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We explore spin dynamics in Cu(1,3-bdc), a quasi-2D topological magnoninsulator. The results show that the thermal evolution of Land\'e $g$-factor($g$) is anisotropic: $g_\textrm{in-plane}$ reduces while$g_\textrm{out-plane}$ increases with increasing temperature $T$. Moreover, theanisotropy of the $g$-factor ($\Delta g$) and the anisotropy of saturationmagnetization ($\Delta M_\textrm{s}$) are correlated below 4 K, but theydiverge above 4 K. We show that the electronic orbital moment contributes tothe $g$ anisotropy at lower $T$, while the topological orbital moment inducedby thermally excited spin chirality dictates the $g$ anisotropy at higher $T$.Our work suggests an interplay among topology, spin chirality, and orbitalmagnetism in Cu(1,3-bdc).

Evidence of Magnon-Mediated Orbital Magnetism in a Quasi-2D Topological Magnon Insulator