[Paper Review] Anomalous nonlinearity of the magnonic edge mode

Mykola Dvornik, Johan Åkerman|arXiv (Cornell University)|Apr 4, 2018

Magnetic properties of thin films3 citations

TL;DR

This paper demonstrates that magnonic edge modes in patterned magnetic nanostructures exhibit anomalous nonlinearity, where the nonlinearity coefficient 𝒩 is amplitude-dependent due to a nonlinear confinement potential. Unlike extended films, edge modes can remain localized even with positive 𝒩 (repulsive magnons), showing spatial expansion for positive 𝒩 and compression for negative 𝒩, enabling all-electrical control of magnetic coupling in nonlinear magnonic networks.

ABSTRACT

Nonlinearity of magneto-dynamics is typically described by a single constant, $\mathcal{N}$, with positive and negative values indicating repulsion and attraction of magnons, respectively. In thin magnetic films with easy-plane magnetic anisotropy, magnon attraction is typically achieved for an in-plane magnetization. At sufficient stimulus, e.g. via application of spin transfer torque, the attraction can give rise to self-localized magnetic solitons, such as spin wave bullets, which shrink as their amplitude increases. In contrast, for an oblique magnetization above a certain critical angle, the repulsion of magnons only allows for propagating modes, which expand when pumped more strongly. Here we demonstrate, both analytically and using micromagnetic simulations, that such a dichotomic description is inadequate for magnonic edge modes, which naturally appear in confined magnetic systems. In particular, we demonstrate that the confinement potential of such modes is nonlinear in nature and its contribution makes $\mathcal{N}$ non-monotonically dependent on their amplitude. As a prominent example, edge modes show compression and expansion for negative and positive $\mathcal{N}$, yet remain localized. In striking contrast to the extended geometries, edge magnons might also repeal even for an in-plane magnetization.

Motivation & Objective

• To understand the nonlinear dynamics of magnonic edge modes in confined magnetic systems, which deviate from standard nonlinear behavior in extended films.
• To identify the origin of non-monotonic nonlinearity in edge modes, particularly the interplay between dynamic and static dipolar fields.
• To demonstrate that edge modes can remain localized under positive nonlinearity (magnon repulsion), defying conventional expectations.
• To enable all-electrical control of mode volume and coupling in magnonic networks via amplitude-dependent nonlinearity.

Proposed method

• Analytical modeling of edge mode nonlinearity using a modified spin wave equation incorporating both dynamic and static dipolar fields.
• Micromagnetic simulations of semi-infinite ferromagnetic nanowires with periodic and absorbing boundary conditions to model edge mode excitation.
• Calculation of the nonlinearity coefficient 𝒩_EDGE as a function of mode amplitude, magnetization angle, and film thickness using the Kittel equation and demagnetizing field components.
• Use of spin-polarized current injection to excite auto-oscillating edge modes and track their spatial and frequency evolution under varying pump currents.
• Comparison of analytical predictions with micromagnetic results to validate the amplitude-dependent nonlinearity model.
• Investigation of mode profile evolution, including center detachment from the edge, under increasing oscillation amplitude.

Experimental results

Research questions

• RQ1 Why do edge modes in nano-patterned magnetic structures exhibit non-monotonic nonlinearity, unlike in extended films?
• RQ2 How does the confinement potential in edge modes contribute to amplitude-dependent nonlinearity?
• RQ3 Can edge modes remain localized under positive nonlinearity (magnon repulsion), contrary to expectations?
• RQ4 What is the role of static dipolar fields in modifying the effective nonlinearity of edge modes?
• RQ5 How does the magnetization angle and film thickness affect the sign and magnitude of the nonlinearity coefficient 𝒩_EDGE?

Key findings

• The nonlinearity coefficient 𝒩_EDGE of edge modes is non-monotonically dependent on amplitude due to a nonlinear confinement potential from static dipolar fields.
• For intermediate film thickness (12 nm), 𝒩_EDGE exhibits a non-monotonic behavior, changing sign from negative to positive with increasing amplitude.
• Edge modes show spatial compression for negative 𝒩 (magnon attraction) and expansion for positive 𝒩 (magnon repulsion), consistent with nonlinear dynamics.
• Despite positive 𝒩, edge modes remain localized due to the stabilizing effect of the nonlinear confinement potential, defying behavior in extended films.
• The mode center detaches from the edge and moves inward with increasing amplitude, a result of the shallowing of the spin wave well due to nonlinear effects.
• The frequency of auto-oscillating edge modes tends toward the bulk FMR frequency ω_B as the precession angle approaches π/2, indicating vanishing nonlinearity at high amplitudes.