Hyperfine fields at nonmagnetic atoms in metallic ferromagnets

The various models used to describe the hyperfine field at nonmagnetic impurities in metallic ferromagnets are discussed. These models fall into two main categories. In one the impurity is considered to introduce a strongly perturbing charge disturbance and solute-host effects are nonseparable. These models use scattering-theory concepts and formalism and the host and impurities are represented by parameters which are difficult to relate to, and often in conflict with other known information about these systems. In the other approach the perturbation of the $s$-conduction-electron polarization caused by the solute is considered to be small enough so that the hyperfine field at the impurity can be separated into a host $s$-conduction-electron polarization contribution and a contribution associated with the impurity atom. This model is formulated in terms of atomic and band properties and thus can give information about the impurity and host wave functions. This separable volume misfit model is modified from earlier presentations to take into account the changes in the $d$-conduction-electron polarization in the vicinity of impurity atoms with $d$ valence electrons. The impurity contribution, also known as the transferred hyperfine field or volume overlap contribution, has been calculated for the $4sp$ and $5sp$ solute atoms in Fe. The main differences from previous calculations of this type are that in order to better represent the solid state of the host we have used a more diffuse $3d$ orbital for the Fe atoms which closely resembles the Fe band orbital. We have also included contributions from the 2nn (2nd nearest neighbor) and 3nn shells. With these improvements we get excellent agreement between the experimental solute-atom contribution obtained from the volume misfit model and the calculated overlap hyperfine fields.