  Iron inclusions embedded inside dust grains play a crucial role in both
internal alignment via Barnett relaxation and external alignment via the
MAgnetically Enhanced RAdiative Torque (MRAT) mechanism. Moreover, inelastic
relaxation is predicted to dominate over Barnett relaxation in driving the
internal alignment of micron-sized and very large grains above $10\mu m$
(VLGs). Yet, a detailed modeling of polarized thermal dust emission from Class
0/I Young Stellar Objects (YSOs) taking into account these effects and their
observational constraints are still lacking. In this paper, we perform
synthetic dust polarization modeling for MHD simulations of an
intermediate-mass YSOs using our updated POLARIS code developed by Giang et al.
(2022). Synthetic polarization results are then post-processed with CASA to
confront ALMA observations. We found that to reproduce the high polarization
degree of $p \sim 5-30\%$ observed in protostellar envelopes by ALMA,
micron-sized and VLGs must contain iron inclusions with $N_{\rm cl} \sim 5 -
10^{4}$ iron atoms per cluster, assuming $30\%$ of iron abundance locked inside
dust grains under the cluster form. Inside the inner $\sim 500$ au region, it
requires inelastic relaxation, larger iron inclusions of $N_{\rm cl} \sim
10^{2}-10^{4}$, and grain growth beyond $\geq 10\mu m$ to reproduce $\sim
3-10\%$ of polarization observed by ALMA. But given such a combination, the
internal alignment and MRAT efficiency acting on VLGs still decrease toward the
center, which produces the decrease of $p(\%)$ with increasing gas density,
reaching $p \sim 1\%$ inside the disk. Additionally, our results show that the
high polarization by ALMA toward YSOs is not totally an artifact caused by the
interferometric filtering, but it could be explained by the efficient magnetic
alignment of SPM grains by MRAT mechanism.
