Coupling of dynamical micromagnetism and a stationary spin drift-diffusion equation: A step towards a fully self-consistent spintronics framework

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.We consider the coupling of the Landau-Lifshitz-Gilbert equation with a quasilinear diffusion equation to describe the interplay of magnetization and spin accumulation in magnetic-nonmagnetic multilayer structures. For this problem, we propose and analyze a convergent finite element integrator, where, in contrast to prior work, we consider the stationary limit for the spin diffusion. Numerical experiments underline that the new approach is more effective, since it leads to the same experimental results as for the model with time-dependent spin diffusion, but allows for larger time-steps of the numerical integrator.The authors acknowledge support from the Vienna Science and Technology Fund (WWTF) under grant MA14-44 (GH, DP, DS), from the Austrian Science Fund (FWF) under grant W1245 (DP, MR), from TU Wien through the innovative projects initiative (DP, MR), from the Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development (CA, DS), through the EPSRC grant EP/K008412/1 (GH), from the Royal Society under grant UF080837 (GH)

Super-harmonic injection locking of nano-contact spin-torque vortex oscillators

Super-harmonic injection locking of single nano-contact (NC) spin-torque vortex oscillators (STVOs) subject to a small microwave current has been explored. Frequency locking was observed up to the fourth harmonic of the STVO fundamental frequency $f_{0}$ in microwave magneto-electronic measurements. The large frequency tunability of the STVO with respect to $f_{0}$ allowed the device to be locked to multiple sub-harmonics of the microwave frequency $f_{RF}$, or to the same sub-harmonic over a wide range of $f_{RF}$ by tuning the DC current. In general, analysis of the locking range, linewidth, and amplitude showed that the locking efficiency decreased as the harmonic number increased, as expected for harmonic synchronization of a non-linear oscillator. Time-resolved scanning Kerr microscopy (TRSKM) revealed significant differences in the spatial character of the magnetization dynamics of states locked to the fundamental and harmonic frequencies, suggesting significant differences in the core trajectories within the same device. Super-harmonic injection locking of a NC-STVO may open up possibilities for devices such as nanoscale frequency dividers, while differences in the core trajectory may allow mutual synchronisation to be achieved in multi-oscillator networks by tuning the spatial character of the dynamics within shared magnetic layers.Comment: 21 pages, 8 figure

Current-driven vortex oscillations in metallic nanocontacts

We present experimental evidence of sub-GHz spin-transfer oscillations in metallic nano-contacts that are due to the translational motion of a magnetic vortex. The vortex is shown to execute large-amplitude orbital motion outside the contact region. Good agreement with analytical theory and micromagnetics simulations is found.Comment: 4 pages, 3 figure

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

Modelling interfacial coupling in thin film magnetic exchange springs at finite temperature

This is the final version of the article. Available from the American Institute of Physics via the DOI in this record.We report a numerical study that demonstrates the interface layer between a soft and hard magnetic phase, the exchange transition layer, is the dominant factor that influences the magnetization reversal process at room temperature and long measurement times. It is found that the exchange transition layer thickness affects the magnetization reversal and the coupling of a bi-layer system by lowering the switching field and changing the angle dependent magnetization reversal. We show that the change in angle dependence of reversal is due to an increased incoherency in the lateral spin behavior. Changing the value of exchange coupling in the exchange transition layer affects only the angle dependent behavior and does not lower the switching field. © 2013 AIP Publishing LLC.We would like to thank the EPSRC for financial support under Grant Nos. EP/G032440/1 and EP/G032300/1, the WWTF Project MA09-029 and the Royal Society UF080837

Direct observation of magnetization dynamics generated by nano-contact spin-torque vortex oscillators

Time-resolved scanning Kerr microscopy has been used to directly image the magnetization dynamics of nano-contact (NC) spin-torque vortex oscillators (STVOs) when phase-locked to an injected microwave (RF) current. The Kerr images reveal free layer magnetization dynamics that extend outside the NC footprint, where they cannot be detected electrically, but which are crucial to phase-lock STVOs that share common magnetic layers. For a single NC, dynamics were observed not only when the STVO frequency was fully locked to that of the RF current, but also for a partially locked state characterized by periodic changes in the core trajectory at the RF frequency. For a pair of NCs, images reveal the spatial character of dynamics that electrical measurements show to have enhanced amplitude and reduced linewidth. Insight gained from these images may improve understanding of the conditions required for mutual phase-locking of multiple STVOs, and hence enhanced microwave power emission.Comment: 10 pages, 3 figure

Auto-oscillation threshold and line narrowing in MgO-based spin-torque oscillators

We present an experimental study of the power spectrum of current-driven magnetization oscillations in MgO tunnel junctions under low bias. We find the existence of narrow spectral lines, down to 8 MHz in width at a frequency of 10.7 GHz, for small applied fields with clear evidence of an auto-oscillation threshold. Micromagnetics simulations indicate that the excited mode corresponds to an edge mode of the synthetic antiferromagnet

Atomistic study on the pressure dependence of the melting point of NdFe12

We investigated, using molecular dynamics, how pressure affects the melting point of the recently theorised and epitaxially grown structure NdFe12. We modified Morse potentials using experimental constants and a genetic algorithm code, before running two-phase solid-liquid coexistence simulations of NdFe12 at various temperatures and pressures. The refitting of the Morse potentials allowed us to significantly improve the accuracy in predicting the melting temperature of the constituent elements

Imaging magnetisation dynamics in nano-contact spin-torque vortex oscillators exhibiting gyrotropic mode splitting

This is the author accepted manuscript. The final version is available from IOP Publishing via the DOI in this record.Nano-contact spin-torque vortex oscillators (STVOs) are anticipated to find application as nanoscale sources of microwave emission in future technological applications. Presently the output power and phase stability of individual STVOs are not competitive with existing oscillator technologies. Synchronisation of multiple nano-contact STVOs via magnetisation dynamics has been proposed to enhance the microwave emission. The control of device-to-device variations, such as mode splitting of the microwave emission, is essential if multiple STVOs are to be successfully synchronised. In this work a combination of electrical measurements and time-resolved scanning Kerr microscopy (TRSKM) was used to demonstrate how mode splitting in the microwave emission of STVOs was related to the magnetisation dynamics that are generated. The free-running STVO response to a DC current only was used to identify devices and bias magnetic field configurations for which single and multiple modes of microwave emission were observed. Stroboscopic Kerr images were acquired by injecting a small amplitude RF current to phase lock the free-running STVO response. The images showed that the magnetisation dynamics of a multimode device with moderate splitting could be controlled by injecting an RF current so that they exhibit similar spatial character to that of a single mode. Significant splitting was found to result from a complicated equilibrium magnetic state that was observed in Kerr images as irregular spatial characteristics of the magnetisation dynamics. Such dynamics were observed far from the nano-contact and so their presence cannot be detected in electrical measurements. This work demonstrates that TRSKM is a powerful tool for the direct observation of the magnetisation dynamics generated by STVOs that exhibit complicated microwave emission. Characterisation of such dynamics outside the nano-contact perimeter permits a deeper insight into the requirements for optimal phase-locking of multiple STVOs that share common magnetic layers.The authors gratefully acknowledge the financial support of the Engineering and Physical Sciences Research Council under grants EP/I038470/1 and EP/K008501/1, the Royal Society under grant UF080837, the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), and the Knut and Alice Wallenberg Foundation (KAW). The authors and co-authors declare that there are no conflicts of interes