Fig. 1

Reference cubic perovskite structure and most relevant atomic distortions. a Sketch of the reference \(Pm\bar 3m\) cubic perovskite cell of RNiO₃ compound with R at the corner, Ni at the center, and O atoms at the middle of the faces, forming corner-shared octahedra surrounding the B atoms. Starting from this reference, three main atomic distortions drive the system successively to the Pbnm and then P2₁/n phases: b anti-phase rotations of oxygen octahedra of same amplitudes about x- and y-axis (R _xy ), c in-phase rotations of oxygen octahedra about z-axis (M _z ), d breathing of the oxygen octahedra (B _OC). The energy wells associated to the freezing of individual distortion of increasing amplitude in the cubic cell are shown for different R cations, associated to distinct tolerance factor t, and either a ferromagnetic (full line) or E′-type antiferromagnetic (dashed line, only for R = Y) spin arrangement: YNiO₃ (t = 0.920, blue); GdNiO₃ (t = 0.938, orange) and SmNiO₃ (t = 0.947, green). The atomic distortions are normalized to their amplitude in the P2₁/n AFM-E′ ground state of YNiO₃. Calculations are done for each compound in a cubic cell that has the same volume as the ground state