Symmetry-forbidden intraband transitions leading to ultralow Gilbert damping in van der Waals ferromagnets

Abstract

Based upon first-principles calculations, we report ultralow Gilbert damping in two-dimensional (2D) van derWaals (vdW) ferromagnets. The low damping occurs at weak scattering because mirror symmetry prohibits intraband transitions. The monotonic dependence on the electronic scattering rate suggests the absent lower limit, in contrast to conventional ferromagnetic materials. Breaking mirror symmetry through magnetization rotation, layer stacking, or structural phase transition significantly increases damping by enabling intraband transitions. Topological nodal lines, also protected by mirror symmetry, contribute substantially to interband-transition-mediated damping, which can be tuned by adjusting the Fermi level. Our findings elucidate the unique characteristics of Gilbert damping in 2D vdW ferromagnets, providing valuable insights for designing low-dimensional spintronic devices with high energy efficiency.

Figures (5)

• Figure 1: (a) Atomic structure of 1QL Fe$_{3}$GaTe$_{2}$. The magnetic moments on the Fe atoms are indicated by black arrows. The blue plane in the middle of the layer highlights the mirror symmetry of the lattice structure. (b) Gilbert damping as a function of the electronic scattering rate for 1QL Fe$_{3}$GaTe$_{2}$ with the out-of-plane (red solid circles) and in-plane magnetization (black solid squares). The dotted and dashed lines represent the contributions from intraband and interband transitions, respectively. The orange and green vertical lines denote two characteristic scattering rates, $\gamma=3$ meV and 20 meV, which are used to calculate the damping in detail.
• Figure 2: (a) Calculated band structure of 1QL Fe$_{3}$GaTe$_{2}$ with out-of-plane magnetization. The red and blue lines denote mirror-symmetric ($a_{n\mathbf k}=-i$) and antisymmetric ($a_{n\mathbf k}=+i$) bands, respectively. Bands calculated with in-plane magnetization are presented in gray. (b) Schematic illustration of energy dissipation during magnetization dynamics in a mirror-symmetric system. (c) Enlarged view of a typical symmetry-protected band crossing, as indicated by the rectangle in (a).
• Figure 3: (a) Gilbert damping for 1QL Fe$_{3}$GaTe$_{2}$ as a function of the tilting angle $\theta$ of the magnetization away from the surface normal, for two scattering rates $\gamma=3$ meV and 20 meV. The intraband and interband contributions to the damping are represented by dotted and dashed curves, respectively. (b) Gilbert damping for Fe$_{3}$GaTe$_{2}$ with varying stacking layers plotted as a function of electrical resistivity.
• Figure 4: (a) Schematic representation of band overlap near their crossing point, with shadows indicating the broadening. Thick black lines show the extent of overlap at various isoenergetic surfaces. (b) Calculated nodal lines for 1QL Fe$_{3}$GaTe$_{2}$ with out-of-plane magnetization in the 2D Brillouin zone. (c) Calculated $\alpha$ as a function of energy at two scattering rates. (d) Calculated $\alpha$ as a function of scattering rate at various energies.
• Figure 5: Calculated damping anisotropy between out-of-plane and in-plane magnetization for Fe$_{3}$GaTe$_{2}$.