Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Phys. Rev. ST AB Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article:

Phys. Rev. B 47, 2626–2635 (1993)

[Issue 5 – 1 February 1993 ]

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Mechanism for non-Heisenberg-exchange coupling between ferromagnetic layers

R. P. Erickson

Naval Research Laboratory, Washington, D.C. 20375

Kristl B. Hathaway and James R. Cullen

Naval Surface Warfare Center, Silver Spring, Maryland 20903

We consider a free-electron model of exchange coupling between transition-metal ferromagnetic films separated by a paramagnetic metal spacer. The minority-spin energy bands in the ferromagnets are matched to those of the paramagnetic spacer. The majority-spin electrons experience a repulsive potential arising from the lack of corresponding states in the spacer. The height of the potential barrier is equal to the exchange-energy gap in the ferromagnets. We show how the model, applicable to a trilayer film such as Fe/Cr/Fe or Co/Ru/Co, generates an infinite sum of terms with coefficients A₁₂,B₁₂, . . . in the coupling energy, extending beyond the Heisenberg-like A₁₂ term of bilinear coupling between the moments of the ferromagnets. Both the A₁₂ and non-Heisenberg (biquadratic) B₁₂ exchange terms oscillate with spacer-layer thickness. We find that the phase of B₁₂ relative to A₁₂ shifts with this thickness, so that at certain regions of spacer-layer thickness, the magnitude of B₁₂ is greater than that of A₁₂, and B₁₂ is of the proper sign to cause 90° coupling between the ferromagnets. These special thicknesses are predicted to appear over a broad range of the ratio of Fermi to exchange-gap energies. Thus, we show from our model that biquadratic, or 90°, coupling between the ferromagnets is intrinsic to itinerant-electron exchange across the paramagnetic spacer.

©1993 The American Physical Society

URL: http://link.aps.org/abstract/PRB/v47/p2626
DOI: 10.1103/PhysRevB.47.2626
PACS: 75.10.-b, 75.30.Et, 75.70.-i

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