Evolution of Spin Wave Modes in Periodically Perturbed Thin Films

Periodic perturbations of a magnetic thin film lead to a dipolar contribution proportional to –k (for ultrathin films: k•d << 1) in the dispersion relation of backward volume spin waves additional to the exchange term, which goes quadratically with k. If the scattering condition is fulfilled, meaning the k-vector matches a multiple of the reciprocal lattice vector g0 = 2π/a0, spin waves can scatter into excited magnonic states. This process is referred to as two-magnon scattering (TMS).
In this work, TMS is investigated by introducing periodic defects by Cr+ ion beam irradiation on the surface of a d = 30 nm thick permalloy (Ni80Fe20) film. Patterning was achieved using a PMMA mask, which was pre-structured by electron beam lithography (EBL) and subsequently exposed to a low energy Cr ion beam. Selecting ion energy and fluence, the effective depth of such perturbations can be controlled to investigate the transition from a surface perturbed thin film towards a full magnonic crystal.
The FMR spectra f(H) (see Fig.1) of different samples with varying perturbation depth h and a periodicity a0 ranging from 200 nm to 400 nm have been measured showing mode splitting at each crossing point of higher spin wave modes with the uniform mode due to TMS. Moreover, brillouin light scattering (BLS) measurements have been performed to directly measure the dispersion relation of such periodically perturbed film.
In a further experiment, the evolution of FMR mode splitting dependent on the perturbation depth h was investigated performing multi-step reactive Ar+ ion beam etching (RIBE) of surface steps on a 30 nm permalloy film.
Theoretical calculations based on a perturbation theory[1,2] are accompanied and reveal a good agreement of experiment and theory (see Fig.1). Amongst that, numerical simulations of the FMR spectra were carried out using the MuMax3 code allowing for deeper understanding of the micromagnetic structure of the observed magnonic modes, such as the visualization of the dynamic magnetization.
This work has been supported by DFG grant no. LE2443/5-1.
References:
[1] P. Landeros and D. L. Mills, Phys. Rev. B 85, 054424 (2012).
[2] R. A. Gallardo, A. Banholzer, K. Wagner, M. Körner, K. Lenz, M. Farle, J. Lindner, J. Fassbender and P. Landeros, New J. Phys 16, 023015 (2013).
[3] M. Körner, K. Lenz, R. A. Gallardo, M. Fritzsche, A. Mücklich, S. Facsko, J. Lindner and J. Fassbender, Phys. Rev. B 88, 054405 (2103).