Magnetic dipole microwave emission from dust grains

Thermal fluctuations in the magnetization of interstellar grains will produce magnetic dipole emission at v ≲ 100 GHz. We show how to calculate absorption and emission from small particles composed of material with magnetic, as well as dielectric, properties. The Kramers-Kronig relations for a dusty medium are generalized to include the possibility of magnetic grains. The magnetic permeability as a function of frequency is discussed for several candidate grain materials. Iron grains, or grains containing iron inclusions, are likely to have the magnetic analog of a Fröhlich resonance in the vicinity of ∼50-100 GHz, which results in a large magnetic dipole absorption cross section. We calculate the emission spectra for various interstellar grain candidates. Although "ordinary" paramagnetic grains or even magnetite grains cannot account for the observed "anomalous" emission from dust in the 14-90 GHz range, stronger magnetic dipole emission will result if a fraction of the grain material is ferromagnetic, as could be the case given the high Fe content of interstellar dust. The observed emission from dust near 90 GHz implies that not more than ∼5% of interstellar Fe is in the form of metallic iron grains or inclusions (e.g., in "GEMS"). However, we show that if most interstellar Fe is in a moderately ferromagnetic material, with the magnetic properties suitably adjusted, it could contribute a substantial fraction of the observed 14-90 GHz emission, perhaps comparable to the contribution from spinning ultrasmall dust grains. The two emission mechanisms can be distinguished by measuring the emission from dark clouds. If ferromagnetic grains consist of a single magnetic domain and are aligned, the magnetic dipole emission will be linearly polarized, with the polarization depending strongly on frequency.