  We study the role of spin-down in driving quark deconfinement in the high
density core of isolated neutron stars. Assuming spin-down to be solely due to
magnetic braking, we obtain typical timescales to quark deconfinement for
neutron stars that are born with Keplerian frequencies. Employing different
equations of state (EOS), we determine the minimum and maximum neutron star
masses that will allow for deconfinement via spin-down only. We find that the
time to reach deconfinement is strongly dependent on the magnetic field and
that this time is least for EOS that support the largest minimum mass at zero
spin, unless rotational effects on stellar structure are large. For a fiducial
critical density of $5\rho_0$ for the transition to the quark phase
($\rho_0=2.5\times10^{14}$g/cm$^3$ is the saturation density of nuclear
matter), we find that neutron stars lighter than $1.5M_{\odot}$ cannot reach a
deconfined phase. Depending on the EOS, neutron stars of more than
$1.5M_{\odot}$ can enter a quark phase only if they are spinning faster than
about 3 milliseconds as observed now, whereas larger spin periods imply that
they are either already quark stars or will never become one.
