  In a newly born (high-temperature and Keplerian rotating) neutron star,
r-mode instability can lead to stellar differential rotation, which winds the
seed poloidal magnetic field ($\sim 10^{11}$ G) to generate an ultra-high
($\sim 10^{17}$ G) toroidal field component. Subsequently, by succumbing to the
Tayler instability, the toroidal field could be partially transformed into a
new poloidal field. Through such dynamo processes, the newly born neutron star
with sufficiently rapid rotation could become a magnetar on a timescale of
$\sim 10^{2-3}$ s, with a surface dipolar magnetic field of $\sim10^{15}$ G.
Accompanying the field amplification, the star could spin down to a period of
$\sim5$ ms through gravitational wave radiation due to the r-mode instability
and, in particular, the non-axisymmetric stellar deformation caused by the
toroidal field. This scenario provides a possible explanation for why the
remnant neutron stars formed in gamma-ray bursts and superluminous supernovae
could be millisecond magnetars.
