On the magnetic excitations in nickel

By comparing measured and calculated versions of the generalized magnetic response function of nickel over a wide range of temperatures it is shown that the much-discussed simple model of an itinerant-electron ferromagnet based on a random-phase-approximation treatment of the Hubbard Hamiltonian accounts, in its essentials, for the magnetism of that substance. Thermal neutron inelastic scattering techniques were used to explore the whole Brillouin zone of wave vectors K in nickel up to energies ▄ω of some 2k _B T _C over the range of temperatures up to 2T _C; the computations were based on direct evaluation of the Lindhard expression for the generalized susceptibility, using a tight-binding band structure, followed by exchange enhancement of the spin part as per Izuyama, Kim and Kubo. The contribution to the neutron scattering from orbital motion of the electrons was estimated to be small, and in a special experimental investigation a satisfactorily low upper limit on this quantity for our present purposes was observed.

In the course of the article we attempt to illuminate with our computational results the theoretical content of the random-phase approximation, and to show how it accounts for spin waves, paramagnons and a variety of other phenomena. For instance at low temperatures, where the collective or spin-wave mode is the most prominent feature, the Stoner-mode states are so strongly mixed with the spin-wave states by the electron-electron interaction that little trace is left of the ‘band of Stoner modes’ often referred to in elementary accounts of this phenomenon. With increase of temperature, the severe broadening of the spin wave and the characteristic style of evolution of the magnetic response function through the critical temperature are correctly predicted, outside a narrow range of conditions about the critical point. The dramatic divergence of the susceptibility characteristic of the phase transition is confined much more closely towards the origin of K,ω space than could be accounted for by free-electron gas theory, and this is explained. On the other hand what appears to be a case of breakdown of the random-phase approximation is detected in the ferromagnetic state, where in a certain set of conditions at large K and small ω an excess of longitudinal spin correlation was measured over that expected theoretically.

Aside from the aforementioned aberrant region, however, absolute agreement between experiment and theory essentially within the statistical error is obtainable by assuming that the effective Coulomb interaction parameter I _eff(K) falls off gently between K=0 and K _max in a manner consistent with the predictions of Singwi et al. ; with increase of temperature, I _eff(0) declines gently and the amount of fall-off with K increases. It is shown that the theory of the Heisenberg ferromagnet fails entirely to account for the observations—indeed, fails to correlate any of the data on nickel—and that at least three-quarters of the known magnetic stiffness of nickel must be due to band-theory effects rather than to Heisenberg-type exchange integrals.