First-principles study of phonons, optical properties, and Raman spectra in ${\text{MgV}}_2{\text{O}}_5$

The electronic properties of ${\text{MgV}}_2{\text{O}}_5$ are calculated in the framework of the all-electron full-potential linearized augmented plane-wave method within density-functional theory. Adopting the experimental lattice parameters, all atomic positions inside the unit cell are optimized. It is shown that this relaxation has a strong effect on the bond lengths and hence the electronic bands. The optical properties are determined within the independent-particle approximation. In addition, the fully symmetric $A_g$ phonon modes are calculated by the frozen phonon approach. For each eigenvector, the dielectric tensor is obtained as a function of the displacement coordinates. Based on these results, the corresponding Raman spectra are determined and discussed in the context of experimental data. Theory is able to either confirm or revise the assignment of the measured spectra. Finally, the calculated properties are compared with those of other vanadium ladder structures.

Figure 1

(Color online) Crystal structure of ${\text{MgV}}_2{\text{O}}_5$ from a slant perspective (Ref. 25). The triangle indicates the $x\text{−}z$ plane that includes both the Mg atom of the upper layer and the two apex oxygens O3 of the lower layer.

Figure 2

(Color online) Relaxation-induced shifts of the atomic positions (magnified by a factor of 5). The labeled sites represent the reference atoms for Table .

Figure 3

(Color online) Upper part: Brillouin zone and $\mathbf{k}$ path used for the band-structure plot. Lower part: band structure and atomic densities of states (in states per eV and unit cell) for relaxed (upper panel) and experimental (Ref. 13) atomic positions (lower panel).

Figure 4

(Color online) Partial densities of states (states per eV and atom) of the relaxed structure, showing the orbital character of the $\text{V}3d$ and the $\text{O}2p$ bands. In the considered energy range no magnesium states are present.

Figure 5

(Color online) Real and imaginary parts of the dielectric function of ${\text{MgV}}_2{\text{O}}_5$ in $xx$, $yy$, and $zz$ polarizations.

Figure 6

(Color online) $A_g$ phonons of ${\text{MgV}}_2{\text{O}}_5$. The arrows show the eigenvectors for each eigenmode, i.e., the direction and magnitude of the atomic displacements weighted by the square root of the corresponding atomic mass.

Figure 7

Theoretical Raman spectra for the $A_g$ modes of ${\text{MgV}}_2{\text{O}}_5$ for $xx$, $yy$, and $zz$ polarizations (upper three panels), compared to unpolarized Raman spectra from experiment (Ref. 16) (lower panel). In the latter, the $A_g$ spectra are superposed by the $B_{1g}$, $B_{2g}$, and $B_{3g}$ modes. All results are obtained for a photon frequency of 2.41 eV (488 nm).

Figure 8

(Color online) Change in the dielectric function with respect to displacements along the eigenvectors, ${\left|d{\epsilon }_{ii}/dQ\right|}^2$, for the $A_g$ eigenmodes of ${\text{MgV}}_2{\text{O}}_5$.