Universal angular magnetoresistance and spin torque in ferromagnetic/normal metal hybrids

The electrical resistance of ferromagnetic/normal-metal $\mathrm{}(F/N)\mathrm{}$ heterostructures depends on the nature of the junctions that may be tunnel barriers, point contacts, or intermetallic interfaces. For all junction types, the resistance of disordered $F/N/F$ perpendicular spin valves as a function of the angle between magnetization vectors is shown to obey a simple universal law. The spin-current induced magnetization torque can be measured by the angular magnetoresistance of these spin valves. The results are generalized to arbitrary magnetoelectronic circuits.