Ansar R. Safin

Mutual phase locking of very nonidentical spin torque nanooscillators via spin wave interaction

In this paper the mutual phase locking theory of very nonidentical spin-torque nanooscillators, which is based on the Slavin-Tiberkevich model, considering the theory of nonlinear oscillations, is developed. Using generalized Adler equation we calculate phase-locking region of the system with spinwave coupling in the parameter plane - distance between nanocontacts and radii difference. We describe trajectories of such a system in the phase space and show the effect of a broadband synchronization. We introduce a generalization of this approach to the ensembles of spin-torque nanooscillators.

A system of phase synchronization of a spin-transfer nano-oscillator

We have studied the dynamics of a spin-torque nanooscillator’s (STNO) phase locked loop (PLL) generating microwave oscillations in a broad range of frequencies under the effect of direct current and external magnetic field. Bifurcations in the system caused by a change in the frequency detuning of synchronized oscillations are considered. Bands of phase locking and synchronism are determined. The existence of a phase locking band in the filterless PLL of STNOs basically distinguishes these oscillators from other types of microwave generators.We have studied the dynamics of a filterless phase-synchronization system (PSS) of a spin-transfer nano-oscillator (STNO) generating microwave oscillations in a broad range of frequencies under the effect of direct current and external magnetic field. Bifurcations in the system caused by a change in the frequency detuning of synchronized oscillations are considered. Bands of phase locking and synchronism are determined. The existence of a phase-locking band in the filterless PSS of STNOs basically distinguishes these oscillators from other types of microwave generators.

Loading characteristics of a spin-transfer nano-oscillator

A family of loading and control characteristics of a spin-transfer nano-oscillator (STNO) at various values of direct current have been constructed by integrating the Landau–Lifshitz–Gilbert–Slonczewski equation. The obtained characteristics are compared to approximated dependences calculated using truncated equations with respect to the first harmonic. An approximate expression is derived for the load resistance ensuring the maximum STNO output power.

Comparison between the Series and Parallel Power Output Summation Arrangements for an Ensemble of Self-oscillators

The parallel and serial arrangements for summing the power outputs in large ensembles of sine-wave self-oscillators (SO) are investigated. The study was prompted by research activities carried out in the field of spintronics and spin-transfer nanooscillators (STNO). The main drawback of such oscillators is a low power level of the generated oscillations (a few hundred of nanowatts); therefore, one of possible ways for increasing the power output of STNO-based devices is combining them into ensembles to synchronize and sum up their power outputs. In summing up the powers of active elements, bridge circuits are used, which provide mutual decoupling and lack of connection through the common load. The use of bridge circuits for summing up the powers of nanoscale oscillators does not seem to be feasible because the number of generators can reach several hundred. In view of this circumstance, a need arises to seek for the best way of combining the generators (the uniting geometry) and the method for arranging their connection with the load. One possible way in which nanooscillators can be interlinked is to unite their current circuits by means of short-circuited connectors to form either a parallel or a series wiring schemes. Abridged equations of ensembles were derived proceeding from the simplified equivalent circuit of a single self-oscillator consisting of an oscillating loop with losses and a nonlinear active element, and the elementary equal-amplitude synchronous modes are investigated. The obtained models were used to construct a family of SO ensemble external load characteristics. In addition, the ensemble operation conditions are found for the case when an arbitrary number of ensemble elements fail in emergency manner. It is shown that if M elements in the ensemble consisting of N self-oscillators fail, their parallel-connected arrangement will remain operable only if N > 2M, whereas the series-connected scheme will remain operable with any N > M. It should be pointed out that the self-excitation condition for the parallel scheme is not fulfilled if M > N/2. If there occurs a short-circuit fault in the parallel scheme and an open-circuit fault in the series scheme, the entire ensemble fails. Therefore it is necessary to use more intricate component combining topologies, e.g., to unite the considered types of ensembles into sub-ensembles. The obtained results are of importance in constructing large ensembles of SOs (specifically, spin-transfer nanooscillators) when the implementation of bridge circuits is impossible.

Theory of spin torque nano-oscillator-based phase-locked loop

In this paper, we propose an approximate nonlinear theory of a phase-locked loop (PLL) of the spin torque nano-oscillator (STNO). We study the nonlinear dynamics of a filterless PLL generating microwave oscillations in a broad range of frequencies under the spin-polarized electrical current and external magnetic field. We consider the bifurcation analysis caused by a change in the frequency detuning of synchronized oscillations. We determine the bands of phase locking and quasi-synchronism, which basically distinguish STNOs from other types of microwave oscillators. Finally, we study the amplitude and phase noises of isochronous and nonisochronous STNO-based PLLs and compare them to the analogous characteristics of an autonomous oscillator.

Features of the mutual synchronization of nanooscillators

In this work, we investigate the mutual synchronization dynamics in the system of two coupled by spin-waves spin transfer nanooscillators (STNOs). We artificially introduce a leader in the network by passing through it the high density of electrical current, which gives the large energy level (large amplitude of oscillations). We identify that the introduction of a leader, an oscillator having large energy level, in the network induces a profound change in the critical interpillar distances on which mutual synchronization occurs as a function of their radius mismatch for different type of network topologies. We calculate the synchronization badwidth between coupled STNOs We find that the emergence of a leader leads to the reduction of synchronization time. We illustrate different type of nonlinear behavior of the two-coupled STNOs with a leader using phase portraits.