Wall and stray-energy comparison in a magnetic particle (${\gamma }_w{A}_w\ge \Delta U_{\mathrm{stray}}$)

A trial domain pattern costs wall energy ${\gamma }_w{A}_w$ and can release stray energy $\Delta U$. For a stable uniform ground state, ${\gamma }_w{A}_w\ge \Delta U$ within that trial model. Substituting the entire initial stray energy assumes that it is nearly all removed; a numerical lower bound independent of the domain geometry does not follow from single-domain observation alone.