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Bias Dependence of Spin Transfer Torque in Magnetic Tunnel Junctions
Ioannis Theodonis 1* , Nicholas Kioussis 2 , Alan Kalitsov 3 , Mairbek Chshiev 4 , W.H. Butler 4
1 Department of Physics, National Technical University Athens, Zografou Campus 15780, Greece
2 Department of Physics, California State University Northridge, CA 91330-8268, USA
3 Theoretische Physik, Universität Kassel, Heinrich-Plett-Strasse 40, 34132 Kassel, Germany
4 MINT Center, University of Alabama, P. O. Box 870209, Tuscaloosa, Alabama, USA
* ytheod@mail.ntua.gr
Spintronics or magnetoelectronics involve the exploitation of the quantum mechanical spin degree of freedom to provide
new functionalities beyond conventional electronics [1]. Excellent magnetoelectronic components are the magnetic tunnel
junctions (MTJ) due to the tunneling magnetoresistance (TMR) effect. The MTJ consists of two ferromagnetic layers
separated by a non magnetic insulating layer (Figure 1) and the TMR effect is the change in the resistance of a MTJ when the
ferromagnetic layers switch their relative polarization alignments from a parallel (P) to an anti-parallel (AP) configuration [2].
MTJ are used in magnetic random access memory (MRAM) devices where information is stored by switching their magnetic
state to the desired configuration.
Recently, the spin-polarized-current-induced magnetization switching in magnetic tunnel junctions, has attracted great
scientific interest, due to its potential application in future spin transfer torque MRAMs [3,4]. As current flows through a
ferromagnetic layer of a MTJ, it becomes spin-polarized and hence it carries angular momentum. The current remains spinpolarized
in the neighboring thin non magnetic insulating layer, so that the angular momentum carried by the current can
interact with the non-collinear magnetization of the subsequent ferromagnetic layer. Consequently, the spin-polarized current
exerts a spin transfer torque [5,6] on the magnetizations of the ferromagnetic layers in the MTJ. For large enough currents,
this torque leads to precession [7] and reversal of the magnetization [8].
T
T
M 2
I
I L
I
R ( )
R ( )
I
I R
I
z
x
y
Left FM
M 1
Insulating
spacer
N
+ -
V
Right FM
I L
R ( )
I
R ( )
I
I R
Figure 1: Schematic structure of the MTJ, consisting of left and
right semi-infinite FM leads separated by a thin non-magnetic
insulating system containing N atomic layers. The
magnetization M 2 of the right FM lead is along the z axis,
whereas the magnetization M 1 of the left lead is rotated by
angle θ around the y axis with respect to M 2 .
Figure 2: Equivalent circuit of the MTJ, with for spinchannel
currents, with angular-dependent resistances.
A critical aspect of MTJ, with great practical importance is the comprehensive understanding of the bias dependence of the
spin transfer torque. We will present a study of the effect of applied bias on the spin transfer torque, with components
T , and perpendicular, T ⊥
, to the interface (Figure 1), in MTJ, using tight-binding calculations and the non-
parallel,
||
equilibrium Keldysh formalism [9]. We predict an anomalous bias dependence [10] of the parallel component of the spin
torque, contrary to the general consensus. First, we demonstrate that depending on the exchange splitting ∆, T
||
may exhibit
an unusual and interesting non-monotonic bias dependence: it may change sign without a sign reversal in bias or current, and
in some cases it may even have a quadratic bias dependence as presented in Figure 3(a). Second, by generalizing the simple
circuit model for the MTJ [11] using angular dependent resistances (Figure 2), we show that T
||
satisfies an expression
involving the difference in spin currents between the parallel and anti-parallel configurations. This result is very important
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