Theoretical investigation of lattice thermal conductivity and electrophononic effects in ${\mathrm{SrTiO}}_3$

We present a theoretical study of the lattice thermal conductivity of ${\mathrm{SrTiO}}_3$ in its antiferrodistortive ferroelastic phase and of its dependence on an applied external electric field, via electrophononic couplings. The calculations are done by using second-principles density-functional theory and the full solution of the Boltzmann transport equation. Our results allow, on one hand, to identify and explain deviations from the usual temperature dependence of the thermal conductivity, revealing Poiseuille flow and a rare umklapp transport regime, in agreement with recent experimental results [Martelli et al., Phys. Rev. Lett. 120, 125901 (2018)]; on the other hand, they show that an external electric field, by reducing the symmetry of the lattice, activates different phonon-phonon scattering processes and thus yields a reduction of the thermal conductivity, supporting the generality of a heat control strategy previously reported by some of us [Seijas-Bellido et al., Phys. Rev. B 97, 184306 (2018)].

Figure 1

Sketch of ${\mathrm{SrTiO}}_3$ in (a) the cubic paraelectric and (b) the AFD ferroelastic phase.

Figure 2

Thermal conductivity of ${\mathrm{SrTiO}}_3$ in the AFD phase as a function of temperature. The faster-than-cubic temperature dependence of $\kappa$ indicates a Poiseuille transport regime where normal processes dominate aharmonic scattering. The $T^3$ dependence expected when phonon transport is limited by boundary scattering is shown for comparison. The thermal conductivity of an isotopically purified sample is shown with a blue solid line (${\overline{\kappa }}_{\text{pure}}$), while ${\overline{\kappa }}_{\text{doped}}$ corresponds to the case of a lanthanum-doped system, ${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$, with $x=0.00085$. A calculation with a boundary scattering of $100\mu \mathrm{m}$ (${\overline{\kappa }}_{100\mu \text{m}}$) is also included to observe the size effects at low temperature. Experimental data (red squares) are taken from Ref. [18].

Figure 3

Variation of the thermal conductivity as a function of temperature for (a) $E_z=2.5\times {10}^{-3}$ V/Å and (b) $E_x=2.5\times {10}^{-3}$ V/Å. The changes are referred to the value of the thermal conductivity ${\kappa }^0$ without field. For comparison the variation of the thermal conductivity of PTO with an electric field of the same value opposed to the polarization ($-E_z$) is shown in (a) and with the same value ($E_x$) in (b) [17].

Figure 4

Thermal conductivity as a function of an external electric field $E_z$ (left) and $E_x$ (right) at $T=100\mathrm{K}$.

Figure 5

Diagonal components of the second-order electrophononic tensor ${\mathbf{\beta }}_{ij,kl}$, as defined in Eq. (2), as a function of temperature.

Figure 6

(a) Phonon band structure of ${\mathrm{SrTiO}}_3$ along the $\mathrm{\Gamma }-X$ direction. (b) Phonon-phonon scattering interaction strength for ${\mathrm{SrTiO}}_3$ with $E_z=0\mathrm{V}/\AA , E_z=2.5\times {10}^{-3}\mathrm{V}/\AA$, and $E_z=4.5\times {10}^{-3}$ V/Å at 100 K.

Figure 7

Thermal conductivity accumulation function for ${\mathrm{SrTiO}}_3$ with $E_x=0$ V/Å and $E_x=2.5\times {10}^{-3}$ V/Å at 100 K. Results for ${\mathrm{PbTiO}}_3$ are shown for comparison.