Momentum-dependent precessional and nutational spin pumping in a honeycomb antiferromagnet

The ultrafast magnetic inertial dynamics on subpicosecond timescales generate an additional high-frequency terahertz nutational resonance. Here, we investigate momentum-resolved spin pumping in a two-dimensional honeycomb antiferromagnet by incorporating spin inertia into the Landau-Lifshitz-Gilbert equation. Using a microscopic two-sublattice model with $J_1$-$J_2$-$J_3$ exchange interactions, we calculate the precessional and nutational magnon spectra and their corresponding intra- and inter-sublattice spin pumping contributions throughout the Brillouin zone. For parameters representative of MnPS${}_3$, we find a pronounced complementary momentum dependence of the two spin pumping channels: the precessional current is strongly suppressed around the $\mathrm{\Gamma }$ point ($0.01\mathrm{\%}$) and increases towards the Brillouin zone boundary ($100\mathrm{\%}$ at $K$ and $87\mathrm{\%}$ at $M$), whereas the nutational current is largest near $\mathrm{\Gamma }$ ($100\mathrm{\%}$) and decreases towards the boundary ($68\mathrm{\%}$ at $K$ and $69\mathrm{\%}$ at $M$). This contrasting momentum dependence provides a means of distinguishing spin nutation from conventional precessional motion. We further demonstrate that the nutational spin pumping current is strongly controlled by the inertial relaxation time $\eta$, in contrast to the comparatively weak $\eta$ dependence of the precessional current. In the small-$\eta$ regime, our analytical results show that the intra-sublattice nutational spin pumping current exhibits a leading-order dependence of $1\mathrm{/}{\eta }^3$. The spin pumping response can also be tuned through the exchange interaction strengths and magnetic moment. Our further results on the magnetic field dependence of spin pumping reveal that the ratio of nutational spin pumping current increases with magnetic field strength, whereas the corresponding precessional counterpart decreases.