Size Limit of Superparamagnetic Inclusions in Dust Grains and Difficulty of Magnetic Grain Alignment in Protoplanetary Disks

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