Magnetic Normal Mode Calculations in Big Systems: A Highly Scalable Dynamical Matrix Approach Applied to a Fibonacci-Distorted Artificial Spin Ice

Abstract

We present a new formulation of the dynamical matrix method for computing the magnetic normal modes of a large system, resulting in a highly scalable approach. The motion equation, which takes into account external field, dipolar and ferromagnetic exchange interactions, is rewritten in the form of a generalized eigenvalue problem without any additional approximation. For its numerical implementation several solvers have been explored, along with preconditioning methods. This reformulation was conceived to extend the study of magnetization dynamics to a broader class of finer-mesh systems, such as three-dimensional, irregular or defective structures, which in recent times raised the interest among researchers. To test its effectiveness, we applied the method to investigate the magnetization dynamics of a hexagonal artificial spin-ice as a function of a geometric distortion parameter following the Fibonacci sequence. We found several important features characterizing the low frequency spin modes as the geometric distortion is gradually increased.

Controlling the three dimensional propagation of spin waves in continuous ferromagnetic films with an increasing out of plane undulation

“…The magnetic parameters were typical for permalloy material: exchange stiffness constant , saturation magnetization and the gyromagnetic ratio . The magnetization maps were the input of the DMM software 55 , 56 , 59 , which computes the frequency and phase profiles of the dynamic magnetization both at any given applied field and wavevector magnitude and direction. In our case the applied field was , while the wavevector magnitude k was taken at discrete points, from 0 to 0.5 with steps of 0.1 in units of the Brillouin zone width, and then converted into absolute values rad/m.…”

Magnetization dynamics in quasiperiodic magnonic crystals

“…This tunability of resonance frequencies and bandwidth depicts the potential application of Fibonacci distorted kagome artificial spin ice in magnonic devices. Moreover, a recent study introduced the dynamical matrix method to calculate the magnetic normal modes of the magnonic system [188]. This method offered a theoretical framework to understand the frequency of SW modes in Fibonacci-distorted artificial spin systems by addressing the generalized eigenvalue problem.…”