Microscopic modelling of correlated low-dimensional systems [Elektronische Ressource] / von Lady-Andrea Salguero

Sujets

• Physik

Informations

• Publié par: goethe_universitat_frankfurt_am_main
• Publié le: 01 janvier 2009
• Nombre de lectures: 15
• Langue: English
• Poids de l'ouvrage: 31 Mo

Extrait

Microscopic Modelling of Correlated
Low-dimensional Systems
Dissertation
zur Erlangung des Doktorgrades
der Naturwissenschaften
vorgelegt beim Fachbereich Physik
der Johann Wolfgang Goethe-Universit at
in Frankfurt am Main
von
Lady-Andrea Salguero
aus Kolumbien
Frankfurt, 2009
D30vom Fachbereich Physik der
Johann Wolfgang Goethe-Universit at als Dissertation angenomen
Dekan: Prof. Dr. Dirk-Hermann Rischke
Gutachter: Prof. Dr. Maria-Roser Valent
Prof. Dr. Michael Lang
Datum der Disputation: 21 January 2009Abstract
The characterization of microscopic properties in correlated low-dimensional materials is
a challenging problem due to the e ects of dimensionality and the interplay between the
many di erent lattice and electronic degrees of freedom. Competition between these factors
gives rise to interesting and exotic magnetic phenomena. An understanding of how these
phenomena are driven by these degrees of freedom can be used for rational design of new
materials, to control and manipulate these degrees of freedom in order to obtain desired
properties. In this work, we study these e ects in materials with small exchange interaction
between the magnetic ions such as metal-organic and inorganic dilute compounds. We
overcome the di culties in studying these kind of materials by combining classical and
quantum mechanical ab initio methods and many-body theory methods in an e ective
theoretical approach. To treat metal-organic compounds we elaborate a novel two-step
methodology which allows one to include quantum e ects while reducing the computational
cost. We show that our approach is an e ective procedure, leading at each step, to additional
insights into the essential features of the phenomena and materials under study.
Our investigation is divided into two parts, the rst one concerning the exploration of the
fundamental physical properties of novel Cu(II) hydroquinone-based compounds. We have
studied two representatives of this family, a polymeric system Cu(II)-2,5-bis(pyrazol-1-yl)-
1,4-dihydroxybenzene (CuCCP) and a coupled system Cu S F N O (TK91). The second2 2 6 8 12
part concerns the study of magnetic phenomena associated with the interplay between
di erent energy scales and dimensionality in zero-, one- and two-dimensional compounds.
In the zero-dimensional case, we have performed a comprehensive study of Cu OCl L4 6 4
with L=diallylcyanamide=NC-N-(CH -CH=CH ) (Cu OCl daca ). Interpretations of2 2 2 4 6 4
the magnetic properties for this tetrameric compound have been controversial and incon-
sistent. From our studies, we conclude that the common models usually applied to this
and other representatives in the same family of cluster systems fail to provide a consistent
ivAbstract v
description of their low temperature magnetic properties and we thus postulate that in such
systems it is necessary to take into account quantum uctuations due to possible frustrated
behavior.
In the one-dimensional case, we studied polymeric Fe(II)-triazole compounds, which are
of special relevance due to the possibility of inducing a spin transition between low and
high spin state by applying a external perturbation. A long standing problem has been a
satisfactory microscopic explanation of this large cooperative phenomenon. A lack of X-ray
data has been one mitigating reason for the absence of microscopic studies. In this work,
we present a novel approach to the understanding of the microscopic mechanism of spin
crossover in such systems and show that in these kind of compounds magnetic exchange
between high spin Fe(II) centers plays an important role.
The correct description of the underlying physics in many materials is often hindered by
the presence of anisotropies. To illustrate this di culty, we have studied a two dimensional
dilute compound K V O which exhibits an unusual spin reorientation e ect when applying2 3 8
magnetic elds. While this e ect can be understood when considering anisotropies in the
system, it is not su cient to reproduce experimental observations. Based on our studies
of the electronic and magnetic properties in this system, we predict an extra exchange
interaction and the presence of an additional magnetic moment at the non-magnetic V site.
This sheds a new light into the controversial recent experimental data for the magnetic
properties of this material.Contents
1 Introduction 1
2 Method 7
2.1 Describing the properties of matter . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Density Functional Theory (DFT) . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Approximations to the Exchange-Correlation energy functional . . . 13
2.2.2 Orbital-dependent functionals: LDA+U method . . . . . . . . . . . 15
2.2.3 Solving the DFT equations: The LAPW and LMTO methods . . . . 16
2.2.4 NMTO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.5 Advantages and disadvantages: LAPW vs. LMTO . . . . . . . . . . 25
2.2.6 Obtaining physical quantities with DFT . . . . . . . . . . . . . . . . 27
2.3 An overview on classical ab initio and molecular dynamics . . . . . . . . . . 29
2.3.1 The DREIDING force eld methods . . . . . . . . . . . . . . . . . . 29
2.3.2 Car-Parinello molecular dynamics . . . . . . . . . . . . . . . . . . . 30
2.4 E ective models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.1 Tight-binding and Hubbard Hamiltonian . . . . . . . . . . . . . . . 31
2.4.2 Spin Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3 Crystal structures of the studied compounds 35
3.1 Triclinic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Monoclinic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Tetragonal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 Low dimensional spin systems 41
4.1 Metal-organic frameworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 1,4-hydroquinone ligands bridging Cu(II)-ions . . . . . . . . . . . . . . . . . 44
4.2.1 CuCCP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.2 TK91 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Competing interactions in low dimensional systems . . . . . . . . . . . . . . 53
4.3.1 ‘Zero-dimensional’ system with frustration . . . . . . . . . . . . . . 53
4.3.2 Spin-Crossover in One-dimensional chains . . . . . . . . . . . . . . . 58
4.3.3 Magnetic anisotropies in a 2D-system . . . . . . . . . . . . . . . . . 66
viContents vii
5 Results and Discussion 73
5.1 Preparation of reliable structures for ab initio calculations . . . . . . . . . . 73
5.2 New class of quantum magnets based on 1,4-hydroquinone ligands . . . . . 76
5.2.1 Geometry relaxation of CuCCP . . . . . . . . . . . . . . . . . . . . . 76
5.2.2 Cu(II)-NH and Cu(II)-CN polymers . . . . . . . . . . . . . . . . . . 822
5.2.3 Cu(II)-H O and Cu(II)-NH . . . . . . . . . . . . . . . . . . . . . . 882 3
5.2.4 TK91 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3 Magnetic phenomena in zero-, one- and two-dimensional compounds . . . . 104
5.3.1 Cu OCl daca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044 6 4
5.3.2 Fe(II)-triazole polymers . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.3.3 K V O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1292 3 8
6 Summary and Outlook 150
A Atomic coordinates for the relaxed CuCCP-based structures 156
B Atomic co for the obtained Fe[CH trz] 1603
C Atomic coordinates for the relaxed K V O compound 1692 3 8
Bibliography 171
List of publications 178
Zusammenfassung 179
Curriculum vitae 185
Acknowledgements 187List of Figures
2.1 Schematic representation of the division of the unit cell done in APW/LAPW
method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Atomic Sphere Approximation (ASA) in which the mu n tin spheres are
chosen to have the same volume as the Wigner-Seitz cell, which leads to
overlapping spheres [77]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1 Representation of a Triclinic unit cell. . . . . . . . . . . . . . . . . . . . . . 36
3.2 The Brillouin zone for a triclinic lattice. In it are shown high symmetry
points: = (0 ; 0; 0), F=(0; 1=2; 0), B=(1=2; 0; 0) and G=(0; 0; 1=2), in units
of (=a, =b, =c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Representation of a primitive monoclinic unit cell. . . . . . . . . . . . . . . 38
3.4 The rst Brillouin zone for a monoclinic lattice. The high symmetry points
chosen in this work are: = (0 ; 0; 0), Y=(0; 1=2; 0), B=(1=2; 0; 0) and
Z=(0; 0; 1=2), in units of (=a, =b, =c). . . . . . . . . . . . . . . . . . . . . 38
3.5 Representation of a primitive tetragonal unit cell. . . . . . . . . . . . . . . . 39
3.6 Schematic representation of the rst Brillouin zone of a primitive tetra-
gonal cell. The high symmetry points chosen in this work are =
(0; 0; 0), Z=(0; 0; 1=2), R=(0; 1=2; 1; 2), A=(1=2; 1=2; 1=2), X=(0; 1=2; 0),
M=(1=2; 1=2; 0) and X=(0; 1=2; 0), in units of (=a, =b, =c). . . . . . . . . 40
4.1 Quinoid linkers: (a) hydroquinone, (b) p benzoquinone, (c)
o benzoquinone. The gure (d) shows a pyrazole ring, which together with
the hydroquinone, is one of the constitue