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Considering the density wave of scalar and pseudoscalar condensates, we studythe response of quark matter to a weak external magnetic field. In an externalmagnetic field, the energy spectrum of the lowest Landau level becomesasymmetric about zero, which is closely related to chiral anomaly. Thisspectral asymmetry gives rise to spontaneous magnetization. This mechanism maybe one of candidates for the origin of the strong magnetic field in magnetars.Furthermore, using the generalized Ginzburg-Landau(gGL) expansion, we show thatmagnetic susceptibility exhibits a peculiar feature

Spontaneous Magnetization of Quark Matter in Inhomogeneous Chiral Phase