Journal of Magnetism and Magnetic Materials 316 (2007) e977–e979 Theoretical investigation of the relationship between spin torque and magnetoresistance in spin-valves and magnetic tunnel junctions A. Manchon a,Ã , N. Strelkov a,b , N. Ryzhanova a,b , A. Vedyayev a,b , B. Dieny a , J.C. Slonczewski c a SPINTEC, URA 2512 CEA/CNRS, CEA/Grenoble, 38054 Grenoble Cedex 9, France b Department of Physics, Lomonosov University, Moscow, Russia c IBM Research Center, Box 218, Yorktown Heights, NY 10598, USA Available online 23 March 2007 Abstract A theoretical study is presented concerning the relationship between spin transfer torque and absolute current-perpendicular-to-plane magnetoresistance in metallic spin-valves (SV) and magnetic tunnel junctions. In a first step, using Valet and Fert Boltzmann-like theory extended to any metallic magnetic multilayers with non-collinear magnetizations, linear relationships between spin torque and absolute current-perpendicular-to-plane giant magnetoresistance are derived numerically, when varying the parameters of the structure one by one. The obtained results are compared with an extension of J.C. Slonczewski’s circuit theory. The latter model gives an analytical expression of this linear dependence. In a second step, using an out-of-equilibrium perturbation formalism (Keldysh technique), we study the tunnel magnetoresistance (TMR) dependence of the spin torque amplitude in magnetic tunnel junctions when varying the parameters one by one in the junction. Once again, linear dependences are obtained, with different characteristics when the TMR vanishes. It is shown that these two equivalent behaviours are associated with different origins of the spin torque. r 2007 Elsevier B.V. All rights reserved. Keywords: Spin transfer; Spin torque; Multilayer; Magnetic tunnel junction; Magnetoresistance 1. Introduction Reciprocally to the influence of the magnetization orientation on a spin-polarized electrical current, the influence of a spin-polarized current on the magnetization orientation has recently been observed [1]. This phenom- enon, known as ‘‘spin transfer torque’’, is due to the transfer of the transverse component of spin current to the local magnetization. It induces magnetization excitations, which eventually lead to magnetization switching. These effects are under investigation in many teams worldwide [2]. Spin transfer torque is of great interest as a new write scheme in magnetic nanostructures especially non-volatile random access memories (MRAM) because it can be used to selectively reverse the magnetization of the free layer in metallic spin-valves (SV) [3] or magnetic tunnel junctions (MTJ) [4]. Thanks to intense effort to reduce the critical current density for current-induced magnetization switch- ing [5], the current threshold has been significantly lowered (10 6 A/cm 2 ) and becomes low enough for practical applications in silicon-based circuits. Spin torque studies may also play an important role in magnetic read-heads, but a detrimental one. Due to the change of technology used in magnetoresistive heads from a geometry of in-plane current to a geometry of perpendi- cular-to-plane current, and because of the high current density used in these sensors (10 8 A/cm 2 ), current- induced excitations due to spin torque can be expected in these systems. These excitations may generate magnetic noise, thus affecting the signal-to-noise ratio. These examples of spintronics applications points out to the necessity of controlling spin torque in very small magnetic devices and in particular finding efficient way to determine the spin torque amplitude. This requires a deeper understanding of the spin torque phenomenon and its relationship with spin-dependent transport phenomena. It has been experimentally shown by Urazhdin et al. [6] that the inverse current threshold varies linearly with giant ARTICLE IN PRESS www.elsevier.com/locate/jmmm 0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2007.03.160 Ã Corresponding author. Tel.: +33 4 38 78 46 91; fax: +33 4 38 78 21 27. E-mail address: aurelien.manchon@cea.fr (A. Manchon).