Spin-Echo and Free-Induction-Decay Measurements in Pure Fe and Fe-Rich Ferromagnetic Alloys: Domain-Wall Dynamics

Abstract

Measurements were made of the free-induction-decay (FID) and spin-echo amplitudes of ${\mathrm{Fe}}^{57}$ in pure Fe and some of its alloys. Complex spectra are observed consisting of many oscillations often covering a range of many Mc/sec. The amplitudes are very dependent on the pulse length $\ensuremath{\tau}$, the applied rf field ${B}_{1}$, and the exciting frequency $\ensuremath{\omega}$. Excellent agreement is found between the experimental and calculated amplitudes when a model for domain-wall motion is used which takes into consideration the following features: 1. There is an averaging over the orientation of ${\mathbf{B}}_{1}$ with respect to the local magnetization. 2. There is a variation of the enhancement factor across the domain wall due to the spin arrangement in the wall. 3. The domain wall is considered to be composed of area segments which are immobile along their perimeters and whose motion resembles that of a vibrating drumhead. 4. These domain-wall segments have a distribution in areas. The restricted motion of the domain walls imposed by the last two features is essential in order to obtain agreement with the experimental results. This is in contrast to the usual model, which represents the domain-wall motion as given by rigid simple-harmonic-like oscillations; such a model shows great discrepancy with the experimental results presented here. In some of the spectra, asymmetries are observed in the variation of the amplitudes as a function of frequency. No satisfactory explanation for these asymmetries is known although some possible sources are suggested. Such asymmetries make it appear very doubtful that the Fe-alloy spectra obtained with this technique can be reliably unfolded to give the variation of the internal field for second- or higher-neighbor impurity atoms. FID amplitude measurements were also made on Fe in an externally applied dc field. No variation in the value of the maximum enhancement factor was observed for dc fields varying from 0 to about 5 kG.