Magnetic structures of 2D and 3D nanoparticles

• New 3D magnetic structures of 3D nanomagnets.
• Bent and S-shaped magnetic vortices and antivortices.
• Flux closure determines these structures.
• New dynamic properties.

The minimization of exchange interactions and dipolar interactions in 2D and 3D nanoparticles is obtained from a powerful variational approach of the local spin Hamiltonian and leads to a different set of equations which correspond to different levels of screening of the long range dipolar interactions. These equations are shown to introduce topological defects which are analyzed on the basis of elementary spin clusters. Four basic topological defects are deduced for 2D nanoparticles, as observed in magnetic samples and simulations and 10 basic topological defects are deduced for 3D nanoparticles. These singularities induce complex variations of magnetization around them and non-linear properties.