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 '' not equal 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 degrees antiferromagnetic order with root 3 x root 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 degrees. 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 degrees - 2 delta, it is 120 degrees + delta between a short and the long one. Only when J '' = J', their magnitudes become equal and the relative angles 120 degrees. 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,I-0)/I-(0,I-1) = 4 sin(2) (pi/6 + delta) presents an experimental measure of the deviation d from the 120 degrees order.