Comparing the orbital angular momentum and magnetic moment of magnon in the Kagome antiferromagnet with negative spin chirality

Abstract

The orbital dynamics of magnons have recently drawn interest due to their potential roles in thermal and orbital transport phenomena in magnetic insulators. In this study, we investigate the orbital magnetic moment (OMM) and orbital angular momentum (OAM) of magnons in a Kagome antiferromagnet with negative vector chirality, focusing on the distinction between thermodynamic and wave-packet-based definitions. We compute the Berry curvature, the OMM, and the OAM in momentum space under an external magnetic field. Our results reveal a quantitative difference between the OMM and OAM, yet their associated Nernst coefficients exhibit similar temperature and field dependence in transport. Our results provide a quantitative comparison between the thermodynamic and wave-packet formulations of magnon orbital dynamics.

Figures (5)

• Figure 1: Magnon band structure of the negative vector chirality Kagome lattice. The solid (dashed) lines represent the results in the absence (presence) of a magnetic field $B_z$. The left insets represent the ground-state spin configuration and the right inset the high symmetry point in the first Brillouin zone of the negative vector chirality Kagome lattice. The magnon band structure is obtained from Eq. (\ref{['eq:Hamiltonian']}) with $J=3.18 \hbox{meV},S=5/2, D_z=-0.062J, D_p=1 \hbox{meV}, B_z = 0\hbox{T} (8\hbox{T})$ to illustrate the gap opening at the $\Gamma$ point.
• Figure 2: Berry curvatures. Left (right) column: magnon Berry curvature texture in the negative vector chirality Kagome lattice at $0.05\,\text{T}$ ($1\,\text{T}$). Each row shows, from top to bottom, the Berry curvature of the [(a),(b)] lowest, [(c),(d)] middle band, and highest band [(e),(f)], respectively. Panels (c) and [(e),(f)] exhibit large negative (positive) Berry curvature values at the $\Gamma$ point.
• Figure 3: Magnon OMM textures. The left and right columns show the magnon OMM in the negative vector chirality kagome lattice at $0.05\,\text{T}$ and $1\,\text{T}$, respectively. Each row corresponds, from top to bottom, to the OMM of the lowest band [(a), (b)], middle band [(c), (d)], and highest band [(e), (f)].
• Figure 4: Magnon OAM textures for each band in the negative vector chirality kagome lattice. The left and right panels show the magnon OAM distributions at $0.05\,\text{T}$ and $1\,\text{T}$, respectively. Panels (a) and (b) correspond to the lowest band, (c) and (d) to the middle band, and (e) and (f) to the highest band.
• Figure 5: (a) Temperature and magnetic field dependences of the total orbital magnetic moment $\left<\mu_{\mathrm{tot}}^{O,z}\right>$ (red) and the total magnon orbital angular momentum $\left< l_{\mathrm{tot}}^{z}\right>$ (blue) (b) Nernst coefficient $\alpha^{\mu_{\mathrm{tot}}^{O,z}}$ (red) of the total orbital magnetic moment and the Nernst coefficient $\alpha^{l_{\mathrm{tot}}^{z}}$ (blue) of the total angular momentum. The red dotted, dashed, and solid lines almost completely overlap.