Simulation of three-dimensional nonperiodic structures of π-vertical Bloch line (pi-VBL) and 2π-VBL (2pi-VBL) in Permalloy films

Three-dimensional magnetic structures of pi-vertical-Bloch line (VBL) and 2pi-VBL are investigated in 80–320-nm-thick Permalloy films using direct integration of the Landau–Lifshitz–Gilbert equation in an 128×128×80 point Cartesian lattice. A pi-VBL reflects the shapes of its adjacent walls, which change with film thickness. The pi-VBL conducts the flux between walls of opposite chirality by letting the magnetization rotate out of the plane of the walls via a vortex structure. The Néel caps switch chirality via a “converging point,” or cross-tie, flux at one surface and a vortex flux, or a swirl, at the other surface. The pi-VBL energy per unit area is 0.44, 0.20, and 0.30 erg/cm2 in 80, 160, and 320 nm films, respectively. The corresponding pi-VBL widths are 88, 60, and 86 nm. A stable winding 2pi-VBL structure was also computed by combining two pi-VBL structures of appropriate chirality. The Néel caps intersect via the pair-(swirl, converging point) like flux at both surfaces. The width of the 2pi-VBL is 140 nm and its energy per unit area is 0.57 erg/cm2.