We report on polarimetric maps made with HAWC+/SOFIA toward Rho Oph A, the densest portion of the Rho Ophiuchi molecular complex. We employed HAWC+ bands C (89 $mu$m) and D (154 $mu$m). The slope of the polarization spectrum was investigated by defining the quantity R_DC = p_D/p_C, where p_C and p_D represent polarization degrees in bands C and D, respectively. We find a clear correlation between R_DC and the molecular hydrogen column density across the cloud. A positive slope (R_DC > 1) dominates the lower density and well illuminated portions of the cloud, that are heated by the high mass star Oph S1, whereas a transition to a negative slope (R_DC < 1) is observed toward the denser and less evenly illuminated cloud core. We interpret the trends as due to a combination of: (1) Warm grains at the cloud outskirts, which are efficiently aligned by the abundant exposure to radiation from Oph S1, as proposed in the radiative torques theory; and (2) Cold grains deep in the cloud core, which are poorly aligned due to shielding from external radiation. To assess this interpretation, we developed a very simple toy model using a spherically symmetric cloud core based on Herschel data, and verified that the predicted variation of R_DC is consistent with the observations. This result introduces a new method that can be used to probe the grain alignment efficiency in molecular clouds, based on the analysis of trends in the far-infrared polarization spectrum.
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