The crystalline solids are often a playground to generate novel quantum states which hold the key for next-generation technological applications in the area of electronics, quantum information, and quantum computation. Specifically, perovskite oxides exhibit a rich spectrum of functional responses including magnetism, ferroelectricity, superconductivity, etc. The functionality of these oxides increases to a great extent as one moves down in the periodic table from 3d, 4d to 5dtransition metals. This is due to the comparable energy scale of several interactions such as Hund’s exchange, spin-orbit coupling (SOC), electron-electron repulsion, and electron hopping strength. The competition among these interactions can lead to a rich phase diagram involving a plethora of novel exotic quantum phases such as Dirac and Weyl semimetals, topological insulators, spin liquid, superconductivity, etc. Apart from competing interactions, reduced dimensionality also brings another degree of freedom to increase the functionality of these systems.
In this talk, we will present the electronic structure and magnetism of perovskite oxides and other oxide materials which is obtained by pursuing model Hamiltonian and density functional studies. For the family of bulk and low-dimensional low-spin d5 perovskite oxides, we present thirteen electronic and magnetic phases in the space spanned by