$\mathrm{C}{\mathrm{a}}_3\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ is an experimentally confirmed hybrid improper ferroelectric material, in which the electric polarization is induced by a combination of the coherent $\mathrm{Ti}{\mathrm{O}}_6$ octahedral rotation and tilting. In this work, we investigate the tuning of ferroelectricity of $\mathrm{C}{\mathrm{a}}_3\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ using isovalent substitutions on Ca sites. Due to the size mismatch, larger/smaller alkaline earths prefer $A^{\prime }/A$ sites, respectively, allowing the possibility for site-selective substitutions. Without extra carriers, such site-selected isovalent substitutions can significantly tune the $\mathrm{Ti}{\mathrm{O}}_6$ octahedral rotation and tilting, and thus change the structure and polarization. Using the first-principles calculations, our study reveals that three substituted cases (Sr, Mg, and Sr+Mg) show divergent physical behaviors. In particular, ${\left(\mathrm{CaTi}{\mathrm{O}}_3\right)}_2\mathrm{SrO}$ becomes nonpolar, which can reasonably explain the suppression of polarization upon Sr substitution observed in experiment. In contrast, the polarization in ${\left(\mathrm{MgTi}{\mathrm{O}}_3\right)}_2\mathrm{CaO}$ is almost doubled upon substitutions, while the estimated coercivity for ferroelectric switching does not change. The ${\left(\mathrm{MgTi}{\mathrm{O}}_3\right)}_2\mathrm{SrO}$ remains polar but its structural space group changes, with moderate increased polarization and possible different ferroelectric switching paths. Our study reveals the subtle ferroelectricity in the $A_3\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ family and suggests one more practical route to tune hybrid improper ferroelectricity, in addition to the strain effect.

• Received 23 January 2018
• Revised 11 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.184105