Inside the electronic structure of the ${\mathrm{Sm}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ garnet: A mixed ab initio and experimental study

A combination of density functional theory (DFT) with experimental methods was used to study the electronic and crystal structure of ${\text{Sm}}_3{\text{Fe}}_5{\text{O}}_{12}$ (SmIG), which was synthesized using a modified sol-gel method. Computational studies were performed within the generalized gradient approximation (GGA), with and without the Hubbard-$U$ correction ($\mathrm{DFT}+U$), to analyze the influence of the on-site repulsion on the band structure and the density of states (DOS) of SmIG, as well as the structural parameters. The calculations were contrasted with experimental results from x-ray diffraction (XRD) and UV-Vis spectra. A Rietveld refinement returned a lattice parameter of 12.5231(3) Å. Synthesis methods seem to have a substantial effect in the band gap of SmIG, as our experimental value of 2.26–2.27 eV differs from the 2.02 eV value previously reported for samples prepared using the traditional solid-state method, despite similar lattice parameters. The DFT-calculated lattice parameters were within 1% of the experimental value. Analytically calculated effective Hubbard-$U$ values were 4.3092 eV for tetrahedral iron, and 6.0926 eV for octahedral iron. A model is proposed to calculate the band gap in ${\text{Sm}}_3{\text{Fe}}_5{\text{O}}_{12}$, taking into account the structure's ferrimagnetism and energy level distribution. A direct transition between minority spin states was found, resulting in a calculated band gap of 2.27 eV, close to the aforementioned value from sol-gel synthesis.

Figure 1

Temperature evolution of the phase composition of samples synthesized using the sol-gel PVA route. All peaks, unless otherwise stated, belong to the garnet phase. At 1150 °C, single-phase ${\text{Sm}}_3{\text{Fe}}_5{\text{O}}_{12}$ is obtained.

Figure 2

SEM micrograph of ${\text{Sm}}_3{\text{Fe}}_5{\text{O}}_{12}$, showing a highly porous morphology. Sample synthesized using the sol-gel PVA procedure and calcined at 1150 °C for 4 h.

Figure 3

Rietveld analysis of a ${\text{Sm}}_3{\text{Fe}}_5{\text{O}}_{12}$ powder diffraction pattern, collected at room temperature. The $Ia\overline{3}d$ space group was used for the structural model. This particular sample was calcined at 1150 °C for 4 h.

Figure 4

Kubelka-Munk transformed reflectance (absorbance) vs wavelength for ${\text{Sm}}_3{\text{Fe}}_5{\text{O}}_{12}$ synthesized by the sol-gel PVA route. The sample was calcined at 1150 °C for 4 h.

Figure 5

Tauc plot for the UV-Vis DRS spectra of ${\text{Sm}}_3{\text{Fe}}_5{\text{O}}_{12}$. The dashed line indicates the extrapolation used for the band-gap value estimation.

Figure 6

Band structure of ${\text{Sm}}_3{\text{Fe}}_5{\text{O}}_{12}$ calculated under the PBE functional. (a) Majority spin channel (spin up). (b) Minority spin channel (spin down).

Figure 7

Projected density of states (PDOS) for ${\text{Sm}}_3{\text{Fe}}_5{\text{O}}_{12}$, calculated under the PBE flavor of the GGA approximation. The sign of the DOS indicates the spin direction. Valence iron states are highly delocalized, indicating that the description of the system can be improved upon. The shaded area corresponds to the total DOS.

Figure 8

$\mathrm{PBE}+U$ band structure of ${\text{Sm}}_3{\text{Fe}}_5{\text{O}}_{12}$. The energy gap in each spin direction is indicated. (a) Majority spin (up). (b) Minority spin (down). A clear improvement in the description of the band gap is observed.

Figure 9

Projected density of states (PDOS) for samarium-iron garnet within the $\mathrm{DFT}+U$ model. A clear improvement is observed in the description of valence iron states, which are now highly localized, as expected. The shaded area represents the total DOS.

Figure 10

Proposed model for the magnetic coupling and energy level distribution ions within the samarium-iron garnet structure. (a) Band structure with the correct band gap for SmIG. Dark green lines denote spin-up bands, while light pink ones correspond to the spin-down channel. The $E_g$ transition happens between spin-down bands at the $\mathrm{\Gamma }$ point. The calculated band-gap value of 2.27 eV is very close to the one we found for sol-gel PVA synthesized SmIG. (b) Energy level distribution for the ground state, as determined from DFT calculations and crystal field theory. (c) Energy level distribution for the first excited state, illustrating charge transfer from oxygen to tetrahedral iron.