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

Abstract

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 ${J}^{\ensuremath{'}}>0$ (nearest neighbor) and ${J}^{\ensuremath{''}}$ (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 ${J}^{\ensuremath{'}}\ensuremath{-}{J}^{\ensuremath{''}}$ 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 ${J}^{\ensuremath{''}}=0$ line (the nearest-neighbor case), and on both sides of it for ${J}^{\ensuremath{''}}\ensuremath{\ne}0$, in an extended region bounded by the critical lines of transition to the gapless antiferromagnetic phases. The gapless phase in the negative ${J}^{\ensuremath{''}}$ region has a coplanar ${120}^{\ensuremath{\circ}}$ antiferromagnetic order with $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ 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 ${120}^{\ensuremath{\circ}}$. The magnetic lattice in this case has a unit cell consisting of three triangles. The other gapless phase, in the positive ${J}^{\ensuremath{''}}$ region, is found to exhibit a different coplanar antiferromagnetic order with ordering wave vector $\mathbf{q}=(0,0)$. 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 ${120}^{\ensuremath{\circ}}\ensuremath{-}2\ensuremath{\delta}$, it is ${120}^{\ensuremath{\circ}}+\ensuremath{\delta}$ between a short and the long one. Only when ${J}^{\ensuremath{''}}={J}^{\ensuremath{'}}$, their magnitudes become equal and the relative angles ${120}^{\ensuremath{\circ}}$. The magnetic lattice in this $\mathbf{q}=(0,0)$ 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 ${I}_{(1,0)}/{I}_{(0,1)}=4{sin}^{2}(\frac{\ensuremath{\pi}}{6}+\ensuremath{\delta})$ presents an experimental measure of the deviation $\ensuremath{\delta}$ from the ${120}^{\ensuremath{\circ}}$ order.