Fluctuations, Higher Order Anharmonicities, and Landau Expansion for Barium Titanate

TL;DR

This paper develops a phenomenological model for ferroelectric phase transitions in barium titanate, emphasizing the importance of eighth-order free energy terms and temperature-dependent coefficients influenced by thermal fluctuations.

Contribution

It introduces a comprehensive Landau expansion including eighth-order terms and explains the temperature dependence of coefficients B_1 and B_2 via polarization fluctuations.

Findings

Eighth-order terms are necessary for accurate phase transition description.

Temperature dependence of B_1 and B_2 aligns with fluctuation contributions.

Theoretical B_1/B_2 ratio matches experimental data.

Abstract

Correct phenomenological description of ferroelectric phase transitions in barium titanate requires accounting for eighth-order terms in the free energy expansion, in addition to the conventional sixth-order contributions. Another unusual feature of BaTiO_3 crystal is that the coefficients B_1 and B_2 of the terms P_x^4 and P_x^2*P_y^2 in the Landau expansion depend on the temperature. It is shown that the temperature dependence of B_1 and B_2 may be caused by thermal fluctuations of the polarization, provided the fourth-order anharmonicity is anomalously small, i. e. the nonlinearity of P^4 type and higher-order ones play comparable roles. Non-singular (non-critical) fluctuation contributions to B_1 and B_2 are calculated in the first approximation in sixth-order and eighth-order anharmonic constants. Both contributions increase with the temperature, which is in agreement with available experimental data. Moreover, the theory makes it possible to estimate, without any additional assumptions, the ratio of fluctuation (temperature dependent) contributions to coefficients B_1 and B_2. Theoretical value of B_1/B_2 appears to be close to that given by experiments.