Ultrafast Relaxation Dynamics of the Antiferrodistortive Phase in Ca Doped ${\mathrm{SrTiO}}_3$

The ultrafast dynamics of the octahedral rotation in $\mathrm{Ca}:\mathrm{SrTi}{\mathrm{O}}_3$ is studied by time-resolved x-ray diffraction after photoexcitation over the band gap. By monitoring the diffraction intensity of a superlattice reflection that is directly related to the structural order parameter of the soft-mode driven antiferrodistortive phase in $\mathrm{Ca}:\mathrm{SrTi}{\mathrm{O}}_3$, we observe an ultrafast relaxation on a 0.2 ps timescale of the rotation of the oxygen octahedron, which is found to be independent of the initial temperature despite large changes in the corresponding soft-mode frequency. A further, much smaller reduction on a slower picosecond timescale is attributed to thermal effects. Time-dependent density-functional-theory calculations show that the fast response can be ascribed to an ultrafast displacive modification of the soft-mode potential towards the normal state induced by holes created in the oxygen $2p$ states.

Figure 1

Transient relative x-ray intensity of the (1.5 0.5 0.5) superlattice reflection of ${\mathrm{Sr}}_{0.97}{\mathrm{Ca}}_{0.03}{\mathrm{TiO}}_3$ upon above band gap excitation with 40 fs pulses centered around 4.66 eV at a temperature of 100 K. For clarity, a constant vertical offset of 0.2 separates traces recorded for different excitation fluences $\varphi$. Error bars indicate x-ray photon counting statistics. Inset: ${\mathrm{SrTiO}}_3$ crystal structure as seen along the $c$ axis (visualized using vesta [21]). $\phi$ measures the antiferrodistortive rotation of the oxygen octahedra (exaggerated) and represents the order parameter. The dashed (solid) black line frames a cubic (tetragonal) unit cell of the high (low) temperature phase along the respective in-plane axes.

Figure 2

Dynamics of the (1.5 0.5 0.5) superlattice reflection measured for temperatures approaching $T_c=280\mathrm{K}$ at an excitation fluence of $\varphi =6\mathrm{mJ}/{\mathrm{cm}}^2$.

Figure 3

DFT phonon dispersion of cubic ${\mathrm{SrTiO}}_3$ for a series of hole dopings (not including longitudinal optical-transverse optical phonon splitting). Inset: Calculated energy change per ${\mathrm{SrTiO}}_3$ cubic unit cell as a function of oxygen displacement $u/u_0$ along the in-plane cubic crystal axes resulting from the octahedral rotation at select hole dopings.

Figure 4

Right $y$ axis: Time-dependent DFT simulation of the transient hole population $\rho (t)$ for excitation with a 110 fs field pulse centered 200 meV above the DFT band gap (see the Supplemental Material [20], Fig. S5). Left $y$ axis: Relative scattering intensity of superlattice peaks associated with the octahedral distortion calculated via Eq. (2) for a parametric change of the double-well potential of Fig. 3 by $\rho (t)$. The curves are labeled by the doping level ${\rho }_{\text{final}}$ reached after the excitation process.