Doping a dipole into an incipient ferroelectric: Route to relaxor ferroelectrics

Abstract

$\mathrm{Ti}{\mathrm{O}}_{2}$ in the rutile phase is known to be an incipient ferroelectric. Considering Nb-Cr codoping we examine if ferroelectricity can be induced at the low doping limit in $\mathrm{T}{\mathrm{i}}_{(1\text{\ensuremath{-}}x)}{(\mathrm{N}{\mathrm{b}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5})}_{x}{\mathrm{O}}_{2}$ ($x=0.05%$, 1%, 5%, and 10%). A relaxor behavior is found in the temperature range 20--120 K which obeys the Vogel-Fulcher relation while pyrocurrent measurements confirm switching of the electric polarization. The spontaneous net polarization is doping dependent with a maximum at 1% and for doping concentrations above 5% is found to be paraelectric. Ab initio density functional theory based calculations suggest that the Nb-Cr pair behaves like a dipole and polarizes the neighboring $\mathrm{Ti}{\mathrm{O}}_{6}$ octahedra, stabilizing a ferroelectric ground state akin to magnetic impurities in dilute magnetic semiconductors. At larger doping concentrations one finds that Nb-Cr clusters result in a vanishing polarization.