Spin waves in metallic iron and nickel measured by soft x-ray resonant inelastic scattering

The spin-wave dispersions in iron and nickel along the [111] direction are determined using soft x-ray resonant inelastic x-ray scattering (RIXS). For iron, a 10-nm thin film was studied and, over the limited q range accessible, the peaks disperse as expected for a spin wave and in agreement with inelastic neutron scattering (INS) results. At the higher q values damping is observed with the peaks weakening and broadening. This damping is less pronounced than in the INS studies. The RIXS results are also compared with ab initio spin fluctuation calculations. The calculations slightly underestimate the energy dispersion and the damping is larger than in the measurement. Nevertheless, the agreement between the RIXS results, INS studies, and the theory is quite satisfactory. For the single crystal of nickel, the measured q dispersion flattens out rapidly and the peaks broaden. The strong damping effect is reproduced by the spin fluctuation calculations but the energy of the peaks is largely overestimated. Nevertheless, the flattening of the dispersion is not reproduced by the calculations and, although similar effects were observed in early INS experiments, they are not seen in more recent work. Possible reasons for this are discussed. These measurements show that using soft x-ray RIXS to study spin fluctuations in metallic systems, which are in general very challenging for the technique, has much promise. More interestingly, since the iron measurements were performed on a 10-nm thin film, the study opens the possibility to study tailor-made thin-film samples, which cannot be easily studied by other techniques. Combining these studies with state-of-the-art ab initio calculations opens up interesting prospects for testing our understanding of spin waves in metallic systems.