Linear-in-temperature resistivity in PdCrO$_2$ from magneto-elastic interactions

The kindred delafossite metals PdCrO$_2$ and PdCoO$_2$ exhibit a strikingly different temperature dependence of the in-plane resistivity at intermediate temperatures. The magnitude of the resistivity in the former displays a sublinear approach to a pronounced T-linear scaling. This difference, apparently linked to antiferromagnetic correlations in PdCrO$_2$, cannot be fully accounted for by conventional scattering mechanisms. Motivated by this puzzle, we consider a particular coupling of electrons to magneto-elastic (EME) interactions in a 3D system composed of alternately stacked layers of itinerant electrons and antiferromagnetic Mott insulators. We show that EME interactions can explain the anomalous transport properties of PdCrO$_2$ and offer several experimental predictions to showcase the effects of the EME coupling.