Plaquette-triplon analysis of magnetic disorder and order in a trimerized spin-1 kagome Heisenberg antiferromagnet

A spin-1 Heisenberg model on trimerized kagome lattice is studied by doing a low-energy bosonic theory in terms of plaquette triplons defined on its triangular unit cells. The model considered has an intratriangle antiferromagnetic exchange interaction J (set to 1) and two intertriangle couplings J^'>0 (nearest neighbor) and J^'' (next nearest neighbor; of both signs). The triplon analysis performed on this model investigates the stability of the trimerized singlet ground state (which is exact in the absence of intertriangle couplings) in the J^'-J^'' plane. It gives a quantum phase diagram that has two gapless antiferromagnetically ordered phases separated by the spin-gapped trimerized singlet phase. The trimerized singlet ground state is found to be stable on J^''=0 line (the nearest-neighbor case), and on both sides of it for J^''≠0, in an extended region bounded by the critical lines of transition to the gapless antiferromagnetic phases. The gapless phase in the negative J^'' region has a coplanar 120^∘ antiferromagnetic order with √3×√3 structure. In this phase, all the magnetic moments are of equal length, and the angle between any two of them on a triangle is exactly 120^∘. The magnetic lattice in this case has a unit cell consisting of three triangles. The other gapless phase, in the positive J^'' region, is found to exhibit a different coplanar antiferromagnetic order with ordering wave vector q=(0,0). Here, two magnetic moments in a triangle are of the same magnitude, but shorter than the third. While the angle between two short moments is 120^∘-2δ, it is 120^∘+δ between a short and the long one. Only when J^''=J^', their magnitudes become equal and the relative angles 120^∘. The magnetic lattice in this q=(0,0) phase has the translational symmetry of the kagome lattice with triangular unit cells of reduced (isosceles) symmetry. This reduction in the point-group symmetry is found to show up as a difference in the intensities of certain Bragg peaks, whose ratio I(1,0)/I(0,1)=4sin²(π6+δ) presents an experimental measure of the deviation δ from the 120^∘ order.