Fluctuations, higher anharmonisms, and the Ginzburg-Landau-Devonshire expansion for barium titanate

We show that the strong temperature dependence of the coefficients B1 and B2 of terms of the form Px4 and Px2Py2 in the Ginzburg-Landau-Devonshire expansion for barium titanate can result from the action of thermal polarization fluctuations if the fourth-order anharmonic constants are anomalously small, i.e., if the nonlinearity of the form P4and higher anharmonisms play comparable roles. We calculate the regular (noncritical) fluctuation contributions to B1 and B2 in the first approximation in the sixth- and eighth-order anharmonic constants. Both contributions increase monotonically with temperature, which agrees with the forms of the experimentally observed temperature dependences of these coefficients. The theory allows finding the ratio of the fluctuation components B1 and B2 without additional assumptions. This ratio also turns out to be very close to the experimental value.