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A ferrimagnetic spin model composed of $S=1/2$ spin-dimers and $S=5/2$spin-chains is studied by combining the bond-operator representation (for$S=1/2$ spin-dimers) and Holstein-Primakoff transformation (for $S=5/2$ spins).A finite interaction $J_{\rm DF}$ between the spin-dimer and the spin chainmakes the spin chains ordered antiferromagnetically and the spin dimerspolarized. The effective interaction between the spin chains, mediated by thespin dimers, is calculated up to the third order. The staggered magnetizationin the spin dimer is shown proportional to $J_{\rm DF}$. It presents aneffective staggered field reacting on the spin chains. The degeneracy of thetriplons is lifted due to the chain magnetization and a mode with longitudinalpolarization is identified. Due to the triplon-magnon interaction, thehybridized triplon-like excitations show different behaviors near the vanishing$J_{\rm DF}$. On the other hand, the hybridized magnon-like excitations open agap $\Delta_A\sim J_{\rm DF}$. These results consist well with the experimentson Cu$_{2}$Fe$_{2}$Ge$_{4}$O$_{13}$.

Cooperative order and excitation spectra in the bicomponent spin networks