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

$\mathrm{Ti}{\mathrm{O}}_2$ 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 $\mathrm{T}{\mathrm{i}}_{\left(1\text{−}x\right)}{\left(\mathrm{N}{\mathrm{b}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5}\right)}_x{\mathrm{O}}_2$ ($x=0.05\%$, 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.

Figure 1

(a) Neutron diffraction of the 1% sample at 6 K with refinement. The inset shows the table with lattice parameters derived from XRD while those indicated with * show 300 K and ‡ denotes 6 K neutron diffraction data. (b) Temperature variation of ε′ of 0.05% sample; inset shows the Arrhenius fit for the high-temperature relaxation.

Figure 2

Temperature variation of ε′ for (a) 0.05%, (b) 1%, and (c) 5% samples and (d) fit for ε′ versus $T\text{−}{T}_m$ plot at 10 kHz. Inset of (a) temperature variation of tanδ and ε″ and inset of (c) plot of ln τ versus T and the solid line is the Vogel-Fulcher fit.

Figure 3

Temperature dependence of the 0.05% sample: (a) spontaneous polarization for various fields, (b) shows the pyrocurrent for different ramp rates, (c) $P_S$ for various dopings; inset is ε′ versus temperature for Cr-only and Nb-only doped samples at 0.05% doping, and (d) phase diagram of the codoped $\mathrm{Ti}{\mathrm{O}}_2$ with doping concentration.

Figure 4

The calculated up (solid line) and down (dashed line) spin projected (a) Ti $d$, (b) Nb $d$, and (c) Cr $d$ partial density of states at 5% of doping. The Ti atom which is just above the Nb atom is the one for which the density of states is shown. The bond lengths of the $\mathrm{TM}{\mathrm{O}}_6$ octahedra are shown along with the magnetic moment.