Physics origin of universal unusual magnetoresistance

The discovery of unusual magnetoresistance (UMR) during the rotation of magnetization in the plane perpendicular to the electric current, which has been typically attributed to the magnetization-dependent interfacial reflection of the spin current, has had a remarkable impact on the understanding and application of a variety of spintronics phenomena. Here, we report that giant UMR occurs also in single-layer magnetic metals and exhibits high-order contributions and a universal sum rule, which agree well with the physics origin of the recently proposed two-vector magnetoresistance that simply considers electron scattering by the magnetization vector and interfacial electric field, without the need for any relevance to the spin/orbital current or crystalline symmetry. Revisiting of the literature data reveals that the most representative data that were used to claim spin Hall magnetoresistance or other magnetoresistances related or unrelated to spin current can be understood unifiedly by using the two-vector MR theory. Experimental and theoretical results against spin-current-related magnetoresistances, but not two-vector magnetoresistance, are discussed.