Abstract:
Oxides are mostly non-toxic and quite abundant in nature. They form an important
class of materials due to their chemical and structural (halite, wurzite, spinel, corrundum,
rutile, perovskite and pyrochlore) diversity. Oxides with transition metal ions
have been studied greatly as these exhibit rich varieties of physical properties such as
metallicity, semiconductivity, insulating, ferromagnetism, antiferromagnetism, ferroelectricity,
antiferroelectricity, piezoelectricity, colossal magnetoresistance, superconductivity,
charge and orbital orderings [1{9] along with a remarkable diversity
in the nature of phase transitions (high-spin/low spin, metal-insulator, magnetic,
ferroelectric and structural transitions) they undergo [2, 4, 5, 10{13].
The macroscopic properties of a material are a consequence of how electrons
and atoms are arranged and held together in a solid. Since the motion of electrons
(atoms) is governed by quantum mechanical laws (Newtonian mechanics), most of
the physical properties can be determined in principle from these laws. Accurate
evaluation of the macroscopic properties of a material directly from the fundamental
equations ( rst-principles) of electrons is of fundamental importance, but also quite
di cult.
