. 2017 Feb 17;8:14282. doi: 10.1038/ncomms14282

Table 6. Total energy difference (ΔE in meV per atom) with respect to the lowest energy structure for NaRRuO₄ in two P 2₁ m and Pca2₁ structures with both FM and AFM spin configurations.

Compound	ΔE
	P2₁m FM	P2₁m AFM	Pca2₁ FM	Pca2₁ AFM
NaLaRuO₄	0	7.3	0.4	6.0	0.91
NaPrRuO₄	0	6.8	0.7	1.8	0.91
NaNdRuO₄	0	6.7	0.3	0.5	0.91
NaGdRuO₄	2.5	8.7	1.4	0	0.85
NaYRuO₄	8.1	14.1	5.5	0	0.84

AFM, antiferromagnetic; FM, ferromagnetic.

All compounds initialized with AFM P Inline graphic 2₁m converged to AFM P2₁2₁2 structures indicating evidence of spin–lattice coupling. Constraining AFM configuration in P2₁m structures (where we fixed the lattice constants to that of FM P2₁m) only resulted in total energies higher than that for AFM P2₁2₁2. Structures with ΔE=0 represent the ground state configuration. Inline graphic is the absolute value for the magnetic moment per Ru-site (in Bohr magnetons) in the corresponding ground state structures.

Table 6. Total energy difference (ΔE in meV per atom) with respect to the lowest energy structure for NaRRuO4 in two P 21 m and Pca21 structures with both FM and AFM spin configurations.

Table 6. Total energy difference (ΔE in meV per atom) with respect to the lowest energy structure for NaRRuO₄ in two P 2₁ m and Pca2₁ structures with both FM and AFM spin configurations.