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Accretion-induced collapse (AIC) from oxygen/neon/magnesium composition whitedwarf (ONeMg WD) + stripped helium (He) star binaries is one promising channelto form peculiar neutron star objects. It has been discussed that the WD'smagnetic field may alter the accretion phase in the WD binary evolution. Byconsidering non-magnetic and sufficiently magnetized WDs, we investigate theevolution of ONeMg WD + He star binaries with detailed stellar evolution andbinary population synthesis simulations. The role of the magnetically confinedaccretion in the possible formation pathway for like millisecond pulsars (MSPs)and magnetars is also studied. Comparing with the case of spherically symmetricaccretion, the mass accumulation efficiency of the WDs is enhanced at low masstransfer rate under the magnetic confinement model. The initial parameter spaceof the potential AIC progenitor systems moves toward shorter orbital period andlower donor mass (but not so significantly) due to the effect of the magneticconfinement. This also allows final MSPs to have lower-mass WD companions andshorter orbital periods. There is no significant difference between theGalactic birthrates of the AIC derived with and without the magneticconfinement, which implies that the magnetic field of the WD does notdramatically change the number of ONeMg WD + He star binaries which can produceAIC. It is worth noting that these conclusions can be applied for the CO(carbon/oxgen) WD + He star binaries as progenitors of type Ia supernovae,because the accretion phases of ONeMg WDs and CO WDs are similar. The Galacticrate of magnetars possibly formed via AIC of highly magnetized WDs is$0.34\times10^{-4}\,{\rm yr}^{-1}$.

The Magnetized White Dwarf + Helium star Binary Evolution with Accretion-induced Collapse