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Alignment of non-spherical grains with magnetic fields is an importantproblem as it lays the foundation of probing magnetic fields with polarizeddust thermal emissions. In this paper, we investigate the feasibility ofmagnetic alignment in protoplanetary disks (PPDs). We use an alignmentcondition that Larmor precession should be fast compared with the dampingtimescale. We first show that the Larmor precession timescale is some threeorders of magnitude longer than the damping time for millimeter-sized grainsunder conditions typical of PPDs, making the magnetic alignment unlikely. Theprecession time can be shortened by superparamagnetic inclusions (SPIs), butthe reduction factor strongly depends on the size of the SPI clusters, which wefind is limited by the so-called "N\'{e}el's relaxation process." Inparticular, the size limit of SPIs is set by the so-called "anisotropic energyconstant" of the SPI material, which describes the energy barrier needed tochange the direction of the magnetic moment of an SPI. For the most commoniron-bearing materials, we find maximum SPI sizes corresponding to a reductionfactor of the Larmor precession timescale of order $10^3$. We also find thatreaching this maximum reduction factor requires fine-tuning on the SPI sizes.Lastly, we illustrate the effects of the SPI size limits on magnetic alignmentof dust grains with a simple disk model, and we conclude that it is unlikelyfor relatively large grains of order 100 $\mu$m or more to be aligned withmagnetic fields even with SPIs.

Size limit of superparamagnetic inclusions in dust grains and difficulty of magnetic grain alignment in protoplanetary disks