Local indirect magnetoelectric coupling at twin walls in CaMnO$_3$

TL;DR

This study addresses whether ferroelastic twin walls in the centrosymmetric antiferromagnet CaMnO3 can host local polarization and magnetization and exhibit a magnetoelectric coupling absent in the bulk. Using density functional theory with PBEsol+U for Mn 3d states, the authors model two ferroelastic wall geometries in the Pnma phase and analyze both collinear and noncollinear magnetic configurations. They find wall-centered polarization and a finite magnetization confined to the wall, enhanced Mn canting, and a strain-mediated coupling between polarization and magnetization driven by octahedral rotations, with the effect strongest for walls displaying larger strain gradients (the 90° wall). The results imply a general mechanism for magnetoelectric effects at ferroelastic domain walls in bulk centrosymmetric antiferromagnets and highlight LaFeO3 as a potential experimental candidate for observing these phenomena.

Abstract

Ferroelastic twin walls in centrosymmetric perovskites can host emergent polar and magnetic properties forbidden in the bulk. We use density functional theory calculations to study the geometry and magnetic properties of ferroelastic domain walls in orthorhombic CaMnO$_3$, which belongs to the most common perovskite space group, $Pnma$. At the wall, the inherent inversion symmetry-breaking induces local polar distortions dependent on the wall geometry, which couple to the magnetic order through the octahedral distortions. Noncollinear calculations reveal enhanced out-of-plane magnetic moments on the Mn atoms and a local, finite magnetization confined to the wall. Strain fields across twin walls thus give rise to coexistence of polarization and magnetization as well as magnetoelectric response that is absent and symmetry-forbidden in bulk CaMnO$_3$. We propose that magnetoelectric coupling and coexisting polarization and magnetization can emerge at twin walls in bulk centrosymmetric antiferromagnets.

Figures (5)

• Figure 1: (a) The distortion modes present in the ground state of CaMnO3. The top octahedron illustrates the rotational modes around each pseudocubic axis, namely the $R_4^+$ (here denoted $R_x$ and $R_y$ by their respective rotational axis), and $M_3^+$ (denoted $M_z$). The bottom figure displays the A-site displacement in the $xy$-plane, decoupled as an $X_y$ and $X_x$-mode along each axis. (b) Dashed lines mark the orthorhombic primitive cell, while solid lines display the strained 40-atom cell. The arc at the lower left vertex indicates the angle $90^\circ-\gamma$, where $\gamma$ is the twin angle. (c)-(d) Relaxed mirror and $90^\circ$ ferroelastic domain wall cells. Black arrows show the octahedral tilting direction resulting from the out-of-phase rotations, and "+" and "-" denote a clockwise or counter-clockwise in-phase rotation around the $z$-axis, prior to relaxation. The black dashed line illustrates the center position of the domain wall. Note that only half of the supercell is displayed here.
• Figure 2: (a)-(b) Order parameter evolution calculated as the rotation angle around the $x$, $y$ and $z$-axes, as a function of the distance through the domain wall cell, for (a) a $90^\circ$ wall and (b) a mirror wall. The location of each domain wall is indicated by the dashed lines. (c)-(d) Polar distortion profiles of each domain wall type for the first domain wall of the cell, denoted "DW1". The distortion is calculated as the displacement of the Mn-atom from the center of mass of the surrounding oxygen octahedron. DW2 shows the same trend, except that the direction of $D_y$ is reversed. For the mirror wall, $D_z$ is also reversed.
• Figure 3: (a) Average Mn-O-Mn bond angles calculated as a function of distance from the first domain wall in each supercell. $\delta$ represents the angles around the axis of in-phase rotations ($z$), while $\phi_\|$ and $\phi_\perp$ are the in-plane angles, parallel and perpendicular to the domain wall. (b) Bond length alteration at each domain wall. $\alpha_\|$ and $\alpha_\perp$ denote the in-plane bond lengths parallel and perpendicular to the domain wall, while $\beta$ is the average bond angle in the $z$ direction. (a)-(b) All values converge to bulk values with the exception of $\alpha_{\perp,90^\circ}$ which is why these have been omitted from the plot.
• Figure 4: (a) Spin orders for the four lowest energy magnetic wall configurations. The cartesian axes coincide with those in Figure \ref{['fig:1']}. The position of the domain wall is indicated by the red plane. (b) Formation energies from placing a magnetic wall at the domain wall as opposed to a bulk structure, for a selection of spin orders, sorted with respect to the mirror domain wall. (c) Polar distortion profiles for the lowest energy magnetic walls for each respective domain wall type. For each magnetic wall the corresponding ground state distortion is shown at a higher transparency for comparison. The data is plotted without fits to hyperbolic functions to highlight the differences between the profiles.
• Figure 5: (a) The initial magnetic order prior to the self-consistent spin rotation. The magnetic domain wall corresponds to a "mirror" symmetric interface (if the spins are not treated as axial vectors). (b) The resulting average magnetization of one unit cell consisting of eight Mn atoms. While $m_x$ and $m_y$ cancel each other, there is a net magnetization, $m_z$, in the out-of-plane direction. Note the break in the $y$-axis scale.