Magnon scattering and transduction in Coulomb-coupled quantum Hall ferromagnets

TL;DR

This work studies how Coulomb interactions in quantum Hall ferromagnets couple spin textures to electric fields in the lowest Landau level at $ν=1$. Using semiclassical spin dynamics and a second-Born analysis, it demonstrates two main results: (i) magnons acquire an electric dipole moment and are deflected by the field of a distant point charge, and (ii) in a bilayer QHFM, Coulomb coupling between coexisting skyrmions enables magnon transduction (spin drag) across layers. The authors provide quantitative estimates for experimental observability, including parameter mappings, transduction efficiencies, and layer-spacing considerations, highlighting a path toward long-range magnonics in 2D materials. Overall, the paper advances the understanding of spin-charge coupled dynamics in topological flat-band magnets and proposes a mechanism for electrically controlled magnonics and interlayer information transfer.

Abstract

The magnetization field of a quantum Hall ferromagnet (QHFM) can host a variety of spin textures, including skyrmions and magnons. When projected into the lowest Landau level with $ν= 1$ filling, the topological (Pontryagin) charge density of the magnetization field is proportional to the electric charge density, allowing for long-range spin-spin interactions. Inspired by recent experimental developments that enable all-electrical magnon generation and detection, in this work we theoretically demonstrate two phenomena that can occur due to Coulomb interactions that are unique to QHFMs: magnons can scatter off of point charges at a distance, and skyrmions can act as transmitters and receivers for magnons to be transduced between separate layers of a bilayer QHFM. The latter Coulomb-mediated spin drag effect occurs at arbitrary distance and could facilitate long-range magnonics, such as detection of spin waves for future experiments in 2D materials.

Figures (9)

• Figure 1: Cartoon of Coulomb-mediated magnon-skyrmion-skyrmion-magnon transduction. Magnons injected in the lower layer induce undulations of the skyrmion core in that layer. These undulations couple via the Coulomb interaction to the noncollinear spin texture in the upper layer (associated e.g. to another proximal skyrmion). The induced core fluctuations in the top-layer core then function as an antenna, emitting directed magnon radiation into the upper layer.
• Figure 2: (Color online) Plane magnons scatter off of the electrical field due to a point charge located at $(x,y,z) = (0,0,l_\perp)$. Despite carrying zero net electric charge, magnons interact with electric fields due to the effective electrical dipole moment proportional to the U(1) spin current, Eq. (\ref{['dipole']}). (a) Snapshot of a numerical simulation. The color indicates the magnitude of the deviation of the spin field from the ferromagnetic ground state $|\psi(x,y)|\equiv\sqrt{m_x^2+m_y^2}$ after plane magnons are driven into the sample from the bottom. The scattering arises due to the electric field of a point charge placed at a distance $l_\perp = 2$ above the plane. The magnon has wavevector $k=1.5708$ and the magnitude of the point charge is $Q=-9$. Here all distances and inverse wavenumbers are measured in units of the magnetic length $l_B = 1$, and charge in units of the electron charge $e > 0$. (b) Analytical result via the second Born approximation for the magnon scattering off of a point charge at $(x,y,z)=(0,0,0)$, with $k=1.5$ and $Q\alpha=-0.8$, where $\alpha$ is defined via Eq. (\ref{['dimparams']}). (c) $k$-space distribution of magnons at end of simulation. Here, $c_\mathbf{k}=\sum\limits_{\mathbf{r}}e^{-2\pi i\mathbf{k\cdot r}/N}\psi(\mathbf{r})$ is the discrete Fourier transform for the mode $\mathbf{k}$ of the magnon field $\psi=m_x+im_y$.
• Figure 3: Interlayer magnon transduction ("spin drag") due to Coulomb-mediated skyrmion-skyrmion interactions. A cartoon of the setup is shown in Figure \ref{['fig:transduction_cartoon']}. We simulate two QHFMs separated by small distance of $0.1 \, l_B$, each with a skyrmion defect of size $\lambda=5\,l_B$. The skyrmion size $\lambda$, defined in Appendix A [Eq. \ref{['skyrmionsize']}], is half of its radius. The defects are vertically stacked and pinned by an impurity potential. Plane-wave magnons are driven from the bottom of the spin field in layer 1. Magnon-skyrmion interactions in that layer produce a dynamic undulation in the skyrmion core, and this acts as a "transmitter" that (via Coulomb interaction) drives core undulations in the layer-2 skyrmion (the "receiver"). The latter produces directed magnon emission in the second layer. (a) Magnitude of the lateral magnetization field $\sqrt{m_x^2+m_y^2}$ in layer 1, in which magnons are driven from the bottom. (b) Magnitude of the lateral magnetization in layer 2, in which magnons can be seen emitted from the skyrmion, towards the upper-left of the magnetization field. Plots (a,b) are taken within a steady state at a late time in the simulation $\tau = 250$. Note that the anisotropy of the transduced spin texture (b) clearly reflects the magnon-skyrmion scattering occuring in the driven layer (a). (c) Initial stable skyrmion texture in each layer. All results have the interlayer "interaction strength" $\alpha_{12} = 1$ [Eq. (\ref{['dimparams']})].
• Figure 4: Parameter dependence of Coulomb-mediated spin-drag simulations I. (a) Magnitude of the difference in the $k$-space distribution of magnons in the receiving layer at the end of a driven simulation versus undriven simulation. The arc shows that transduced magnons in the second layer share the wavenumber $k_0\approx0.90841 \, l_B^{-1}$ of the skyrmion-scattered magnons in the driving layer (not shown). (b) Transduction ratio $T$ [Eq. (\ref{['transductionRT']})] versus driven magnon wavenumber $k_0$ and interlayer spacing $l_\perp$ for various simulations, with skyrmion size $\lambda=5\,l_B$, interaction parameter $\alpha=1$, and Gaussian pinning potential in each layer. Note that the $k$-values deviate by about $5\%$ from the continuum quadratic dispersion for high $k$, since they obey the lattice magnon dispersion relation Eq. \ref{['dispersion']}. (c) Average magnong scattering angle $\phi$ in layer 2 versus driven magnon wavenumber $k_0$ and interlayer spacing $l_\perp$ for various simulations, with skyrmion size $\lambda=5\,l_B$, interaction parameter $\alpha=1$, and Gaussian pinning potential in each layer. The scattering profile of transduced magnons always resembles that of the driving layer, see Figs. \ref{['fig:main-results-transduction']}(a,b), independent of the spacing. This shows that its behavior under different $k_0$ is similar to the single-layer case for the magnon-skyrmion scattering shown in Sec. \ref{['sec:SLDyn']}
• Figure 5: Parameter dependence of Coulomb-mediated spin-drag simulations II. (a) Transduction ratio $T$ versus skyrmion size $\lambda$. Smaller core sizes enhance the Coulomb interaction, producing larger transduction ratios. (b) Transduction ratio $T$ versus lateral interlayer skyrmion core separation $R=\sqrt{l_\perp^2+l_\text{offset}^2}$ and interlayer spacing $l_\perp$, showing a roughly inverse relation $T\sim 1/R$ for large distances. (c) Transduction ratio $T$ versus incident magnon amplitude $|\psi|=\sqrt{m_x^2+m_y^2}$. Note that the ratio is approximately independent of perturbation magnitude, suggesting that transduction occurs as an effective electrodynamic linear response of the composite two-skyrmion, two-layer system. The interlayer interaction parameter $\alpha_{12}=1$ and the driven magnon wavenumber is $k_0 \approx 1.047 \, l_B^{-1}$.