  We explore magnetic field effects on the nuclear matter based on the skrymion
crystal approach for the first time. It is found that the magnetic effect plays
the role of a catalyzer for the topological phase transition (topological
deformation for the skyrmion crystal configuration from the skrymion phase to
half-skyrmion phase). Furthermore, we observe that in the presence of the
magnetic field, the inhomogeneous chiral condensate persists both in the
skyrmion and half-skyrmion phases. Explicitly, as the strength of magnetic
field gets larger, the inhomogeneous chiral condensate in the skyrmion phase
tends to be drastically localized, while in the half-skyrmion phase the
inhomogeneity configuration is hardly affected. It also turns out that a large
magnetic effect in a low density region distorts the baryon shape to an
elliptic form but the crystal structure is intact. However, in a high density
region, the crystal structure is strongly effected by the strong magnetic
field. A possible correlation between the chiral inhomogeneity and the
deformation of the skrymion configuration is also addressed. The results
obtained in this paper might be realized in the deep interior of compact stars.
