Anharmonic phonon properties in Eu_0.5Ba_0.5TiO₃

Phonon properties have been studied using reduced sound velocity of Eu_0.5Ba_0.5TiO₃ (EBTO). To achieve this aim, the anharmonic phonon-phonon interaction and the spin-phonon interaction were used. It was shown that the reduced sound velocity of multiferroic EBTO exhibits a kink at T_N = 1.9 K. This anomalously reduced sound velocity can be interpreted as an effect of vanishing magnetic ordering above T_N. What’s more, the ferroelectric subsystem cannot be influenced by the magnetic subsystem above T_N for T_N ≪T_C in the EBTO. It was found that the reduced sound velocity decreases as T increases near ferroelectric transition TC. That is to say, the sound velocity softens near ferroelectric transition TC. It is also noteworthy that the reduced sound velocity softens when the RE (the coupling between the ferroelectric pseudo-spins and phonons), V⁽³⁾ and |V⁽⁴⁾| (the third- and fourth-order atomic force constants of the anharmonic phonons, respectively) increase. These conclusions are all in good accordance with the experimental data and theoretical results.