Applications of gradient descent method to magnetic Skyrmion problems

The conjugate gradient (CG) method, a standard and vital way of minimizing the energy of a variational state, is applied to solve several problems in Skyrmion physics. The single-Skyrmion profile optimizing the energy of a two-dimensional chiral magnet is found without relying on specific boundary conditions. The two-dimensional Skyrmion lattice and three-dimensional hedgehog crystal state is recovered with efficiency using the modified CG (p-GD) method. The p-GD method is proposed as a complement to the traditional Monte Carlo annealing method, which still gives better results for the ground state but at the far greater cost in computation time.