First-principles calculations of the electronic structure and magnetism of nanostructured $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ microgranules and nanoparticles

A detailed study of the structural and magnetic properties of inverse spinel $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ nanoparticles and nanostructured $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ microgranules is made by the first-principles calculations. We have estimated the relative strengths of crystal fields, exchange fields, and magnetic exchange interactions using the electronic structure calculations and electron density maps. We find that the electron-electron correlation plays a significant role in obtaining the correct ground-state structure. A significant local structural distortion at the octahedral site and “inverted” sublattice occupancy in $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ affects the magnetic exchange interactions substantially. The trends in magnetic exchange interactions are analyzed in terms of structural parameters and the features of their electronic structures and magnetic properties. We find that Fe states in $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ are extremely localized, irrespective of the symmetry of the site. Also, Co and Fe ions prefer their high-spin configurations with higher spin moments at octahedral sites.

Figure 1

The crystal structure of CF1 (a), where octahedral, tetrahedral, and oxygen atoms are shaded in pink, brown, and red, respectively, and the crystal structure of CF2 (b), where octahedral, tetrahedral, and oxygen atoms are shaded in sky blue, blue, and red, respectively.

Figure 2

The neighborhood around the tetrahedral and octahedral sites in CF1 (a) and CF2 (b) along with bond angles and bond lengths. The calculated bond lengths and bond angles obtained from first-principles calculations are shown for (c) CF1 and (d) CF2 structures.

Figure 3

The electron density (ED) plots in the $yz$ plane taken at the $x=0$ intercept for both CF1 (b, c) and CF2 (e, f) along with a corresponding section of the unit cell for CF1 (a) and CF2 (d).

Figure 4

The electron density (ED) plots in the $yz$ plane taken at the $x$ intercept of $x=0.125$ (a), $x=0.375$ (b), $x=0.625$ (c), and $x=0.875$ (d) for CF1.

Figure 5

The unit cell of CF1 in the $yz$ plane, taken at an $x$ intercept of $x=0.125$ (a), $x=0.375$ (b), $x=0.625$ (c), and $x=0.875$ (d) for clarification.

Figure 6

The electron density (ED) plots in the $yz$ plane taken at the $x$ intercept of $x=0.125$ (a), $x=0.375$ (b), $x=0.625$ (c), and $x=0.875$ (d) for CF2.

Figure 7

The unit cell of CF2 in the $yz$ plane, taken at the $x$ intercept of $x=0.125$ (a), $x=0.375$ (b), $x=0.625$ (c), and $x=0.875$ (d) for clarification.

Figure 8

The site-projected density of states for CF1 (a) and CF2 (b), where identified tetrahedral and octahedral density of states are shown in the middle and bottom panel, whereas the upper panel indicates the total density of states.