Table 4. The total energy difference and thermodynamic stability for different known and predicted RP phases from Quantum ESPRESSO63.
| RP oxides | Crystal symmetries from phonon calculations (ΔE) | Machine learning (ΔE) | ΔED | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| P4/nmm | Pmn21 | Pc |
P 21m
|
P 2m
|
I 2m
|
Pnma | P21212 | Pbcm | Pca21 | ||
| Known composition | |||||||||||
| Ca2IrO4 (Pbca) | — | — | — | — | — | — | — | — | — | — | +34 |
| Ca2IrO4 (I4/mmm) | — | — | — | — | — | — | — | — | — | — | +156 |
| New predictions | |||||||||||
| Stannates | |||||||||||
| NaLaSnO4 | 2.3 | 1.7 | 1.7 | 0 | 2.4 | 2.1 | 2.3 | 0 | 0.9 | 0.3 | +68.6 |
| NaPrSnO4 | 9.5 | 9.3 | 9.3 | 0 | 9.5 | 3.4 | 9.5 | 0 | 3.4 | 2.9 | +79.9 |
| NaNdSnO4 | 14.7 | 14.7 | 15.4 | 0 | 14.4 | 3.9 | 14.7 | 0 | 5.4 | 1.3 | +81.2 |
| NaGdSnO4 | 40.2 | 34.8 | 34.5 | 0 | 28.0 | 5.4 | 35.2 | 0 | 14.6 | 10.9 | +75.6 |
| NaYSnO4 | 46.8 | 37.1 | 36.4 | 0 | 32.5 | 5.9 | 37.6 | 0 | 16.6 | 11.7 | +73.6 |
| Ruthenates | |||||||||||
| NaLaRuO4 | 5.7 | 5.1 | 5.1 | 0 | 4.9 | 2.6 | 5.1 | 0 | 0.5 | 0.4 | +72.2 |
| NaPrRuO4 | 15.5 | 14.9 | 14.9 | 0 | 10.9 | 4.6 | 14.9 | 0 | 1.8 | 0.7 | +78.3 |
| NaNdRuO4 | 21.1 | 20.4 | 20.4 | 0 | 13.8 | 5.0 | 21.1 | 0 | 2.8 | 0.3 | +53.3 |
| NaGdRuO4 | 46.1 | 41.7 | 41.7 | 1.0 | 26.6 | 7.1 | 43.2 | 1.03 | 8.9 | 0 | −14.1 |
| NaYRuO4 | 179.9 | 47.6 | 47.6 | 2.6 | 32.7 | 8.8 | 49.2 | 2.6 | 11.4 | 0 | −1.3 |
DFT, density-functional theory; RP, Ruddlesden-Popper; OQMD, Open Quantum Materials Database.
The total energy difference ΔE (in units of meV per atom) is taken with respect to the lowest energy phase. Crystal symmetry with ΔE=0 is identified as the ground state structure. For all ruthenates, we imposed ferromagnetic spin order on the Ru atom. ΔED in meV per atom is the total energy difference calculated from DFT for a decomposition reaction obtained from OQMD50,51. Negative and positive values for ΔED indicate that the compound is thermodynamically stable and unstable, respectively. Corresponding decomposition reactions are given in Supplementary Note 4. For Ca2IrO4, space groups Pbca and I4/mmm are the theoretical ground state and high-symmetry structures15, respectively. Furthermore, in stannates structures initialized with Pnma symmetry converged to P21/m when R=La, Pr or Nd. Similarly, in ruthenates Pc structure converged to P1 when R=Pr, Gd or Y.