Giant Electrophononic Response in ${\mathrm{PbTiO}}_3$ by Strain Engineering

We demonstrate theoretically how, by imposing epitaxial strain in a ferroelectric perovskite, it is possible to achieve a dynamical control of phonon propagation by means of external electric fields, which yields a giant electrophononic response, i.e., the dependence of the lattice thermal conductivity on external electric fields. Specifically, we study the strain-induced manipulation of the lattice structure and analyze its interplay with the electrophononic response. We show that tensile biaxial strain can drive the system to a regime where the electrical polarization can be effortlessly rotated and thus yield giant electrophononic responses that are at least one order of magnitude larger than in the unstrained system. These results derive directly from the almost divergent behavior of the electrical susceptibility at those critical strains that drive the polarization on the verge of a spontaneous rotation.

Figure 1

(Top panel) Lattice parameters and (main panel) components of the polarization, $\mathbf{P}$ and diagonal terms of the electrical susceptibility tensor $\mathit{\chi }$, as a function of the substrate lattice parameter $a_{\mathrm{sub}}$. The applied strain referred to the lattice parameter of the zero kelvin cubic phase is shown in the axis above the top panel.

Figure 2

Thermal conductivity and first-order electrophononic coefficient ${\alpha }_{ii,i}$ as a function of the substrate lattice parameter $a_{\mathrm{sub}}$. The polarization direction is represented to indicate when $\mathbf{E}$ is perpendicular or in the plane of $\mathbf{P}$. The fluctuation of $\mathit{\alpha }$ far from the critical points is caused by the error associated to the polynomial fitting of Eq. (1).

Figure 3

Relative change of the thermal conductivity as a function of an applied electric field for different values of the biaxial strain. Solid lines show the response in ${\kappa }_{zz}$ when a electric field perpendicular to the $z$ axis is applied. Dashed lines show the electrophononic response in ${\kappa }_{xx}$ when the electric field is applied parallel to the $z$ axis.

Figure 4

(Left) First-order electrophononic coefficient ${\alpha }_{ii,j}$, with $i\ne j$, and (right) second-order electrophononic coefficient, ${\beta }_{ii,ii}$ and ${\beta }_{ii,jj}$, with $i\ne j$, as a function of the substrate lattice parameter $a_{\mathrm{sub}}$. The polarization direction is represented to indicate when $\mathbf{E}$ is perpendicular or in the plane of $\mathbf{P}$.

Figure 5

Reduction of the lattice thermal conductivity as function of strain for electric fields of $E_i=5\times {10}^4\mathrm{V}/\mathrm{cm}$ along the $x$ axis (top) and the $z$ axis (bottom). The same electrophononic response for ${\kappa }_{xx,x}$ and ${\kappa }_{xx,z}$ is found for ${\kappa }_{yy,y}$ and ${\kappa }_{yy,z}$.