Macroscopic Polarization from Antiferrodistortive Cycloids in Ferroelastic ${\mathrm{SrTiO}}_3$

Based on a first-principles based multiscale approach, we study the polarity $P$ of ferroelastic twin walls in ${\mathrm{SrTiO}}_3$. In addition to flexoelectricity, which was pointed out before, we identify two new mechanisms that crucially contribute to $P$: a direct “rotopolar” coupling to the gradients of the antiferrodistortive oxygen tilts, and a trilinear coupling that is mediated by the antiferroelectric displacement of the Ti atoms. Remarkably, the rotopolar coupling presents a strong analogy to the mechanism that generates a spontaneous polarization in cycloidal magnets. We show how this similarity allows for a breakdown of macroscopic inversion symmetry (and therefore a macroscopic polarization) in a periodic sequence of parallel twins. These results open new avenues towards engineering pyroelectricity or piezoelectricity in nominally nonpolar ferroic materials.

Figure 1

(a),(b) Schematic illustration (not to scale) of the two different types of TBs considered in this work, respectively HH (a) and HT (b). Sr (large green balls), O (small red balls), and the oxygen octahedra are shown; the dashed square indicates the primitive cell of the cubic reference phase; the arrows indicate the local tilt vector. (c) Evolution of ${\varphi }_s$ and ${\varphi }_r$ across the two TBs. A local decomposition of the tilt vector (black arrows) into $s$ (green) and $r$ (red) is also shown. The shaded area indicates the nominal wall thickness $2\xi$. (d) Amplitude of the $u_{\mathrm{Ti}}$ mode in arbitrary units. The inset illustrates the AFE character of the Ti displacements, resembling spins in a $G$-type antiferromagnet. The length scale is in units of $\xi$.

Figure 2

(a) Domain wall thickness $2\xi$ as a function of temperature. (b) Formation energy per surface unit as a function of temperature.

Figure 3

(a) Polarization profile across the two DWs; the dashed line refers to the result $B$, i.e., without including $u^{\mathrm{Ti}}$ in the simulation. (b): Total polarization integrated across the DW as a function of the addition of different couplings in the Hamiltonian. The empty and filled symbols refer to the results obtained while excluding or including the biquadratic and electrostrictive terms. The polarization vector is always oriented towards the apex of the twin boundary.