We present a theoretical proposal for the design of a thermal switch based on the anisotropy of the thermal conductivity of PbTiO3 and the possibility to rotate the ferroelectric polarization with an external electric field. Our calculations are based on an iterative solution of the phonon Boltzmann Transport Equation and rely on interatomic force constants computed within an efficient second-principles density functional theory scheme. We also characterize the hysteresis cycle of the thermal conductivity in the presence of an applied electric field and show that the response time would be limited by the speed of the ferroelectric switch itself and thus the switch can operate in the high-frequency regime.

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