Paramagnetic resonance in dilute iron group fluorides. II. Wave functions of the magnetic electrons

Abstract

The data on the g, A and D tensors and on the fluorine hyperfine structure coupling tensors for paramagnetic ions in a ZnF$_{2}$ lattice are interpreted in terms of 3d orbitals augmented by attached fluorine wave functions of appropriate symmetry. It is suggested that fluorine 3s and 3p functions are required, in addition to the 2s and 2p functions usually assumed, to give quantitative agreement between the fluorine h.f.s. coupling and the spin-orbit coupling reduction effects. The presence of n = 3 functions also renders the dependences on internuclear distance more easily understood. Charge transfer by $\pi $- and $\sigma $-bonding seems to be of the same order, but the s-electron contact interaction of the $\sigma $-bonding electrons gives the dominant h.f.s. interaction. Particularly complete analyses are possible for Mn$^{2+}$ and Fe$^{2+}$. In these cases, we estimate that the magnetic electrons have a probability of about 6% of being in fluorine n = 2 orbitals, about the same of being in fluorine n = 3 orbitals, roughly 25% of being in the overlap region, leaving only about (60 $\pm $ 10)% probability of being on the central ion. The charge transfer in the case of Co$^{2+}$ is believed to be less, and perhaps more typical of the situation when the ions are in their own lattices, with proper lattice parameter. The absence of resolved fluorine h.f.s. with Cr$^{3+}$ is consistent with the absence of d$\gamma $ electrons in the 3d$^{3}$ configuration in an octahedral environment.