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Conductance and Exchange Coupling of Two Ferromagnets Separated by a Tunneling Barrier
Slonczewski, J.C., 1989. Conductance and Exchange Coupling of Two Ferromagnets Separated by a Tunneling Barrier. Phys. Rev. B 39, 6995
Essay about this article
In 1989 John Slonczewski wrote a seminal paper to discuss Tunneling Magnetoresistance (TMR) in Magnetic Tunnel Junctions (MTJs) in which he introduced spin currents to analyze both interlayer-coupling between magnetic electrodes in equilibrium, as well as an out of equilibrium coupling that later came to be known as spin transfer torque; see the next section 14. He described the spin current not only by its magnitude as is needed for understanding spin accumulation and Current Perpendicular to the Plane Magnetoresitance (CPP-MR), but by its polarization, a three dimensional vector describing the orientation of the plane of spin polarization of the current. Whereas this polarization does not play a role in the magnitude of the TMR in tunnel junctions, it is necessary to explain the current induced torque that a current exerts on the magnetic electrodes as we see in the next section.
The concept of using spin currents to calculate interlayer exchange coupling in MTJs was readily extended in 1993 to metallic spacers and multilayers by Erickson, Hathaway and Cullen [1]. Slonczewski related the coupling to the torque exerted by one magnetic layer on another in the absence of a current; to calculate this he determined the spin-flip current between two layers when they were in equilibrium [indeed, even though there is no charge current, a spin current can exist in equilibrium]. This current gives the rate of change of the spin density, which, from the equation of continuity of the spin density, is the torque acting on a layer.
While this coupling monatomically decays in MTJs, it oscillates with spacer layer thickness in metallic systems. Back in 1964-66 when Neél’s group was studing interlayer coupling in multilayers [see Section 3] they always found a ferromagnetic rather than oscillatory coupling. Eventually it was recognized this was caused by pinholes of ferromagnetic material in the nominally nonmagnetic metallic spacer; however there was a theoretical analysis that rationalized this monatomic variation from an analysis of the Ruderman-Kittel interaction through the metallic spacer layer. A year later Doug Mills, amongst others, showed this conclusion was arrived at by an incorrect counting of states participating in the coupling; when properly done they demonstrated these “evanescent” contributions [non-oscillatory] cancelled and only the usual oscillatory coupling coming from states around the Fermi level remained [2].
For completeness I should mention that in his seminal 1989 paper Slonczewski also derived expressions for the TMR of an MTJ in terms of the wave vectors of the tunneling electrons in the metallic electrodes; the polarization of the density of states of the electrodes, i.e., the difference in the densities for spin parallel and antiparallel to the magnetization; and the height of the barrier of the insulating spacer layer above the Fermi level of the electrons in the electrodes. While based on a free electron model for the electrodes and a square barrier profile for the spacer, Slonczewski’s expressions for the TMR have been extensively used by experimentalists to understand their data. To determine the TMR he calculated the conductivity of a MTJ for parallel and antiparallel alignment of the electrodes. This is determined from the charge, not the spin, current.
References
[1] R.P. Erickson, Kristl B. Hathaway and James R. Cullen, Phys. Rev.B 47, 2626 (1993).
[2] A. Bardasis, D.S. Falk, R.A. Ferrell, M.S. Fullenbaum, R.E. Prange and D.L. Mills, Phys. Rev. Lett. 14, 298 (1965).
Discussion Question
How should one modify Slonczewski’s calculation of interlayer coupling in tunnel junctions to determine this coupling for metallic multilayers?
The above article is reprinted with permission from the author Slonczewski, J.C., 1989.Conductance and Exchange Coupling of Two Ferromagnets Separated by a Tunneling Barrier. Phys. Rev. B 39, 6995. Copyright (1989) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.
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