Origin of Effective Fields in Magnetic Materials

The origin of the effective magnetic fields at the nuclei of magnetic materials which have been determined by Mössbauer, nuclear magnetic resonance, electron paramagnetic resonance, specific heat, and nuclear polarization methods is investigated theoretically by means of the exchange polarization mechanism. Exchange-polarized iron series Hartree-Fock calculations were carried out for (a) free ions and neutral atoms, (b) ions in a (crude) crystalline field (as in a salt), and (c) spin densities and configurations which conform with energy band and neutron magnetic scattering observations for the ferromagnetic metals. The effective field data for metals, ferrites, rare-earth garnets, and salts are then discussed and it is shown that the dominant contribution to the effective field (in almost every case) arises from the (exchange) polarization of the core electrons by the spin density of the unpaired outer electrons. For the transition metals, the role of the conduction electrons is analyzed including some new contributions not previously considered. The data for ions like ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Mn}}^{++}$ may be understood mainly on the basis of the core polarization term but such factors as covalent bonding, charge transfer, crystal field effects (such as distortions from cubic symmetry) must also be included. For ions like ${\mathrm{Fe}}^{++}$ and ${\mathrm{Co}}^{++}$ the (large) field due to unquenched orbital angular momentum must also be considered and several cases in which the orbital field dominates are discussed. The exchange polarization method and the accuracy of the analytic spin-polarized Hartree-Fock functions are discussed with regard to the sensitivity of the internal field to orbital descriptions, the effect of crystalline environments, and to expansion and contraction of the spin density. Each factor is investigated in detail by means of accurate exchange-polarized calculations. In conjunction with these studies a restricted Hartree-Fock calculation for ${\mathrm{Mn}}^{++}$ was carried out (and is reported as an Appendix) which is more accurate than existing calculations and indicates the accuracy of earlier analytic Hartree-Fock calculations.