Figure 1

(a) Magnetic unit cells of the two $E$-phase domains in ${\mathrm{HoMnO}}_3$ corresponding to the ($E_1$, 0, $-P_a$) and (0, $E_2$, $P_a$) solutions of (2). The arrows on the Mn atoms denote the directions of their spins. The FE displacements are not shown, but the direction of $\mathbf{P}$ is indicated. (b) The simple sine-wave magnetic structure of ${\mathrm{HoMnO}}_3$ for $T_L<T<T_N=42.2–47.5\mathrm{K}$ [16]. (c) The $E$-phase magnetic structure below $T_L$.Reuse & Permissions

Figure 2

(a) The starting configuration of a Mn-O-Mn bond. Numbers 1–4 enumerate the O atoms surrounding one Mn. (b) An MC snapshot of the IMF $E$-phase at $T=0.01$. The ferromagnetic zigzag chain links are shown as solid lines. The displacements of the oxygen atoms are exaggerated. (c) Left. The local arrangement of the Mn-O bonds with disordered Mn spins (full circles). Right. Oxygen displacements (arrows) within the chains of opposite Mn spins (open and crossed circles) in the $E$-phase (see also Refs. 3, 15). (d) MC results for the polarization at $T=0.01$ for different values of $J_{\mathrm{AF}}$.Reuse & Permissions