  Located in the Large Magellanic cloud and mostly irradiated by a massive-star
cluster R$\,$136, 30 Doradus is an ideal target to test the leading theory of
the grain alignment and rotational disruption by RAdiative Torques (RATs).
Here, we use publicly available polarized thermal dust emission observations of
30 Doradus at 89, 154, and 214$\,\mu$m using SOFIA/HAWC+. We analyse the
variation of the dust polarization degree ($p$) with the total emission
intensity ($I$), the dust temperature ($T_{\rm d}$), and the gas column density
($N_{\rm H}$) constructed from ${\it Herschel}$ data. The 30 Doradus complex is
divided into two main regions relative to R$\,$136, namely North and South. In
the North, we find that the polarization degree first decreases and then
increases before decreasing again when the dust temperature increases toward
the irradiating cluster R$\,$136. The first depolarization likely arises from
the decrease of grain alignment efficiency toward the dense medium due to the
attenuation of the interstellar radiation field and the increase of the gas
density. The second trend (the increase of $p$ with $T_{\rm d}$) is consistent
with the RAT alignment theory. The final trend (the decrease of $p$ with
$T_{\rm d}$) is consistent with the RAT alignment theory only when the grain
rotational disruption by RATs is taken into account. In the South, we find that
the polarization degree is nearly independent of the dust temperature, while
the grain alignment efficiency is higher around the peak of the gas column
density and decreases toward the radiation source. The latter feature is also
consistent with the prediction of the rotational disruption by RATs.
