Scaling analysis and application: Phase diagram of magnetic nanorings and elliptical nanoparticles

The magnetic properties of single-domain nanoparticles with different geometric shapes, crystalline anisotropies, and lattice structures are investigated. A recently proposed scaling approach is shown to be universal and in agreement with dimensional analysis coupled with the assumption of incomplete self-similarity. It is used to obtain phase diagrams of magnetic nanoparticles featuring three competing configurations: in-plane ferromagnetism, out-of-plane ferromagnetism, and vortex formation. The influence of the vortex core on the scaling behavior and phase diagram is analyzed. Three-dimensional phase diagrams are obtained for cylindrical nanorings depending on their height and outer and inner radii. The triple points in these phase diagrams are shown to be in a linear relationship with the inner radius of the ring. Elliptically shaped magnetic nanoparticles are also studied. A new parametrization for double vortex configurations is proposed, and regions in the phase diagram where the double vortex is a stable ground state are identified.