Exchange Explosions: Magnetization Dynamics during Vortex-Antivortex Annihilation

A magnetic vortex and an antivortex can annihilate, resulting in a homogeneous magnetization. A detailed description of the magnetization dynamics of such annihilation processes is obtained by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. We show that, depending on the relative polarization of the vortex-antivortex pair, the annihilation process is either a continuous transformation of the magnetic structure or it involves the propagation of a micromagnetic singularity (Bloch point) causing a burstlike emission of spin waves. These results provide new insight into a fundamental micromagnetic process that has recently been proposed for a controlled generation of spin waves.

Figure 1

Schematics of a magnetic (a) vortex and (b) an antivortex structure. In the core of the (anti)vortex, the magnetization is perpendicular to the plane. (c) Schematic representation on the definition of the winding number.

Figure 2

Magnetization dynamics of the domain structure conversion from a cross-tie wall structure to a vortex state. The polarization of the vortices is parallel to the one of the central antivortex. Ten snapshots are taken at five different times [(a),(f): 0 ps; (b),(g): 30 ps; (c),(h): 70 ps; (d),(i): 90 ps; (e),(j): 125 ps]. In (a)–(e), the $y$ component of the magnetization is shown with a color code going from blue ($-100\%$) over green (0%) to red ($+100\%$). In the bottom row, the same magnetic structures are displayed with an isosurface representation. The meaning of the isosurfaces is described in more detail in the text.

Figure 3

Dynamics of a vortex-antivortex annihilation process with opposite polarization. In (a)–(e), a visualization with isosurfaces has been used, as done previously in the bottom row in Fig. 2. The configurations are shown at (a),(f) 5 ps, (b),(g) 110 ps, (c),(h) 135 ps, (d),(i) 138 ps, and (e),(j) 141 ps. In the bottom row, (f)–(j) show magnified top views on the region of interest. In addition, the isosurfaces $m_z=0$ are displayed as green ribbons in these panels.

Figure 4

Temporal evolution of the system’s energy during the annihilation processes. In the case of antiparallel polarization, the formation of the BP initiates a rapid decay of the energy. In contrast to this, the energy decreases continuously during the annihilation process with parallel polarization.