Micromagnetic understanding of stochastic resonance driven by spin-transfer-torque (original) (raw)

In this paper, we employ micromagnetic simulations to study non-adiabatic stochastic resonance (NASR) excited by spin-transfer torque in a super-paramagnetic free layer nanomagnet of a nanoscale spin valve. We find that NASR dynamics involves thermally activated transitions among two static states and a single dynamic state of the nanomagnet and can be well understood in the framework of Markov chain rate theory. Our simulations show that a direct voltage generated by the spin valve at the NASR frequency is at least one order of magnitude greater than the dc voltage generated off the NASR frequency. Our computations also reproduce the main experimentally observed features of NASR such as the resonance frequency, the temperature dependence and the In the superparamagnetic regime, for each value of the direct current density in the OFF dc ON J J J < < interval, random thermal torques induce asynchronous jumps between D and AP states governed by Kramer transition rates (diffusion over potential barriers) between a fixed point of dynamics (AP) and a limit cycle (D). Our data show that the dwell times in the D-state D τ and in the AP state AP τ strongly depend on dc J . In particular, for dc J near ON J , the free layer spends most of its time in the D state, while for dc J near OFF J FIG. 5: (Color online) (a) Dc voltage as function of frequency of the applied alternating current calculated for two direct current densities and temperatures, dc J =0.35×10 8 A/cm 2 (T=100K) and dc J =0.39×10 8 A/cm 2 (T=50K); (b) time traces of the average x-component of the magnetization for dc J =0.35×10 8 A/cm 2 (T=100K) at two different ac current frequencies, AC f =2.75GHz (top) and AC f =6GHz (bottom); (c) V DC-max as function of the direct current density calculated at T=100K and T=0K; (d) Temperature dependence of V DC-max for three direct current densities, dc J =0.35, 0.39, and 0.43×10 8 A/cm 2 (the curves are vertically offset by 10 µV for clarity). 20 FIG. 6: Time evolution of dc voltage computed for dc J =0.39×10 8 A/cm 2 , T=100K, M J =0.1×10 8 A/cm 2 and f AC =2.50 GHz. FIG. 7: (Color online)(a) Trajectory of the average magnetization vector at the nonadiabatic stochastic resonance (NASR) for dc J =0.35×10 8 A/cm 2 , T=100K, M J =0.1×10 8 A/cm 2 and f AC =2.75GHz. (b) Zero-temperature magnetization trajectories in the D and the AP (AP-AC) states for the drive frequency of f AC =2.75GHz.