Currents and torques in metallic magnetic multilayers

A theory is given for electron transport across a very thin non-magnetic metallic spacer joining two ferromagnetic metals whose moment vectors include a general angle. An assumed condition of negligible interfacial reflection for majority-spin electrons is approached by certain multilayer compositions including the experimentally important composition Co/Cu. Analytic formulas based on a non-spin-diagonal density operator inside the spacer connect the spin-channel currents and electro-chemical voltages across the spacer. The quantum-mechanically derived torques on sublayer moments agree with a previous macroscopic relation. The single additional parameter of the resulting macroscopic magnetoelectronic transport formulation depends only on bulk electron structure of the spacer. Illustrative application of the new connection formulas to the special case of two equal thin ferromagnets predicts closely related expressions for angular dependences of magnetoresistance and current-driven torque. A simple relation between magnetoresistance and asymmetry of exciting currents holds for this case. © 2002 Published by Elsevier Science B.V.