µMAG Standard Problem #3

μMAG Standard Problem #3 determines the single domain limit of a cubic magnetic particle — the critical edge length $L$ (in units of exchange length $l_{\mathrm{ex}} = \sqrt{A / K_m}$, where $K_m = \frac{1}{2} \mu_0 M_s^2$) at which the “flower state” and “vortex state” have equal total energy.

The uniaxial anisotropy constant is $K_u = 0.1,K_m$ with the easy axis along $z$. All energies are normalised by $K_m L^3$.

The expected result is $L \approx 8.47,l_{\mathrm{ex}}$.

Submissions#

Convergence of critical size#

Convergence of total energy at transition#

Flower state partial energies#

Vortex state partial energies#

Convergence data: Martins, Ribeiro, Freitas#

Convergence data: Bjork, Poulsen, Insinga#