Precessional switching of thin nanomagnets: analytical study

We study analytically the precessional switching of the magnetization of a thin macrospin. We analyze its response when subjected to an external field along its in-plane hard axis. We derive the exact trajectories of the magnetization. The switching versus non switching behavior is delimited by a bifurcation trajectory, for applied fields equal to half of the effective anisotropy field. A magnetization going through this bifurcation trajectory passes exactly along the hard axis and exhibits a vanishing characteristic frequency at that unstable point, which makes the trajectory noise sensitive. Attempting to approach the related minimal cost in applied field makes the magnetization final state unpredictable. We add finite damping in the model as a perturbative, energy dissipation factor. For a large applied field, the system switches several times back and forth. Several trajectories can be gone through before the system has dissipated enough energy to converge to one attracting equilibrium state. For some moderate fields, the system switches only once by a relaxation dominated precessional switching. We show that the associated switching field increases linearly with the damping parameter. The slope scales with the square root of the effective anisotropy. Our simple concluding expressions are useful to assess the potential application of precessional switching in magnetic random access memories

Lineshape distortion in a nonlinear auto-oscillator near generation threshold: Application to spin-torque nano-oscillators

The lineshape in an auto-oscillator with a large nonlinear frequency shift in the presence of thermal noise is calculated. Near the generation threshold, this lineshape becomes strongly non-Lorentzian, broadened, and asymmetric. A Lorentzian lineshape is recovered far below and far above threshold, which suggests that lineshape distortions provide a signature of the generation threshold. The theory developed adequately describes the observed behavior of a strongly nonlinear spin-torque nano-oscillator.Comment: 4 pages, 3 figure

Auto-oscillation threshold, narrow spectral lines, and line jitter in spin-torque oscillators based on MgO magnetic tunnel junctions

We demonstrate spin torque induced auto-oscillation in MgO-based magnetic tunnel junctions. At the generation threshold, we observe a strong line narrowing down to 6 MHz at 300K and a dramatic increase in oscillator power, yielding spectrally pure oscillations free of flicker noise. Setting the synthetic antiferromagnet into autooscillation requires the same current polarity as the one needed to switch the free layer magnetization. The induced auto-oscillations are observed even at zero applied field, which is believed to be the acoustic mode of the synthetic antiferromagnet. While the phase coherence of the auto-oscillation is of the order of microseconds, the power autocorrelation time is of the order of milliseconds and can be strongly influenced by the free layer dynamics

Current-driven microwave oscillations in current perpendicular-to-plane spin-valve nanopillars

We study the current and temperature dependences of the microwave voltage emission of spin-valve nanopillars subjected to an in-plane magnetic field and a perpendicular-to-plane current. Despite the complex multilayer geometry, clear microwave emission is shown to be possible and spectral lines as narrow as 3.8 MHz (at 150 K) are observed.Comment: To appear in Applied Physics Letter

Phase Coherent Precessional Magnetization Reversal in Micro-scopic Spin Valve Elements

We study the precessional switching of the magnetization in microscopic spin valve cells induced by ultra short in-plane hard axis magnetic field pulses. Stable and highly efficient switching is monitored following pulses as short as 140 ps with energies down to 15 pJ. Multiple application of identical pulses reversibly toggles the cell's magnetization be-tween the two easy directions. Variations of pulse duration and amplitude reveal alter-nating regimes of switching and non-switching corresponding to transitions from in-phase to out-of-phase excitations of the magnetic precession by the field pulse. In the low field limit damping becomes predominant and a relaxational reversal is found allowing switching by hard axis fields below the in-plane anisotropy field threshold.Comment: 17 pages, 4 figure

Quantized spin wave modes in magnetic tunnel junction nanopillars

We present an experimental and theoretical study of the magnetic field dependence of the mode frequency of thermally excited spin waves in rectangular shaped nanopillars of lateral sizes 60x100, 75x150, and 105x190 nm2, patterned from MgO-based magnetic tunnel junctions. The spin wave frequencies were measured using spectrally resolved electrical noise measurements. In all spectra, several independent quantized spin wave modes have been observed and could be identified as eigenexcitations of the free layer and of the synthetic antiferromagnet of the junction. Using a theoretical approach based on the diagonalization of the dynamical matrix of a system of three coupled, spatially confined magnetic layers, we have modeled the spectra for the smallest pillar and have extracted its material parameters. The magnetization and exchange stiffness constant of the CoFeB free layer are thereby found to be substantially reduced compared to the corresponding thin film values. Moreover, we could infer that the pinning of the magnetization at the lateral boundaries must be weak. Finally, the interlayer dipolar coupling between the free layer and the synthetic antiferromagnet causes mode anticrossings with gap openings up to 2 GHz. At low fields and in the larger pillars, there is clear evidence for strong non-uniformities of the layer magnetizations. In particular, at zero field the lowest mode is not the fundamental mode, but a mode most likely localized near the layer edges.Comment: 16 pages, 4 figures, (re)submitted to PR

Agility of vortex-based nanocontact spin torque oscillators

We study the agility of current-tunable oscillators based on a magnetic vortex orbiting around a point contact in spin-valves. Theory predicts frequency-tuning by currents occurs at constant orbital radius, so an exceptional agility is anticipated. To test this, we have inserted an oscillator in a microwave interferometer to apply abrupt current variations while time resolving its emission. Using frequency shift keying, we show that the oscillator can switch between two stabilized frequencies differing by 25% in less than ten periods. With a wide frequency tunability and a good agility, such oscillators possess desirable figures of merit for modulation-based rf applications.Comment: 3 pages, 3 figure

Frequency shift keying in vortex-based spin torque oscillators

Vortex-based spin-torque oscillators can be made from extended spin valves connected to an electrical nanocontact. We study the implementation of frequency shift keying modulation in these oscillators. Upon a square modulation of the current in the 10 MHz range, the vortex frequency follows the current command, with easy identification of the two swapping frequencies in the spectral measurements. The frequency distribution of the output power can be accounted for by convolution transformations of the dc current vortex waveform, and the current modulation. Modeling indicates that the frequency transitions are phase coherent and last less than 25 ns. Complementing the multi-octave tunability and first-class agility, the capability of frequency shift keying modulation is an additional milestone for the implementation of vortex-based oscillators in RF circuit.Comment: 6 pages, 5 figure