Brillouin light scattering investigation of magnetostatic modes in symmetric and asymmetricNiFe∕Cu∕NiFetrilayered wires

Abstract

The peculiarities of magnetostatic resonances of trilayered wires ($700\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ wide) consisting of two ferromagnetic permalloy layers, coupled by dipolar interaction across a nonmagnetic Cu spacer, have been comprehensively studied both experimentally and theoretically. Both a symmetric structure, $\mathrm{Ni}\mathrm{Fe}(30\phantom{\rule{0.3em}{0ex}}\mathrm{nm})∕\mathrm{Cu}(10\phantom{\rule{0.3em}{0ex}}\mathrm{nm})∕\mathrm{Ni}\mathrm{Fe}(30\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$, and an asymmetric one, $\mathrm{Ni}\mathrm{Fe}(10\phantom{\rule{0.3em}{0ex}}\mathrm{nm})∕\mathrm{Cu}(10\phantom{\rule{0.3em}{0ex}}\mathrm{nm})∕\mathrm{Ni}\mathrm{Fe}(30\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$, were analyzed. Brillouin light scattering (BLS) from thermally excited spin waves, has been performed as a function of the incidence angle of light and of the intensity of the external applied field. A number of discrete peaks, corresponding to the resonant frequencies of the trilayered structures have been observed in BLS spectra. To achieve a satisfactory interpretation of the experimental results, substantial improvements of previous theoretical models were necessary. In this case, in fact, due to the rather large value of the ferromagnetic layers thickness, the dipole interaction between magnetic layers associated with the nondiagonal terms of the tensorial Green's functions (describing a dynamic dipolar magnetic field induced by one magnetic layer in the other one) gives significant contributions to the resonant frequencies.