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Register a new userMutual Synchronization of Spin-Torque Oscillators within a Ring Array
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An array of spin torque nano-oscillators (STNOs), coupled by dipolar interaction and arranged on a ring, has been studied numerically and analytically. The phase patterns and locking ranges are extracted as a function of the number $N$, their separation, and the current density mismatch between selected subgroups of STNOs. If $Ngeq 6$ for identical current densities through all STNOs, two degenerated modes are identified an in-phase mode (all STNOs have the same phase) and an out-of-phase mode (the phase makes a 2$pi$ turn along the ring). When inducing a current density mismatch between two subgroups, additional phase shifts occur. The locking range (maximum current density mismatch) of the in-phase mode is larger than the one for the out-of-phase mode and depends on the number $N$ of STNOs on the ring as well as on the separation. These results can be used for the development of magnetic devices that are based on STNO arrays.
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This paper micromagnetically studies the magnetization dynamics driven by the spin-Hall effect in a Platinum/Permalloy bi-layer. For a certain field and current range, the excitation of a uniform mode, characterized by a power with a spatial distribution in the whole ferromagnetic cross section, is observed. We suggest to use the ferromagnet of the bi-layer as basis for the realization of an array of spin-torque oscillators (STOs): the Permalloy ferromagnet will act as shared free layer, whereas the spacers and the polarizers are built on top of it. Following this strategy, the frequency of the uniform mode will be the same for the whole device, creating an intrinsic synchronization. The synchronization of an array of parallely connected STOs will allow to increase the output power, as necessary for technological applications.
We are reporting a new type of synchronization, termed dancing synchronization, between two spin-torque nano-oscillators (STNOs) coupled through spin waves. Different from the known synchronizations in which two STNOs are locked with various fixed relative phases, in this new synchronized state two STNOs have the same frequency, but their relative phase varies periodically within the common period, resulting in a dynamic waving pattern. The amplitude of the oscillating relative phase depends on the coupling strength of two STNOs, as well as the driven currents. The dancing synchronization turns out to be universal, and can exist in two nonlinear Van der Pol oscillators coupled both reactively and dissipativly. Our findings open doors for new functional STNO-based devices.
A mutual synchronization of spin-torque oscillators coupled through current injection is studied theoretically. Models of electrical coupling in parallel and series circuits are proposed. Solving the Landau-Lifshitz-Gilbert equation, excitation of in-phase or antiphase synchronization, depending on the ways the oscillators are connected, is found. It is also found from both analytical and numerical calculations that the current-frequency relations for both parallel and series circuits are the same as that for a single spin-torque oscillator.
We investigate analytically and numerically the synchronization dynamics of dipolarly coupled vortex based Spin-Torque Nano Oscillators (STNO) with different pillar diameters. We identify the critical interpillar distances on which synchronization occurs as a function of their diameter mismatch. We obtain numerically a phase diagram showing the transition between unsynchronized and synchronized states and compare it to analytical predictions we make using Thiele approach. Our study demonstrates that for relatively small diameters differences the synchronization dynamics can be described qualitatively using Adler equation. However when the diameters difference increases significantly, the system becomes strongly non-Adlerian.
We have proposed a method to synchronize multiple spin-transfer torque oscillators based on spin pumping, inverse spin Hall, and spin Hall effects. The proposed oscillator system consists of a series of nano-magnets in junction with a normal metal with high spin-orbit coupling, and an accumulative feedback loop. We conduct simulations to demonstrate the effect of modulated charge currents in the normal metal due to spin pumping from each nano-magnet. We show that the interplay between the spin Hall effect and inverse spin Hall effect results in synchronization of the nano-magnets.
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