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A spin-1 Heisenberg model on trimerized Kagom\'e lattice is studied by doinga low-energy bosonic theory in terms of plaquette-triplons defined on itstriangular unit-cells. The model has an intra-triangle antiferromagneticexchange interaction, $J$ (set to 1), and two inter-triangle couplings,$J^\prime>0$ (nearest-neighbor) and $J^{\prime\prime}$ (next-nearest-neighbor;of both signs). The triplon analysis of this model studies the stability of thetrimerized singlet (TS) ground state in the $J^\prime$-$J^{\prime\prime}$plane. It gives a quantum phase diagram that has two gaplessantiferromagnetically (AF) ordered phases separated by the spin-gapped TSphase. The TS ground state is found to be stable on $J^{\prime\prime}=0$ line(the nearest-neighbor case), and on both sides of it for $J^{\prime\prime}\neq0$, in an extended region bounded by the critical lines of transition to thegapless AF phases. The gapless phase in the negative $J^{\prime\prime}$ regionhas a $\sqrt{3}\times\sqrt{3}$ coplanar $120^\circ$-AF order, with all themoments of equal length and relative angles of $120^\circ$. The other AF phase,in the positive $J^{\prime\prime}$ region, is found to exhibit a differentcoplanar order with ordering wave vector ${\bf q}=(0,0)$. Here, two magneticmoments in a triangle are of same magnitude, but shorter than the third. Whilethe angle between the two short moments is $120^\circ-2\delta$, it is$120^\circ+\delta$ between a short and the long one. Only when$J^{\prime\prime}=J^\prime$, their magnitudes become equal and therelative-angles $120^\circ$. This ${\bf q}=(0,0)$ phase has the translationalsymmetry of the Kagom\'e lattice with isosceles triangular unit-cells. Theratio of the intensities of certain Bragg peaks, $I_{(1,0)}/I_{(0,1)} =4\sin^2{(\frac{\pi}{6}+\delta)}$, presents an experimental measure of thedeviation, $\delta$, from the $120^\circ$ order.

Plaquette-triplon analysis of magnetic disorder and order in a trimerized spin-1 Kagom\'e antiferromagnet