Microscopic Modelling of Correlated Low-dimensional Systems

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List of Figures xii 5.37 Spin resolved density of states for Fe 3d states for our Fe(II)-triazole model with different dF e−N distances. It is shown explicitly the spin up (upper panels) and spin down (lower panels) contributions. The first three structures in the upper part of the figure, correspond to the spin state S=0, the three last figures in the lower part correspond to the spin state S=2. . . . . . . . 122 5.38 Crystal field splitting ∆ vs. Fe-N distances. . . . . . . . . . . . . . . . . . . 123 5.39 Ground state energies as function Fe-N distance, for the set of model structures obtained within GGA-sp in the FP-LAPW basis set. . . . . . . . . . . 124 5.40 Magnetic susceptibility of Fe[(hyetrz)3](4-chlorophenylsulfonate)2·H2O. . . . 126 5.41 Building units of K2V3O8. (a) VO5-square pyramid. (b) VO4 tetrahedra . . 129 5.42 Band structure for K2V3O8 in the AFM configuration. The bars indicate the dominant band character in the local coordina te frame of V1. The selected path correspond to Γ(0,0,0)-X(0,1/2,0)-M(1/2,1/2,0)-Γ-Z(0,0,1/2)- R(0,1/2, 1/2)-A(1/2, 1/2, 1/2)-M in units of (π/a, π/b, π/c). . . . . . . . . . 131 5.43 Orbital resolved DOS for the AFM configuration in the spin up channel for V atoms (above) and O atoms (below). The K contribution to the DOS in this energy range is very small and thus it have been omitted for simplicity. 132 5.44 Crystal field splitting obtained from the GGA results, calculated in the local reference system of V1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.45 Chosen paths for the calculation of the J superexchange parameters in K2V3O8.134 5.46 3D charge density calculated in the GGA approximation. (above) the charge density is calculated for and isovalue ρ=0.005 e/˚A 3 , (below) the charge density is calculated with a smaller isovalue ρ=0.002 e/˚A 3 in order to show the small charge around the O atoms which coordinate with the non-magnetic V atoms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.47 Components of the Dzyaloshinskii-Moriya vectors in the basal plane of K2V3O8. Shown are the VO4 square pyramids and the VO5 tetrahedra. . . 137 5.48 Band structure for the AFM configuration (a) with the inclusion of SO coupling along the crystallographic axis c and (b) with the inclusion of SO along the c-axis and the on-site Coulomb repulsion U (U=4.5 eV) simultaneously. 139 5.49 Dependence of the spin and orbital magnetic moment of V1 (in units of µB) with U in the LDA+U calculation with inclusion of SO coupling. . . . . . . 140 5.50 Schematic representation of the different spin configurations studied in (a) reference [75] and (b) our model. The spheres represent the magnetic vanadium atoms with different spins (represented by different colors) . . . . . . 143 5.51 Comparison between the proposed model [75], an isolated dimer and a square lattice models with the experimental data. . . . . . . . . . . . . . . . . . . . 144 5.52 Susceptibility per site calculated with exact diagonalization for two different lattice sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.53 Susceptibility per spin calculated for the 2D square lattice without (upper panel) and with (lower panel) the extra superexchange term. . . . . . . . . 146 5.54 Comparison between theoretical and experimental specific heat results given in reference [101]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
List of Tables 4.1 Bond lengths and angles in TK91 . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 Characteristic intracluster distances (dintra (˚A)) and angles (in degrees ( ◦ )) for Cu4OCl6daca4 at T=80 K and T=340 K. Also shown a comparison of the distances between the centers of the molecules in the unit cell (dinter). . 54 5.1 Comparison of the values (given in meV) for the Cu–Cu hopping integrals calculated with the NMTO downfolding method for the relaxed CuCCP, Cu(II)-NH2 and Cu(II)-CN structures. The subscripts i= 1,2,3,7,8,12 denote the ith Cu–Cu nearest neighbors. Note that t4, t5, t6 are missing since these values are less than one hundredth of 1 meV in the calculation. See Figure 5.4. 85 5.2 Lattice parameters for the structure CuCCP and models CuCCP-H2O and CuCCP-NH3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.3 Comparison of the Cu-Cu distances between CuCCP and models CuCCP- H2O and CuCCP-NH3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.4 Values for the Cu–Cu hopping integrals calculated with the NMTO downfolding method for the relaxed CuCCP, Cu(II)-H2O and Cu(II)-NH3 structures. The values are given in meV. The subscripts i = 1, 2, 3, 7, 8, 12 denote the ith nearest neighbors. See Fig. 5.4. . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.5 Values for the Cu–Cu hopping integrals given in eV. The subscripts i= 1,2,3,denote the ith Cu–Cu nearest neighbors. Also shown the Cu-Cu distances corresponding to these paths. . . . . . . . . . . . . . . . . . . . . . . 100 5.6 Magnetic moment (µ(mB/atom)) within the muffin-tin radii (rrmt) and its % of the total moment. For the interstitial the moment is normalized per formula unit (f.u=CuO0.25Cl1.5 daca) . . . . . . . . . . . . . . . . . . . . . 103 5.7 Lattice parameters of the constructed Fe(II)-triazole structures . . . . . . . 113 5.8 Hopping parameters obtained between the Fe 3d orbitals in our constructed models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.9 Comparison between distances and angles in K2V3O8 before and after the relaxation. The labelling of the atoms is according to Figure 5.41. . . . . . 130 5.10 Comparison between the experimental and calculated hopping parameters for K2V3O8. The label of the parameters correspond to the paths showed in Figure 5.45. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 xiii
Page 1 and 2: Microscopic Modelling of Correlated
Page 3 and 4: I declare that I wrote this work my
Page 5 and 6: Abstract v description of their low
Page 7 and 8: Contents vii 5 Results and Discussi
Page 9 and 10: List of Figures ix 4.7 (above) (a)
Page 11: List of Figures xi 5.16 Cu Wannier
Page 15 and 16: List of Abbreviations 1D . . . . .
Page 17 and 18: Dedicated to Fernando-Andres Salgue
Page 19 and 20: Chapter 1: Introduction 2 are being
Page 21 and 22: Chapter 1: Introduction 4 external
Page 23 and 24: Chapter 2 Method Our understanding
Page 25 and 26: Chapter 2: Method 8 system at any t
Page 27 and 28: Chapter 2: Method 10 The functional
Page 29 and 30: Chapter 2: Method 12 and to use it
Page 31 and 32: Chapter 2: Method 14 2.2.2 Orbital-
Page 33 and 34: Chapter 2: Method 16 linearized for
Page 35 and 36: Chapter 2: Method 18 and relativist
Page 37 and 38: Chapter 2: Method 20 the fact that
Page 39 and 40: Chapter 2: Method 22 The basis func
Page 41 and 42: Chapter 2: Method 24 • If these b
Page 43 and 44: Chapter 2: Method 26 LAPW and LMTO
Page 45 and 46: Chapter 2: Method 28 2.3 An overvie
Page 47 and 48: Chapter 2: Method 30 2.4 Effective
Page 49 and 50: Chapter 2: Method 32 HSO = λ(L ·
Page 51 and 52: Chapter 3 Crystal structures of the
Page 53 and 54: Chapter 3: Crystal structures of th
Page 55 and 56: Chapter 3: Crystal structures of th
Page 57 and 58: Chapter 4 Low dimensional spin syst
Page 59 and 60: Chapter 4: Low dimensional spin sys
Page 61 and 62: Chapter 4: Low dimensional spin sys
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Chapter 4: Low dimensional spin sys
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Chapter 5 Results and Discussion 5.
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Chapter 5: Results and Discussion 7
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Chapter 6 Summary and Outlook The t
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Chapter 6: Summary and Outlook 150
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Chapter 6: Summary and Outlook 152
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Appendix A: Atomic coordinates for
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Appendix A: Atomic coordinates for
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Appendix B: Atomic coordinates for
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Appendix C Atomic coordinates for t
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Bibliography [1] F. H. Allen, O. Ke
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Bibliography 170 [34] R. C. Dickins
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Bibliography 172 [75] M. D. Lumsden
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Bibliography 174 [116] R. L. Wither
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Zusammenfasung Niedrigdimensionale
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Zusammenfasung 178 Quantenspinssyst
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Zusammenfasung 180 Clustern zeigen,
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Experience: Curriculum vitae Name:
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I would like to thank: Acknowledgme
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Microscopic Modelling of Correlated Low-dimensional Systems

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