Unidirectional gliding of a cycloidal spin structure by an AC magnetic field

TL;DR

The paper examines a cycloidal spin structure stabilized by interfacial DMI in a ferromagnetic thin film and develops a collective-coordinate Lagrangian framework to describe its dynamics under a weak AC magnetic field. It identifies unidirectional gliding governed by two coupled-mode subsystems, leading to two resonance frequencies that maximize the average velocity, and confirms these predictions with micromagnetic simulations. Additionally, the authors show that Rashba-induced non-adiabatic spin-motive forces generate a substantial DC voltage per cycle, enabling the spin structure to function as a magnetic rectifier for energy harvesting. The work provides both fundamental insight into CSS dynamics and a potential pathway for AC-to-DC conversion in spintronic devices, with practical implications for devices operating under ambient electromagnetic radiation.

Abstract

The dynamics of a cycloidal spin structure driven by an AC magnetic field is theoretically studied in the weak-field limit. A specific model Hamiltonian describing the cycloidal spin structure in a ferromagnetic thin film is constructed, and its dynamics is analyzed using the collective-coordinate approach within the Lagrangian formalism. We demonstrate that the cycloidal spin structure exhibits a unidirectional gliding motion under an AC magnetic field, and an expression for the average velocity is derived as a function of the magnitude, the direction, and the frequency of the AC magnetic field. We compare our theoretical predictions with the results of micromagnetic simulations and identify two resonance frequencies determined by the eigenenergies of the excitation modes. Furthermore, evaluating spin motive forces induced by the dynamics reveals a substantial DC voltage, which may be exploited in energy-harvesting devices utilizing ambient electromagnetic radiation.

Figures (9)

• Figure 1: Simple schematics of the ground states for different DMI constants, $D$. The color of arrows represents $m_z$ and red (blue) color indicates $m_z=+1\,(-1)$. From top to middle, $D$ increases from $D_1\,(<D_c)$ to $D_2$. From middle to bottom, $D$ increases from $D_2$ to $D_3$, i.e., $D_1<D_c<D_2<D_3$.
• Figure 2: Potentials of two operators, $\hat{H}_\theta$ [Eq. (\ref{['H_theta']})] and $\hat{H}_\phi$ [Eq. (\ref{['H_phi']})], and the difference between them, $\Delta(x)$ [Eq. (\ref{['delta']})], for one period, where $U_0=1/\lambda^2$. The left panel shows the potential when $D=1.01D_c$, and the right panel illustrates it when $D=1.5D_c$.
• Figure 3: Plots showing how the modes used in the theory modify the ground state in components of the magnetization unit vector. $s_{i}(x,\kappa)$ is a function proportional to $u_{i}(s,\kappa)$ [Eqs. (\ref{['ansatz1']}) and (\ref{['ansatz2']})] for $D=2.858\,\mathrm{mJ/m^2}$.
• Figure 4: Schematics explaining how the rotational modes operate on the CSS. Top (Middle) figure illustrates how $X$ ($\pi_z$) rotates the CSS about the $y$ ($z$) -axis. Bottom figure shows the rotation about the $x$-axis by $\pi_x$.
• Figure 5: The plots of the average velocity, $\bar{V}$ [Eq. (\ref{['avgvel']})], for (a) all solid angles from the theory and the comparison with simulations for (b) red dashed line ($\Theta=\pi/4$) and (c) blue dashed line ($\Phi=\pi$), where $D=2.858\,\mathrm{mJ/m^2}$, $f=10\,\mathrm{GHz}$ and $H=30\,\mathrm{mT}$.