Improper origin of polar displacements at CaTiO${}_3$ and CaMnO${}_3$ twin walls

Recent interest in novel functionalities arising at domain walls of ferroic materials naturally calls for a microscopic understanding. To this end, first-principles calculations have been performed in order to provide solid evidence of polar distortions in the twin walls of nonpolar CaTiO${}_3$ and magnetic CaMnO${}_3$. We show that such polar displacements arise from rotation and/or tilting octahedral distortions—cooperatively acting at the twin wall in both considered systems—rather than from a proper secondary ferroelectric instability, as often believed. Our results are in excellent agreement with experimental observations of domain walls in CaTiO${}_3$. In addition, we show that magnetic properties at the twin wall in CaMnO${}_3$ are also modified, thus suggesting an unexplored route to achieve and detect multiferroic ordering in a single-phase material.

Figure 1

(a) Ball-and-stick model of a CaTi(Mn)O${}_3$ supercell. (b) Top view highlighting the ferroelastic domains, with orthorhombic cells mirrored with respect to the $\left[1\overline{1}0\right]$ plane, and the twin angle of CaTiO${}_3$. Yellow and red balls refer to Ca and O atoms, respectively, while Ti (Mn) ions are inside purple octahedra. (c),(d) Layer-averaged rotational order parameters as a function of the distance from the twin wall and associated offcentering of $B$-site ions estimated from the center-of-mass of oxygen octahedra for (c) CTO and (d) CMO. The DW profile of the polar offcenterings was fitted via a function $D_y\left(X\right)=D_0{\text{sech}}^2\left(\frac{X}{{\xi }_D}\right)$ [7].

Figure 2

(a) Sketch of the two different choices of unit cells used for the calculation of polarization via Born effective charges. The polarization profile in the supercell is then evaluated as sketched in (b). (c) Total polarization profile at the CTO twin wall and contributions assigned to different ions; empty and solid symbols refer to different choices of the unit cell, referring respectively to $A$-site and $B$-site centered cells.

Figure 3

Antipolar displacements of Ca ions in the bulk $Pbnm$ structure of Ca$B$O${}_3$, showing the two kinds of modulated collective antiferrodistortive distorsions (a) ${\mathit{A}}^{001}$ and (b) ${\mathit{A}}^T\left(X\right)$. (c) Antipolar displacements at the considered twin wall, separating two twin domains characterized by different AFD polarizations; the emergence of the third local displacement induced by the local rotational pattern is also highlighted. (d) DW profile of bulk antipolar order parameters in CTO, describing antipolar displacements of Ca ions evaluated in the local center of mass of each CaO${}_{12}$ dodecahedron. (e) Layered-averaged polar offcentering ${\mathit{D}}^{\text{Ca}}$ of Ca ions, compared with the DW profile of the antipolar OP ${\mathit{A}}^{100}$ that is expected to develop only at the wall.

Figure 4

(a) Sketch of the evaluated DW exchange couplings at the interface; the domain wall between two AFM-G domains with all parallel-spin bonds across the DW, labeled as FM${}_X$ configuration, is also highlighted. (b),(c) Mn offcentering profile when the magnetic domain wall is assumed to be on top of the ferroelastic twin boundary [(b) DW+MW] and of the bulk lattice structure [(c) MW], compared to the single AFM-G magnetic domain with ferroelastic twin wall (dotted lines).