Injection locking at 2f of spin torque oscillators under influence of noise

M. TORTAROLO; C. DIEUDONNÉ; M. QUINSAT; L. BUDA-PREJBEANU; M. C. CYRILLE; J. A. KATINE; U. EBELS

Autrans

Workshop; XVIe Colloque Louis Néel; 2014

CNRS

A spin polarized current passing through a magnetic multilayered nanosystem can drive its magnetization into large amplitude periodic oscillations[1,2], when the spin polarized current is large enough to compensate the natural damping. These spin transfer driven magnetization oscillations are promising for several applications for current controlled microwave oscillators. Nevertheless, one of the main issues that remains to be addressed for these spin transfer torque oscillators (STOs) is their relative large linewidth. One possibility to reduce the linewidth is to couple either different layers within an oscillator, or to couple several oscillators. As a first step to understand the conditions for synchronization of several oscillators by their own emitted rf current, we studied the synchronization of an STO to a microwave power source, with known spectral specifications. Here we focus on standard in-plane magnetized oscillators (in-plane polarizer and in-plane free layer), for which an in-plane precession (IPP) mode is stabilized. The injection locking of such an in-plane magnetized STO to an external microwave current at two times the generated frequency (2f) was demonstrated both numerically and by experiments[3]. However, the linewidth in the locked regime was reduced only by a factor of ten. This raises the question on the role of external noise and the conditions to achieve a true phase-locking. In order to address this question we investigate the phase noise and the transient behavior to the locked state for the synchronization at 2f. The numerical analysis of the phase noise in the synchronized state predicts a crossover of a 1/f2 dependence for frequency locking to a 1/f0 for phase locking by increasing the microwave current. This crossover indicates a truly phase locked state. Experimentally we find for MTJ nanopillars that while a complete synchronization is achieved in the frequency, the system is not in a truly phase locked regime. While it is possible to reduce the phase noise by synchronization only a 1/f2 phase noise dependence was observed. In order to understand the effects of thermal fluctuations in the synchronized state, we developed an analytical model for the IPP mode, for f and 2f synchronization, which reveals clearly that synchronization at 2f occurs only for non-isochronous oscillators. As in a previous existing model[4] at f, it was found that at 2f, the phase approaches its locked state exponentially and oscillating. However, the threshold of microwave current between a pure exponential approach to an oscillatory approach is different for synchronization at f and 2f. The correlation between the transient behavior and the phase noise diagrams will be discussed. [1] J. C. Slonzewski, J. Magn. Magn. Mater. 159 L1 (1996) [2] L. Berger, Phys. Rev. B 54, 9353 (1996) [3] Quinsat et al., App. Phys. Lett 97, 182507 (2010) [4] A. Slavin and V. Tiberkevich, IEEE Transactions in Magnetics, Vol. 45, NO. 4 (2009)