Thermodynamic properties of temperature graded ferroelectric film

Effects of quantum fluctuation and four-spin interaction on the polarization and pyroelectric coefficient of temperature graded ferroelectric film are investigated, based on the transverse Ising model by taking into account the four-spin interaction. It is found that the magnitude and the sign of the polarization gradient are dependent on the imposed temperature gradient, and both the quantum fluctuation and four-spin interaction play an important role in the thermodynamic properties of the temperature graded film. With increasing strength of the quantum fluctuations the sharp peak of the pyroelectric coefficient shifts to lower temperatures. Also the four-spin interaction increases the mean polarization and makes the smooth pyroelectric peak at low temperature more pronounced. Furthermore, the graded ferroelectric film shows the characteristic feature of a first-order phase transition when the four-spin interaction is larger than a critical value, which is dependent on the temperature gradient and the quantum fluctuation.