  Magnetic dipole emission (MDE) from interstellar magnetic nanoparticles is an
important Galactic foreground in the microwave frequencies, and its
polarization level may pose great challenges for achieving reliable
measurements of cosmic microwave background (CMB) B-mode signal. To obtain
theoretical constraints on the polarization of MDE, we first compute the degree
of alignment of big silicate grains incorporated with magnetic inclusions. We
find that, in realistic conditions of the interstellar medium, thermally
rotating big grains with magnetic inclusions are weakly aligned and achieve
{\it alignment saturation} when the magnetic alignment rate becomes much faster
than the rotational damping rate. We then compute the degree of alignment for
free-flying magnetic nanoparticles, taking into account various interaction
processes of grains with the ambient gas and radiation field, including neutral
collisions, ion collisions, and infrared emission. We find that the rotational
damping by infrared emission can significantly decrease the degree of alignment
of small particles from the saturation level, whereas the excitation by ion
collisions can enhance the alignment of ultrasmall particles. Using the
computed degrees of alignment, we predict the polarization level of MDE from
free-flying magnetic nanoparticles to be rather low. Such a polarization level
is within the upper limits measured for anomalous microwave emission (AME),
which indicates that MDE from free-flying iron particles may not be ruled out
as a source of AME. We also quantify spinning dust emission from free-flying
iron nanoparticles with permanent magnetic moments and find that its emissivity
is one order of magnitude lower than that from spinning polycyclic aromatic
hydrocarbons (PAHs). Finally, we compute the polarization spectra of spinning
dust emission from PAHs for the different interstellar magnetic fields.
