First-principles study of misfit strain-stabilized ferroelectric SnTiO${}_3$

Toxicity of lead and bismuth has motivated an active search for isovalent ferroelectric oxides free of these elements. Using first-principles density-functional calculations, we survey Sn(ii) titanates with SnTiO${}_3$ stoichiometry to evaluate the phase stability of polar and nonpolar polymorphs: we predict a tetragonal perovskite $P4mm$ phase with a large axial ratio ($c/a=1.134$) and ferroelectric polarization (1.28 C/m${}^2$) to be the ground-state equilibrium structure. We also show that heteroepitaxial thin films of perovskite SnTiO${}_3$ promote the stereochemical lone-pair activity and simultaneously enable control over the direction of the net electric polarization and magnitude of the electronic band gap. Finally, we examine the consequence of antisite defects on the polar cation displacements by studying the substitution of Sn on Ti sites. We demonstrate that local metallic screening resulting from site substitution diminishes the magnitude of the polar distortions but does not completely quench it. Based on these calculations, we suggest that polar perovskite SnTiO${}_3$ ferroelectrics are viable thin-film alternatives to Pb- and Bi-containing oxides.

Figure 1

Pair distribution functions (PDFs) $g\left(r\right)$ of the three lowest-energy SnTiO${}_3$ polymorphs, $P4mm$, $Cm$, and LN-type $R3c$, resolved by pair atomic types (black/shaded for Sn-Ti, red/diagonal-striped for Sn-O, green/checkered for Ti-O, and blue/vertical-striped for O-O). The PDF of the Sn-Ti substitutional defect (see Sec. 7) is indicated by the dashed line in the $P4mm$ frame.

Figure 2

Unstable phonon-mode frequencies $\omega$ at $\Gamma$ and various (tetragonal) BZ-boundary $\mathbf{q}$ points of the paraelectric perovskite SnTiO${}_3$ under biaxial strain $\varepsilon$. Imaginary frequencies associated with unstable modes are plotted as negative numbers below the horizontal zero line. $\mathbf{q}$ points $X=(\frac{1}{2},0,0)$, $M=(\frac{1}{2},\frac{1}{2},0)$, $R=(\frac{1}{2},0,\frac{1}{2})$, or $A=(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ are marked in brackets after the instability label subscripts, which indicate the sense of direction: axial ($\alpha$) or ($\alpha ,\beta$) ionic motion for the FE and AFE ones, single ($\alpha$) or an equivalent set ($\alpha ,\beta$) of rotational axes for the AFD ones; here $\alpha ,\beta =x,y,z.$

Figure 3

Polarization (left vertical axis) and tetragonality (right vertical axis, star data points) of epitaxially strained $P4mm$ and $Cm$ SnTiO${}_3$ phases as functions of biaxial misfit strain $\varepsilon$. Polarization of the $R3c$ LN-type structure is also marked on the left as an open square for comparison. The shaded area outlines the region of the $Cm$ phase stability.

Figure 4

Valence-band maxima (VBM) [circles] and conduction-band minima (CBM) [squares] of epitaxially strained $P4mm$ and $Cm$ SnTiO${}_3$ phases as functions of biaxial strain. Data for the corresponding $P4/mmm$ structures are also shown in dotted lines. Open (red) square and circle at zero strain mark the VBM and CBM positions in the cubic $Pm\overline{3}m$ structure.

Figure 5

Evolution of the Ti $d_{xy}$ and O $p_x$ orbital projected density of states (PDOS) in epitaxially strained $P4mm$ and $Cm$ SnTiO${}_3$ with biaxial strain. Data for the corresponding $P4/mmm$ structures are also shown in dotted lines. See Sec. 6 for more details.