Fig. 4: Phase transitions and magnetic interactions in ETO under pressure, from DFT calculations.

a The energy difference between FM and AFM showing a clear magnetic phase transition. The star represents the experimental negative pressure. b Atom displacement along z-direction (OOP direction) showing a clear ferroelectric phase transition. The inset shows a schematic diagram for the movement of atoms under pressure. c Schematic diagram with a G-type AFM magnetic configuration adopted for ETO, with different interactions. J1m (m = 1,2) refers to the nearest interactions, J2n (n = 1,2) refers to the next-nearest interactions, and J33 refers to the next-next-nearest interactions. d Calculated variation of magnetic exchange coefficients of ETO under different pressures.