# Analytical and numerical $K_u - B$ phase diagrams for cobalt nanostructures: stability region for a Bloch skyrmion

## TL;DR

This paper analytically and numerically constructs phase diagrams for cobalt nanostructures, identifying stability regions for skyrmions, vortices, and ferromagnetic states under varying anisotropy and magnetic fields.

## Contribution

It introduces a method to calculate magnetic phase diagrams for cobalt nanostructures, highlighting stability regions for skyrmions and other magnetic configurations.

## Key findings

- Stability regions for Bloch skyrmions, vortices, and ferromagnetic states identified.
- Phase diagrams constructed as functions of anisotropy and magnetic field.
- Results enable control of skyrmion formation in cobalt nanostructures.

## Abstract

In this letter we calculate the energies corresponding to the different magnetic phases present in a ferromagnetic cylinder by means of analytical calculations. From the comparison of these energies, it is possible to construct magnetic phase diagrams as a function of the uniaxial anisotropy of the sample and the external magnetic field applied. As proof of concept, we analyzed the magnetic phase diagrams for a cobalt dot of 240 nm in diameter and 70 nm in length, with an easy axis parallel to the dot axis, and with a magnetic field applied towards or perpendicular to this axis. From these diagrams we have obtained the stability regions for a Bloch skyrmion (Sk), a vortex core (VC) and a ferromagnetic (F) configuration, which can point in any $\psi$ direction. Our results provide a pathway to engineer the formation and controllability of a skyrmion in a ferromagnetic dot to different anisotropy constants and magnetic fields.