Period doubling toward chaos in a driven magnetic macrospin

The Landau-Lifshitz-Gilbert equation is analyzed in the case of a configuration involving easy plane isotropy under the influence of a sinusoidally oscillating magnetic field and a demagnetizing field. Through the use of numerical techniques, chaotic behavior is found and analyzed. By reducing the system to a discrete map (numerically), bifurcation diagrams for the system are computed. The system is found to exhibit a period doubling cascade route to chaos, and it obeys certain convergence rules for chaotic transitions outlined by Feigenbaum. A connection is drawn between the route to chaos and the geometry of the system, and comparisons are made with similar systems. Within the chaotic regime, windows of arbitrarily large period are suspected to exist, and explicitly illustrated and discussed for a period three window.