Fig. 1: Lattice and magnetic structure of PrO₂.

a The distorted crystal structure below 120 K. Yellow balls are Pr, the oxygens positions in the ideal cubic fluorite structure (small white circles) and the corresponding oxygen positions in the distorted structure (red balls) are connected by lines representing the shift due to the distotion (the shift’s magnitude is enhanced with respect to the experimental one for clarity); b Observed antiferromagnetic order at 1.5 K, Ref. ¹⁷, which is also the ground state predicted from the nearest-neighbour multipolar superexchange interactions calculated in this work (only Pr atoms are shown for clarity); c Predicted antiferromagnetic order in PrO₂ under external magnetic field of 5 Tesla applied in the [110] direction (indicated in the plot by the black arrow).