P. K. Muduli

Spin torque oscillator frequency versus magnetic field angle: The prospect of operation beyond 65 GHz

We study the impact of the magnetic field angle on the oscillation frequency of a nanocontact spin torque oscillator (STO) in magnetic fields up to 2.1 T. A model based on a single nonlinear, nonpr ...

Experimental evidence of self-localized and propagating spin wave modes in obliquely magnetized current-driven nanocontacts.

Through detailed experimental studies of the angular dependence of spin wave excitations in nanocontact-based spin-torque oscillators, we demonstrate that two distinct spin wave modes can be excited, with different frequency, threshold currents, and frequency tunability. Using analytical theory and micromagnetic simulations we identify one mode as an exchange-dominated propagating spin wave, and the other as a self-localized nonlinear spin wave bullet. Wavelet-based analysis of the simulations indicates that the apparent simultaneous excitation of both modes results from rapid mode hopping induced by the Oersted field.

Nonlinear frequency and amplitude modulation of a nanocontact-based spin-torque oscillator

We study the current-controlled modulation of a nanocontact spin-torque oscillator. Three principally different cases of frequency nonlinearity (d(2)f/dI(dc)(2) being zero, positive, and negative) ...

Mutually synchronized bottom-up multi-nanocontact spin–torque oscillators

Spin-torque oscillators offer a unique combination of nanosize, ultrafast modulation rates and ultrawide band signal generation from 100 MHz to close to 100 GHz. However, their low output power and large phase noise still limit their applicability to fundamental studies of spin-transfer torque and magnetodynamic phenomena. A possible solution to both problems is the spin-wave-mediated mutual synchronization of multiple spin-torque oscillators through a shared excited ferromagnetic layer. To date, synchronization of high-frequency spin-torque oscillators has only been achieved for two nanocontacts. As fabrication using expensive top-down lithography processes is not readily available to many groups, attempts to synchronize a large number of nanocontacts have been all but abandoned. Here we present an alternative, simple and cost-effective bottom-up method to realize large ensembles of synchronized nanocontact spin-torque oscillators. We demonstrate mutual synchronization of three high-frequency nanocontact spin-torque oscillators and pairwise synchronization in devices with four and five nanocontacts.

Spin-Torque and Spin-Hall Nano-Oscillators

This paper reviews the state of the art in spin-torque and spin-Hall-effect-driven nano-oscillators. After a brief introduction to the underlying physics, the authors discuss different implementations of these oscillators, their functional properties in terms of frequency range, output power, phase noise, and modulation rates, and their inherent propensity for mutual synchronization. Finally, the potential for these oscillators in a wide range of applications, from microwave signal sources and detectors to neuromorphic computation elements, is discussed together with the specific electronic circuitry that has so far been designed to harness this potential.

Frequency modulation of spin torque oscillator pairs

The current controlled modulation of nanocontact based spin torque oscillator (STO) pairs is studied in both the synchronized and nonsynchronized states. The synchronized state shows a well behaved modulation and demonstrates robust mutual locking even under strong modulation. The power distribution of the modulation sidebands can be quantitatively described by assuming a single oscillator model. However, in the nonsynchronized state, the modulation sidebands are not well described by the model, indicating interactions between the two individual nanocontact STOs. These findings are promising for potential applications requiring the modulation of large synchronized STO arrays.

Bias dependence of perpendicular spin torque and of free- and fixed-layer eigenmodes in MgO-based nanopillars

We have measured the bias voltage and field dependence of eigenmode frequencies in a magnetic tunnel junction with MgO barrier. We show that both free layer (FL) and reference layer (RL) modes are excited, and that a crossover between these modes is observed by varying external field and bias voltage. The bias voltage dependence of the FL and RL modes are shown to be dramatically different. The bias dependence of the FL modes is linear in bias voltage, whereas that of the RL mode is strongly quadratic. Using modeling and micromagnetic simulations, we show that the linear bias dependence of FL frequencies is primarily due to a linear dependence of the perpendicular spin torque on bias voltage, whereas the quadratic dependence of the RL on bias voltage is dominated by the reduction of exchange bias due to Joule heating, and is not attributable to a quadratic dependence of the perpendicular spin torque on bias voltage.

Spin-torque oscillator linewidth narrowing under current modulation

We study the behavior of the linewidth of a nanocontact based spin torque oscillator (STO) under application of a radio frequency (100 MHz) modulating current. We achieve a significant (up to 85%) reduction in the STO linewidth when it is modulated across a region of high nonlinearity. The mechanism responsible for the linewidth reduction is the nonlinear frequency shift under the influence of current modulation, which reduces the nonlinear amplification of the linewidth. The reduction in the linewidth during modulation can be quantitatively calculated from the free-running behavior of the STO.

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.

Spin Torque Oscillators and RF Currents—Modulation, Locking, and Ringing

We study the interaction between a nano-contact spin torque oscillator (STO) and injected radio-frequency and microwave currents. Modulation of the STO signal is observed over a wide frequency range from 100 MHz to 3.2 GHz. The modulation sidebands agree well with macrospin simulations. When the injected microwave frequency approaches that of the STO, we observe injection locking, frequency pulling/pushing, and intermodulation peaks. While the intermodulation peaks are reasonably well reproduced by macrospin simulations, they do not follow the Adlers model. We argue that this discrepancy is due to intrinsic ringing effects stemming from the internal dynamics of the STO.