Magnetic excitations in nickel and iron

Abstract

A reanalysis of existing relevant experimental data shows that at low temperatures (T<or=0.4TC) the variation of magnetisation with temperature can be well explained, for both Ni and Fe, by adding a T2 term to the usual Bloch T3/2 spin-wave term. In the particular case of Ni such a procedure now reconciles the values of the spin-wave stiffness constant as deduced from magnetisation and neutron measurements. The T2 term is thought to arise from Stoner nonspin-flip excitations rather than Stoner spin-flip excitations since the latter are found to be unimportant at low temperatures. At higher temperatures collective excitations in the molecular field (as distinct from single-site spin reversals in such a field) and Stoner spin-flip excitations contribute to the decrease of the spontaneous magnetisation. Regarding the former as some sort of an 'optic' spin-wave mode with a quadratic dispersion relation, a cross-over point between the resulting two spin-wave modes in Ni is obtained at about the same wavevector (0.47 AA-1) and energy (120 meV or 29 THz) as has been found in recent neutron measurements of the spin-wave dispersion curves. A similar cross-over is predicted to occur for pure Fe at a wavevector of about 0.74 AA-1 and an energy of about 166 meV (40 THz). It is further suggested that the intersection of the acoustic spin-wave mode with the Stoner spin-flip excitations should occur at energies much higher than the cross-over energies.