  The radiative torque (RAT) alignment of interstellar grains with ordinary
paramagnetic susceptibilities has been supported by earlier studies. The
alignment of such grains depends on the so-called RAT parameter $q^{\max}$ that
is determined by the grain shape. In this paper, we elaborate our model of RAT
alignment for grains with enhanced magnetic susceptibility due to iron
inclusions, such that RAT alignment is magnetically enhanced for which we term
MRAT mechanism. Such grains can get aligned with high angular momentum at the
so-called high-J attractor points, achieving a high degree of alignment. Using
our analytical model of RATs we derive the critical value of the magnetic
relaxation parameter $\delta_{m}$ to produce high-J attractor points as
functions of $q^{\max}$ and the anisotropic radiation angle relative to the
magnetic field $\psi$. We find that if about $10\%$ of total iron abundance
present in silicate grains are forming iron clusters, it is sufficient to
produce high-J attractor points for all reasonable values of $q^{\max}$. To
calculate the degree of grain alignment, we carry out numerical simulations of
MRAT alignment by including stochastic excitations from gas collisions and
magnetic fluctuations. We show that large grains can achieve perfect alignment
when the high-J attractor point is present, regardless of the values of
$q^{\max}$. Our obtained results pave the way for physical modeling of
polarized thermal dust emission as well as magnetic dipole emission. We also
find that millimeter-sized grains in accretion disks may be aligned with the
magnetic field if they are incorporated with iron nanoparticles.
