Crystal field analysis of the 3d N ions at low symmetry sites including the ‘‘imaginary’’ terms

Abstract

The crystal field (CF) package applicable to orthorhombic or higher symmetry has been extended to enable calculations of energy levels and ligand field states for 3dN ions in crystals at arbitrary symmetry sites by taking into account the contributions of the ‘‘imaginary’’ CF terms. The full Hamiltonian matrix, including the electrostatic terms, Trees correction, the spin–orbit interaction, and the ligand field terms, is diagonalized within the whole 3dN configuration. Several techniques based on the transformation properties of the crystal field Hamiltonian have been devised to test the package for internal consistency. The package is especially suitable for analysis of the low symmetry effects for transition metal ions at sites with the tetragonal and trigonal symmetry involving the imaginary CF terms as well as monoclinic and triclinic symmetry. It can be useful in analyzing the electron paramagnetic resonance spectra of 3dN ions and in correlating the ligand field parameters with the spin Hamiltonian parameters.