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 field-driven ferromagnetic resonance can occur with substantial spatial coherency at 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. The obtained deeply nonlinear ferromagnetic resonance regime is probed by a new spectroscopic technique based on the application of a second excitation field. This enables to resonantly drive slow coherent magnetization nutations around the large angle periodic trajectory. Our experimental findings are well accounted for by an analytical model derived for systems with uniaxial symmetry. They also provide new means for controlling highly nonlinear magnetization dynamics in nanostructures, which open interesting applicative opportunities in the context of magnetic nanotechnologies. Spectroscopy based on the resonant interaction of electromagnetic fields with material media has been of tremendous impact on the development of physics since the beginning of the 20th century and remains of crucial importance till nowadays in the study of nanotechnologies. In this area, a central role is played by magnetic resonance spectroscopy, which includes various techniques such as nuclear magnetic resonance (NMR), electron paramagnetic resonance (EPR), and ferromagnetic resonance (FMR), all based on the excitation of the Larmor precession of magnetic moments around their equilibrium position [1].FMR differs from NMR and EPR by the fact that in ferromagnetic media, magnetic moments are coupled by strong exchange interactions which tend to align them, leading to a large macroscopic spontaneous magnetization. In these conditions, magneto-dipolar effects become important and determine large internal fields which enrich both the ground state, that can be spatially non-uniform, and the dynamics of magnetic moments. The complex interactions taking place in the media can be described by an appropriate effective field which sets the time scale of the magnetization precession, and which itself depends on the magnetization, making the dynamics, for sufficiently large deviations from the ground state, highly nonlinear [2]. A special role in FMR is also played by the spin-waves (SWs), which are the collective eigenmodes associated to small magnetization oscillations around the equilibrium configuration [3]. When pumping fields excite SWs well above their thermal amplitudes, a rich variety of phenomena emerges, such as the formation of dynamical solitons [4,5], SW turbulences and chaos [4,[6][7][8], and Bose-Einstein condensation of magnons [9], the quanta of SWs.Recent developments in magnetic nanotechnologies have also demon...

Derivation of magnetic inertial effects from the classical mechanics of a circular current loop

“…This is coherent with the classical forms of the LLG equation, as generally used in micromagnetism [26,27]. As discussed in the Introduction, the problem of the inertial effect in the dynamics of magnetization has been investigated in recent literature [45][46][47][48][49][50][51][52][53][54][55]. In these works, an evolution equation for the magnetization has been proposed.…”

“…The origin of the differences between our approach and previous works is due to the fact that in Refs. [45][46][47][48][49][50][51][52][53][54][55] the intrinsic rotational motion of the charge defining the magnetic dipole is not considered as a basic assumption and therefore the inertial and Lorentz forces are introduced in a different way. An alternative approach useful to better draw a comparison with the equation proposed by Wegrowe and co-workers is discussed in the next Section.…”

“…It is important to remark that these inertial terms and the Lorentz terms due to the reorientation are both of the order of 1/ω and therefore they are often neglected in practical applications. Nevertheless, the possible use of magnetic fields with extremely high frequencies (at pico-and femto-second time scales) has recently generated a wide interest for the generalization of the LLG equation with inertial effects [45][46][47][48][49][50][51][52][53][54][55]. In this context, our approach yields two generalized sets of second order differential equations for the magnetization dynamics, including the inertial effects and the Lorentz terms due to the reorientation.…”

Quantum Paradigm of the Foldover Magnetic Resonance

“…The H up field corresponds to the end point of the second branch of the solution and is located relatively close to the linear resonance field. This model describes well the results of experiments with a nanosized YIG sample [37]. But this does not apply to macroscopic samples.…”

Parametric resonance of spin waves in ferromagnetic nanowires tuned by spin Hall torque

“…Despite these challenges, a quantitative description of magnetization dynamics in nanomagnets is critically needed for design and optimization of nanoscale spintronic devices [23][24][25][26] such as spin torque memory (STT-MRAM) [27][28][29], spin torque nano-oscillators [30][31][32][33][34][35][36] and ultrasensitive spintronic sensors [37]. Operation of all these practical spintronic devices critically depends on details of linear and nonlinear [38] magnetization dynamics in nanomagnets [39].…”