Comparison of the paramagnetic spin fluctuations in nickel with asymptotic renormalization-group theory

The paramagnetic spin fluctuations in Ni have been investigated at small momentum q and energy transfer Latin small letter h with strokeω by means of inelastic-neutron-scattering techniques. For fixed energy transferred from the neutron to the spin system [S(q,ω=const)], peaks at finite momentum are observed. Their positions are very sensitive to the low-intensity parts of the magnetic cross section. The results are compared with an analytical expression for the dynamical correlation function for an isotropic ferromagnet introduced by Iro. The agreement with the theory is good near Tc for excitation energies 1 meV ≤Latin small letter h with strokeω<kBTc50 meV. Further away from Tc serious discrepancies occur, mainly because the spin fluctuations slow down more quickly than expected on the basis of mode-mode coupling or renormalization-group theory. If the experimentally determined scaling function is used, then the results can be well parametrized. The additional slowing down, which affects also the line shape at Tc, is most likely caused by the interaction of the 3d moments with the conduction electrons, i.e., by an itinerant effect. We have also extracted from our data the asymptotic behavior of the scattering function at very large energy transfers, i.e., SI(q,ω→)ω-(z+4)/z at Tc and the results are in reasonable agreement with renormalization-group theory. No indications for a breakdown of dynamical scaling has been found within the q and E ranges investigated.