Non-white frequency noise in spin torque oscillators and its effect on spectral linewidth

We measure the power spectral density of frequency fluctuations in nanocontact spin torque oscillators over time scales up to 50 ms. We use a mixer to convert oscillator signals ranging from 10 GHz to 40 GHz into a band near 70 MHz before digitizing the time domain waveform. We analyze the waveform using both zero crossing time stamps and a sliding Fourier transform, discuss the different limitations and advantages of these two methods, and combine them to obtain a frequency noise spectrum spanning more than five decades of Fourier frequency $f$. For devices having a free layer consisting of either a single Ni$_{\text{}80}$Fe$_{\text{}20}$ layer or a Co/Ni multilayer we find a frequency noise spectrum that is white at large $f$ and varies as \emph{$1/f$} at small $f$. The crossover frequency ranges from \approx\unit[10^{4}]{Hz} to \approx\unit[10^{6}]{Hz} and the $1/f$ component is stronger in the multilayer devices. Through actual and simulated spectrum analyzer measurements, we show that $1/f$ frequency noise causes both broadening and a change in shape of the oscillator's spectral line as measurement time increases. Our results indicate that the long term stability of spin torque oscillators cannot be accurately predicted from models based on thermal (white) noise sources

Frequency Modulation of Spin-Transfer Oscillators

Spin-polarized dc electric current flowing into a magnetic layer can induce precession of the magnetization at a frequency that depends on current. We show that addition of an ac current to this dc bias current results in a frequency modulated (FM) spectral output, generating sidebands spaced at the modulation frequency. The sideband amplitudes and shift of the center frequency with drive amplitude are in good agreement with a nonlinear FM model that takes into account the nonlinear frequency-current relation generally induced by spin transfer. Single-domain simulations show that ac current modulates the cone angle of the magnetization precession, in turn modulating the frequency via the demagnetizing field. These results are promising for communications and signal processing applications of spin-transfer oscillators.Comment: 13 pages, 3 Figure

Time domain measurement of phase noise in a spin torque oscillator

We measure oscillator phase from the zero crossings of the voltage vs. time waveform of a spin torque nanocontact oscillating in a vortex mode. The power spectrum of the phase noise varies with Fourier frequency $f$ as $1/f^2$, consistent with frequency fluctuations driven by a thermal source. The linewidth implied by phase noise alone is about 70 % of that measured using a spectrum analyzer. A phase-locked loop reduces the phase noise for frequencies within its 3 MHz bandwidth.Comment: 6 pages, 5 figures, supplementary material. Submitted to {Appl. Phys. Lett.

Synchronization of spin-torque driven nanooscillators for point contacts on a quasi-1D nanowire: Micromagnetic simulations

In this paper we present detailed numerical simulation studies on the synchronization of two spin-torque nanooscillators (STNO) in the quasi-1D geometry: magnetization oscillations are induced in a thin NiFe nanostripe by a spin polarized current injected via square-shaped CoFe nanomagnets on the top of this stripe. In a sufficiently large out-of-plane field, a propagating oscillation mode appears in such a system. Due to the absence of the geometrically caused wave decay in 1D systems, this mode is expected to enable a long-distance synchronization between STNOs. Indeed, our simulations predict that synchronization of two STNOs on a nanowire is possible up to the intercontact distance 3 mkm (for the nanowire width 50 nm). However, we have also found several qualitatively new features of the synchronization behaviour for this system, which make the achievement of a stable synchronization in this geometry to a highly non-trivial task. In particular, there exist a minimal distance between the nanocontacts, below which a synchronization of STNOs can not be achieved. Further, when the current value in the first contact is kept constant, the amplitude of synchronized oscillations depends non-monotonously on the current value in the second contact. Finally, for one and the same currents values through the contacts there might exist several synchronized states (with different frequencies), depending on the initial conditions.Comment: 13 pages with 4 figurews, recently submitted to PR

Broadband Ferromagnetic Resonance Linewidth Measurement of Magnetic Tunnel Junction Multilayers

The broadband ferromagnetic resonance (FMR) linewidth of the free layer of magnetic tunnel junctions is used as a simple diagnostic of the quality of the magnetic structure. The FMR linewidth increases near the field regions of free layer reversal and pinned layer reversal, and this increase correlates with an increase in magnetic hysteresis in unpatterned films, low frequency noise in patterned devices, and previous observations of magnetic domain ripple by use of Lorentz microscopy. Postannealing changes the free layer FMR linewidth indicating that considerable magnetic disorder, originating in the exchange-biased pinned layer, is transferred to the free layer.Comment: 13 pages, 4 figure

Switching Distributions for Perpendicular Spin-Torque Devices within the Macrospin Approximation

We model "soft" error rates for writing (WSER) and for reading (RSER) for perpendicular spin-torque memory devices by solving the Fokker-Planck equation for the probability distribution of the angle that the free layer magnetization makes with the normal to the plane of the film. We obtain: (1) an exact, closed form, analytical expression for the zero-temperature switching time as a function of initial angle; (2) an approximate analytical expression for the exponential decay of the WSER as a function of the time the current is applied; (3) comparison of the approximate analytical expression for the WSER to numerical solutions of the Fokker-Planck equation; (4) an approximate analytical expression for the linear increase in RSER with current applied for reading; (5) comparison of the approximate analytical formula for the RSER to the numerical solution of the Fokker-Planck equation; and (6) confirmation of the accuracy of the Fokker-Planck solutions by comparison with results of direct simulation using the single-macrospin Landau-Lifshitz-Gilbert (LLG) equations with a random fluctuating field in the short-time regime for which the latter is practical

Current-Driven Microwave Dynamics in Magnetic Point Contacts as a Function of Applied Field Angle

We have measured microwave frequency, current-driven magnetization dynamics in point contacts made to Co90Fe10/Cu/ Ni80Fe20 spin valves as a function of applied field strength and angle relative to the film plane. As the field direction is varied from parallel to nearly perpendicular, the device power output increases by roughly two orders of magnitude while the frequencies of the excitations decrease. For intermediate angles the excited frequency does not monotonically vary with applied current and also exhibits abrupt, current-dependent jumps. For certain ranges of current, and applied field strength and direction, the excitation linewidths decrease to a few megahertz, leading to quality factors over 18,000

Magnetism and the Weiss Exchange Field - A Theoretical Analysis Inspired by Recent Experiments

The huge spin precession frequency observed in recent experiments with spin-polarized beams of hot electrons shot through magnetized films is interpreted as being caused by Zeeman coupling of the electron spins to the so-called Weiss exchange field in the film. A "Stern-Gerlach experiment" for electrons moving through an inhomogeneous exchange field is proposed. The microscopic origin of exchange interactions and of large mean exchange fields, leading to different types of magnetic order, is elucidated. A microscopic derivation of the equations of motion of the Weiss exchange field is presented. Novel proofs of the existence of phase transitions in quantum XY-models and antiferromagnets, based on an analysis of the statistical distribution of the exchange field, are outlined.Comment: 36 pages, 3 figure

Superconducting Transition Edge Sensor Using Dilute AlMn Alloys

We have fabricated a bolometer using a transition-edge sensor (TES) made of Al doped with Mn to suppress the superconducting critical temperature (Tc) of Al from ∼1Kto∼100mK. The resulting detector exhibits low-frequency noise consistent with theory, with a noise-equivalent power of 7.5×10−18W/√Hz. The addition of Mn impurities did not significantly increase the heat capacity of the TES. In addition, the detector is surprisingly insensitive to applied magnetic fields. The use of AlMn alloy films in arrays of TES detectors has advantages in simplicity of fabrication when compared to traditional bilayer fabrication techniques