Investigation of structural, electronic and magnetic properties of spinels by using density functional theory (PhD)

Abstract

The aim of the thesis is to study the structural, electronic and magnetic properties of spinels by using ab initio electronic structure calculations. In our research, we have applied density functional theory (DFT), DFT+U and DFT+dynamical-mean-field (DMFT) methods to resolve the various fundamental issues reported experimentally and theoretically in V and Cr spinels. The present thesis is divided into seven chapters. In chapter one, we discuss the basic physics that is required tounder stand the materials understudy, these are (i) historical aspects and structure of spinel compounds, (ii) details of strongly correlated materials including the definition of geometrical frustration and its effect on physical properties, (iii) crystal field splitting and Jahn-Teller effect in transition metal oxides, (iv) importance of orbital and spin degrees of freedom in deciding the various phenomena observed in the strongly correlated systems, (v) methods of calculating orbital ordering (OO) in these materials and describe the detailed issues of structural, electronic and magnetic properties of V and Cr spinels that are the subject of present thesis. After this chapter, we discuss a brief theoretical background of electronic structure calculations based on DFT, DFT+U and DFT+DMFT approaches along with the relevant computational methods in chapter two. Chapter three explains the OO and cubic to tetragonal distortion in V and Cr spinels. In this chapter, we first study the long issue related to the OO in V spinels by using density matrices of V atoms computed in DFT+U method. In the absence of spin-orbit coupling (SOC),we have predicted the anti-ferro OO in the global (local octahedral) coordinate system where dxz and dyz (dxz+dyz anddxz- dyz) or bitals are mainly occupied at the neighboring V sites for all the compounds. Then, we apply the spin unpolarized DFT calculations to understand a contentious issue of cubic to tetragonal distortion in V and Cr spinels and found that the main cause for such a distortion in these spinels are the effect of ionic sizes. The role of orbital degrees of freedom in investigating the magnetic properties of geometrically frustrated V spinels are discussed in chapter four,using DFT+U+SOC calculations. In this chapter, we address the issue related to the in consistency about the degree of geometrical frustration in these spinels, which arises from the two experimental results: (i) frustration indices and (ii) magnetic moments. The inclusion of the orbital and spin angular momentafor calculating the frustration indices improve the understanding about the degree of geometrical frustration in these compounds. As compared to ZnV2O4, the calculated values of the frustration indices (fJ) are largest for MgV2O4 and smallest for CdV2O4 for 3.3≤ U ≤5.3 eV. In this range ofU, we have also found the calculated values of∆M2=Mtotal-Mexp (where, Mtotal=Mspin-|Morbital|) to be largest for MgV2O4 and smallest for CdV2O4. Hence, the consistency about the degree of geometrical frustration, which arises from the fJ as well asfromthe∆M2 is achieved and improves the understanding about the degree of geometrical frustration in these compounds. In chapter five, we investigate the applicability of the DFT+U method in understanding the electronic and magnetic properties of a geometrically frustrated V and Cr compounds, where the delicate balance of electrons,lattice,orbital and spininter actions play an important role in deciding its physical properties. Firstly, we describes the limitations of unconstrained (normal) DFT+U method in predicting the electronic and magnetic ground state of a geometrically frustrated ZnV2O4 compound. Our work clearly suggests that the unconstrained DFT+U calculations are not the correct methods for predicting the experimentally observed anti-ferromagnetic ground state of this system, while constrained DFT+U calculations give it for wide parameter range of U. Hence, it is suggested that the constrained DFT+U calculations should be preferred, if one wants to predict the real magnetic ground state of an unknown complex system, as small change in the magnetic moments of magnetic atoms in various spin configurations may lead to the prediction of wrong ground state of the compound. Secondly, we apply constrained DFT+U method to understand the inconsistency reported by Yaresko in the theoretically estimated sign of nearest neighbour exchange coupling constant (i.e. Curie-Weiss temperature) and variation of its magnitude with increasing U in Cr spinels and found that such inconsistency is resolved by using this approach. Electronic structure study of V spinels by using DFT and DFT+DMFT approaches is explained in chapter 6. In the first part this chapter, we discuss the degree of localization of V 3d electrons in V spinels based on calculated values of t Uef f ratio (wheret andUef f are the transfer integral between neighbouring sites and on-site effective Coulomb interaction, respectively) and found that the degree of localization of these electrons is largest for CdV2O4 and smallest for ZnV2O4 as compared to MgV2O4. In the second part of this chapter, we study the electronic structure of V spinels by using DFT and DMFT, where the self-consistently calculated material specific parameters,Uef f and Hund’s coupling, J are used. Corresponding to these parameters, we have found that the main features, such as insulating band gaps, degree of itinerancy of V 3d electrons and position of the lower Hubbard band, are closely matched with the experiment data. At last in chapter seven, we summarizes the thesis,with a brief overview of the significant conclusions drawn and give direction for future work.