  One of recent surprising discoveries is the unusual anisotropic
magnetoresistance (UAMR) 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 UAMR 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 UAMR. Our findings provide an efficient way of searching and
optimizing materials with large UAMR, important in the design of
high-performance spintronic devices.
