Infrared optical and inelastic X-ray scattering spectra have been systematically investigated in combination with first-principles calculations for paraelectric and antiferromagnetic perovskite SrBaMnO single crystals, which are close to a ferroelectric transition arising from off-center displacement of magnetic Mn ions. One optical phonon rapidly softens toward zero frequency at room temperature with increasing . 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. Below the antiferromagnetic-transition temperature, the soft mode hardens with decreasing temperature and then resoftens toward the lowest temperature.
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