${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x\mathrm{Ti}{\mathrm{O}}_3$: An $\mathrm{XY}$ Quantum Ferroelectric with Transition to Randomness

A series of twenty homogeneous ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x\mathrm{Ti}{\mathrm{O}}_3$ mixed crystals has been measured dielectrically between 4.2 and 300 K. In the tetragonal phase, the dielectric constant perpendicular to the $c$ axis becomes peaked above $x_c=0.0018\mathrm{}$, the quantum mechanical onset for displacive ferroelectricity. The polarization $\perp c$ can be switched between the two equivalent $a$ axes, i.e., the system is an $\mathrm{XY}$, $n=2\mathrm{}$, quantum ferroelectric. Above $x_r=0.016\mathrm{}\pm 0.002$, the $\epsilon \mathrm{}\left(T\right)\mathrm{}$ peaks round in a distinct manner which we attribute to the onset of a random-field-induced domain state.