Spin-polarized energy-band structure, conduction-electron polarization, spin densities, and the neutron magnetic form factor of ferromagnetic gadolinium

Conduction-electron polarization, spin densities, and neutron magnetic scattering in ferromagnetic Gd metal were studied using the spin-polarized augmented-plane-wave (APW) method in a warped-muffin-tin-potential formulation. The spin-up and spin-down bands were found to be very similar in shape to the bands from a paramagnetic calculation, with the exchange splitting proportional to the amount of d character in the bands. It was also found that the conduction-electron spin density determined from the APW wave functions is of mostly d character. This dominance of the d-like wave functions for the spin-dependent interactions is explained by (i) the much greater overlap of the 4f states with the d-like wave functions as compared to the s-p wave functions; (ii) the nearly complete d character of the bands in the region of the Fermi surface. The magnetic form factor was calculated from the conduction-electron spin density and compared with the recent neutron magnetic - form - factor measurement of Moon, Koehler, Cable, and Child. The calculated spin density was found to have the same shape as the "diffuse" density derived by Moon et al. (including a negative but much smaller in magnitude spin density at the c site in the unit cell). After the inclusion of core - polarization effects we conclude that large nonspherical contributions with Y33-Y3-3, and Y40 angular dependence are needed to explain the experimental results.