Decoherence and Mode Hopping in a Magnetic Tunnel Junction Based Spin Torque Oscillator

We discuss the coherence of magnetic oscillations in a magnetic tunnel junction based spin torque oscillator as a function of the external field angle. Time-frequency analysis shows mode hopping between distinct oscillator modes, which arises from linear and nonlinear couplings in the Landau-Lifshitz-Gilbert equation, analogous to mode hopping observed in semiconductor ring lasers. These couplings and, therefore, mode hopping are minimized near the current threshold for the antiparallel alignment of free-layer with reference layer magnetization. Away from the antiparallel alignment, mode hopping limits oscillator coherence.

Figure 1

(a) Experimental (circles) and calculated (solid line) resistance versus the in-plane field angle $\phi$ at $H=450\mathrm{Oe}$; $\phi =180°$ corresponds to AP alignment of FL and RL. Inset: Magnetoresistance loop measured at $\phi =180°$. (b) Map of power (dB) vs frequency ($f$) and $\phi$ for $I=8\mathrm{mA}$ and $H=450\mathrm{Oe}$.

Figure 2

Wigner distribution (first column), and normalized autocorrelation envelope (second column) at (a), (b) 140°, (c), (d) 196°, and (e), (f) 220° for $I=8\mathrm{mA}$ and $H=450\mathrm{Oe}$. Red lines are exponential fits to experimental autocorrelation envelope (dashed lines).

Figure 3

Coherence time ${\tau }_c$ (filled symbols) and average dwell time $t_{\mathrm{ave}}$ (open symbols) vs $I$ at 140° (black squares), 196° (red circles), and 220° (blue triangles). Inset: Corresponding $1/t_{\mathrm{ave}}$ vs $I$ showing a clear angular dependence of $1/t_{\mathrm{ave}}$ for $I\to 0$.

Figure 4

Wigner transforms of micromagnetic time traces of average FL magnetization at $T=0\mathrm{K}$ (left) and $T=300\mathrm{K}$ (middle). The right side represents the Fourier transform (FFT) of the 100 ns-long time trace at 300 K. The top row is for 140°; the bottom row is for 180°. The bias current was 8 mA.

Figure 5

(a) $1/(\pi {\tau }_c)$ vs current at 140° (black squares), 196° (red circles), and 220° (blue triangles). Solid lines are fits to the subthreshold region; intercepts with the horizontal axis indicate threshold currents. (c) Power restoration rate ${\Gamma }_p$ vs current at 140° (black squares), 196° (red circles), and 220° (blue triangles). Solid lines are visual guides. Right: Normalized power distribution function and fits at (b) 140°, (d) 196°, and (e) 220°.