coupling is weak FM. Calculated results indicate that the spin-dimer on the rung plays an crucial role in the electronic structure and magnetic characteristics of the ladder structural compound CaV_2O_5. The spin-dimer forms spin-singlet along with temperature descending, which brings on the nonmagnetic ground state of the system. There is a spin gap between the ground state and the first excited state. The existence of inter-ladder weak FM interactions results in an obvious decrease of the spin gap.
Third, the electronic structure, magnetic property and origin of ferroelectricity in multiferroic material PbVO_3 are investigated. Four typical spin ordering states in perovskite compound are considered during the study process. The FM state of the tetragonal phase displays a half-metallic characteristic. The insulating ground state of tetragonal phase has been reproduced successfully in the framework of the band theory by introducing the experimentally observed AFM spin configuration, which is characterized by C-type two-dimensional AFM magnetic ordering in the ab plane. The crystal-field splitting associated with the magnetic ordering lead to the insulating behavior in tetragonal PbVO_3. The 3d electrons of the V4+ ions occupy the dxy orbital and hybridize with O px/py orbitals to form the two-dimensional C-AFM magnetic coupling. The V atom and vertical O atom in the VO5 square-pyramid form a very short V-O bond, which results in strong hybridization effects between O 2p and V 3d states. The hybridization effects weaken the short-range repulsion and reduce the system energy, which is favored by the ferroelectric (FE) distortion of the tetragonal phase. In addition, the lone paired state of the Pb 6s orbitals hybridize with O 2p states, which also reduce the system energy and enhance the stability of the tetragonal FE structure. The equilibrium unit cell volume V and bulk modulus B at ambient pressure are deduced by fitting the equation of states (EOS) for the tetragonal and cubic phases PbVO_3. The calculated results are 72.58 and 59.79 A~3, 41 and 163 GPa for the tetragonal and cubic phases PbVO_3, respectively. The bulk modulus of tetragonal phase is remarkable smaller than that of the cubic phase, which implies the former is much more compressible relative to the latter. The tetragonal phase transforms to a cubic perovskite structure corresponding to the FE to paraelectric (PE) phase transition at 1.25 GPa. The discontinuous changes of the lattice parameters indicate the first-order phase transition characteristic. The phase transition accompanies by coordinate environment transformation from VO5 square-pyramid to VO6 octahedron for the V~(4+) ions, which give rise to the volume collapse and dramatic changes of the lattice parameters. Electronic structure calculations reveal that the FM state is the ground state of the cubic phase, which exhibits the representative characteristic of FM half metal. The majority-spin states display metallic character, whereas the minority-spin states have an energy gap around the Fermi level (E_F). As a result, only electrons of majority-spin states contribute toward conduction electrons yielding 100% spin polarization at the E_F. The theoretical calculations predict that the cubic phase PbVO_3 is a possible candidate material for applications in spintronics.
引文
1 Y. Tokura and N. Nagaosa, Orbital Physics in Transition-Metal Oxides [J]. Science, 2000, 288: 462-468.
2 C. Felser, G. H. Fecher, and B. Balke, Spintronics: A Challenge for Materials Science and Solid-State Chemistry [J]. Angew. Chem. Int. Ed. 2007, 46, 668-699.
3 C. H. Bennett and D. P. DiVincenzo, Quantum information and computation [J]. Nature 2000, 404, 247-255.
4黄昆,韩汝琦.固体物理学[M].北京:高等教育出版社, 2001.
5吴代鸣,固体物理基础[M].北京:高等教育出版社, 2007.
6 H. A. Jahn and E. Teller, Stability of Polyatomic Molecules in Degenerate Electronic States. I. Orbital Degeneracy [J]. Proc. R. Soc. A 1937, 161, 220-235.
7冯端,金国钧,凝聚态物理学(上卷) [M].北京:高等教育出版社,2003.
8 M. Getzlaff, Fundamentals of Magnetism [M]. Springer Berlin Heidelberg, 2008.
9杜菲,关联电子体系新奇磁学性质的研究[M].长春:吉林大学, 2007.
10 Nicola A. Hill, Why Are There so Few Magnetic Ferroelectrics [J]. J. Phys. Chem. B 2000, 104, 6694-6709.
11 J. St?hr, H. C. Siegmann, Magnetism: From Fundamentals to Nanoscale Dynamics [M]. Berlin Heidelberg: Springer, 2006.
12 H. Ibach, H. Lüth, Solid-State Physics:An Introduction to Principles of Materials Science [M]. New York: Springer Berlin Heidelbeg, 2003.
13 P. Fulde, Electron Correlations in Molecules and Solids [M]. Berlin Heidelberg New York: Springer, 1991.
14 J. H. Van Vleck, Models of Exchange Coupling in Ferromagnetic Media [J]. Rev. Mod. Phys. 1953, 25, 220-227.
15 J. C. Slater. The Ferromagnetism of Nickel [J]. Phys. Rev. 1936, 49, 537-545.
16 J. C. Slater. The Ferromagnetism of Nickel. II. Temperature Effects [J]. Phys. Rev. 1936, 49, 931-937.
17 W. Heisenberg, Zur Theorie des Ferromagnetismus [J]. Z. Phys. 1928, 49, 619-636.
18 L. J. de Jongh, Magnetic Properties of Layered Transition Metal Compounds [M]. Kluwer, Dordrecht: Springer, 1990.
19 E. Lieb, Inorganic Electronic Structure and Spectroscopy, Volume I: Methodology [M]. New York: Plenum, 1995.
20 S. Blundell, Magnetism in condensed matter (Oxford Master Series in Condensed Matter Physics) [M]. Oxford: Oxford University Press, 2001.
21 T. Moriya, Anisotropic Superexchange Interaction and Weak Ferromagnetism [J]. Phys. Rev.1960, 120, 91-98.
22 T. Moriya, New Mechanism of Anisotropic Superexchange Interaction [J]. Phys. Rev. Lett. 1960, 4, 228-230.
23 J. B. Goodenough,Theory of the Role of Covalence in the Perovskite-Type Manganites [La, M(II)]MnO3 [J]. Phys. Rev. 1955, 100: 564– 573.
24 J. B. Goodenough, An interpretation of the magnetic properties of the perovskite-type mixed crystals La1-xSrxCoO3-λ[J]. J. Phys. Chem. Solids 1958, 6: 287-297.
25 J. Kanamori, Superexchange interaction and symmetry properties of electron orbitals [J]. J. Phys. Chem. Solids 1959, 10: 87-98.
26 P. W. Anderson, Theory of Magnetic Exchange Interactions: Exchange in Insulators and Semiconductors [J]. Solid State Phys. 1963, 14: 99-214.
27 M.-H. Whangbo, H.-J. Koo and D. Dai, Spin exchange interactions and magnetic structures of extended magnetic solids with localized spins: theoretical descriptions on formal, quantitative and qualitative levels [J]. J. Solid State Chem. 2003, 176: 417-481.
28 Ibério de P. R. Moreira and Francesc Illas, A unified view of the theoretical description of magnetic coupling in molecular chemistry and solid state physics [J]. Phys. Chem. Chem. Phys., 2006, 8, 1645– 1659
29 D. C. Johnston, T. Saito, M. Azuma, M. Takano, T. Yamauchi, and Y. Ueda, Modeling of the magnetic susceptibilities of the ambient- and high-pressure phases of (VO)2P2O7 [J]. Phys. Rev. B 2001, 64, 134403.
30 (a) R. K. Nesbet, The Heisenberg exchange operator for ferromagnetic and antiferromagnetic systems [J]. Ann. Phys. 1958, 4, 87-103. (b) R. K. Nesbet, Molecular Model of the Heisenberg Exchange Interaction [J]. Phys. Rev. 1961, 122, 1497-1508.
31 A. J. W. Wachters and W. C. Nieupoort, Selected Topics in Molecular Physics [M]. Weinheim: Chemie, 1972.
32 P. J. Hay, J. C. Thibeault, and R. Hoffmann, Orbital interactions in metal dimer complexes [J]. J. Am. Chem. Soc. 1975, 97, 4884-4899.
33 O. Kahn and B. Briat, Exchange interaction in polynuclear complexes. Part 1.—Principles, model and application to the binuclear complexes of chromium(III) [J]. J. Chem. Soc., Faraday Trans. 2 1976, 72, 268-281.
34 L. Noodleman, Valence bond description of antiferromagnetic coupling in transition metal dimmers [J]. J. Chem. Phys. 1981, 74: 5737-5743.
35 L. Noodleman and E. R. Davidson, Ligand spin polarization and antiferromagnetic coupling in transition metal dimers [J]. Chem. Phys. 1986, 109: 131-143.
36 L. Noodleman and D. A. Case, Density-functional theory of spin polarization and spin couplingin iron-sulfur clusters [J]. Adv. Inorg. Chem. 1992, 38: 423470.
37 Ph. De Loth, P. Cassoux, J. P. Daudley, and J. P. Malrieu, Ab initio direct calculation of the singlet-triplet separation in cupric acetate hydrate dimmer [J]. J. Am. Chem. Soc. 1981, 103, 4007-4016.
38 R. Hoffmann, An Extended Hückel Theory. I. Hydrocarbons [J]. J. Chem. Phys. 1963, 39, 1397-1412.
39 D. Dai and M.-H. Whangbo, Spin-Hamiltonian and density functional theory descriptions of spin exchange interactions [J]. J. Chem. Phys. 2001, 114, 2887-2897.
40 F. Illas, I. de P. R. Moreira, C. de Graaf, and V. Barone, Magnetic coupling in biradicals, binuclear complexes and wide-gap insulators-a survey of ab initio wave function and density functional theory approaches [J]. Theor. Chem. Acc. 2000, 104, 265-272.
41 A. Bencini, F. Totti, C. A. Daul, K. Doclo, P. Fantucci, and V. Barone, Density Functional Calculations of Magnetic Exchange Interactions in Polynuclear Transition Metal Complexes [J]. Inorg. Chem. 1997, 36, 5022-5030.
42 F. Illas, J. Casanovas, M. A. Garcia-Bach, R. Caballol, and O. Castell, Towards an ab initio description of magnetism in ionic solids [J]. Phys. Rev. Lett. 1993, 71, 3549-3552.
43 C. de Graaf, I. de P. R. Moreira, F. Illas, and R. L. Martin, Ab initio study of the magnetic interactions in the spin-ladder compound SrCu2O3 [J]. Phys. Rev. B 1999, 60, 3457-3464.
44 J. Li, L. Noodleman, and D. A. Case, in Inorganic Electronic Structure and Spectroscopy, Volume 1: Methodology, edited by E. I. Solomon and A. B. P. Lever (Wiley, New York, 1999), pp. 661–724.
45 A. I. Liechtenstein, M. I. Katsnelson, V. P. Antropov, V. A. Gubanov, Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys [J]. J. Mag. Mag. Mater. 1987, 67: 65-74.
46 A. I. Liechtenstein, V.I. Anisimov, J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators [J]. Phys. Rev. B 1995, 52: R5467-5470.
47 M. A. Korotin, I. S. Elfimov, V. I. Anisimov, M. Troyer, and D. I. Khomskii. Exchange Interactions and Magnetic Properties of the Layered Vanadates CaV2O5, MgV2O5, CaV3O7, and CaV4O9 [J]. Phys. Rev. Lett. 1999, 83: 1387-1390.
48 M. A. Korotin, V. I. Anisimov, T. Saha-Dasgupta, and I. Dasgupta, Electronic structure and exchange interactions of the ladder vanadates CaV2O5 and MgV2O5 [J]. J. Phys.: Condens. Matter 2000, 12:113-124.
49 O. K. Andersen, C. Arcaangeli, R. W. Tank, T. Dasgupta, G. Krier, O. K. Jepsen, I. Dasgupta, Tight-Binding Approach to Computational Materials Science, Materials Research Society, Warrendale, , pp. 3-34. 1997.
50 V. I. Anisimov, J. Zaanen, O. K. Andersen, Band theory and Mott insulators: Hubbard U insteadof Stoner I [J], Phys. Rev. B 1991, 44: 943-954.
51 D. Dai, M.-H. Whangbo, Spin exchange interactions of a spin dimer Analysis of broken-symmetry spin states in terms of the eigenstates of Heisenberg and Ising spin Hamiltonians [J]. J. Chem. Phys. 2003, 118: 29-39.
52 D. Dai, M.-H. Whangbo, Spin-Hamiltonian and density functional theory descriptions of spin exchange interactions [J]. J. Chem. Phys. 2001, 114: 2887-2893.
53 A. Chartier, P. D’Arco, R. Dovesi, V. R. Saunders, Ab initio Hartree-Fock investigation of the structural, electronic, and magnetic properties of Mn3O4 [J]. Phys. Rev. B 1999, 60: 14042-14048.
54 M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, J. Chazelas,Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices [J]. Phys. Rev. Lett. 1988, 61: 2472-2475.
55 G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn, Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange [J]. Phys. Rev. B 1989, 39: 4828-4830.
56 Albert Fert, Nobel Lecture: Origin, development, and future of spintronics [J]. Rev. Mod. Phys. 2008, 80: 1517.
57 Gus L. W. Hart,Computational materials science: Out of the scalar sand box [J].Nature Materials 7, 426-427 (2008)
58 Smolinski H, Gros C, Weber W, Peuchert U, Roth G, Weiden M, and Geibel C. NaV2O5 as a Quarter-Filled Ladder Compound [J]. Phys. Rev. Lett. 1998, 80: 5164-5167.
1冯端、金国钧.凝聚态物理学(上卷) [M].北京:高等教育出版社, 2003.
2 (a) R. G. Parr, W. Yang. Density Functional Theory of Atoms and Molecules [M]. New York: Oxford, 1989; (b) R. M. Dreizler, E. K. U. Gross, Density Functional Theory, Springer-Vertag, Berlin (1990). R. M. Dreizler, E. K. U. Gross, Density Functional Theory [M]. Berlin: Springer-Vertag, 1990.
3 (a) P. A. M. Dirac.The principles of quantum mechanics [M]. Oxford: Clarendon Press, 1985; (b)曾谨言,量子力学[M].北京:科学出版社, 2000.
4 W. Kohn. Nobel Lecture: Electronic structure of matter—wave functions and density functionals [J]. Rev. Mod. Phys. 1999, 71: 1253-1266.
5 M. Born and R. Oppenheimer. Zur Quantentheorie der Molekeln. Ann. Phys. (Leipzig) 1927, 84 (20): 457.
6 M. Born, K. Huang. Dynamical Theory of Crystal Lattices [M]. Oxford: Oxford Universities Press, 1954.
7 J. C. Slater. Wave Functions in a Periodic Potential [J]. Phys. Rev. 1937, 51: 846-851.
8 M. Levy. Approach to Melting in Ammonia as a Critical Transition [J]. Phys. Rev. A 1982, 26: 1200-1208.
9 V. Fock, Z. Phys. 1930, 61: 209.
10 T. Koopmans,über die Zuordnung von Wellenfunktionen und Eigenwerten zu den Einzelnen Elektronen Eines Atoms [J]. Physica, 1934, 1: 104-113.
11吴代鸣.固体物理学[M].长春:吉林大学出版社, 1996.
12李正中.固体物理[M].北京:高等教育出版社, 2002.
13 H. Thomas.The calculation of atomic fields [J]. Proc. Camb. Phil. Soc, 1927, 23: 542-548.
14 E. Fermi. Un Metodo Statistico per la Determinazione di alcune Priorieta dell'Atome [J]. Accad. Naz. Lincei, 1927, 6: 602-607.
15 P. Hohenberg, W. Kohn. Inhomogeneous electron gas [J]. Phys. Rev. B 1964, 136: 864-871.
16 W. Kohn, L. J. Sham. Self-Consistent Equations Including Exchange and Correlation Effects [J]. Phys. Rev. A 1965, 140: 1133-1138.
17 K. Capelle, G.Vignale. Nonuniqueness of the Potentials of Spin-Density-Functional Theory [J]. Phys. Rev. Lett. 2001, 86: 5546-5549.
18 E .Runge, E. K. U. Gross. Density-Functional Theory for Time-Dependent Systems [J]. Phys. Rev. Lett 1984, 52: 997-1000.
19 E. K. U. Gross, W. Kohn. Local density-functional theory of frequency-dependent linear response [J]. Phys. Rev. Lett. 1985, 55: 2850-2852.
20 W. Yang, P. W. Ayers, and Q. Wu. Potential Functionals: Dual to Density Functionals andSolution to the v-Representability Problem [J]. Phys. Rev. Lett. 2004, 92: 146404.
21 M. Lüders, A. Ernst, W. M. Temmerman, Z. Szotek and P. J. Durham, Ab initio angle-resolved photoemission in multiple scattering formulation [J]. J. Phys.: Condens. Matter 2001, 13: 8587-8606.
22 R. Stowasser, R.Hofmann.What Do the Kohn?Sham Orbitals and Eigenvalues Mean? [J]. J. Am. Chem. Soc. 1999, 121: 3414-3420.
23 J. C. Slater. A Simplification of the Hartree-Fock Method [J]. Phys. Rev. 1951, 81: 385-390.
24 D. M. Ceperley, B. L. Alder. Ground State of the Electron Gas by a Stochastic Method [J]. Phys. Rev. Lett. 1980, 45: 566-569.
25 T. P. Perdew, A. Zunger. Self-interaction correction to density-functional approximations for many-electron systems [J]. Phys. Rev. B 1981, 23: 5048-5079.
26 J. C. Slater. Quantum Theory of Molecular and Solids [M]. Vol. 4, McGraw-Hill, 1974.
27 S. H. Vosko, L. Wilk, and M. Nusair. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis [J]. Can. J. Phys. 1980, 58: 1200-1211.
28 R. M. Martin, Electronic Structure: Basic Theory and Practical Methods [M]. New York: Cambridge University Press, 2004.
29 W. Kohn, Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms [J]. Phys. Rev. Lett. 1996, 76: 3168-3171.
30 A. D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior [J]. Phys. Rev. A 1988, 38: 3098-3100.
31 K. Burke, J. P. Perdew, and Y. Wang, Electronic Density Functional Theory: Recent Progress and New Direction [M]. Plenum, 1998.
32 J. P. Perdew. Density-functional approximation for the correlation energy of the inhomogeneous electron gas [J]. Phys. Rev. B 1986, 33: 8822-8824.
33 J. P. Perdew, K. Burke, and M. Ernzerhof. Generalized Gradient Approximation Made Simple [J]. Phys. Rev. Lett. 1996, 77: 3865-3868.
34 C. Lee, W. Yang, and R. G. Parr. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density [J]. Phys. Rev. B 1984, 37: 785-789.
35 C. Filippi, C. J. Umrigar, M. Taut. Comparison of exact and approximate density functionals for an exactly soluble model [J]. J. Chem. Phys. 1994, 100: 1290-1295.
36 X. Xu, W. A. Goddard III. The X3LYP Extended Density Functional for Accurate Descriptions of Nonbond Interactions (London Forces, electrostatics, and hydrogen bonding), spin states, and Thermochemical Properties [J]. Proc. Natl. Acad. Sci. USA, 2004, 101: 2673-2677.
37 J. P. Perdew, S. Kurth , A. Zupan, P. Blaha. Accurate Density Functional with Correct Formal Properties: A Step Beyond the Generalized Gradient Approximation [J]. Phys. Rev.Lett. 1999, 82:2544-2547.
38 J. Tao, J. P. Perdew, V. N. Staroverov and G. E. Scuseria. Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids [J]. Phys. Rev. Lett. 2003, 91: 146401.
39 S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne. First principles methods using CASTEP [J]. Z. Kristallogr, 2005, 220: 567-570.
40 Y. Wang, N. S. Rogado, R. J. Cava, and N. P. Ong, Spin entropy as the likely source of enhanced thermopower in NaxCo2O4 [J]. Nature, 2003, 423: 425-428.
41 D. R. Hamann, M. Schluter, C. Chiang. Norm-Conserving Pseudopotentials [J]. Phys. Rev. Lett. 1977, 43: 1494-1497.
42 D. Vanderbilt. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism [J]. Phys. Rev. B 1990, 41: 7892-7895.
1 R. E. Peierls, Quantum Theory of Solids [M]. Oxford: Oxford University Press, 1955.
2固体物理学黄昆原著,韩汝琦改编北京:高等教育出版社.
3 M. Dressel, Peierls Instability and Charge Density Waves, http://www.pi1.physik.uni-stuttgart.de/glossar/Peierls_e.php
4 P. B. Littlewood and V. Heine, The effect of electron-electron interactions on the Peierls transition in metals with strong nesting of Fermi surfaces [J]. J. Phys. C: Solid State Phys 1981, 14: 2493-2949.
5 J. E. Hirsch, Effect of Coulomb Interactions on the Peierls Instability [J]. Phys. Rev. Lett. 1983, 51: 296-299.
6 E. B. Kolomeisky and J. P. Straley, Phase Transition in the Peierls Model and the Possibility of One-Dimensional Melting [J]. Phys. Rev. Lett. 1996, 76: 2930-2933.
7 J.W. Bray et al. Extended linear chain compounds [M] edited by J. S. Miller, New York: Plenum, 1993.
8 E. Pyette, Peierls instability in Heisenberg chains [J]. Phys. Rev. B 1974, 10: 4637-4642.
9 M. C. Cross and D. S. Fisher, A new theory of the spin-Peierls transition with special relevance to the experiments on TTFCuBDT [J]. Phys. Rev. B 1979, 19: 402-419.
10 Anthony F. De Lia, Dynamical studies of antiferromagnetic exchange interactions in low dimensional quantum spin systems [D]. Florida: The Florida State University, 2003.
11 M. Hase, I. Terasaki, and K. Uchinokura, Observation of the spin-Peierls transition in linear Cu2+ (spin-?) chains in an inorganic compound CuGeO3 [J]. Phys. Rev. Lett. 1993, 70: 3651-3654.
12 J. P. Boucher and L. P. Regnault, The Inorganic Spin-Peierls Compound CuGeO3 [J]. J. de Physique I 1996, 6: 1939-1966.
13 Isobe M and Udea Y. Magnetic Susceptibility of Quasi-One-Dimensional Compoundα'- NaV2O5 - Possible Spin-Peierls Compound with High Critical Temperature of 34 K [J]. J. Phys. Soc. Jpn. 1996, 65: 1178-1181.
14 M. Isobe, C. Kagami, and Y. Ueda, Crystal growth of new spin-Peierls compound NaV2O5 [J]. J. Crystal Growth, 1997, 181: 314-317.
15 (a) Carpy P A, Casalot A, Pouchard M, Galy J and Hagenmuller P. Electric and magnetic properties of the oxyfluoride vanadium bronzes alpha'-NaV2O5-XFX [J]. J. Solid State Chem. 1972, 5: 229-238. (b) Carpy P A and Galy J. Affinement de la structure cristalline du bronze NaV2O5 [J]. Acta Crystallogr. Sect. B: Struct. Crystallogr. Cryst. Chem. 1975, 31: 1481-1482.
16 Bonner J C and Fisher M E. Linear Magnetic Chains with Anisotropic Coupling [J]. Phys. Rev.1964, 135: A640-A658.
17 (a) Meetsma A, de Boer J L, Damascelli A, Jegoudez J, Revcolevschi A and Palstra T T M. Inversion Symmetry in the Spin-Peierls Compoundα'-NaV2O5 [J]. Acta Crystallogr. Sect.C 1998, 54: 1558-1561. (b) von Schnering H G, Grin Y, Kaupp M, Somer M, Kremer R K, Jepsen O, Chatterji T and Weiden M [J]. Z. Kristallogr. 1998, 213: 246. (c) Chatterji T, Li? K D, McIntyre G J, Weiden M, Hauptmann R and Geibel C. The ground state of NaV2O5 [J]. Solid State Commun. 1998, 108: 23-26.
18 Smolinski H, Gros C, Weber W, Peuchert U, Roth G, Weiden M, and Geibel C. NaV2O5 as a Quarter-Filled Ladder Compound [J]. Phys. Rev. Lett. 1998, 80: 5164-5167.
19 Ohama T, Yasuoka H, Isobe M and Ueda Y. Mixed valency and charge ordering inα′-NaV2O5 [J]. Phys. Rev. B 1999, 59: 3299-3302.
20 Konstantinovi? M J, Popovi? Z V, Vasil’ev A N, Isobe M and Ueda Y. First evidence for charge ordering in NaV2O5 from Raman spectroscopy [J]. Solid State Commun. 1999, 112: 397-402.
21 Damascelli A, Presura C, van der Marel D, Jegoudez J and Revcolevschi A. Optical spectroscopic study of the interplay of spin and charge inα′-NaV2O5 [J]. Phys. Rev. B 2000, 61: 2535-2552.
22 Y. Fujii, H. Nakao, T. Yosihama, M. Nishi, K. Nakajima, K. Kakurai, M. Isobe, Y. Ueda, and H. Sawa, New Inorganic Spin-Peierls Compound NaV2O5 Evidenced by X-Ray and Neutron Scattering [J]. J. Phys. Soc. Japan 1997, 66: 326-329.
23 Yosihama T, Nishi M, Nakajima K, Kakurai K, Fujii Y, Isobe M, Kagami C and Ueda Y. Spin Dynamics in NaV2O5–Inelastic Neutron Scattering [J]. J. Phys. Soc. Jpn. 1998, 67: 744-747.
24 Fischer M, Lemmens P, Els G, Güntherodt G, Sherman E Ya, MorréE, Geibel C and Steglich F. Spin-gap behavior and charge ordering inα′-NaV2O5 probed by light scattering [J]. Phys. Rev. B 1999, 60: 7284-7294.
25 Lüdecke J, Jobst A, van Smaalen S, MorréE, Geibel C and Krane H G Acentric Low-Temperature Superstructure of NaV2O5 [J]. Phys. Rev. Lett. 82: 3633-3636.
26 J. L. de Boer, A. Meetsma, J. Baas and T. T.Palstra, Spin-Singlet Clusters in the Ladder Compound NaV2O5 [J]. Phys. Rev. Lett. 2000, 84: 3962-3965.
27 Sawa H, Ninomiya E, Ohama T, Nakao H, Ohwada K, Murakami Y, Fujii Y, Noda Y, Isobe M and Ueda Y. Low-Temperature Structure of the Quarter-Filled Ladder Compoundα'-NaV2O5 [J]. J. Phys. Soc. Jpn. 2002, 71: 385-388.
28 Lohmann M, Krug von Nidda H A, Eremin M V, Loidl A, Obermeier G and Horn S Charge Order in NaV2O5 Studied by EPR [J]. Phys. Rev. Lett. 2000, 85: 1742-1745
29 Nakao H, Ohwada K, Takesue N, Fujii Y, Isobe M, Ueda Y, Zimmermann M V, Hill J P, Gibbs D, Woicik J C, Koyama I and Murakami Y X-Ray Anomalous Scattering Study of aCharge-Ordered State in NaV2O5 [J]. Phys. Rev. Lett. 2000, 85 4349-4352.
30 van Smaalen S, Daniels P, Palatinus L and Kremer R K. Orthorhombic versus monoclinic symmetry of the charge-ordered state of NaV2O5 [J]. Phys. Rev. B, 2002, 65: 060101.
31 Ohwada K, Fujii Y, Katsuki Y, Muraoka J, Nakao H, Murakami Y, Sawa H, Ninomiya E, Isobe M and Ueda Y. Charge-Order Pattern of the Low-Temperature Phase from a Monoclinic Single Domain of NaV2O5 Uniquely Determined by Resonant X-Ray Scattering[J]. Phys. Rev. Lett. 2005, 94: 106401.
32 Fertey P, Poirier M, Castonguay M, Jegoudez J and Revcolevschi A. Ultrasonic evidence of a spin-Peierls transition inα′-NaV2O5 [J]. Phys. Rev. B 1998, 57:13698-13701.
33 M. K¨oppen, D. Pankert, R. Hauptmann, M. Lang, M. Weiden, C. Geibel, and F. Steglich .Interference of a first-order transition with the formation of a spin-Peierls state inα′-NaV2O5 [J]. Phys. Rev. B 1998, 57: 8466-8471.
34 D. K. Powell, J.W. Brill, Z. Zeng, and M. Greenblatt. Specific heat ofα′-NaV2O5 at its spin-Peierls transition [J]. Phys. Rev. B 1998, 58: 2937-2940.
35 E. Postolache, D. K. Powell, G. Popov, R. C. Rai, M. Greenblatt, and J. W. Brill. Comparison of Young's modulus and specific heat anomalies at the magnetic transition inα′-NaV2O5 [J]. Solid State Sci. 2000, 2: 759-766.
36 J. Hemberger, M. Lohmann, M. Nicklas, A. Loidl, M. Klemm, G. Obermeier,and S. Horn .Thermodynamic, transport and magnetic properties ofα'-NaV2O5 [J]. Europhys. Lett. 1998, 42: 661-666.
37 D. C. Johnston, R. K. Kremer, M. Troyer, X. Wang, A. Kl¨umper, S. L. Bud’ko, A. F. Panchula, and P.C. Pantfield. Thermodynamics of spin S=? antiferromagnetic uniform and alternating-exchange Heisenberg chains [J]. Phys. Rev. B 2000, 61: 9558-9606.
38 W. Schnelle, Yu. Grin, and R. Kremer. Specific heat ofα′-NaV2O5 in magnetic fields up to 16 T [J]. Phys. Rev. B 1999, 59: 73-76.
39 L. N. Bulaevskii, A. I. Buzdin, and D. I. Khomskii, Spin-peierls transition in magnetic field [J]. Solid State Commun. 1978, 27: 5-10.
40 M. C. Cross. Effect of magnetic fields on a spin-Peierls transition [J]. Phys. Rev. B 1979, 20: 4606-4611.
41 P. Fertey, M. Poirier, and M. Castonguay, Ultrasonic evidence of a spin-Peierls transition inα′-NaV2O5 [J]. Phys. Rev. B 1998, 57: 13698-13701.
42 Vasil’ev A N , Pryadun V V, Khomskii D I, Dhalenne G, Revcolevschi A, Isobe M and Ueda Y. Anomalous Thermal Conductivity of NaV2O5 as Compared to Conventional Spin-Peierls System CuGeO3 [J]. Phys. Rev. Lett. 1998, 81: 1949-1952.
43 Smirnov A I, Popova M N, Sushkov A B, Golubchik S A, Khomskii D I, Mostovoy M V, Vasil’ev A N, Isobe M and Ueda Y. High-frequency dielectric and magnetic anomaly at the phasetransition in NaV2O5 [J]. Phys. Rev. B 1999, 59: 14546-14551.
44 Wu H and Zheng Q Q, Electronic structure of the spin-Peierls system NaV2O5 [J]. Phys. Rev. B 1999, 59:15027-15032.
45 Yaresko A N, Antonov V N, Eschrig H, Thalmeier P and Fulde P. Electronic structure and exchange coupling inα′-NaV2O5 [J]. Phys. Rev. B 2000, 62: 15538-15546.
46 Spitaler J, Sherman E Y, Evertz H G and Ambrosch-Draxl C. Optical properties, electron-phonon coupling, and Raman scattering of vanadium ladder compounds [J]. Phys. Rev. B 2004, 70: 125107.
47 (a) Golubchik S A, Isobe M, Ivlev A N, Mavrin B N, Popova M N, Sushkov A B, Ueda Y and Vasil’ev A N. Raman, Infrared and Optical Spectra of the Spin-Peierls Compound NaV2O5 [J]. J. Phys. Soc. Jpn. 1999, 66: 4042-4046. (b) Golubchik S A, Isobe M, Ivlev A N, Mavrin B N, Popova M N, Sushkov A B, Ueda Y and Vasil’ev A N. Errata: Raman, Infrared and Optical Spectra of Spin-Peierls Compound NaV2O5 [J] J. Phys. Soc. Jpn. 1999, 68: 318.
48 Damascelli A, van der Marel D, Grüninger M, Presura C, Palstra T T M, Jegoudez J and Revcolevschi A. Direct Two-Magnon Optical Absorption inα′-NaV2O5:“Charged”Magnons [J]. Phys. Rev. Lett. 1998, 81: 918-921.
49 Long V C, Zhu Z, Musfeldt J L, Wei X, Koo H J., Whangbo M H, Jegoudez J and Revcolevschi A. Polarized optical reflectance and electronic band structure ofα′-NaV2O5 [J]. Phys. Rev. B 1999, 60: 15721-15727.
50 (a) Zhang G P, Callcott T A, Woods G T, Lin L, Sales Brian, Mandrus D and He J. Electron Correlation Effects in Resonant Inelastic X-Ray Scattering of NaV2O5 [J]. Phys. Rev. Lett. 2002, 88: 077401. (b) Zhang G P, Callcott T A, Woods G T, Lin L, Sales Brian, Mandrus D and He J. Erratum: Electron Correlation Effects in Resonant Inelastic X-Ray Scattering of NaV2O5 [J]. Phys. Rev. Lett 2002, 88: 189902(E)
51 (a) Zhang G P, Woods G T, Shirley E L, Callcott T A, Lin L, Chang G S, Sales B C, Mandrus D and He J, Orbital-resolved soft x-ray spectroscopy in NaV2O5 [J]. Phys. Rev. B 2002, 65: 165107. (b) Woods G T, Zhang G P, Callcott T A, Lin L, Chang G S, Sales B C, Mandrus D and He J. Site-selected O 2p densities of states in NaV2O5 determined from angular-dependent X-ray absorption and emission spectra [J]. Phys. Rev. B 2002, 65: 165108.
52 Zhang G P and Callcott T A .Resolving d-d transitions in NaV2O5 using angle-resolved resonant inelastic x-ray scattering at the V L edge [J]. Phys. Rev. B 2006, 73: 125102.
53 Presura C, van der Marel D, Dischner M, Geibel C and Kremer R K .Optical properties and electronic structure ofα′-Na1-xCaxV2O5 [J]. Phys. Rev. B 2000, 62:16522-16527.
54 Presura C, van der Marel D, Damascelli A and Kremer R K .Low-temperature ellipsometry ofα′-NaV2O5 [J]. Phys. Rev. B 2000, 61: 15762-15765.
55 Konstantinovi? M J, Popovi? Z V, Moshchalkov V V, Presura C, Gaji? R, Isobe M and Ueda Y .Optical properties ofα′-NaxV2O5 [J]. Phys. Rev. B 2002, 65: 245103.
56 (a) Duda L C, Schmitt T, Nordgren J, Kuiper P, Dhalenne G and Revcolevschi A .Low-Energy Excitations in Resonant Inelastic X-Ray Scattering ofα′-NaV2O5 [J]. Phys. Rev. Lett. 2004, 93: 169701. (b) van Veenendaal M and Fedro A J. Comment on“Electron Correlation Effects in Resonant Inelastic X-ray Scattering of NaV2O5”[J]. Phys. Rev. Lett. 2004, 92: 219701.
57 (a) Zhang G P, Callcott T A, Woods G T, Lin L, Sales B C, Mandrus D and He J. Zhang et al. Reply [J]. Phys. Rev. Lett. 2004, 93: 169702. (b) Zhang G P, Callcott T A, Woods G T, Lin L, Sales B C, Mandrus D and He J .Zhang et al. Reply [J]. Phys. Rev. Lett. 2004, 92: 219702.
58 Mila F, Millet P and Bonvoisin J. Exchange integrals of vanadates as revealed by magnetic-susceptibility measurements of NaV2O5 [J]. Phys. Rev. B 1996, 54: 11925-11928.
59 Kobayashi K, Mizokawa T, Fujimori A, Isobe M and Ueda Y. Single-Particle Excitations in One-Dimensional Mott-Hubbard Insulator NaV2O5 [J]. Phys. Rev. Lett. 1998, 80: 3121-3124.
60 Aichhorn M, Sherman E Y and Evertz H G. Single-particle spectral function of quarter-filled ladder systems [J]. Phys. Rev. B 2005, 72: 155110.
61 S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne. First principles methods using CASTEP [J]. Z. Kristallogr. 2005, 220: 567-570.
62 Perdew J P, Burke S and Ernzerhof M. Generalized Gradient Approximation Made Simple [J]. Phys. Rev. Lett. 1996, 77: 3865-3868.
63 Perdew J P and Wang Y. Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation [J]. Phys. Rev. B 1986, 33: 8800-8802.
64 D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism [J]. Phys. Rev. B 1990, 41: 7892-7895.
65 Popovi? Z S and Vukajlovi? F R A. Comparative Study of Coulomb-Correlated Electronic Structure of the Spin-Gapped Compoundα′-NaV2O5 in Pmmn and P21mn Crystal Structure [J]. J. Phys. Soc. Jpn. 2002, 71: 2720-2729.
66 Katoh N, Miyazaki T and Ohno T. First-principles study on the insulating state ofα′-NaV2O5 [J]. Phys. Rev. B 1999, 59: 12723-12727.
67 Galy J, Vanadium pentoxide and vanadium oxide bronzes-Structural chemistry of single (S) and double (D) layer MxV2O5 phases [J]. J. Solid State Chem. 1992, 100: 229-245.
68 P. Ravindran, R. Vidya, O. Eriksson, and H. Fjellv?g, Magnetic-instability-induced giant magnetoelectric coupling [J]. Adv. Mater. 2008, 20: 1353-1356 .
69 T. Ohama, H. Yasuoka, M. Isobe and Y. Ueda, The d Orbital Character in the Spin-PeierlsSystem NaV2O5 [J]. J. Phys. Soc. Jpn. 1997, 66: 3008-3011.
70 Suaud N and Lepetit M B. Ab Initio Evaluation of the Charge Ordering inα′-NaV2O5 [J]. Phys. Rev. Lett. 2002, 88: 056405.
71 Hozoi L, Nishimoto S and Yamasaki A. Near degeneracy and pseudo Jahn-Teller effects in mixed-valence ladders: The phase transition in NaV2O5 [J]. Phys. Rev. B 2005, 72: 195117.
72 (a) Hozoi L, de Vries A H, van Oosten A B, Broer R, Cabrero J and de Graaf C. Theoretical Characterization of the Ground and Optically Excited States ofα′-NaV2O5 [J]. Phys. Rev. Lett. 2002, 89: 076407. (b) Hozoi L, Presura C, de Graaf C and Broer R. Electronic structureα′-NaV2O5: Wave-function-based embedded-cluster calculations [J]. Phys. Rev. B 2003, 67: 035117.
73 Horsch P and Mack F. A new view of the electronic structure of the spin-Peierls compound -α′-NaV2O5 [J]. Eur. Phys. J. B 1998, 5: 367-370.
74 Suaud N and Lepetit M B .Ab initio evaluation of local effective interactions inα′-NaV2O5 [J]. Phys. Rev. B 2000, 62: 402-409.
75 Popovi? Z S and Vukajlovi? F R. Coulomb-correlated band structure of one-dimensional spin-Peierlsα′-NaV2O5 [J]. Phys. Rev. B 1999, 59: 5333-5340.
76 Korbel P, Wójcik W, Klejnberg A, Spalek J, Acquarone M and Lavagna M. Antiferromagnetism of almost localized fermions: Evolution from Slater-type to Mott-Hubbard gap [J]. Eur. Phys. J. B 2003, 32: 315-322.
77 Moukouri S and Jarrell M. Absence of a Slater Transition in the Two-Dimensional Hubbard Model [J]. Phys. Rev. Lett. 2001, 87: 167010.
78 Slater J C. Magnetic Effects and the Hartree-Fock Equation [J]. Phys. Rev. 1951, 82: 538-541.
79 Riera J, Poilblanc D. Coexistence of charge-density wave and spin-Peierls orders in quarter-filled quasi-one-dimensional correlated electron systems [J]. Phys. Rev. B 1999, 59: 2667-2675.
1 E. Manousakis, The spin-? Heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides [J]. Rev. Mod. Phys. 1991, 63: 1-62.
2 H. Bethe, On the theory of metals. I. Eigenvalues and eigenfunctions of the linear atom chain [J]. Z. Phys. 1931, 71: 205-226.
3 E. Dagotto, Spin-gap and superconductivity in ladder compounds [J]. Journal of Electron Spectroscopy and Related Phenomena 2001, 117–118: 223–236.
4 M. Azuma, Z. Hiroi, M. Takano, K. Ishida and Y. Kitaoka. Observation of a Spin Gap in SrCu2O3 Comprising Spin-? Quasi-1D Two-Leg Ladders [J]. Phys. Rev. Lett. 1994, 73: 3463-3466.
5 E. Dagotto, J. Riera and D. J. Scalapino. Superconductivity in ladders and coupled planes [J]. Phys. Rev. B 1992, 45: 5744-5747.
6 E. Dagotto and A. Moreo. Zero-temperature properties of the two-dimensional Heisenberg antiferromagnet: A numerical study [J]. Phys. Rev. B 1988, 38: 5087-5090.
7 T. Barnes, E. Dagotto, J. Riera and E. Swanson. Excitation spectrum of Heisenberg spin ladders [J]. Phys. Rev. B 1993, 47: 3196-3203.
8 S. Gopalan, T.M. Rice and M. Sigrist. Spin ladders with spin gaps: A description of a class of cuprates [J]. Phys. Rev. B 1994, 49: 8901-8910.
9 R.M. Noack, S.R. White and D.J. Scalapino. Correlations in a Two-Chain Hubbard Model [J]. Phys. Rev. Lett. 1994, 73: 882-885.
10 M. Onoda and N. Nishiguchi, Crystal Structure and Spin Gap State of CaV2O5 [J]. J. Solid State Chem. 1996, 127, 359-362.
11 H. Smolinski, C. Gros, W. Weber, U. Peuchert, G. Roth, M. Weiden, and C. Geibel, NaV2O5 as a Quarter-Filled Ladder Compound [J]. Phys. Rev. Lett. 1998, 80: 5164-5167.
12 H. Iwase, M. Isobe, Y. Ueda, and H. Yasuoka, Observation of Spin Gap in CaV2O5 by NMR [J]. J. Phys. Soc. Jpn. 1996, 65: 2397-2400.
13 Y. Ueda, Vanadate Family as Spin-Gap Systems [J]. Chem. Mater. 1998, 10: 2653-2664.
14 S. Miyahara, M. Troyer, D. C. Johnston, and K. Ueda, Quantum Monte Carlo Simulation of the Trellis Lattice Heisenberg Model for SrCu2O3 and CaV2O5 [J]. J. Phys. Soc. Jpn. 1998, 67: 3918-3923.
15 P. Millet, C. Satto, J. Bonvoisin, B. Normand, K. Penc, M. Albrecht, and F. Mila, Magnetic properties of the coupled ladder system MgV2O5 [J]. Phys. Rev. B 1998, 57: 5005-5008.
16 M. A. Korotin, I. S. Elfimov, V. I. Anisimov, M. Troyer, and D. I. Khomskii, Exchange Interactions and Magnetic Properties of the Layered Vanadates CaV2O5, MgV2O5, CaV3O7, and CaV4O9 [J]. Phys. Rev. Lett. 1999, 83: 1387-1390.
17 M. A. Korotin, V. I. Anisimov, T. Saha-Dasgupta, and I. Dasgupta, Electronic structure andexchange interactions of the ladder vanadates CaV2O5 and MgV2O5 [J]. J. Phys.: Condens. Matter 2000, 12:113-124.
18 M. Konstantinovi?, Z. V. Popovi?, M. Isobe, and Y. Ueda, Raman scattering from magnetic excitations in the spin-ladder compounds CaV2O5 and MgV2O5 [J]. Phys. Rev. B 2000, 61: 15185-15188.
19 C. de Graaf, L. Hozoi and R. Broer, Magnetic interactions in calcium and sodium ladder vanadates [J]. J. Chem. Phys. 2004, 120: 961-967.
20 H.-J. Koo, M.-H. Whangbo, Analysis of the spin–spin interactions in layered oxidesα′-NaV2O5, CaV2O5 and MgV2O5 and the spin-Peierls distortion inα′-NaV2O5 by molecular orbital, Madelung energy and bond valence sum calculations [J]. Solid State Commun. 1999, 111: 353-360.
21 M.-H. Whangbo, H.-J. Koo and D. Dai, Spin exchange interactions and magnetic structures of extended magnetic solids with localized spins: theoretical descriptions on formal, quantitative and qualitative levels [J]. J. Solid State Chem. 2003, 176: 417-481.
22 J. Spitaler, E. Ya. Sherman, H. G. Evertz, and C. Ambrosch-Draxl, Optical properties, electron-phonon coupling, and Raman scattering of vanadium ladder compounds [J]. Phys. Rev. B 2004, 70:125107.
23 S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, First principles methods using CASTEP [J]. Z. Kristallogr. 2005, 220: 567-570.
24 John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Generalized Gradient Approximation Made Simple [J]. Phys. Rev. Lett. 1996, 77: 3865-3868.
25 John P. Perdew and Wang Yue, Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation [J]. Phys. Rev. B 1986, 33: 8800-8802.
26 D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism [J]. Phys. Rev. B 1990, 41: 7892-7895.
27 R. S. Mulliken, Electronic Population Analysis on LCAOMO Molecular Wave Functions. I [J]. J. Chem. Phys., 1955, 23: 1833-1846.
28 L. Noodleman, Valence bond description of antiferromagnetic coupling in transition metal dimmers [J]. J. Chem. Phys. 1981, 74: 5737-5743.
29 L. Noodleman and E. R. Davidson, Ligand spin polarization and antiferromagnetic coupling in transition metal dimers [J]. Chem. Phys. 1986, 109: 131-143.
30 L. Noodleman and D. A. Case, Density-functional theory of spin polarization and spin coupling in iron-sulfur clusters [J]. Adv. Inorg. Chem. 1992, 38: 423470.
31 E. R. Davidson and S. Chakravorty, A test of the Hirshfeld definition of atomic charges and moments [J]. Theor. Chim. Acta 1992, 83: 319-330.
32 M. D Segall, C. J. Pickard, R. Shah, M. C. Payne, Population analysis in plane wave electronic structure calculations [J]. Mol. Phys. 1996, 89: 571-577.
33 M. D. Segall, R. Shah, C. J. Pickard, M. C. Payne, Population analysis of plane-wave electronic structure calculations of bulk materials [J]. Phys. Rev. B, 1996, 54: 16317-16320.
34 P. Ravindran, R. Vidya, O. Eriksson, and H. Fjellv?g, Magnetic- Instability-Induced Giant Magnetoelectric Coupling [J]. Adv. Mater. 2008, 20: 1353-1356.
35 T. Ohama, H. Yasuoka, M. Isobe and Y. Ueda, The d Orbital Character in the Spin-Peierls System NaV2O5 [J]. J. Phys. Soc. Jpn. 1997, 66: 3008-3011.
36 T. Ohama, M. Isobe, and Y. Udea, 3d Orbital State in CaV2O5 [J]. J. Phys. Soc. Jpn. 2000, 69: 1574-1575.
37 M. Imada, A. Fujimori, and Y. Tokura, Metal-insulator transitions, Rev. Mod. Phys. 1998, 70: 1039-1263.
38 F. Gebhard, The Mott Metal-Insulator Transition: Models and Methods [M]. Springer Berlin/Heidelberg, 1997.
39 de Boer, J. H., and E. J. W. Verway, Semi-conductors with partially and with completely filled 3d-lattice bands [J] Proc. Phys. Soc. London, Sect. A 1937, 49: 59-71.
40 N F Mott and R Peierls, Discussion of the paper by de Boer and Verwey [J] Proc. Phys. Soc. London, Ser. A 1937, 49: 72-73.
41 N. F. Mott, The Basis of the Electron Theory of Metals, with Special Reference to the Transition Metals [J], Proc. Phys. Soc. London, Ser. A 1949, 62: 416-422.
42 N. F. Mott, The transition to metallic conduction in semiconductors [J] Can. J. Phys. 1956, 34: 1356-1357.
43 N. F. Mott, The transition to the metallic state [J] Philos. Mag. 1961, 6: 287-309.
44 N. F. Mott, Metal-Insulator Transitions [M]. Taylor and Francis, London/Philadelphia). 1990.
45 J. C. Slater, Magnetic Effects and the Hartree-Fock Equation [J]. Phys. Rev. 1951, 82: 538– 541.
46 K. Terakura, T. Oguchi, A. R. Williams, and J. Kübler, Band theory of insulating transition-metal monoxides: Band-structure calculations [J]. Phys. Rev. B 1984, 30: 4734-4747.
47 K. Terakura, A. R. Williams, T. Oguchi, and J. Kübler,Transition-Metal Monoxides: Band or Mott Insulators [J] Phys. Rev. Lett. 1984, 52: 1830– 1833.
48 G. A. Sawatzky and J. W. Allen, Magnitude and Origin of the Band Gap in NiO [J] Phys. Rev. Lett. 1984, 53: 2339-2342.
49 J. B. Goodenough,Theory of the Role of Covalence in the Perovskite-Type Manganites [La, M(II)]MnO3 [J]. Phys. Rev. 1955, 100: 564– 573.
50 J. B. Goodenough, An interpretation of the magnetic properties of the perovskite-type mixed crystals La1-xSrxCoO3-λ[J]. J. Phys. Chem. Solids 1958, 6: 287-297.
51 J. Kanamori, Superexchange interaction and symmetry properties of electron orbitals [J]. J. Phys. Chem. Solids 1959, 10: 87-98.
52 P. W. Anderson, Theory of Magnetic Exchange Interactions:Exchange in Insulators and Semiconductors [J]. Solid State Phys. 1963, 14: 99-214.
53 H. B. Yahia, E. Gaudin, J. Darriet, M. Banks, R. K. Kremer, A. Villesuzanne and M.-H. Whangbo. Synthesis, Crystal Structure, Magnetic Properties, and Electronic Structure of the New Ternary Vanadate [J]. Inorg. Chem. 2005, 44: 3087-3093.
54 V. Bellini, A. Olivieri and F. Manghi, Density-functional study of the Cr8 antiferromagnetic ring [J]. Phys. Rev. B 2006, 73: 184431.
55 H. J. Xiang, C. Lee, and M. -H. Whangbo, Absence of a spiral magnetic order in Li2CuO2 containing one-dimensional CuO2 ribbon chains [J]. Phys. Rev. B 2007, 76: 220411(R).
56 H. J. Xiang, S. -H. Wei, and M. -H. Whangbo, Origin of the Structural and Magnetic Anomalies of the Layered Compound SrFeO2: A Density Functional Investigation [J]. Phys. Rev. Lett. 2008, 100, 167207.
57 A. N. Vasil'ev, M. M. Markina, and E. A. Popova, Spin gap in low-dimensional magnets (Review) [J] Low Temp. Phys. 2005, 31: 203-223.
1 H. Schmid. Multi-ferroic Magnetoelectrics [J]. Ferroelectrics, 1994, 162: 317-338.
2 Nicola A. Hill, Alessio Filippetti. Why are there any magnetic ferroelectrics? [J]. Journal of Magnetism and Magnetic Materials, 2002, 242-245: 976–979.
3 N. A. Spaldin,and M. Fiebig, The renaissance of magnetoelectric multiferroics [J]. Science, 2005, 309: 391– 392.
4 J. F. Scott, Data storage - Multiferroic memories [J]. Nature Mater. 2007, 6: 256-257.
5 M. Gajek, M. Bibes, S. Fusil, K. Bouzehouane, J. Fontcuberta, A. Barthélémy and A. Fert, Tunnel junctions with multiferroic barriers [J]. Nature Mater. 2007, 6: 296–302.
6 J. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D. G. Schlom, U. V. Waghmare, N. A. Spaldin, K. M. Rabe, M. Wuttig, R. Ramesh, Epitaxial BiFeO3 multiferroic thin film heterostructures [J]. Science 2003, 299: 1719–1722.
7 Fiebig, M., Lottermoser, Th., Fro¨hlich, D., Goltsev, A. V. and Pisarev, R. V. Observation of coupled magnetic and electric domains [J]. Nature 2002, 419: 818–820 .
8 T. Zhao, A. Scholl, F. Zavaliche, K. Lee, M. Barry, A. Doran, M. P. Cruz, Y. H. Chu, C. Ederer, N. A. Spaldin, R. R. Das, D. M. Kim, S. H. Baek, C. B. Eom and R. Ramesh. Electrical control of antiferromagnetic domains in multiferroic BiFeO3 films at room temperature [J]. Nature Materials, 2006, 5: 823-829.
9 Cheong, S.-W. & Mostovoy, M. Multiferroics: A magnetic twist for ferroelectricity [J]. Nature Mater. 2007, 6: 13–20.
10 R. Ramesh and N. A. Spaldin. Multiferroics- Progress and prospects in thin films [J]. Nature Mater. 2007, 6: 21-29.
11 T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima and Y. Tokura. Magnetic control of ferroelectric polarization [J]. Nature, 2003, 426: 55–58.
12 N. Ikeda, H. Ohsumi, K. Ohwada, K. Ishii, T. Inami, K. Kakurai, Y. Murakami, K. Yoshii, S. Mori, Y. Horibe and H. Kit?. Ferroelectricity from iron valence ordering in the charge-frustrated system LuFe2O4 [J]. Nature, 2005, 436: 1136–1138.
13 N. A. Hill, Why are there so few magnetic ferroelectrics? [J]. J. Phys. Chem. B, 2000, 104: 6694–6709.
14 N. A. Spaldina and W. E. Pickett. Computational design of multifunctional materials [J]. Journal of Solid State Chemistry, 2003, 176: 615–632.
15 C. Ederer, and N. A. Spaldin, Recent progress in first-principles studies of magnetoelectric multiferroics [J]. Curr. Opin. Solid State Mater. Sci. 2005, 9: 128–139.
16 R. V. Shpanchenko, V. V. Chernaya, A. A. Tsirlin, P. V. Chizhov, D. E. Sklovsky, E. V. Antipov, E. P. Khlybov, V. Pomjakushin, A. M. Balagurov, J. E. Medvedeva, E. E. Kaul, and C. Geibel.Synthesis, Structure, and Properties of New Perovskite PbVO3 [J]. Chem. Mater. 2004, 16: 3267-3273.
17 A. A. Belik, M. Azuma, T. Saito, Y. Shimakawa, and M. Takano, Crystallographic Features and Tetragonal Phase Stability of PbVO3, a New Member of PbTiO3 Family [J]. Chem.Mater. 2005, 17: 269-273.
18 K. Oka, I. Yamada, M. Azuma, S. Takeshita, K. H. Satoh, A. Koda, R. Kadono, M. Takano, and Y. Shimakawa. Magnetic Ground-State of Perovskite PbVO3 with Large Tetragonal Distortion [J]. Inorg. Chem., 2008, 47: 7355-7359.
19 A. A. Belik, S. Iikubo, K. Kodama, N. Igawa, S. Shamoto, S. Niitaka, M. Azuma, Y. Shimakawa, M. Takano, F. Izumi, and E. T. Muromachi. Neutron Powder Diffraction Study on the Crystal and Magnetic Structures of BiCoO3 [J]. Chem. Mater. 2006, 18: 798-803.
20 Y. Uratani, T. Shishidou, F. Ishi, and T. Oguchi. First-Principles Predictions of Giant Electric Polarization [J]. Jpn. J. Appl. Phys. 2005, 44: 7130-7133.
21 L. W. Martin, Q. Zhan, Y. Suzuki, R. Ramesh, M. Chi, N. Browning, T. Mizoguchi, and J. Kreisel. Growth and structure of PbVO3 thin films [J]. Appl. Phys. Lett. 2007, 90: 062903.
22 A. Kumar,N. J. Podraza, S. Denev, J. Li, L. W. Martin,Y. H. Chu, R. Ramesh, R. W. Collins, and V. Gopalan. Linear and nonlinear optical properties of multifunctional PbVO3 thin films [J]. Appl. Phys. Lett. 2008, 92: 231915.
23 A. Kumar, L. W. Martin, S. Denev, J. B. Kortright, Y. Suzuki, R. Ramesh, and V. Gopalan. Polar and magnetic properties of PbVO3 thin films [J]. Phys. Rev. B 2007,75: 060101(R).
24 D. J. Singh. Electronic structure and bond competition in the polar magnet PbVO3 [J]. Phys. Rev. B 2006, 73: 094102 .
25 A. A. Tsirlin, A. A. Belik, R. V. Shpanchenko, E. V. Antipov, E. T.-Muromachi, and H. Rosner. Frustrated spin-? square lattice in the layered perovskite PbVO3 [J]. Phys. Rev. B 2008, 77: 092402.
26 S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne. First principles methods using CASTEP [J]. Z. Kristallogr. 2005, 220: 567-570 .
27黄祖飞. LiMnO2体系结构与性能的第一性原理研究[D].吉林:吉林大学, 2006.
28王一.高压提高PbTe热电效率的第一性原理研究[D].吉林:吉林大学, 2008.
29 I. Solovyev, N. Hamada, K. Terakura. t2g versus all 3d localization in LaMO3 perovskites (M=Ti–Cu): First-principles study [J] .Phys. Rev. B 1996, 53: 7158-7170.
30 S. K. Mishra, G. Ceder. Structural stability of lithium manganese oxides [J]. Phys. Rev. B 1999, 59: 6120-6130.
31 J. P. Perdew, K. Burke, and M. Ernzerhof. Generalized Gradient Approximation Made Simple [J] .Phys. Rev. Lett. 1996, 77: 3865-3868.
32 D. Vanderbilt. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism [J].Phys. Rev. B 1990, 41: R7892-7895 .
33 K. Terakura, A. R. Williams, T. Oguchi, and J. Kübler. Transition-Metal Monoxides: Band or Mott Insulators [J]. Phys. Rev. Lett. 1984, 52: 1830-1833.
34 K. Terakura, T. Oguchi, A. R. Williams, and J. Kübler. Band theory of insulating transition-metal monoxides: Band-structure calculations [J]. Phys. Rev. B 1984, 30: 4734-4747.
35 H. Smolinski, C. Gros, W. Weber, U. Peuchert, G. Roth, M. Weiden, and C. Geibel. NaV2O5 as a Quarter-Filled Ladder Compound [J]. Phys. Rev. Lett. 1998, 80: 5164-5167.
36 M. Onoda and N. Nishiguchi. Crystal Structure and Spin Gap State of CaV2O5 [J]. J. Solid State Chem. 1996, 127: 359-362.
37 M A Korotin, V I Anisimov, T Saha-Dasgupta and I Dasgupta. Electronic structure and exchange interactions of the ladder vanadates CaV2O5 and MgV2O5 [J]. J. Phys.: Condens. Matter 2000, 12: 113-124.
38 P. Millet, C. Satto, J. Bonvoisin, B. Normand, K. Penc, M. Albrecht, and F. Mila. Magnetic properties of the coupled ladder system MgV2O5 [J]. Phys. Rev. B 1998, 57: 5005-5008.
39 J. Spitaler, E. Ya. Sherman, and C. Ambrosch-Draxl. First-principles study of phonons, optical properties, and Raman spectra in MgV2O5 [J]. Physical Review B 2008, 78: 064304.
40 M. A. Korotin, I. S. Elfimov, V. I. Anisimov, M. Troyer, and D. I. Khomskii. Exchange Interactions and Magnetic Properties of the Layered Vanadates CaV2O5, MgV2O5, CaV3O7, and CaV4O9 [J]. Phys. Rev. Lett. 1999, 83: 1387-1390.
41 W. E. Pickett, Impact of Structure on Magnetic Coupling in CaV4O9 [J]. Phys. Rev. Lett. 1997, 79: 1746-1749.
42 P. Ravindran, R. Vidya, O. Eriksson, and H. Fjellv?g, Magnetic-instability-induced giant magnetoelectric coupling [J]. Adv. Mater. 2008, 20: 1353-1356 .
43 R. C. Rai, J. Cao, J. L. Musfeldt, D. J. Singh, X. Wei, R. Jin, Z. X. Zhou, B. C. Sales, and D. G. Mandrus. Magnetodielectric effect in the S=? quasi-two-dimensional antiferromagnet K2V3O8 [J]. Phys. Rev. B 2006, 73: 075112.
44迟振华,靳常青.单相磁电多铁性体研究进展[J].物理学进展,2007, 27: 225-238.
45 R. E. Cohen. Origin of ferroelectricity in perovskite oxides [J]. Nature (London), 1992, 358: 136-138.
46 R. E. Cohen, H. Krakauer. Electronic structure studies of the differences in ferroelectric behavior of BaTiO3 and PbTiO3 [J]. Ferroelectrics, 1992, 136: 65-83.
47 D.I. Khomskii. Multiferroics: Different ways to combine magnetism and ferroelectricity [J]. Journal of Magnetism and Magnetic Materials, 2006, 306: 1–8.
48 P. Baettig, C. F. Schelle, R. LeSar, U. V. Waghmare, and N. A. Spaldin, Theoretical Prediction of New High-Performance Lead-Free Piezoelectrics [J]. Chem. Mater. 2005, 17: 1376-1380.
49 N. A. Hill, P. Baettig and C. Daul. First Principles Search for Multiferroism in BiCrO3 [J]. J .Phys. Chem. B. 2002, 106: 3383-3388.
50 R. Seshadri and N. A. Hill. Visualizing the Role of Bi 6s“Lone Pairs”in the Off-Center Distortion in Ferromagnetic BiMnO3 [J]. Chem. Mater. , 2001, 13: 2892-2899.
51 J. B. Neaton1, C. Ederer, U. V. Waghmare, N. A. Spaldin, and K. M. Rabe, First-principles study of spontaneous polarization in multiferroic BiFeO3 [J]. Phys. Rev. B. 2005, 71: 014113.
52 B. G. Pfrommer, M. Cote, S. G. Louie, and M. L. Cohen. Relaxation of Crystals with the Quasi-Newton Method [J]. J. Comput. Phys. 1997, 131: 133-140.
53 F. D. Murnaghan, The Compressibility of Media under Extreme Pressures [J]. Proc. Natl. Acad. Sci. U. S. A., 1944, 30: 244-247.
54肖衍繁,李文斌.物理化学[M].天津:天津大学出版社, 1997.
55 A. Sani, M. Hanfland and D. Levy, Pressure and Temperature Dependence of the Ferroelectric–Paraelectric Phase Transition in PbTiO3 [J]. J. Solid State Chem. 2002, 167: 446-452.
56 R. A. de Groot, F. M. Mueller, P. G. van Engen, and K. H. J. Buschow. New Class of Materials: Half-Metallic Ferromagnets [J]. Phys. Rev. Lett. 1983, 50: 2024-2027.
57 S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study [J]. Phys. Rev. B 1998, 57:1505-1509.
58冯端,金国钧,凝聚态物理学(上卷) [M].北京:高等教育出版社, 2003.
59 K. Ramesha, R. Seshadri, C. Ederer, T. He, M. A. Subramanian. Experimental and computational investigation of structure and magnetism in pyrite Co1?xFexS2 Chemical bonding and half-metallicity [J]. Phys. Rev. B 2004, 70: 214409
60 S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger. Spintronics: A Spin-Based Electronics Vision for the Future [J]. Science, 2001, 294: 1488-1495.
61 I. ?uti?, J. Fabian, and S. D. Sarma. Spintronics: Fundamentals and applications [J]. Rev. Mod. Phys. 2004, 76: 323- 410.
62 C. Felser, G. H. Fecher, and B. Balke, Spintronics: A Challenge for Materials Science and Solid-State Chemistry [J]. Angew. Chem. Int. Ed. Engl. 2007, 46: 668-669 .
63 L. Wang, T. Y. Chen, C. Leighton. Spin-dependent band structure effects and measurement of the spin polarization in the candidate half-metal CoS2 [J]. Phy. Rev. B 2004, 69: 094412.
64 S. P. Lewis, P. B. Allen, T. Sasaki. Band structure and transport properties of CrO2 [J]. Phys. Rev. B 1997, 55: 10253-10260.
65 M. I. Katsnelson, V. Yu. Irkhin, L. Chioncel, A. I. Lichtenstein, R. A. de Groot. Half-metallic ferromagnets: From band structure to many-body effects [J].Rev. Mod. Phys. 2008, 80: 315.
66 M. J. M. de Jong and C. W. J. Beenakker. Andreev Reflection in Ferromagnet-SuperconductorJunctions [J]. Phys. Rev. Lett. 1995, 74:1657 -1660.
67 J. -H. Park, E. Vescovo, H. -J. Kim, C. Kwon, R. Ramesh, and T. Venkatesan. Direct evidence for a half-metallic ferromagnet [J].Nature, 1998, 392: 794-796 .
68 K. E. H. M. Hanssen and P. E. Mijnarends. Positron-annihilation study of the half-metallic ferromagnet NiMnSb: Theory [J]. Phys. Rev. B 1986, 34: 5009-5016.