High-Field Studies of Band Ferromagnetism in Fe and Ni by Mössbauer and Magnetic Moment Measurements

Abstract

High-field susceptibility ${\ensuremath{\chi}}_{\mathrm{HF}}$ in Fe and Ni (at 4.2, 77, and 300\ifmmode^\circ\else\textdegree\fi{}K) and high-field M\"ossbauer studies in Fe at 4.2\ifmmode^\circ\else\textdegree\fi{}K are reported and related to the band structure of Fe and Ni and to band models of ferromagnetism. The M\"ossbauer effect was employed to measure the change in the hyperfine field ${H}_{n}$ at the $^{57}\mathrm{Fe}$ nucleus with application of an external field. Assuming ${H}_{n}$ to be proportional to the bulk magnetization, a microscopic equivalent to ${\ensuremath{\chi}}_{\mathrm{HF}}$ is obtained. We also show how the high-field data may be used alternatively to determine the nuclear $g$ factor. The macroscopic differential magnetic moment measurements are presented along with an extensive discussion of the experiments to 150 kG. We find ${\ensuremath{\chi}}_{\mathrm{HF}}=4.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ emu/cc for Fe and 1.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ emu/cc for Ni at 4.2\ifmmode^\circ\else\textdegree\fi{}K, where ${\ensuremath{\chi}}_{\mathrm{HF}}$ is averaged from 50-150 kG. The interpretation of these low-temperature data (when reasonable estimates of Van Vleck susceptibility are made) indicates holes in both spin bands of Fe and a full band of one spin in N, in agreement with the accepted band theory picture for these metals and with recent spin-polarized and pseudopotential band calculations for magnetic Fe and Ni. The differential magnetic moment measurements at higher temperatures are in reasonable agreement with predictions of spin-wave theory. In the Appendices we include: (a) a tabulation of the fielddependent terms which enter into the spin-wave description of the magnetization and their derivatives with respect to field and temperature, (b) a discussion of depolarization effects and their influence on the approach to saturation, and (c) a discussion of the dependence of the magnetic moment measurements on sample positioning errors.