Chaotic Dynamics of Spin-Valve Oscillators

Recent experimental and theoretical studies on the magnetization dynamics driven by an electric current have uncovered a number of unprecedented rich dynamic phenomena. We predict an intrinsic chaotic dynamics that has not been previously anticipated. We explicitly show that the transition to chaotic dynamics occurs through a series of period doubling bifurcations. In chaotic regime, two dramatically different power spectra, one with a well-defined peak and the other with a broadly distributed noise, are identified and explained.

Figure 1

Chaotic-nonchaotic phase diagram. Two lines are the boundary of chaos determined by the Melnikov integral. Chaos is possible only within the region bounded by these two lines. The dark region represents a positive value of the largest Lyapunov exponent, i.e., chaos. The parameters are chosen similar to a permalloy film: damping constant $\alpha =0.02$, anisotropy constant $H_K=0$, demagnetization field $4\pi M_s=8400\mathrm{Oe}$, and $\gamma =1.7\times {10}^{-7}{\mathrm{Oe}}^{-1}{\mathrm{s}}^{-1}$. The amplitude and the frequency of the ac current are $a_{\mathrm{ac}}=20\mathrm{Oe}$ and $\omega =15\mathrm{GHz}$.

Figure 2

(a) Lyapunov spectra for $226\mathrm{Oe}<a_j<233\mathrm{Oe}$; (b) the regular nonchaotic trajectory for $a_j=227.5\mathrm{Oe}$; (c) chaotic trajectory for $a_j=232.5\mathrm{Oe}$. The magnetic field is 200 Oe. All parameters are the same as in Fig. 1.

Figure 3

Period doubling bifurcation cascade. The dashed lines indicate the critical values of the dc current where the bifurcation occurs. All parameters are the same as in Fig. 2.

Figure 4

Trajectories and their corresponding $M_z$-component power spectra of two types of chaos. Upper panels: $a_j=262.5\mathrm{Oe}$; the largest Lyapunov exponent is 0.86. Lower panels: $a_j=261.0\mathrm{Oe}$; the largest Lyapunov exponent is 1.56. All parameters are the same as in Fig. 2.