Crystal field splitting

When we put a transition metal ion in a crystal, the systematics of the corresponding electron states changes. For isolated atoms or ions we have spherical symmetry, and the corresponding states are characterized by the principal quantum number n, by orbital moment l and, with spin–orbit coupling included, by the total angular momentum J. When the atom or ion is in a crystal, the spherical symmetry is violated; the resulting symmetry is the local (point) symmetry determined by the structure of the crystal. Thus, if a transition metal ion is surrounded by a regular octahedron of anions such as O2− (Fig. 3.1) (this is a typical situation in many TM compounds, e.g. in oxides such as NiO or LaMnO3), the d levels which were fivefold degenerate in the isolated ion (l = 2; lz = 2, 1, 0, −1, −2) are split into a lower triplet, t2g, and an upper doublet, eg (Fig. 3.2). The corresponding splitting is caused by the interaction of d-electrons with the surrounding ions in the crystal, and is called crystal field (CF) splitting. The type of splitting and the character of the corresponding levels is determined by the corresponding symmetry. The detailed study of such splittings is a major field in itself, and is mostly treated using group-theoretical methods.