Critical Neutron Scattering in SrTiO3and KMnF3

Abstract

The accepted view of the dynamics of the structural phase transition in SrTi${\mathrm{O}}_3$ ($T_c\sim 100°$ K) and KMn${\mathrm{F}}_3$ ($T_c\sim 186°$ K) had been that of a soft zone-boundary ($\overrightarrow{\mathrm{q}}={\overrightarrow{\mathrm{q}}}_R$) phonon driving the transition with a frequency ${\omega }_{\infty }$ that goes to zero as $T\to T_c$ from above. Recently, Riste et al. observed in the neutron-scattering spectra of SrTi${\mathrm{O}}_3$ a temperature-dependent central component centered around $\omega =0\mathrm{}$ and $\overrightarrow{\mathrm{q}}={\overrightarrow{\mathrm{q}}}_R$ in addition to the phonon sidebands centered around $\omega ={\omega }_{\infty }$. We report on higher-resolution neutron studies of the central component and sidebands in SrTi${\mathrm{O}}_3$, as well as the observation of a central peak in KMn${\mathrm{F}}_3$. The central component is interpreted as arising from a low-frequency resonance in the self-energy of the soft mode and is characterized by a frequency ${\omega }_0$ related to ${\omega }_{\infty }$ by the anharmonic coupling constant $\delta$, ${\omega }_0^2={\omega }_{\infty }^2-{\delta }^2$. The temperature behavior of the SrTi${\mathrm{O}}_3$ spectra as $T$ decreases shows a rapid increase in the intensity of the central component as the sideband frequency ${\omega }_{\infty }$ decreases. Near $T_c$, the intensity of the central peak diverges and ${\omega }_{\infty }$ approaches a finite limiting value. Since ${\omega }_0^{-2\mathrm{}}$ is proportional to the total intensity, the diverging intensity implies that ${\omega }_0\to 0$ as $T\to T_c$. It is shown that the temperature dependence of ${\omega }_0^2$ is stronger than that predicted from mean-field theory. The energy width of the central component is <0.02 meV and we observe a narrow temperature-dependent $q$ width. In KMn${\mathrm{F}}_3$, the central component is clearly seen even though the soft phonons are already overdamped at 40 °K from $T_c$. The observed spectra have a similar behavior with decreasing temperature as studied in SrTi${\mathrm{O}}_3$.