Analytical description of the size effect on pyroelectric and electrocaloric properties of ferroelectric nanoparticles

Using Landau-Ginzburg-Devonshire theory and effective medium approximation, we analytically calculate typical dependences of the pyroelectric and electrocaloric coefficients on external electric field, temperature, and radius of spherical single-domain ferroelectric nanoparticles. The considered physical model corresponds to the nanocomposite with a small fraction of ferroelectric nanoparticles. Within the framework of the analytical model, we establish how the size changes determine the temperature and field behavior of pyroelectric and electrocaloric coefficients on the example of $\mathrm{BaTi}{\mathrm{O}}_{3}$ nanoparticles covered by a semiconducting shell and placed in a dielectric polymer. We show that by changing the particle size one can induce maxima of the pyroelectric coefficient and electrocaloric temperature variation, control their width and height. Obtained analytical expressions allow selecting the interval of particle sizes, voltage, and/or temperature for which the pyroelectric energy conversion and electrocaloric coefficient are optimal for applications. The observed size effect opens the possibility to control pyroelectric and electrocaloric properties of ferroelectric nanocomposites that can be important for their advanced applications in energy convertors and cooling systems.