Formation mechanism of polar nanoregion in heterovalent doped incipient ferroelectrics

Incipient ferroelectric SrTiO${}_3$ is known as the structural competition between the ferroelectric polar displacement of Ti ion and antiferrodistortive (AFD) rotation of TiO${}_6$ octahedron. Pr-doped SrTiO${}_3$ (SPTO) possesses relaxor-type ferroelectricity and exhibits both enhanced ferroelectric polar and antiferrodistortion. Here, we use double-edge X-ray absorption spectroscopy fine structure (XAFS: XANES & EXAFS) to investigate the local structure of the SPTO relaxor and the co-existing nature of these two structural distortions. The enhanced local polar is observed by the increment of the A${}_2$ peak of Ti $K$-edge XANES spectra, whose intensity is proportional to the displacement value of the Ti ion. The exact value of Ti displacement is obtained by geometrical analysis of the Ti $K$-edge EXAFS spectra. Sr $K$-edge EXAFS results show the angle of the AFD rotation of TiO${}_6$ octahedron is also increased with Pr doping. With the help of the $abinitio$ calculation, the existence of V${}_{\mathrm{Sr}}^{\prime \prime }$, which is produced by charge compensation after the substitution of Pr${}^{3+}$ on the Sr${}^{2+}$ site (Pr${}_{\mathrm{Sr}}^{•}$), is confirmed by the decreased A${}_4$ peak of Ti $K$-edge XANES. These results explain that the simultaneous enhancement of the ferroelectric polar and the antiferrodistortion in the SPTO relaxor originates from the co-work of the point defects of Pr${}_{\mathrm{Sr}}^{•}$ and V${}_{\mathrm{Sr}}^{\prime \prime }$. Based on our results, a structural mechanism of the PNR formation in the SPTO relaxor is proposed. This study elucidates the mechanism of the heterovalent doping-induced relaxor property in SrTiO${}_3$ and paves the way to induce relaxor property in other incipient ferroelectrics by doping engineering.