Soft phonon mode coupled with antiferromagnetic order in incipient-ferroelectric Mott insulators Sr _1-xBa _xMnO ₃

Infrared optical and inelastic x-ray scattering spectra have been systematically investigated in combination with first-principles calculations for paraelectric and antiferromagnetic perovskite Sr _1-xBa _xMnO ₃ (x=0-0.3) single crystals, which are close to a ferroelectric transition arising from off-center displacement of magnetic Mn4 ⁺ ions. All the phonon dispersions measured for the parent compound of x=0 agree well with the results of the first-principles calculation. As the Ba concentration increases, one optical phonon rapidly softens toward zero frequency at room temperature, while the other phonons are almost unchanged. This soft-mode behavior is also reproduced by the first-principles calculations, from which we have predicted the vibration mode of all the optical phonons. The results of the infrared measurements at various temperatures indicate that only the soft phonon mode shows marked temperature variation relevant to the antiferromagnetic transition for all x, whereas other optical modes are almost independent of temperature. The conventional evolution of a soft phonon with decreasing temperature is prevented by the onset of the magnetic order. Below the antiferromagnetic-transition temperature, the soft mode hardens with decreasing temperature and then resoftens toward the lowest temperature. A similar temperature dependence was observed in the nonzero-momentum region by means of the inelastic x-ray scattering measurements, although its magnitude decreases as the momentum is increased from zero. Such a nonmonotonic temperature profile of the soft-mode energy is well explained on the basis of a phenomenological spin-phonon coupling model, which suggests the largest coupling constant yet attained.