Spin angular momentum transfer in the Einstein-de Haas effect

Abstract

We investigate spin angular momentum transfer in the Einstein-de Haas effect within prototypical magnetic crystals, focusing on its partition between phonons and rigid-body rotation. Using the Eckart frame to decouple local vibrations (phonons) from rigid-body rotation, we demonstrate that spin angular momentum is simultaneously transferred into both phonons and rigid-body rotation in an asymmetric way: rigid-body rotation acquires the dominant share of angular momentum, while phonons absorb most of the resulting kinetic energy. This divergent transfer of angular momentum and energy identifies phonons as direct and indispensable participants in the Einstein-de Haas dynamics. Furthermore, we find that pseudo-dipolar anisotropy and Dzyaloshinskii-Moriya interaction exert distinct control over the angular momentum transfer. Stronger pseudo-dipolar anisotropy increases the total amount of transferred angular momentum, whereas stronger Dzyaloshinskii-Moriya interaction accelerates the transfer rate and increases the proportion of phonon angular momentum. Our work clarifies the microscopic picture of the Einstein-de Haas effect and enables targeted angular-momentum control in magneto-mechanical devices.

Figures (4)

• Figure 1: Schematic of atoms (gray spheres) with total spins (large gradient arrow), local atomic rotations (red circles), and rigid-body rotation in the Eckart frame. The direction normal to the disc is the z direction.
• Figure 2: Angular momentum transfer from spins to mechanical motions in Fe nanodisc. (a) Initial spin configuration. Arrows represent normalized spin vectors, with color indicating the z component from -1 (blue) to +1 (red). (b) Transfer between spin angular momentum ($\bm{S}$) and mechanical angular momentum ($\bm{L}$). (c) Decomposition of mechanical angular momentum into phononic contributions ($\bm{L}_\mathrm{spin}$ and $\bm{L}_\mathrm{orbital}$) and rigid-body rotation ($\bm{L}_\mathrm{rigid}$). (d) XY-plane circular trajectory of a representative atom. Black dots show instantaneous positions along the time evolution, and the purple curve shows the projected trajectory onto the xy plane.
• Figure 3: Time evolution of energies in the Fe nanodisc. (a) Energy components (shown with constant offsets for clarity): total energy $E$, kinetic energy $E_\mathrm{T}$, Embedded-Atom-Method (EAM) potential $E_\mathrm{V}$, and magnetic energy $E_{\mathrm{M}}$ (including $E_{\mathrm{EX}}$, $E_{\mathrm{PDA}}$, $E_{\mathrm{DMI}}$, and $E_{\mathrm{Z}}$).(b) Comparison between $E_\mathrm{T}$ and its rigid-body rotational component $E_\mathrm{TR}$. The inset shows the evolution of $E_\mathrm{TR}$ on a separate scale.
• Figure 4: Effects of DMI and PDA on the dynamics of angular momentum transfer. $D/J$ and $g/J$ are varied from 0.1 to 1.0, with parameters taken from Ref. TRANCHIDA2018406. (a) Initial demagnetization time $t_1$ for different $D/J$ and $g/J$. (b, c) Fourier spectra of the total transferred angular momentum $\left|\Delta S_z(t)\right|$. (d-f) $D/J$ dependence of the Fourier spectra for $\bm{L}_{\mathrm{ph}}/\bm{L}$, $\bm{L}_{\mathrm{spin}}/\bm{L}$, and $\bm{L}_{\mathrm{orbital}}/\bm{L}$. (g–i) Same as (d–f) but for varying $g/J$. Bar color in (b–i) indicates $D/J$ or $g/J$ from 0.1 (blue) to 1 (red).