ELECTRONIC STRUCTURE ABD MAGNETIC PROPERTIES OF CERTAIN STRONGLY CORRELATED LAYERED SYSTEMS

Abstract

Both theoreticians and experimentalists have always been curious about knowing the electronic behavior in solids. Usual band theory of solids [1] was the biggest achievement in solid state physics which could best explain the electronic properties of solids. Band theory is based on the fact that in a solid, the individual atomic orbitals overlap to form energy bands separated by band gaps. This theory could beautifully explain the division of solid state materials into metals, semiconductors and insulators [1–3]. For example, if highest occupied band is partially filled, the material would exhibit metallic behavior whereas if the same is completely filled, the material would be insulating. Even though this theory was tremendously successful in explaining a number of metals, semi-metals, semiconductors and insulators, there was a class of materials for which band theory was found to be inadequate. This new class of materials is known as strongly correlated electronic systems. These are narrow band systems with partially filled d or f shells in which on-site electron-electron Coulomb repulsion is significantly higher than that in the large bandwidth materials. Due to the strong on-site electron-electron Coulomb repulsion (or correlations) even the materials containing half filled bands behave as insulators which otherwise as per band theory should behaved as good metals. These strongly correlated systems exhibit a large number of exotic properties such as high Tc superconductivity [4–7], colossal magneto resistance [8–10], heavy fermionic behavior [11–14], metal-insulator transition without disorder [15,16], charge, orbital and magnetic orders [17, 18] and many more. The widely used theoretical models such as tight binding approximation [1, 2], Hartree-Fock approximation [19], and local density approximation [20,21] successfully explained the materials which are not strongly correlated. However, these models failed to explain the electronic properties of strongly correlated electronic systems. New theoretical model which considers strong electron correlations explicitly were supposed to accurately describe the electronic and magnetic properties of such systems. Mott hypothesis [22] was the first theoretical approach which brought in the concept of electron correlations. Hubbard model [23–26], Falicov Kimball Model [15, 16], periodic Anderson lattice model etc. which followed Mott’s hypothesis gave the mathematical formulation of electron correlations in the form of a model Hamiltonian which could be used under various approximations to understand the electronic properties of these systems. Currently the most widely used first principles method for electronic band strcuture calculations of solids is density functional theory (DFT) [21] which has also incorporated the electron correlations (i.e. LDA+U) in an approximate way. Very recent development of dynamical mean field theory (DMFT) [27] is a state of the art theoretical technique which is being applied to various correlated systems with remarkable success. Though DFT-based methods consider electron correlations in an approximate way, they usually give accurate estimates for a number of physical and chemical properties of such systems in their ground states. Properties such as electronic band structure, density of states, elastic constants, dielectric functions, ground state magnetic and orbital order etc. match with the experimental observation quite well [28]. In density functional theory, Kohn-Sham ansatz [29] technique is the most widely used one for solving the many body Hamiltonian of the system. Among the large number of strongly correlated electronic systems, some of the most widely studied ones are the layered materials such as cuprate superconductors [30], bilayer manganites [31] etc. In these layered systems the two dimensional transition metal oxides layers play a crucial role in governing the physical properties. The two dimensional layers formed by the transition metal ions can have bipartite as well as non bipartite lattice (i.e. square lattice and triangular lattice). Transition metal layer in cuprates [32] and nickelates [33] form two dimensional square lattice whereas in NaTiO2 [34, 35] and NaVO2 [36,37], NaCrS2 [38] etc., transition metal layers form two dimensional triangular lattice. In triangular lattice systems containing transition metal ions, in addition to correlations there exists geometrical frustration (GF). GF [39] arises when all the nearest neighbor magnetic interactions are not satisfied. GF is not only limited to two dimensional layered systems, the phenomenon may also happen in three dimensional structure such as magnetic spinel compounds with pyrochlore lattice [17, 18, 40, 41]. Generally, frustration is caused either by competing interactions or by the geometry of the compounds [42,43]. It may exist both in bipartite lattice as well as in non-bipartite lattice. These systems are studied with particular interest because they give rise to a large number of degenerate ground states such as spin/orbital liquid states. To remove the GF, crystal structure often distorts itself to lower the symmetry. Orbital degree of freedom can also play very important role in removing the GF leading to orbital order [35, 36, 44]. Orbital ordering is analogous to magnetic ordering. The only difference is that in orbital ordering we consider the ordering of orbitals instead of spins. Orbital ordering may occur because of Jahn-Teller distortion or by electronic super-exchange phenomena. In the present thesis, the work is mainly done on the strongly correlated layered compounds having triangular lattice and square lattice. First principle density functional theory calculations have been performed to study various physical properties such as magnetic order, orbital order, metal-insulator transition etc. of triangular lattice compounds NaTiO2 [34], NaVO2 [36], NaMnO2 [45, 46], NaNiO2 [47]. Full potential linearized augmented plane wave method as implemented in WIEN2K code [48] was used for these calculations. There are certain layered materials such as manganites, GdI2 etc. where it has been found from experiments and previous theoretical studies [49, 50] that they contain two types of electrons: itinerant and localized. In these type of materials, the origin of many interesting phenomena such as metal-insulator transition, charge, orbital and magnetic orders etc. is associated with a strong interaction between itinerant and localized electrons. Therefore, it has been proposed that the low energy physics of these systems can be studied using Falicov-Kimball model. A part of the present thesis is devoted to study the ground state properties of the Falicov-Kimball model for compounds having square lattices using numerical technique such asMonte-Carlo on a finite size lattice with periodic boundary condition. The present thesis consists of six chapters. Brief outline of each chapter is described below. Chapter 1 This chapter is mainly devoted to the introduction of strongly correlated electronic systems like layered transition metal oxides. We have discussed in this chapter, what is strong correlations and how these materials such as transition metal oxides differ from other layered materials such as graphene which are not strongly correlated. We have also given a brief introduction to geometric frustration, as the main part of the thesis is devoted to study systems where both strong correlations and geometrical frustration are present. To study the electronic and magnetic properties of these compounds in detail, we have used DFT calculations. We have, therefore, briefly discussed the theoretical background of DFT. In this theory, to solve Hamiltonian of many body problem of a solid, various approximations are used. We have done a brief review of these approximations such as local spin density approximation (LSDA), generalized gradient approximation, LSDA+U etc. which are used to model the exchange correlation functional [21]. The basis set considered in our calculations consists of linearized augmented plane waves [51]. We have also discussed its advantages over augmented plane wave basis. Another important theoretical model to study strongly correlated compounds containing both itinerant and localized electrons is Falicov-Kimball model which we have studied in the later part of this thesis for layered materials having square lattices. Therefore, we have included a brief review of Falicov-Kimball model and previous theoretical results reported in literature. Details of the numerical technique used by us for our calculations are also discussed. Chapter 2 Recently McQueen et al. [36] have observed that there exist two successive orbital order transitions in NaVO2. On the basis of their experimental observations on NaVO2, McQueen et al. have proposed possible orbital order in the low temperature monoclinic phase of NaTiO2 as this compound also undergoes a similar structural transition as NaVO2. The high resolution neutron diffraction patterns show that NaTiO2 has rhombohedral symmetry in its high temperature phase. As the temperature is lowered, there is a phase transition from high temperature rhombohedral phase with space group R¯3m to low temperature monoclinic phase with space group C2/m. In view of the recent experimental predictions, we have studied in the present chapter, the nature of orbital ordering in low temperature monoclinic phase of NaTiO2, using density functional theory calculations. The orbital order observed in our calculations in the low temperature structure of NaTiO2 is found to be consistent with the predictions of McQueen et al. The low temperature phase is also found to be metallic within LSDA+U which is also consistent with the experimental observations on NaTiO2. An LDA plus dynamical mean-field calculation showed considerable transfer of spectral weight from the Fermi level but no metal-insulator transition, confirming the bad metallic behavior observed in transport measurements [52]. Chapter 3 This chapter is mainly devoted to the high temperature rhombohedral phase of NaTiO2. Previous theoretical calculation predicted this system to be insulating whereas experimental observations indicate a bad metallic state. Also as discussed above, geometrical frustration in this compound may lead to degenerate ground states. If such states are accessible by tuning an external parameter such as pressure, temperature or magnetic field, one can consider using the system as a switch or memory device in spintronics/ electronics applications. Our first principle DFT calculations on the high temperature phase of layered triangular lattice system NaTiO2, which is discussed in this chapter, have revealed that there exist competing electronic states which are very close by in energy. We have observed the presence of two distinct electronic states in this system; one is insulating with a1g orbital fully occupied and the other is metallic with partially occupied doubly degenerate eg ′ orbitals. We observed that the system can make transitions between these two electronic states at room temperature via distortions of the oxygen octahedra. It has also been observed from our calculations that over a reasonably large range of U (correlations) values there exist such competing electronic states. On the basis of these observations, a possible explanation for the anomalous specific heat jump at the structural transition is discussed in terms of orbital fluctuation [53]. Chapter 4 In this chapter, we have done the comparative study of the electronic structure and magnetic properties of certain other layered transition metal oxides which are iso-structural to NaTiO2. NaVO2, NaMnO2 and NaNiO2 are all such compounds from the same family, where structural transition from high temperature rhombohedral phase to the low-temperature monoclinic phase occurs. In view of the recent experiments by McQueen et al. and the proposed orbital orders for NaVO2, we have calculated the electronic structures of this compound in its high, intermediate and low temperature phases. We estimated the energy scales of trigonal and tetragonal distortions and studied the orbital orders in low and intermediate temperature phase. We have compared our results with those predicted from experiments and with that of NaTiO2. We have also studied the ground state magnetic properties of NaVO2, NaMnO2 and NaNiO2. Various energy scales such as crystal field splitting, Jahn-Teller splitting, exchange splitting etc. are estimated and compared for these systems [54]. Chapter 5 In this chapter, we have studied spinless Falicov-Kimball model for layered materials having square lattices away from half filling. We have used exact numerical diagonalization technique with Monte Carlo algorithm to study the ground state phase diagram of spinless Falicov-Kimball model for more than half filling and less than half filling limits. In present chapter we present the effect of electron correlation on ground state phase diagram. Depending on the value of correlations U and the filling of localized f-electrons and itinerant d- electrons, we have observed various ordered phases formed by the localized electrons such as diagonal, axial-stripe and segregated phases [55].