  An ionization front (IF) surrounding an H II region is a sharp interface
where a cold neutral gas makes transition to a warm ionized phase by absorbing
UV photons from central stars. We investigate the instability of a
plane-parallel D-type IF threaded by parallel magnetic fields, by neglecting
the effects of recombination within the ionized gas. We find that weak D-type
IFs always have the post-IF magnetosonic Mach number $\mathcal{M}_{\rm M2} \leq
1$. For such fronts, magnetic fields increase the maximum propagation speed of
the IFs, while reducing the expansion factor $\alpha$ by a factor of
$1+1/(2\beta_1)$ compared to the unmagnetized case, with $\beta_1$ denoting the
plasma beta in the pre-IF region. IFs become unstable to distortional
perturbations due to gas expansion across the fronts, exactly analogous to the
Darrieus-Landau instability of ablation fronts in terrestrial flames. The
growth rate of the IF instability is proportional linearly to the perturbation
wavenumber as well as the upstream flow speed, and approximately to
$\alpha^{1/2}$. The IF instability is stabilized by gas compressibility and
becomes completely quenched when the front is D-critical. The instability is
also stabilized by magnetic pressure when the perturbations propagate in the
direction perpendicular to the fields. When the perturbations propagate in the
direction parallel to the fields, on the other hand, it is magnetic tension
that reduces the growth rate, completely suppressing the instability when
$\mathcal{M}_{\rm M2}^2 < 2/(\beta_1 - 1)$. When the front experiences an
acceleration, the IF instability cooperates with the Rayleigh-Taylor
instability to make the front more unstable.
