Electronic Structure of Strongly Correlated Systems

Table 1

3𝑑 orbital contribution to the formation of Fe_𝐵 minority spin states with occupancy 𝑛 evaluated by diagonalization of the occupation matrix [155]. Although one of the 𝑡_2𝑔↓ states of 𝐵1 and 𝐵4 sites is almost occupied with 𝑛≥0.7 𝑒 the 𝑡_2𝑔 minority spin occupancies of 𝐵2 and 𝐵3Fe³⁺ cations are less than 0.1𝑒. The occupied 𝑡_2𝑔↓ states of 𝐵1 and 𝐵4Fe²⁺ cations are predominantly of 𝑑_𝑥𝑧±𝑑_𝑦𝑧 and 𝑑_{𝑥2−𝑦2} characters, respectively. The sum of 𝑡_2𝑔 (𝑒_𝑔) occupations is given in the last column.

Fe𝐵 ion	Sym.	𝑡2𝑔			𝑒𝑔			∑𝑡2𝑔
		𝑦𝑧	𝑧𝑥	𝑥^2−𝑦^2	3𝑧^2−𝑟^2	𝑥𝑦	𝑛	(∑𝑒𝑔)
Fe𝐵1𝑎	𝑡2𝑔	−0.47	−0.80	0.34	0.00	−0.07	0.81	0.89
		0.86	−0.33	0.40	−0.01	0.01	0.04
		−0.21	0.49	0.84	−0.01	0.04	0.04
	𝑒𝑔	0.04	0.06	0.01	−0.49	−0.87	0.15	0.26
		−0.02	−0.03	−0.02	−0.87	0.48	0.11
Fe𝐵1𝑏	𝑡2𝑔	−0.47	0.83	0.28	−0.03	0.12	0.71	0.79
		0.83	0.31	0.46	0.00	0.00	0.04
		0.30	0.45	−0.84	0.00	0.02	0.04
	𝑒𝑔	−0.05	0.11	0.02	0.55	−0.83	0.15	0.27
		0.01	−0.04	0.00	0.83	0.55	0.12
Fe𝐵2𝑎	𝑡2𝑔	0.00	0.91	0.41	0.00	0.00	0.09	0.24
		−0.99	0.00	0.01	0.00	0.00	0.08
		−0.01	0.41	−0.91	−0.04	0.00	0.07
	𝑒𝑔	−0.01	0.00	0.00	0.00	0.99	0.27	0.52
		0.00	−0.02	0.04	−0.99	0.00	0.25
Fe𝐵2𝑏	𝑡2𝑔	0.00	−0.90	0.45	0.01	0.00	0.09	0.23
		−0.99	−0.01	−0.03	0.00	−0.05	0.07
		0.03	−0.45	−0.89	−0.04	0.00	0.07
	𝑒𝑔	0.00	−0.01	−0.04	0.99	0.00	0.26	0.52
		−0.05	0.00	0.00	0.00	0.99	0.26
Fe𝐵3	𝑡2𝑔	0.79	−0.18	0.53	−0.09	0.24	0.17	0.36
		−0.22	0.73	0.63	0.13	−0.10	0.11
		0.52	0.65	−0.55	−0.08	−0.04	0.08
	𝑒𝑔	−0.21	0.12	0.04	−0.91	0.35	0.25	0.49
		0.13	−0.11	0.11	−0.39	−0.90	0.24
Fe𝐵4	𝑡2𝑔	−0.55	−0.18	0.82	−0.02	0.02	0.80	0.87
		0.51	−0.85	0.16	0.01	−0.04	0.04
		0.66	0.50	0.55	−0.03	0.01	0.03
	𝑒𝑔	−0.01	−0.02	−0.03	−0.99	−0.12	0.13	0.25
		−0.02	0.03	0.02	0.12	−0.99	0.11