Abstract Since there is a large population of massive O/B stars and putative neutron stars (NSs) located in the vicinity of the Galactic Center (GC), intermediate-mass X-ray binaries (IMXBs) constituted by an NS and a B-type star probably exist there. We investigate the evolutions of accreting NSs in IMXBs (similar to M82 X-2) with a ~ 5.2 M⊙ companion and orbital period ≃ 2.53 d. By adopting a mildly super-Eddington rate Ṁ = 6 × 10−8M⊙ yr−1 for the early Case B Roche-lobe overflow (RLOF) accretion, we find that only in accreting NSs with quite elastic crusts (slippage factor s = 0.05) can the toroidal magnetic fields be amplified within 1 Myr, which is assumed to be the longest duration of the RLOF. These IMXBs will evolve into NS+white dwarf (WD) binaries if they are dynamically stable. However, before the formation of NS+WD binaries, the high stellar density in the GC will probably lead to frequent encounters between the NS+evolved star binaries (in post-early Case B mass transfer phase) and NSs or exchange encounters with other stars, which may produce single NSs. These NSs will evolve into magnetars when the amplified poloidal magnetic fields diffuse out to the NS surfaces. Consequently, our results provide a possible explanation for the origin of the GC magnetar SGR 1745–2900. Moreover, the accreting NSs with s > 0.05 will evolve into millisecond pulsars (MSPs). Therefore, our model reveals that the GC magnetars and MSPs could both originate from a special kind of IMXB.

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