Fig. 3
From: Magnetization reversal driven by low dimensional chaos in a nanoscale ferromagnet
Qualitative sketches of the magnetization trajectories in the (ϕ, mz)-plane. (ϕ is the azimuthal angle around the z-axis). a Conservative trajectories (α = 0, βac = 0, designated by superscript (0)). Γ1, Γ2 are constant energy trajectories and Γ is the heteroclinic trajectory (separatrix). b Damping dominated dynamics (\(\alpha > 0,\beta _{{\mathrm{ac}}} < \beta _x^{{\mathrm{crit}}}\), d > 0). Here xd1, xd2 are saddle equilibria; xs1, xs2 are node-type equilibria; \(W_1^s\) is stable manifold associated with xd1; \(W_2^u\) is unstable manifold associated with xd2; d is the splitting of the manifolds. c Heteroclinic tangle formation \(\left( {\alpha > 0,\beta _{{\mathrm{ac}}} > \beta _x^{{\mathrm{crit}}}} \right)\). The manifold intersection points xa, xb, xc are generated by iterating the stroboscopic map, Eq. (3). Intersecting stable and unstable manifolds form lobes. Blue regions indicate capturing lobes that keep the magnetization inside the given potential well while red regions show escaping lobes that bring magnetization outside of the well. The colored arrows indicate the transformation of one lobe into another under the action of the map, Eq. (3)
