  It has been proposed that accretion-induced collapse (AIC) of massive white
dwarfs (WDs) is an indispensable path for the formation of neutron star (NS)
binaries. Although there are still no direct evidence for the existence of AIC
events, several kinds of NS systems are suggested to originate from the AIC
processes. One of the representative evidence is the detection of the strong
magnetic field and slow spin NSs with ultra-light companions (<=0.1 Msun) in
close orbits. However, previous studies cannot explain the formation of AIC
events with such low-mass companions. In the present work, we evolve a series
of ONe WD+He WD systems to the formation of AIC events (named as the He WD
donor channel), and the NS binaries behave as ultra-compact X-ray binaries when
the He WDs refill their Roche-lobes. We found that the ONe WD+He WD systems a
possible channel for the formation of the newly formed NS+ultra-light companion
systems just after the AIC event. Although there are some other inconsistent
properties, the detected companion mass and orbital period of 4U 1626-67 (one
of the newly formed NS binaries with ultra-light companions) can be reproduced
by the He WD donor channel. In addition, combined with previous
asteroseismology results, we speculate that an UCXB source (XTE J1751-305) may
originate from the He WD donor channel.
