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

Abstract

A spin-1 Heisenberg model on trimerized Kagomé lattice is studied by doing a low-energy bosonic theory in terms of plaquette-triplons defined on its triangular unit-cells. The model has an intra-triangle antiferromagnetic exchange 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 the trimerized singlet (TS) ground state in the $J^{\prime }$-$J^{\prime \prime }$ plane. It gives a quantum phase diagram that has two gapless antiferromagnetically (AF) ordered phases separated by the spin-gapped TS phase. 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 $J^{\prime \prime }\ne 0$, in an extended region bounded by the critical lines of transition to the gapless AF phases. The gapless phase in the negative $J^{\prime \prime }$ region has a $\sqrt{3}\times \sqrt{3}$ coplanar $120^{\circ }$-AF order, with all the moments 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 different coplanar order with ordering wave vector $\mathbf{q}=(0,0)$. Here, two magnetic moments in a triangle are of same magnitude, but shorter than the third. While the 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 the relative-angles $120^{\circ }$. This $\mathbf{q}=(0,0)$ phase has the translational symmetry of the Kagomé lattice with isosceles triangular unit-cells. The ratio 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 the deviation, $\delta$, from the $120^{\circ }$ order.

15 pages, 12 figures

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