Figure 3. Structural distortions and screening length.

(a) Relaxed geometry of the (002) plane of a 2 × 2 × 1 supercell of YMnO₃ with the perfect structure faded in the background for comparison. Y atoms above the (002) Mn–O plane are projected onto the plane. (b) Unrelaxed structure in upper left panel compared with relaxed structures around O_i in the three triple-well positions around the ²/₃, ²/₃, ¹/₂ position. The green arrows on O_i indicate the displacement towards the two Mn⁴⁺. Bond lengths between O_i and Mn are given in Å. (c) YMnO₃ with O_i (green sphere in the (002) Mn–O layer) viewed along the b-direction. (d) Apical and planar tilting angles of the trigonal bipyramids. O1 and O2; and O3 and O4 being apical and planar oxygens, respectively. (e) Displacements of ions with respect to the perfect structure as a function of distance from O_i. The red symbols represent atoms in the same Mn–O layer as O_i is positioned, the blue symbols represent the apical oxygens and the yttrium atoms closest to the Mn–O layer with O_i, and the green symbols show atoms in the adjacent Mn–O layers. The structural screening length is indicated by a vertical dotted line.