Unified Semi-Classical Theory of Parallel and Perpendicular Giant Magnetoresistance in Superlattices
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V.V. USTINOV AND E.A. KRAVTSOV Institute of Metal Physics, GSP- 170, Ekaterinburg, 620219, Russia
ABSTRACT
The giant magnetoresistance in magnetic superlattices for the current perpendicular to and in the layer planes is studied within a unified semi-classical approach that is based on the Boltzman equation with exact boundary conditions for the spin-dependent distribution functions of conduction electrons. We show that the main differences between the in-plane and perpendicular-to-plane magnetoresistance result from the fact that they originate from different interface processes responsible for spin-dependent scattering. A correlation between the giant magnetoresistance and the superlattice magnetization is also discussed and it is shown that its study has much potential for yielding information about properties of spin-dependent scattering in magnetic superlattices.
INTRODUCTION A great deal of attention has been devoted recently to the giant magnetoresistance (GMR) that is observed in magnetic superlattices for the current flowing in the layer planes 1 (CIP case) and perpendicular to the layer planes 2 (CPP case). When experimental results for the CIP case are compared with those for the CPP one, it is apparent that, although both the CIP and CPPGMR are accounted for by spin-dependent scattering, they differ essentially in general behavior (GMR magnitude, magnetic field, thickness and temperature dependences). In order to appreciate physical mechanisms for this difference, the CIP and CPP-GMR should both be considered within a unified theory.
MODEL Consider an infinite superlattice composed of single-domain ferromagnetic layers with magnetic moments in the layer plane, each layer being L in thickness. The nonmagnetic-spacer thickness is assumed negligible compared with L. Neighboring magnetic moments are considered to be rotated through an angle 6 relative to each other, ( being equal to 66 in the initial state. An external magnetic field H applied in the layer plane rotates the magnetizations to the parallel arrangement and changes the angle 0-=-19(). When the magnetic field is strong enough (H_>H.), 311
Mat. Res. Soc. Symp. Proc. Vol. 384 01995 Materials Research Society
the magnetizations are forced to lie in the same direction (0-0). The relative superlattice magnetization p is given as p(IH)=A/I-)/A=cos(6/2) where Mis the superlattice magnetization and A4 is the saturation magnetization. We define the maximum magnetoresistance ratio as AG = - pG(0)] / pG(O) and the relative magnetoresistance as 8a(h) = Voa(M) - pG( 0 )] / VoG(-) - p0 (0)] . Here G defines the geometry under discussion (CIP or CPP). Having obtained 6P(H) and 1(411) from experimental pG(H) and AMu) dependences, one can find a correlation between P0 and p and eliminate the common variable H When experimental data are represented in the form 6Vu), they should be compared with results of the present theory to estimate microscopic parameters of spindependent scattering.
Semi-classicalformalism In our approach the electron energy spectrum
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