Nutation Spectroscopy of a Nanomagnet Driven into Deeply Nonlinear Ferromagnetic Resonance

Abstract

Strongly out-of-equilibrium regimes in magnetic nanostructures exhibit novel properties, linked to the nonlinear nature of magnetization dynamics, which are of great fundamental and practical interest. Here, we demonstrate that ferromagnetic resonance driven by microwave magnetic fields can occur with substantial spatial coherency at an unprecedented large angle of magnetization precessions, which is normally prevented by the onset of spin-wave instabilities and magnetization turbulent dynamics. Our results show that this limitation can be overcome in nanomagnets, where the geometric confinement drastically reduces the density of spin-wave modes. When the obtained deeply nonlinear ferromagnetic resonance regime is perturbed, the magnetization undergoes eigenoscillations around the steady state due to torques tending to restore the stable large-angle periodic trajectory. These eigenoscillations are substantially different from the usual spin-wave modes around the ground state because their existence is connected to the presence of a large coherent precession. They are experimentally investigated by a new spectroscopic technique based on the application of a second microwave excitation field that is tuned to resonantly drive them. This two-tone spectroscopy enables us to show that they consist in slow coherent magnetization nutations around the large-angle steady precession, whose frequencies are set by the balance of restoring torques. Our experimental findings are well accounted for by an analytical model derived for systems with uniaxial symmetry. They also provide a new means for controlling highly nonlinear magnetization dynamics in nanostructures, opening interesting applicative opportunities in the context of magnetic nanotechnologies.

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Plain Language Summary

Similar to a spinning top, the natural dynamics of the magnetization vector in ferromagnetic media, called ferromagnetic resonance, corresponds to a small-angle precession around its equilibrium position. Remarkably, this behavior is highly nonlinear as the angle of precession is increased, yielding a series of interesting phenomena, such as spin-wave turbulence and chaos. This complexity can also be detrimental to the reliable control of nanomagnetic devices. It is thus important to establish how far from equilibrium magnetic nanostructures can be driven before the coherent magnetization dynamics becomes highly perturbed by the onset of spin-wave instabilities. Here, we demonstrate that magnetization precession can occur with substantial spatial coherency at unprecedented large angles.

We investigate a magnetic nanodisc of yttrium iron garnet with very low spin-wave damping, where the geometric confinement substantially suppresses nonlinear spin-wave interactions. Using a strong microwave field, it is possible to excite the deeply nonlinear regime of ferromagnetic resonance. When this resonance is perturbed, the magnetization should oscillate around the steady state as a result of torques that tend to restore the stable large-angle periodic trajectory. To unveil these oscillations, we apply a second, weaker excitation field that lets us resonantly drive slow coherent magnetization nutations around the large-angle periodic trajectory, similar to those performed by a spinning top around its precession axis.

The resonant excitation of these nutations can also be used to control the bistability of nonlinear magnetization dynamics. More broadly, the novel approach of nutation spectroscopy in ferromagnetic resonance should allow a deeper understanding of highly nonlinear regimes of magnetization dynamics, which are pertinent for the operations of nanomagnetic devices.