Phonon dispersion, Raman spectra, and evidence for spin-phonon coupling in ${\mathrm{MnV}}_2{\mathrm{O}}_4$ from first principles

${\mathrm{MnV}}_2{\mathrm{O}}_4$ in the spinel structure is known to exhibit coupled orbital and spin ordering and its Raman spectra show interesting anomalies in its low-temperature phase. With a goal to explain this behavior involving coupled spins and phonons, we determine here the spin-phonon couplings in ${\mathrm{MnV}}_2{\mathrm{O}}_4$ from a theoretical analysis of its phonon spectra and their dependence on spin ordering and electron correlations, obtained from first-principles density functional theoretical calculations. Using these in an analysis based on a Landau-like theory, we uncover the mechanism governing the Raman anomalies observed in its low-temperature phase.

Figure 1

(a) Crystallographic unit cell and (b) primitive cell of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ compound. Oxygen octahedra (tetrahedra) around V (Mn) ions are shown in gray (cyan-blue).

Figure 2

Total phonon DOS is shown for (a) GGA and (b) $\mathrm{GGA}+U$ calculations in FiM configuration. Unstable modes with imaginary frequencies (given as negative) are observed only in GGA calculations. Projected DOS of Mn, V, and O atoms within $\mathrm{GGA}+U$ calculations in (c) FiM and (d) FM states.

Figure 3

Electronic band structure of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ in FiM state within (a) GGA and (b) $\mathrm{GGA}+U$ calculations.

Figure 4

Total and projected electronic DOS of Mn, V, and O atoms of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ in (a) FiM and (b) FM states within $\mathrm{GGA}+U$ calculations. DOSs on the positive $Y$ axis represent up-spin states, while DOSs on the negative $Y$ axis represent down-spin states.

Figure 5

Calculated Raman spectrum for light in the $X^{\prime }{Y}^{\prime }$ and XY polarization. Raman peaks with red (blue) color are observed in $X^{\prime }{Y}^{\prime }$ (XY) polarization.

Figure 6

Atomic displacements of $B_g$ phonons responsible for the Raman peaks associated with the four $B_g$ modes at (a) $181{\mathrm{cm}}^{-1}\left[B_g\left(1\right)\right]$, (b) $367{\mathrm{cm}}^{-1}\left[B_g\left(2\right)\right]$, (c) $440{\mathrm{cm}}^{-1}\left[B_g\left(3\right)\right]$, and (d) $539{\mathrm{cm}}^{-1}\left[B_g\left(4\right)\right]$.

Figure 7

Phonon dispersion of FiM (red solid lines) and FM (black dotted linens) states of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ in its tetragonal phase.

Figure 8

The Hellman-Feynman forces on the oxygen ions in the FM configuration of the relaxed FiM configuration (crystallographic unit cell). The forces are drawn with golden arrows and give the lowest-order spin-phonon coupling.

Figure 9

Relative change in phonon frequency (${\mathrm{\Delta }}_{\mathrm{rel}}=\frac{{\omega }_{\mathrm{FiM}}-{\omega }_{\mathrm{FM}}}{{\omega }_{\mathrm{FiM}}}\times 100\%$) calculated at the zone center (a) $\mathrm{\Gamma }$ and zone boundary points (b) $N$, (c) $X$, (d) $Z$.

Figure 10

Temperature dependence of phonon modes [(a) 178 ${\mathrm{cm}}^{-1}$ (for ${\mathrm{\Delta }}_{\lambda }=-6{\mathrm{cm}}^{-1}$) and (b) 70 ${\mathrm{cm}}^{-1}$ (for ${\mathrm{\Delta }}_{\lambda }=7{\mathrm{cm}}^{-1}$)] obtained for three choices of $m\left(T\right)$ (see text). “Exp” refers to use of experimental $m\left(T\right)$ [45] in our analysis [Eq. (7)] to determine $\omega \left(T\right)$ corresponding to FiM spin ordering, and $\beta$ is the critical exponent.