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We present a novel method to measure the strength of interstellar magneticfields based on ultraviolet (UV) polarization of starlight, which is in partproduced by weakly aligned, small interstellar grains. We begin withcalculating degrees of alignment of small (size $a\sim 0.01\mu$m) and verysmall ($a\sim 0.001\mu$m) grains in the interstellar magnetic field due to theDavis-Greenstein paramagnetic relaxation and resonance paramagnetic relaxation.We compute the degrees of paramagnetic alignment with the ambient magneticfield $B$ using Langevin equations. In this paper, we take into account variousprocesses essential for the dynamics of small grains, including infrared (IR)emission, electric dipole emission, plasma drag and collisions with neutral andionized species. We find that the alignment of small grains is necessary toreproduce the observed polarization in the UV, although the polarizationarising from these small grains is negligible at the optical and IRwavelengths. Based on fitting theoretical models to observed extinction andpolarization curves, we find that the best-fit model requires a higher degreeof alignment of small grains for the case with the peak wavelength ofpolarization $\lambda_{\max}<0.55\mu$m, which exhibits an excess UVpolarization relative to the Serkowski law, compared to the typical case$\lambda_{\max}=0.55\mu$m. We interpret the correlation between the systematicincrease of the UV polarization relative to maximum polarization (i.e. of$p(6\mu m^{-1})/p_{\max}$) with $\lambda_{\max}^{-1}$ by appealing to thehigher degree of alignment of small grains. We identify paramagnetic relaxationas the cause of the alignment of small grains and utilize the dependence of thedegree of alignment on the magnetic field strength $B$ to suggest a new way tomeasure $B$ using the observable parameters $\lambda_{\max}$ and $p(6\mum^{-1})/p_{\max}$.[Abridged]

Paramagnetic alignment of small grains: a novel method for measuring interstellar magnetic fields