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