Table 1 Summary of the results of selected materials considered in this study.

Material	SG	B-3d	B’-4d/5d	B	B’	M	MS	AHC	AHC\({}_{\max }\)(ΔE)	ANC	ANC\({}_{\max }\)(ΔE)
		site	site	(μ_B)	(μ_B)	(μ_B/f.u.)		(S cm⁻¹)	(S cm⁻¹)	(A m⁻¹ K⁻¹)	(A m⁻¹ K⁻¹)
Ba₂FeMoO₆	225	Fe³⁺ – 3d⁵	Mo⁵⁺ – 4d¹	3.97	−0.40	3.99	FiM	6.94	37 (0.20)	0.04	−0.18 (0.20)
Ba₂CoMoO₆	225	Co²⁺ – 3d⁷	Mo⁶⁺ – 4d⁰	2.70	0.03	2.99	FM	0.00	0.00	0.00	0.00
Ba₂MnMoO₆	225	Mn²⁺ – 3d⁵	Mo⁶⁺ – 4d⁰	4.54	0.11	4.99	FM	0.00	0.00	0.00	0.00
Ba₂FeReO₆	225	Fe³⁺ – 3d⁵	Re⁵⁺ – 5d²	3.90	−0.92	3.06	FiM	33.43	329 (0.20)	0.04	−1.20 (0.14)
Ba₂MnReO₆	225	Mn²⁺ – 3d⁵	Re⁶⁺ – 5d¹	4.52	−0.66	4.03	FiM	278	536 (0.03)	1.52	−2.10 (0.10)
Ba₂NiReO₆	225	Ni²⁺ – 3d⁸	Re⁶⁺ – 5d¹	1.70	0.71	2.95	FM	−495	−571 (0.01)	0.220	2.51 (0.05)
Ba₂NiWO₆	225	Ni²⁺ – 3d⁸	W⁶⁺ – 5d⁰	1.71	0.06	2.01	FM	0.00	0.00	0.00	0.00
Sr₂NiMoO₆	87	Ni²⁺ – 3d⁸	Mo⁶⁺ – 4d⁰	1.67	0.07	2.00	FM	0.00	0.00	0.00	0.00
Sr₂FeMoO₆	87	Fe³⁺ – 3d⁵	Mo⁵⁺ – 4d¹	4.06	−0.55	3.99	FiM	73.68	99 (0.17)	0.03	0.94 (0.16)
Sr₂CoOsO₆	87	Co²⁺ – 3d⁷	Os⁶⁺ – 5d²	2.68	−1.18	1.16	FiM	300	517 (0.12)	−1.61	3.13 (0.20)
Sr₂CoReO₆	87	Co²⁺ – 3d⁷	Re⁶⁺ – 5d¹	2.44	−0.44	2.03	FiM	−22	200 (0.19)	−0.52	−1.97 (0.20)
Sr₂CrOsO₆	87	Cr³⁺ – 3d³	Os⁵⁺ – 5d³	2.74	−1.79	0.18	FiM	0.00	0.00	0.00	0.00
Sr₂NiOsO₆	87	Ni²⁺ – 3d⁸	Os⁶⁺ – 5d²	1.68	1.22	3.84	FM	176	206 (−0.08)	−0.66	−2.60 (−0.19)
Sr₂NiReO₆	87	Ni²⁺ – 3d⁸	Re⁶⁺ – 5d¹	1.67	−0.65	1.03	FiM	447	447	−0.30	2.54 (0.01)

Listed are the space group (SG), charge state, and electron occupancy at the B-3d and B’-4d/5d sites, the magnetic moment at the B-3d and B’-4d/5d sites, theoretical magnetization per formula unit (f.u.), magnetic ground state (MS), AHC, maximum AHC, ANC, and maximum ANC. The maximum values are obtained in an energy window of 200 meV around the Fermi level. ΔE indicates the energy distance in eV of the maximum values with regard to the Fermi level.

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