Magnetic dipole emission (MDE) from interstellar magnetic nanoparticles is potentially an important Galactic foreground in the microwave frequencies, and its polarization level may pose great challenges for achieving reliable measurements of cosmic microwave background B-mode signal. To obtain realistic predictions for the polarization of MDE, we first compute the degree of alignment of big silicate grains incorporated with magnetic inclusions. We find that thermally rotating big grains with magnetic inclusions are weakly aligned and can achieve 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 rotational emission from free-flying iron nanoparticles with permanent magnetic moments and find that its emissivity is about one order of magnitude lower than that from spinning polycyclic aromatic hydrocarbons.
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