DENSITY FUNCTIONAL THEORY AND MONTE CARLO STUDY OF CERTAIN MAGNETIC AND MULTIFERROIC MATERIALS

Abstract

The fundamental objects which cause the magnetism in the solids are the ions with unpaired electrons having non-zero magnetic moments that often manifest quite different phenomena when they are placed together and interact with each other compared to when they are isolated or non-interacting. This demonstrates the diverse nature of magnetic moment interaction (exchange interaction) that leads to the varieties of magnetic properties observed in solids. As the localized magnetic moments are an essential ingredient of magnetism in solids (particularly in insulator), electron correlation (i.e. electron-electron Coulomb interaction) plays a crucial role in stabilizing the localized moments in solids. Therefore, the magnetism and electron correlation are strongly interconnected in solids. Solids in which electron correlation is very large, called strongly correlated electronic systems (SCES), display a wide range of fascinating phenomena such as metal-insulator transition, Kondo effect, colossal magnetoresistance, high-temperature superconductivity, heavy-fermion behaviour, etc. However, understanding these SCES is not simple as the ordinary band theory, widely used to determine the electrical property of materials, fails in determining their insulating states. Thus, the first and foremost challenge is the description of their electronic structure which challenges our understanding of solids. Consistent prolonged research efforts have been made to develop new concepts to address the complex issues in SCES. However, the understanding is still in progress. Hence, studying magnetic properties of SCES is currently a topic of immense interest among researchers. In contrast to ordinary band insulators, where the band gap arises from the periodic potentials, the insulating state in SCES purely comes from the strong electron correlations. Such electron correlation was not accounted for in the band theory. In order to describe these system, we have to start from the many-body Hamiltonian which was first proposed by Hubbard in 1963 famously known as Hubbard Hamiltonian or Hubbard Model. Materials consisting of ions with partially filled d-orbitals such as in transition metal based compounds or partially filled f-orbitals as in Rare-earth based compounds fall under the SCES due to the narrow bands of d- and f-states causing strong electron-electron interaction. The scope of this thesis also falls broadly in to this topic where we have studied electronic structure and magnetic properties of certain SCES as discussed below to understand the underlying mechanism behind certain experimental observations reported in the literature in these systems. This thesis is focused primarily on the understanding the mechanism behind certain magnetic phenomena such as non-collinear magnetic order, spin reorientation etc. in some transition metal based compounds which contain strongly correlated d-bands. Systems considered in our work involve both frustrated and non-frustrated lattice geometries. Computational techniques such as density functional theory (DFT) and Monte-Carlo (MC) are employed to study both zero ii temperature as well as finite temperature properties. Through our study we reveal very fascinating interplay among various degrees of freedom such as spin, orbital and lattice in our chosen systems giving rise to very interesting complex magnetic behaviour. For our study presented in this thesis we have considered spinel vanadate CoV2O4, oxygen deficient layered perovskite compound YBaCuFeO5 and two other perovskites such as LaVO3 and LaTiO3. To probe the electronic structure and magnetic ground state, we have used density functional theory (DFT), a first-principles approach, for our studies. DFT codes like VASP, WIEN2K, and ELK have been utilized for our calculations. While VASP uses psuedopotential+ plane wave method, both WIEN2K and ELK codes use full potential linearized augmented plane wave method. We have used various approximations within the framework of DFT such as LSDA, LSDA+U, LSDA+U+SO, GGA, GGA+U and GGA+SO+U. In addition to the firstprinciples DFT approach, we have also employed the probabilistic approach (Monte-Carlo method) to study the thermodynamics of our systems. For this we have developed our in-house Monte Carlo (MC) codes Ether for our studies. Code ‘Ether’ has the capability to perform the MC simulations on any lattice network (including frustrated networks like pyrochlore lattice). Further, we have also developed various post-processing tools to analyze our observed MC data.