First-principles study of phonon properties in magnetic double-layer manganites

We have studied the lattice dynamical properties of the tetragonal double-layer manganite system La${}_{2-2x}$Sr${}_{1+2x}$Mn${}_2$O${}_7$ ($x=0.4$) within the framework of density functional perturbation theory, using a mixed-basis pseudopotential method and the virtual-crystal approximation for modeling the alloy. Performing phonon dispersion calculations for both ferromagnetic (FM) and nonmagnetic (NM) ground states in the plane $q_z=0$ revealed a strong influence of the magnetic order on high-frequency modes which involve oxygen vibrations with Mn-O bond-stretching modulations. They can be traced back to changes in the dynamical coupling of medium-ranged bonds like Mn-Mn or O-O, while the nearest-neighbor Mn-O bonds remain practically unchanged. Electronically they originate from a replacement of the predominant Mn $d\left(t_{2g}\right)$ orbital polarization in the NM phase by a $d\left(e_g\right)$-type polarization in the FM phase. Good agreement is found between theoretical predictions for phonon frequencies and intensities in the [110] direction and a previous neutron scattering experiment performed in the FM phase. Finally, calculations of the electron-phonon interaction revealed that dips in the dispersion of the high-frequency bond-stretching branches are connected to an enhanced electron-phonon coupling, but on average only a moderate coupling constant of $\lambda =0.65$ is obtained.

Figure 1

La${}_{2-2x}$Sr${}_{1+2x}$Mn${}_2$O${}_7$ crystal structure (Ref. 5).

Figure 2

Calculated phonon dispersion of La${}_{1.2}$Sr${}_{1.8}$Mn${}_2$O${}_7$ for the symmetry classes (a) ${\Sigma }_1$ to ${\Sigma }_4$ along $\left[\xi \xi 0\right]$ and (b) ${\Delta }_1$ to ${\Delta }_4$ along $\left[\xi 00\right]$. Results for the FM case (black solid lines) are compared with those from a NM calculation (red dashed lines).

Figure 3

Top view of the first MnO octahedral layer showing the high-frequency phonon modes at the (a) M point and (b) X point for each symmetry class. The in-plane oxygen is denoted by O${}_3$, while the out-of-plane oxygen O${}_2$ sits on top of Mn.

Figure 4

Average force constants for (a) FM (black solid line) and NM (red dashed line) phases. Bonds are ordered by increasing bond length. Each set of average force constants is normalized to the FM value of the shortest bond. Labels (1) to (6) denote those bonds which are most effected by spin polarization. (b) Cartoon of these bonds.

Figure 5

Calculated phonon dispersion (lines) for the [$\xi$$\xi$0] direction (a) transverse ${\Sigma }_3$ and (b) longitudinal ${\Sigma }_1$ in comparison with inelastic neutron scattering data (open circles: bond-stretching, filled circles: bond-bending modes) (Ref. 12). Dynamical structure factor calculations (vertical lines) at two reciprocal lattice points, $\mathit{\tau }=\left(330\right)$ and $\mathit{\tau }=\left(440\right)$, are included (where $\mathbf{Q}=\mathit{\tau }+\mathbf{q}$). Dashed lines denote the dispersion of the main bond-bending spectral weight.

Figure 6

Calculated e-ph induced linewidths ${\gamma }_{\mathbf{q}\lambda }$ (half-width at half-maximum) of the high-frequency Mn-O bond-stretching modes for both transverse ${\Sigma }_3$ and longitudinal ${\Sigma }_1$ polarizations in the FM phase.