Engineering spin-wave spectrum via the magnetization inertia tensor

TL;DR

This work addresses spin-wave engineering in two-sublattice ferromagnets by incorporating the full magnetic inertia tensor, including cross-sublattice and chiral components. Using linear spin-wave theory and inertial Landau-Lifshitz-Gilbert dynamics, the authors derive a fourth-order dispersion with four magnon branches and show that DMI induces nonreciprocity while cross-sublattice and chiral inertia provide tunable control, including a crossing between the upper precessional and lower inertial bands. They also show that unequal sublattice moments open a zone-edge gap and that inertial magnons can have higher group velocities and reduced damping, with chiral inertia enabling nonreciprocal behavior even without DMI. Together these results establish magnetic inertia as a versatile tool for magnonic band engineering, nonreciprocal transport, and ultrafast spintronic applications.

Abstract

Magnetic inertial dynamics has recently been predicted and experimentally demonstrated in two-sublattice ferromagnets such as CoFeB and NiFe permalloy. In this work, we investigate the spin-wave spectrum of such systems by incorporating the complete magnetic inertia tensor. By decomposing the tensor into symmetric and antisymmetric components, we identify isotropic, anisotropic, and chiral contributions to magnetic inertia. Within linear spin-wave theory, we find that the spectrum comprises two precessional and two inertial magnon bands. Remarkably, the upper precessional band intersects the lower inertial band within the Brillouin zone. Both cross-sublattice and chiral components of the inertia tensor act as effective control parameters for tuning these magnonic band structures. Furthermore, we show that the inertial spin-wave spectrum becomes nonreciprocal along propagation directions where the Dzyaloshinskii-Moriya interaction is finite. Strikingly, a similar nonreciprocity can also arise purely from chiral inertia, even in the absence of Dzyaloshinskii-Moriya interaction. Our findings establish magnetic inertia as a new pathway to engineer nonreciprocal magnon transport and ultrafast spintronic functionalities.

Figures (9)

• Figure 1: Sketch of a two-dimensional rectangular lattice. The ground state of the two-sublattice ferromagnet is shown in the $x$-direction with green arrows belonging to sublattice $A$ and brown arrows belonging to sublattice $B$. ${\bm\delta}_1$ and ${\bm \delta}_2$ represent the nearest-neighbor lattice vectors. The nearest neighbor exchange coupling constants are represented as $J$, with $J_{xx}$ and $J_{yy} = J_{zz}$. The Dzyaloshinskii-Moriya interaction is denoted by $\bm{D}$.
• Figure 2: Spin-wave spectrum along the $k_x$ obtained from Eq. (\ref{['Eq12']}), setting $k_z = 0$. The solid and dashed lines represent + and - branches of the dispersion relation. The other parameters are $\eta = 100$ fs, $\eta^\prime = 0$, $C^\prime = 0$, and $M_A = 2\,\,\mu_B$, $M_B = 2.6$$\mu_B$.
• Figure 3: Spin-wave spectrum along $k_z$ obtained from Eq. (\ref{['Eq12']}), setting $k_x = 0$. The solid and dashed lines represent + and - branches of the dispersion relation. The other parameters are $\eta = 100$ fs, $\eta^\prime = 0$, $C^\prime = 0$, and $M_A = 2\,\,\mu_B$, $M_B = 2.6$$\mu_B$.
• Figure 4: Spin-wave dispersion along $k_x$, setting $k_z = 0$ obtained via solution of Eq. (\ref{['Eq12']}). The following inertial parameters have been used (a) $\eta = 100$ fs, $\eta^\prime = 0$ fs, $C^\prime = 0$ fs (b) $\eta = 100$ fs, $\eta^\prime = 10$ fs, $C^\prime = 0$ fs, and (c) $\eta = 100$ fs, $\eta^\prime = 0$ fs, $C^\prime = 10$ fs. The other parameters are in Table \ref{['tab:1']}.
• Figure 5: Magnon group velocity along $k_x$, setting $k_z = 0$ obtained via solution of Eq. (\ref{['Eq12']}). The following inertial parameters have been used (a) $\eta = 100$ fs, $\eta^\prime = 0$ fs, $C^\prime = 0$ fs (b) $\eta = 100$ fs, $\eta^\prime = 10$ fs, $C^\prime = 0$ fs, and (c) $\eta = 100$ fs, $\eta^\prime = 0$ fs, $C^\prime = 10$ fs. The other parameters are summarized in Table \ref{['tab:1']}.