  Supernova remnants (SNRs) are well-recognised dust producers, but their net
dust production rate remains elusive due to uncertainties in grain properties
that propagate into observed dust mass uncertainties, and determine how
efficiently these grains are processed by reverse shocks. In this paper, we
present a detection of polarised dust emission in the Crab pulsar wind nebula,
the second SNR with confirmed polarised dust emission after Cassiopeia A. We
constrain the bulk composition of the dust with new SOFIA/HAWC+ polarimetric
data in band C 89 um and band D 154 um. After correcting for synchrotron
polarisation, we report dust polarisation fractions ranging between 3.7-9.6 per
cent and 2.7-7.6 per cent in three individual dusty filaments at 89 and 154 um,
respectively. The detected polarised signal suggests the presence of large (>
0.05-0.1 um) grains in the Crab Nebula. With the observed polarisation, and
polarised and total fluxes, we constrain the temperatures and masses of
carbonaceous and silicate grains. We find that the carbon-rich grain mass
fraction varies between 12 and 70 per cent, demonstrating that carbonaceous and
silicate grains co-exist in this SNR. Temperatures range from 40 K to 70 K and
from 30 K to 50 K for carbonaceous and silicate grains, respectively. Dust
masses range from 10^{-4} Msol to 10^{-2} Msol for carbonaceous grains and to
10^{-1} Msol for silicate grains, in three individual regions.
