Dimensional Effect in Magnetoresistance in the Three-Layer Magnetic Films

Based on the generalized Dieny formula [1], [2], a theoretical analysis of the dependence of the magnetoresistance ratio $\delta$, which quantities the effect of giant magnetoresistance (GMR) in a magnetically ordered three-layer film with a thickness $D=d_{m1}+d_{n}+d_{m2}, (d_{m1}$ and dm2 - thickness of the basic and covering magnetic layers of the metal, respectively, dn thickness of the non-magnetic layer), on the thickness of the covering magnetic layer dm2 was performed. It was shown that in the case of performing inequalities $d_{m2}\lt \lt (d_{n}+d_{m1}), (d_{m2}\gt \gt (d_{n}+d_{m1}))$ the value of $\delta$ is negligible due to shunting the resistance of the covering layer with the resistances of the basic layer and the non-magnetic layer (shunting the resistance of the basic layer and the non-magnetic layer with the resistance of the covering magnetic layer). If the equality $d_{m2}=(d_{n}+d_{m1})$ is met, the value of $\delta$ becomes the maximum (amplitude) value due to the absence of a shunting effect.