Angular-dependent spin dynamics of a triad of permalloy macrospins

Abstract

We experimentally and theoretically characterize the angular dependent microwave response of three-macrospin-vertex structures that can serve as a node in various spin ice lattices. The macrospins consist of patterned permalloy thin films with an elliptical cross-section together with an in-plane aspect ratio allowing an Ising-like behavior together with bulk modes as low-frequency excitations in the field range of interest. Various branches of the frequency-magnetic field curves display atypical behaviors and discontinuities, together with softening due to macrospin reversals. The overall behavior observed accurately corresponds to a superposition of the spectra of the individual macrospins. The measured ferromagnetic resonance spectra are in good agreement with theoretical modeling. In particular, they reveal a close correlation between the field direction (relative to the individual macrospins), and the corresponding frequency-magnetic field curve; i.e., between the geometry and the magnetic response.

Geometrical frustration and competing orders in the dipolar trimerized triangular lattice

“…Newly emerging coherent x-ray scattering techniques [56] appear to be the best method for shedding light on these open questions. Three-nanomagnet trimers and kagome-based artificial spin ice systems also pose an intriguing case for studies on spin dynamics [31,57,58] and the dipolar trimerized triangular lattice will be an interesting addition to those investigations.…”

Influence of the Vertex Region on Spin Dynamics in Artificial Kagome Spin Ice

“…As remarked in Refs. [24] and [25], as far as the fundamental modes are concerned, the macrospins behave largely independently of each other, and hence the full FMR spectrum can be thought of as the superposition of the single frequency curves of each single macrospin, as taken alone. In particular, in those works it was demonstrated that, when the field is applied at an angle lower than 45 • with respect to the macrospin axis, the corresponding fundamental mode dispersion is almost linear.…”

“…When the angle is around 75 • , the curve initially (i.e., at high field values) shows a linear behavior and then (on approaching zero field) reaches a plateau. When the angle gets very close or equal to the critical value of 90 • , the frequency curve displays a W -shape behavior 24,25 .…”

“…Details of the specific shape of the curves (linear, sub-linear or reaching a minimum before increasing with field again in a "W-shape") are extensively discussed in Ref. [25]. These symmetry considerations are also directly applicable to the experimental data; however, in contrast to the micromagnetic simulations, the effective coupling of the microwave magnetic field changes as the in-plane angle is rotated.…”

Ferromagnetic resonance spectra of permalloy nano-ellipses as building blocks for complex magnonic lattices

“…[1][2][3][4] The magnetic response of the individual segments themselves is also of interest, and the case of permalloy ellipses has been studied via Brillouin scattering for magnetic fields along the in-plane principal axes, [5][6][7][8] and via the timeresolved magneto-optic Kerr effect (TR-MOKE). 9 We recently completed a study of the microwave response of three-fold, 120°-symmetric, clusters of such ellipses 10 and their angular dependence 11 ; our future intension is to incorporate these vertices into honeycomb or Kagome spin-ice lattices. But prior to this, it is important to characterize the behavior of the isolated elements used to assemble these structures, so as to examine the extent to which the responses of the individual ellipses govern the overall response of the clusters and, ultimately, lattices assembled from them.…”