Density functional study for structural, electronic, magnetic and chemical bonding properties of geometrically-frustrated CdCr₂O₄

Spinels are an attracting class of materials that demonstrate rich complex behaviors at ground states. Among spinel materials, chromium spinels span an enormous range of magnetic exchange strengths and different magnetic ground states. Spinel oxides AB2O4 with magnetic Bcations have received special attention due to their identification by three-dimensional geometrical frustration. The physics of frustrated magnetism is a subject of existing interest. Spinel oxides with Cr3+ ions on the B sites are good examples to study the frustration. Geometrically frustrated spinel CdCr2O4 has been chosen as a model system to study because it has a well-defined magnetic order with a single ordering wave vector. Spinel CdCr2O4 is a magnetic compound that crystallizes into a cubic spinel structure, and the magnetic properties stem from the Cr3+ magnetic ions, that are a three-dimensional network of corner-sharing tetrahedral.In the present work, density functional calculations are performed to investigate the effects of magnetic ordering on the electronic structure and bonding properties of CdCr2O4 with non-magnetic Cd cations and magnetic Cr cations from a pyrochlore lattice, by examining the crystal structure of spinel CdCr2O4 and followed byanalyzing the electronic and magnetic properties that are important in magnetic spinel oxides. The structural, electronic, and chemical bonding properties of geometrically frustrated spinel CdCr2O4with cubic (Fd3̅̅̅̅m)and tetragonal (I41amd⁄) structures have been calculated using density functional method combined with the spin-polarized theory, and compared the results in both cubic and tetragonal structures for different magnetic orderings. Density functional theory applied with the ground-state theory recovered in the zero temperature limit. In order to optimize the crystal structures of spinel CdCr2O4, the plane-wave Ultrasoft pseudopotential technique is used within the generalized gradient approximation. XCrySDen graphic software is applied asa crystalline and molecular structure visualization program to visualize this system. In order to calculate the total energy, the exchange and correlation functional is described within the generalized gradient approximation based on exchange-correlation energy optimization. The optimization of atomic positions and cell parameters is approved through the minimization of energy using Hellman-Feynman forces acting on atoms with the Broyden-Flecher-Goldfarb-Shanno scheme and to get the actual relaxed atomic positions and cell parameters for each element the PWscf (VC-relax) input code is applied. To search for the most stable structure of spinel CdCr2O4 in term of magnetic ordering, the lowest energy in each structure with different magnetic ordering is calculated. What is important for this work is to converge the parameters by applying the scf convergence test, in order to find the actual kinetic energy cut off and k-point in different crystal structures and also to determine the structural properties of spinel CdCr2O4, in term of lattice parameters, symmetry properties and charge density distributions in different magnetic configurations. Fallowing that, the effect of magnetism is obtained and analyzed on the basis of total density of states, projected density of states, and charge density distribution within paramagnetic, ferromagnetic and antiferromagnetic orderings using density functional calculations and understanding of the principles of Quantum ESPRESSO in magnetic materials. In continue, to complete the findings of the electronic density of states for spinel CdCr2O4, the density of states for each atom is calculated, in order to analyze the band gap in each state, separately. Finally, the electronic charge density distribution in the (1 1 0) crystallographic planes are obtained, for both cubic and tetragonal structures, to explain and compare the bonding properties of spinel CdCr2O4 in paramagnetic, ferromagnetic and antiferromagnetic orderings.

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