Dynamics of Macrospins: Symmetric and Asymmetric Frustrated Structures

Systems with frustrated magnetic interactions, such as artificial spin ice arrays, have recently attracted much attention, particularly with respect to the field dependencies of the quasi-static magnetic response and accompanying magnetic instabilities. The dynamic behavior of the underlying macrospins is also of interest, but has received much less attention, especially with respect to soft mode behavior near instabilities. Here we will describe results on the microwave absorption spectrum of an array of 15 nm thick, three-petal (120°-symmetric) rose-like structures consisting of elongated, nearly-contacting, Permalloy elliptical dots. The structures were patterned using e-beam lithography on top of a coplanar waveguide, thereby achieving maximal coupling and sensitivity[1]. Larger arrays were also prepared on which static magnetization measurements were performed. Ferromagnetic resonance spectra were collected while continuously sweeping between large positive and negative fields, together with the opposite direction, for a broad range of closely spaced frequencies. The data reveal several modes, with frequency/field trajectories persisting through field reversal, after which they soften and disappear below certain critical fields. Calculations based on the dynamical matrix method[2] and the discrete dipole approximation were performed which show excellent agreement with the experimentally observed results for both the dynamic and static response of our arrays, including the positions of the instabilities. The angular dependence of both the static and dynamic behavior is also investigated. Finally, we will describe changes in the dynamic and static magnetization behaviors induced by reducing the aspect ratio of one of the petals as compared with the fully symmetric geometry. **Work at Northwestern and Kentucky supported under NSF grants DMR 1507058 and DMR 1506979, respectively. Work at Argonne supported by the US Department of Energy, Office of Science, Materials Science and Engineering Division. [1] M. B. Jungfleisch et. al., Phys. Rev. B 93, 100401(R) (2016). [2] L. Giovannini, F. Montoncello, and F. Nizzoli, Phys. Rev. B 75, 024416 (2007)