Kumari, Spriha
(2019)
*Study of Electronic Structure of 3d and 5d Transition Metal Compounds.*
PhD thesis, lndian Institute of Science Education and Research Kolkata.

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## Abstract

Transition metal oxides (TMOs ) constitutes various compounds with a wide range of unique and fascinating electronic properties such as metal-insulator transitions (MIT), low dimensionality, periodic lattice distortion, superconductivity and many more. The root cause of these complex properties is partially filled d or f bands of transition metal cations. These partially filled d band materials are referred to as strongly correlated systems because of strong electron correlation that arises due to narrow d band. To understand the physics of TMOs, this thesis is primarily focused on studying their underlying electronic structure by theoretical calculations along with spectroscopic studies. Among all the interesting properties, MIT in these systems has attracted a lot of attention because of its fundamental importance as well as technological applications. In this thesis, we mainly concentrated on 3d and 5d transition metal compounds and studied the electronic structure of various TMOs and tungsten bronzes. Among various TMOs, I have studied the electronic structure of perovskite (ABO₃type structure) vanadium (V) and titanium (Ti) oxides with the partially filled 3d band. Strong electron correlation due to narrow d band and disorder effect due to random potential are two main cause of MIT in our 3d systems. MIT due to strong electron correlation is known as Mott-Hubbard transitions whereas, MIT due to disorder fall under the category of Anderson transitions. We have chosen our systems where the correlation strength increases from correlated metals to Mott-Hubbard type insulators. In bronzes, we have investigated the electronic structure of sodium tungsten bronzes and phosphate tungsten bronzes. These materials are called bronze because of the metallic luster of tungsten compounds. Electronic structure of sodium tungsten bronzes is studied with oxygen vacancy defects to understand the discrepancy in experimental band structure determined by angleresolved photoemission spectroscopy (ARPES). On the other hand, phosphate tungsten bronzes are low dimensional systems, which show unusual physical properties. These strongly correlated and low dimensional systems have always been at the frontier research in solid state physics. Low dimensional systems have a strong structural anisotropy, which can be seen from their transport properties and they exhibit unusual physical properties, such as anomalous magnetic properties, metal-insulator, and metal-metal transition, periodic lattice distortion, and charge density wave phase (CDW) transition etc.. We have examined the electronic structure of monophosphate tungsten bronzes with pentagonal tunnels (MPTBp) and monophosphate tungsten bronzes with hexagonal tunnels (MPTBh) to understand the observed anomaly in its transport properties. There are few basic differences in terms of crystal structure between MPTBh and MPTBp. In MPTBh the junction between two octahedral layers, the octahedra and tetrahedra corner share to form hexagonal tunnels, where the A cations are placed. The symmetry of such kind of structure is dependent on the A cation and doping, x value. In MPTBp the octahedral strings are connected together by PO₄ tetrahedra in a zig-zag fashion, while in MPTBh these strings remain parallel from one ReO3 type layer to the next layer. CDW explains the electronic aspects of structural stability and in the CDW phase, the structural distortion is stabilized by the opening of energy gaps at the Fermi level, which lowers the total energy of the system. This gap is a consequence of the periodicity of the distortion, and so the CDW optimally occurs at a wave vector, which nests large parts of the Fermi surfaces (FSs). It has been found that most CDW states are derived from nesting of the Fermi surfaces (FSs). These fascinating materials open up new opportunities for research and therefore to understand the rich physics and the origin of various interesting physical properties of TMOs and bronzes, the study of the electronic structure of these systems is of extreme importance from both fundamental and technical point of view. The electronic structure of these TMOs and bronzes has been studied by both angle-integrated and angle-resolved photoemission spectroscopy (ARPES). I have also performed theoretical electronic band structure calculations using ab-initio full-potential linearized augmented plane-wave (FP-LAPW) method within density functional theory (DFT) framework. I have synthesized polycrystalline samples by solid state reaction route in our laboratory and characterized them using x-ray diffraction (XRD) and followed by Rietveld refinement. For a detailed and better understanding, I have analyzed the experimental results and compared with our theoretical calculations. The present thesis has been divided into eight chapters. Chapter 1 presents a general introduction about the transition metal oxides and bronzes which includes their crystal structure, various properties, and applications. I have discussed the theory of metals and insulators in band picture as well as in the context of Hubbard model. I have also described the metal-insulator transition phenomena and discussed three different models of MIT relevant to our study namely Mott Hubbard, Anderson and Peierls transitions. In the last part of this chapter, I have given a brief introduction about all the works carried out in the course of this thesis. Chapter 2 includes various experimental methods employed to study the electronic structure of TMOs and bronzes. Here, I explained the solid state synthesis route used to prepare polycrystalline samples reported in this thesis. In order to characterize the samples, we have used the XRD technique and hence I have described the basic principle and experimental setup of XRD at IISER Kolkata. The basic principle of resistivity is also discussed. The final section of this chapter describes the theory of photoemission spectroscopy (PES) including both angleintegrated and angle-resolved photoemission spectroscopy. A general introduction about photoemission experimental setup is also given in this chapter. I have also briefly described the photoemission setup at TLS-21B1 beamline, NSRRC synchrotron, Taiwan and APE beamline, Elettra synchrotron, Italy where we have performed the photoemission experiments. Brief theory of electronic structure calculations has been given in Chapter 3, which includes basic principle for the tight binding method and density functional theory used to calculate theoretical band structure, the density of states (DOS) and Fermi surfaces. In Chapter 4, we have investigated the electronic structure of strongly correlated TMOs having 3d¹ electronic configuration namely SrVO₃, CaVO₃ and YTiO₃. SrVO₃ and CaVO₃ are strongly correlated metals whereas YTiO₃ is a Mott-Hubbard insulator with a band gap of ~ 0.7eV. The magnetic ground state of YTiO3 is ferromagnetic with Tc = 30 K. We have performed the ab-initio all-electron FP-LAPW band-structure calculations within DFT framework to understand the electronic structure of these systems. Our GGA calculation well explained the metallic ground state of SrVO₃ and CaVO₃ however it failed to give the correct insulating ground state of YTiO₃. YTiO₃ turns out to be metallic in GGA calculation. To get the correct insulating ground state of YTiO3 we have introduced electronic (U) and exchange (J) correlation energy in our GGA calculation. We have performed various GGA+U calculation with a systematic variation of both U and J correlation energy parameters. A series of calculation with different Ueff (U-J) in GGA+U approximation has been carried out to understand the effect of electron correlation on the electronic structure. GGA+U calculation with optimized U and J values succeeded in describing the insulating electronic structure and the correct ferromagnetic ground state of YTiO₃. We have also tried to understand the effect of disorder on the strongly correlated system by doping titanium (Ti) in CaVO₃ compound i.e. CaV(₁−x)TixO₃. In this system, both disorder and electron correlation are present simultaneously. The one end member, CaVO₃ is a strongly correlated metal, whereas the other end member, CaTiO₃ is a band insulator and Ti doping in CaVO3 leads to the substitution of Ti(4+) for V(4+), which perturbs the periodic potential of the narrow π* band and introduces strong disorder in the system. It has been found that CaV(₁−x)TixO₃ shows metal-insulator transition at x ~ 0.2. We have performed the photoemission experiments on CaV(₁−x)TixO₃ (x = 0, and 0.2) to investigate the effect of disorder in this compound. We have also varied the incident photon energy to understand the surface and bulk electronic structures of these systems. Electronic structure of strongly correlated transition metal compounds is largely influenced by the influence of electron correlation energy (U) and exchange-correlation energy (J) as explained before. In Chapter 5, we have studied the electronic structure of strongly correlated transition metal compounds with 3d² electronic configuration. i.e. RVO₃ (R = La and Y) using FP-LAPW method within DFT. It has been found that both LaVO3 and YVO₃ are Mott- Hubbard insulators with a band gap of 1.1 eV and 1.2 eV, respectively. To understand the role of U and J on the electronic structure of these two compounds, we have performed various DFT calculations with GGA and GGA+U formalism. Electronic band structure calculated with generalized gradient approximation (GGA) formalism shows metallic character for both the compounds. Hence in order to obtain the correct insulating ground state of LaVO₃ and YVO₃ we have approached the GGA+U formalism and to get the optimal U value for the onsite coulomb potential, we have performed a series of GGA+U calculations by varying the Ueff (the difference between U and J) parameter keeping J fixed. By keeping the Ueff value fixed obtained from the above procedure we have also varied the exchange parameter J, (though not as strong as that of U) keeping Ueff fixed to see its influence on the band gaps of LaVO₃ and YVO₃. Our GGA+U approach has succeeded in describing the correct ground state yielding insulating band structures for both LaVO₃ and YVO₃ and we see that both the U and J have a great impact on the electronic structure of these two compounds. We also tried to understand the ground state spin ordering of these compounds by calculating the total energy in various antiferromagnetic (AFM) configurations with GGA+U formalism using our optimized U and J values. LaVO₃ has C-type AFM ordered state below 140 K, whereas YVO₃ has G-type AFM ordered state below 77 K. We calculated the total energy per unit formula for various AFM configurations i.e. C-type, A-type, and G-type. In the next two chapters of this thesis, we focused our attention on transition metal oxide bronzes namely sodium tungsten bronzes and phosphate tungsten bronzes. In Chapter 6, I have investigated the electronic structure of tungsten bronzes, WO3 and sodium tungsten bronzes, NaxWO₃. This alkali-doped tungsten bronze shows many interesting chemicals, electrical and optical properties which can lead to various technological applications. When Na is doped into WO₃ lattice it shows very interesting optical and electronic properties. At the same time the room temperature crystal structure of NaxWO₃ changes from monoclinic, to orthorhombic, to tetragonal, and finally to cubic with increasing x. Additionally, NaxWO₃ undergoes an MIT when Na is doped into the WO₃ lattice. It becomes nonmetallic for low Na-doping and metallic for x ≥ 0.25. We have studied the electronic structure of tungsten bronzes, WO₃ and sodium tungsten bronzes NaxWO₃ with oxygen vacancy defects to understand the discrepancy in experimental ARPES band structure and theoretical band calculations. The main objective of this research work has been focused on the investigation of the effect of oxygen vacancy in WO₃ and NaxWO₃. In order to investigate the role of oxygen vacancies in WO₃ and NaWO₃, we have performed extensive ab-initio self-consistent electronic-structure calculations on WO₃ and NaWO₃ with single- and double-oxygen-vacancy defects within the generalized gradient approximation (GGA) formalism of density functional theory. The density of states of WO₃ and NaWO3 with single and double oxygen vacancy defects shows in-gap states and the energy positions of the in-gap states are sensitive to the oxygen vacancy concentrations. The evolution of the induced states occurs from the unpaired electrons donated by the oxygen vacancy. In case of NaWO₃, the in-gap states are formed close to the valence band, which are pushed towards the conduction band with the increase in oxygen vacancies, whereas in WO₃ system the states are formed mostly in the mid-gap region. Hence, this work well explained the discrepancy in experimental band dispersion measurements from ARPES with that of theoretical band calculations of WO₃ and NaWO₃. The families of Phosphate tungsten bronzes are quasi-low dimensional systems and form tunnel structures. These quasi-low-dimensional systems show interesting exotic physical properties, which are often characterized by CDW mechanism. In Chapter 7, we have devoted our attention to the study of quasi-low dimensional systems and presented the result of our study on monophosphate tungsten bronze using ARPES. We have investigated the electronic structure of m = 4 members of monophosphate tungsten bronzes with pentagonal tunnels (MPTBp) i.e. of P₄W₈O₃₂. P₄W₈O₃₂ has an orthorhombic crystal structure and the structure of this compound is built up of WO₆ octahedra which form ReO₃ type slabs and these slabs are interconnected to each other by PO₄ tetrahedra such that pentagonal tunnels are created at the junction. We have also investigated the electronic structure of monophosphate tungsten bronzes with hexagonal tunnels (MPTBh) for m = 4, A = Na and x = 1.6 i.e. Na₁.₆ P₄W₈O₃₂. Na₁.₆ P₄W₈O₃₂ has a monoclinic crystal structure. These compounds show anomalies in their electrical resistivity which indicates the existence of electronic instabilities. Our theoretical calculations show that the pentagonal P₄W₈O₃₂ structure is more stable and exists in reality due to the lowest ground state energy of pentagonal- over hexagonal- tunnel structure. However, the monophosphate tungsten bronzes with hexagonal tunnels (MPTBh) structures become stable with Na doping. We have measured experimental ARPES spectra at different temperatures of the hexagonal tunnel- Na₁.₆ P₄W₈O₃₂. The experimentally determined band dispersion has an overall fair agreement with our theoretical band calculations. We have also calculated the FSs for the pentagonal tunnel- P₄W₈O₃₂ and hexagonal tunnel- Na₂P₄W₈O₃₂ which elucidate the origin of an anomaly in the transport properties of such systems. We found flat regions with hole pockets around X point of Brillouin zone in the calculated FSs which can be nested to establish the CDW states in these systems. Measurements carried out on the hexagonal tunnel- Na₁.₆ P₄W₈O₃₂ at different temperatures show a depletion of the density of electronic states below the anomaly temperature of 90 K at band crossing points. Our experimental ARPES results suggest that the possible CDWs associated with the incommensurate nesting vector(s) are largely responsible for the anomalous transport properties in the hexagonal tunnel- Na₁.₆ P₄W₈O₃₂. At final, Chapter 8 summarizes the whole research work along with the conclusions of all results carried out in this thesis.

Item Type: | Thesis (PhD) |
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Additional Information: | Supervisor: Dr. Satyabrata Raj |

Uncontrolled Keywords: | 3d Transition Metal Compounds; 5d Transition Metal Compounds; Electronic Structure; Hexagonal Phosphate Tungsten Bronzes; Pentagonal Phosphate Tungsten Bronzes; Sodium Tungsten Bronze; Transition Metal Compounds |

Subjects: | Q Science > QC Physics |

Divisions: | Department of Physical Sciences |

Depositing User: | IISER Kolkata Librarian |

Date Deposited: | 28 Jun 2019 11:13 |

Last Modified: | 28 Jun 2019 11:14 |

URI: | http://eprints.iiserkol.ac.in/id/eprint/828 |

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