One of the recent surprising discoveries is the crystal-axis dependent anisotropic magnetoresistance (CAMR) that depends on two magnetization components perpendicular to the current differently, in contrast to the conventional anisotropic magnetoresistance (AMR) that predicts no change in resistance when the magnetization varies in the plane perpendicular to the current. Using density functional theory and Boltzmann transport equation calculations for bcc Fe, hcp Co, and bcc FeCo alloys, we show that CAMR can be accounted by the magnetization-dependent spin-orbit interactions (SOI): Magnetization-dependent SOI modifies electron energy bands that, in turn, changes resistance. A phenomenological model reveals the intrinsic connection between SOI and order-parameters. Such a mechanism is confirmed by the strong biaxial stain effect on CAMR. Our findings provide an efficient way of searching and optimizing materials with large CAMR, important in the design of high-performance spintronic devices.

Physical  Review B 108, L020401 (2023)