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Interlayer exchange coupling between two ferromagnetic layers across a spacer layer has been intensively investigated within the last few decades. It was discovered that the interlayer exchange coupling across most 3d, 4d, and 5d nonmagnetic metallic spacer layers oscillates between antiferromagnetic and ferromagnetic as a function of spacer layer thickness (1,2). This discovery enabled the control of antiferromagnetic coupling between two ferromagnetic films, which is now used in most spintronic devices (3).
Until recently, the greatest interest has been in the bilinear term of the coupling, where the energy per area is linear in the directions of magnetizations in both magnetic layers. With this form of the interaction, positive values of the bilinear coupling favor parallel alignment of the magnetizations and negative values favor antiparallel alignment. In our recent work (4), we demonstrated that electronic stricture calculation methods can accurately predict the values of the bilinear coupling in Co/Ru/Co systems. In this work we extend our study to the biquadratic term of the coupling, which favors perpendicular orientations of two magnetizations. Biquadratic coupling is believed to have a separate origin from the bilinear coupling, and produced by the presence of disorder (extrinsic coupling). We show, however, that the intrinsic biquadratic term of coupled magnetic layers with perpendicular magnetizations may be of similar magnitude as the extrinsic one, but have both positive and negative values of the coupling. This can lead to both enhancement or reduction of experimentally observed biquadratic coupling.
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