Disentangling the physical contributions to the anomalous Hall effect and domain wall resistance in isoelectronic L1$_{0}$-FePd and L1$_{0}$-FePt alloys

We analyze the origin of the electrical resistance arising in domain walls of perpendicularly magnetized materials by considering a superposition of anisotropic magnetoresistance and the resistance implied by the magnetization chirality. The domain wall profiles of L1$_{0}$-FePd and L1$_{0}$-FePt are determined by micromagnetic simulations based on which we perform first principles calculations to quantify electron transport through the core and closure region of the walls. The wall resistance, being twice as high in L1$_{0}$-FePd than in L1$_{0}$-FePt, is found to be clearly dominated in both cases by a high gradient of magnetization rotation, and not by the spin-orbit interaction driven anisotropic magnetoresistance effect. Concerning the anomalous Hall effect on the other hand, we show that difference in spin-orbit interaction strength of Pt and Pd atoms leads to a pronounced cross-over from an extrinsic side jump mechanism in L1$_{0}$-FePd to an intrinsic Berry-phase anomalous Hall effect in L1$_{0}$-FePt.