Deviations fromT32Law for Magnetization of Ferrometals: Ni, Fe, and Fe+3% Si

The variation with temperature of the magnetizations of single crystals of Ni, Fe, and Fe+3 wt% Si are studied. New data for Fe and Fe(Si) is presented along with previously reported measurements for Ni. These data were obtained by means of the pyromagnetic effect at various applied fields and in the temperature range 4.2-140, 30, and 120°K for the Fe, Fe(Si), and Ni crystals, respectively. The observed departures from $T^{\frac{3}{2}}$ behavior are well described by spin-wave theory. Attempts to ascribe some of the measured variation of the magnetization to Stoner-type excitations or to variation of the moment per atom due to lattice expansion are mainly unsuccessful. The coefficients of the $T^{\frac{3}{2}}$ term appropriate for zero spin-wave energy gap are $C=7.5\mathrm{}\pm 0.2, 3.4\pm 0.2, \mathrm{and} 4.4\pm 0.2\times {10}^{-6\mathrm{}} {\mathrm{deg}}^{-\frac{3}{2}}$ for Ni, Fe, and Fe(Si), respectively. The coefficients of the $T^{\frac{5}{2}}$ term for zero gap are determined only for the Ni and Fe crystals as $D=(1.5\mathrm{}\pm 0.2)\times {10}^{-8\mathrm{}} {\mathrm{deg}}^{-\frac{5}{2}} \mathrm{and} (1\mathrm{}\pm 1)\times {10}^{-9\mathrm{}} {\mathrm{deg}}^{-\frac{5}{2}}$, respectively. The measured variation of the spin-wave energy gap with applied field is consistent with the known $g$ values of 2.19 and 2.09 for Ni and Fe. The magnitude of the gap at zero field is fully explained by the effects of magnetocrystalline anisotropy and magnetic-dipolar coupling. The values of the $C$ and $D$ coefficients are compared with results from independent experiments and are discussed in relation to theories of ferromagnetism in metals.