Softening of spin waves calculated under a Hamiltonian approach: importance for information delivery, and in the understanding of reversal avalanches in macrospin networks

Spin waves (SWs) have became the subject of an intense theoretical and experimental investigation due to ‎their potentiality as dissipationless information carriers for spintronic logic gates and waveguides. ‎Differently from the Fourier analysis of a system’s magnetic response after proper excitation, the ‎Hamiltonian approach [1] allows the computation of the whole set of SW modes, independently ‎of the excitation symmetry and action, as an eigenvalue/eigenvector problem; moreover, the ‎modes can be in principle computed arbitrarily close to the critical field for any magnetization ‎change (“transition”), e.g. magnetization reversal, vortex-to saturation transition, etc. The last property is ‎particularly suitable to the calculation of soft modes [2], i.e. SWs with a frequency going to zero ‎at the critical field: at the critical field, this modes are known to trigger the transition by ‎transferring their symmetry to the static magnetization, determining a specific instability that ‎leads the system to reconfigure in a different way. Besides the theoretical interest in describing ‎many kind of changes of the magnetization configuration, soft modes have surprising properties of ‎great importance for spintronics, as a asymmetric broadening of their bandwidth [3] (with different ‎group velocity in different directions), and for a dynamic explanation of the complexity of reversal ‎avalanches (Dirac strings) in macrospin networks like artificial quasicrystals and artificial spin ices [4]. [1] L. Giovannini, F. Montoncello and F. Nizzoli, Phys. Rev B 75, 024416 (2007) [2] F. Montoncello et al., Phys. Rev. B 77, 214402 (2008) [3] F. Montoncello and L. Giovannini, Appl. Phys. Lett. 104, 242407 (2014) [4] F. Montoncello et al., Journal of Magnetism and Magnetic Materials 423, 158 (2017)