  We elucidate magnetic effects in the Skyrmion system to probe into the dense
nuclear matter. We find a deformed $\pi^0$ dipole structure of a Skyrmion and
quantify nontrivial rearrangements of the confining pressure distribution. We
confirm an isospin-dependent baryon spectrum from the anomaly-induced action.
We then extend our scope to stacked Skyrme Crystal layers to scrutinize phases
of magnetized nuclear matter. We observe a quantized magnetic flux and identify
a phase transition from a crystalline state to a $\pi^0$ domain wall
corresponding to a topological transmutation from $\pi_3(S^3)$ to $\pi_1(S^1)$.
We establish the phase diagram, which could be explored also in analogous
systems with two-component Bose-Einstein condensates.
