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Figure 7
(Left) The movements of atom Ca2 from the prototype structure within space group A21am when displaced along the x, y and z directions, as seen in the [110] projection. Colour coding is Ca blue, Mn magenta and oxygen red; perovskite/rocksalt layers are labelled P and R, respectively. There are eight symmetrically equivalent Ca2 atoms in the unit cell, which lie in the rocksalt layers, while Ca1 atoms lie in the perovskite layers. (Right) Three δij patterns ([\bar{2}]24, 004, 2[\bar{2}]4) showing the resulting changes in intensity (yellow = positive, blue = negative). Displacement of Ca2 along x breaks mirror symmetry and produces antisymmetric δij patterns. Displacement of Ca2 along y moves atoms at different depths in opposite directions, maintaining mirror symmetry in the projection and δij patterns, while displacement along z moves Ca2 away from the perovskite layers, also maintaining mirror symmetry. See also the video and Fig. S4 in the supporting information.

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