Spin Configurations and the Dynamic Response of Antiferromagnetically Coupled Systems
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SPIN CONFIGURATIONS AND THE DYNAMIC RESPONSE OF ANTIFERROMAGNETICALLY COUPLED SYSTEMS
F.C. Nirtemann, R.L. Stamps, and R.E. Camley Department of Physics, University of Colorado at Colorado Springs, Colorado Springs, CO 80933-7150
ABSTRACT We present a calculation of spin waves in coupled multilayered structures which is based on exact evaluation of both exchange and dipolar fields. The ground state spin configuration in antiferromagnetically coupled multilayers can differ significantly from the uniformly canted ground state usually assumed. This non-uniform ground state is found to radically alter the character of the spin wave modes and sometimes lead to a strong localization of the wave to the outermost magnetic films of the multilayer. I. INTRODUCTION The discovery of antiferromagnetic coupling between ferromagnetic films across nonmagnetic layers [1] has raised several important questions and resulted in a number of exciting potential applications. Even though the actual spin configuration often plays a very important role in the most interesting properties of these systems [2-4], to date theoretical investigations [5-7] of giant magnetoresistance and dynamic response of antiferromagnetically coupled systems have assumed orly the simplest possible magnetic ground states. In a recent paper [8], we showed that multilayered systems of antiferromagnetically coupled films will have complicated groundstates that are strongly field dependent. Some of these groundstates are quite different from the groundstate assumed by previous theoretical studies of these systems. In the present work we discuss the effects of the correct groundstate on the linear dynamic magnetic behavior of multilayer systems. In this paper we present a microscopic calculation of spin wave frequencies in magnetic multilayer structures which makes no restrictions on the allowed ground state magnetic configurations. We will use this model to discuss the effects of complicated ground states on spin wave frequencies and characteristics. II. THEORY The geometry of the multilayer is shown in Fig. 1. The axis of the multilayer lies along the y direction, an external applied magnetic field Ho is directed along the z axis and the magnetizations in each layer lie in the xz plane some angle cc from the z axis. The magnetic layers are identified by the integer n and the angle a for the magnetization of each layer by the
Mat. Res. Soc. Symp. Proc. Vol. 313. ©1993 Materials Research Society
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subscript n. The number of atomic layers in each magnetic film is N and there are a total of L magnetic layers in the multilayer. The number of atomic layers in each non-magnetic film is Ns. For simplicity we assume that the lattice is simple cubic with spacing a. For future reference, we also define a wavevector q that lies in the xz plane at an angle 0 from the z axis. We now review the important features of the ground state configurations. If lanI were independent of position then the magnetization of each film would be canted away from the applied field directio
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