Nonlinear Dynamics of the Spin-Injection Oscillator
Ansar R. Safin1
Department of Radio Engineering and Electronics, National Research University “MPEI”,Moscow-111250 Russia
*
Corresponding author’s e-mail:arsafin@gmail.com, Tel.: +7-9060656045; Fax: +7-4956994066
1
Abstract
An approximate analytic approach describing excitation
of spin waves by spin-polarized current in the spin-injection
multilayered microwave oscillators is presented. This
approach is based on the method of slowly varying
amplitudes for the spin waves in nanooscillators, and uses
the idea that transversal spin-transfer torque and
nonequilibrium longitudinal spin-injection mechanisms
create in an effective negative damping for spin wave
modes. Nonlinear dynamics and main bifurcations of such
an oscillators are presented.
Keywords: Magnetization dynamics, nonlinear oscillators,
spin-transfer torque, spin injection, spin waves.
dynamics. We found the initial condition area that leads
to a stable limit cycle (see the trajectory I, II on figure 1),
and leads to the multistable behavior (see trajectory’s III,
IV on figure 1).
A simplified mathematical model of the spin-injection
oscillator dynamics considered the method of slowly varying
amplitudes in term of spin wave complex amplitudes. In this
approach, we calculate the critical electric current, at which
nonlinear oscillations start in such a system. It was found that for
this type of oscillator’s bifurcation (critical) value of the current is
much smaller (in the simplest case on two orders) than for a
standard oscillator, based on the spin-transfer torque mechanism.
Introduction
IT was theoretically discovered by J. Sconczewski
and L. Berger [1]-[2] that spin-polarized electric current passing
through a multilayered magnetic nanostructures can transfer its
angular momentum from one layer to another, and can lead to
the generation of spin waves at microwave frequencies.
Another mechanism of electrical current effect switching of the
ferromagnetic multilayer based on the sd-exchange eneregy
was proposed in [3] due to injection of nonequilibrium
longitudinal spins into the layer.
Recently [4], it was developed an analytic nonlinear
theory of current-induced microwave excitation in magnetic
films based on the classical Hamiltonian formalism for the spin
waves using only transversal spin-transfer torque mechanism
(without using the spin-injection mechanism). This theory
showed a good qualitative, and explanation of experimental
facts when the influence of the spin-transfer torque effect
dominates the spin-injection. In a most literature, these two
effects were studied separately. However, in real case both two
effects are to be taken into account simultaneously. In this work,
we develop a nonlinear analytic theory of current-induced
microwave excitations in multilayered magnetic structures
with these two physical mechanisms.
Nonlinear dynamics
Using the numerical simulations of a
generalized Landau-Lifshitz-Gilbert equation with two
additional terms, which are characterized the influence of
spin transfer torque and spin-injection mechanisms, was
analyzed. This analysis showed the existence of
the multistable trajectories in the phase space, which
leads to the chaotic behavior of the magnetization
Fig. 1: Attractors of the spin-injection oscillator for several
initial conditions with standard physical parameters
Acknowledgment
This work was supported in part by the Russian
Foundation for basic research under Grant No. 10-02-01403, and
in part by the Department of Radio Engineering and Electronics in
National Research University “MPEI”.
References
[1] J. C. Slonczewski, “Current driven excitation of magnetic
multilayers,” J. Magn. Magn. Mater., vol. 159, pp. L1-L7, Jun. 1996.
[2] L. Berger, “Emission of spin waves by a magnetic multilayer
traversed by a current,” Phys. Rev. B, vol. 54, pp. 9252-9358, Oct. 1996.
[3] Yu. V. Gulyaev, P. E. Zilberman, A. I. Panas, and E. M. Epshtein,
“Spintronics: exchange switching of ferromagnetic metallic junctions
at a low current density,” Phys. Usp, vol. 52, pp.359-368, Apr. 2009.
[4] A. Slavin, and V. Tiberkevich, “Excitation of spin waves by
spin-polarized current in magnetic nano-structures,” IEEE Trans.
Magn., vol. 44, no. 7, pp.1916-1927, July 2008.