We study the evolution of magnetoresistance with temperature in thin film bilayers consisting of platinum and the antiferromagnet Cr$_2$O$_3$ with its easy axis out of the plane. We vary the temperature from 20 - 60{deg}C, close to the Neel temperature of Cr$_2$O$_3$ of approximately 37{deg}C. The magnetoresistive response is recorded during rotations of the external magnetic field in three mutually orthogonal planes. A large magnetoresistance having a symmetry consistent with a positive spin Hall magnetoresistance is observed in the paramagnetic phase of the Cr$_2$O$_3$, which however vanishes when cooling to below the Neel temperature. Comparing to analogous experiments in a Gd$_3$Ga$_5$O$_{12}$/Pt heterostructure, we conclude that a paramagnetic field induced magnetization in the insulator is not sufficient to explain the observed magnetoresistance. We speculate that the type of magnetic moments at the interface qualitatively impacts the spin angular momentum transfer, with the $3d$ moments of Cr sinking angular momentum much more efficiently as compared to the more localized $4f$ moments of Gd.
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