Halfvortices in flat nanomagnets

We discuss a new type of topological defect in XY systems where the O(2) symmetry is broken in the presence of a boundary. Of particular interest is the appearance of such defects in nanomagnets with a planar geometry. They are manifested as kinks of magnetization along the edge and can be viewed as halfvortices with winding numbers \pm 1/2. We argue that halfvortices play a role equally important to that of ordinary vortices in the statics and dynamics of flat nanomagnets. Domain walls found in experiments and numerical simulations are composite objects containing two or more of these elementary defects. We also discuss a closely related system: the two-dimensional smectic liquid crystal films with planar boundary condition.Comment: 7 pages, 8 figures, To appear as a chapter in Les Houches summer school on Quantum Magnetis