Excitation of propagating spin waves in ferromagnetic nanowires by microwave voltage-controlled magnetic anisotropy.

Roman Verba,Mario Carpentieri,Vasil Tiberkevich,Andrei Slavin,Giovanni Finocchio

doi:10.1038/srep25018

Abstract

The voltage-controlled magnetic anisotropy (VCMA) effect, which manifests itself as variation of anisotropy of a thin layer of a conductive ferromagnet on a dielectric substrate under the influence of an external electric voltage, can be used for the development of novel information storage and signal processing devices with low power consumption. Here it is demonstrated by micromagnetic simulations that the application of a microwave voltage to a nanosized VCMA gate in an ultrathin ferromagnetic nanowire results in the parametric excitation of a propagating spin wave, which could serve as a carrier of information. The frequency of the excited spin wave is twice smaller than the frequency of the applied voltage while its amplitude is limited by 2 mechanisms: (i) the so-called “phase mechanism” described by the Zakharov-L’vov-Starobinets “S-theory” and (ii) the saturation mechanism associated with the nonlinear frequency shift of the excited spin wave. The developed extension of the “S-theory”, which takes into account the second limitation mechanism, allowed us to estimate theoretically the efficiency of the parametric excitation of spin waves by the VCMA effect.

Highlights

Exact manifestation of these nonlinear phenomena depends on the strength of the microwave driving signal, SW spectrum of a magnetic sample and peculiarities of the parametric interaction between the driving signal and parametric SWs in a given sample geometry
The “S-theory” shows that the amplitudes of the excited SWs are limited by the “phase mechanism”[23], which is the disappearance of the phase correlation between the pumping signal and the excited SWs due to the nonlinear interaction between the SWs
The conclusions of the conventional “S-theory”[23] cannot be directly translated to our case of voltage-controlled magnetic anisotropy (VCMA)-induced parametric excitation of SWs, where the ferromagnetic sample has to be quasi-one-dimensional in order to guarantee a definite direction of the SW propagation[21], and the microwave parametric pumping is localized in the region of the VCMA gate electrode

Summary

Introduction

Exact manifestation of these nonlinear phenomena depends on the strength of the microwave driving signal, SW spectrum of a magnetic sample and peculiarities of the parametric interaction between the driving signal and parametric SWs in a given sample geometry. In our current work we study the peculiarities of the parametric excitation of SWs at a VCMA interface using the micromagnetic simulations. As it is shown below, in a real nanowire geometry the achievable magnitudes of the electric field of the microwave parametric pumping could reach the magnitudes that are above the threshold of parametric excitation, but are sufficient to sustain a stable generation of SWs propagating far away from the region of pumping localization and having narrow frequency linewidth. The comparison of our simulation results with the analytical results obtained using the modified “S-theory” demonstrates that in one-dimensional nanoscale ferromagnets the amplitudes of the parametrically excited SWs are limited by the classical “phase mechanism” (characteristic for the “S-theory” in bulk ferromagnets23), but, by an additional limiting mechanism caused by the dependence of the SW group velocity on the SW amplitude, which appears due to a non-zero nonlinear SW frequency shift

Methods

Results

Conclusion