High-frequency nonlinear microwave response in quantum paraelectric potassium tantalate

We have investigated the microwave echoes in a quantum paraelectric (QPE) KTaO3 to clarify the phonon anharmonicity at low temperatures. When applying two microwave pulses (9.4 GHz), a strong echo signal can be generated below 18 K. The intensity depended exponentially on the pulse interval and was independent of an external magnetic-field strength. When the temperature was increased, the phase relaxation time of the echo became faster, which obeyed the Ahrenius law with the activation energy of about 0.4 meV. A simple model, considering piezoelectric interaction in the ferroelectric micro-domains and the nonlinear electrostriction, is proposed and applied to reproduce successfully the echo time-profile. The nonlinearity should originate from the strong anharmonicity of the phonons in QPE.