  QCD matter in strong magnetic field exhibits a rich phase structure. In the
presence of an external magnetic field, the chiral Lagrangian for two flavors
is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous
coupling of the neutral pion $\pi_0$ to the magnetic field via the chiral
anomaly. Due to this term, the ground state is inhomogeneous in the form of
either chiral soliton lattice (CSL), an array of solitons in the direction of
magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions
supported by $\pi_3[{\rm SU}(2)] \simeq {\mathbb Z}$ appear inside the solitons
as topological lumps supported by $\pi_2(S^2) \simeq {\mathbb Z}$ in the
effective worldvolume theory of the soliton. In this paper, we determine the
phase boundary between the CSL and DWSk phases beyond the single-soliton
approximation, within the leading order of chiral perturbation theory. To this
end, we explore a domain-wall Skyrmion chain in multiple soliton
configurations. First, we construct the effective theory of the CSL by the
moduli approximation, and obtain the ${\mathbb C}P^1$ model or O(3) model,
gauged by a background electromagnetic gauge field, with two kinds of
topological terms coming from the WZW term: one is the topological lump charge
in 2+1 dimensional worldvolume and the other is a topological term counting the
soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are
superconducting rings and their sizes are constrained by the flux quantization
condition. The negative energy condition of the lumps yields the phase boundary
between the CSL and DWSk phases. We find that a large region inside the CSL is
occupied by the DWSk phase, and that the CSL remains metastable in the DWSk
phase in the vicinity of the phase boundary.
