Abstract
The ground state of the spin$-1/2$ kagome antiferromagnet remains uncertain despite decades of active research. Here we step aside from this debated question to address the ground-state nature of a related, and potentially just as rich, system made of corner-sharing triangles: the square-kagome lattice (SKL). Our work is motivated by the recent synthesis of a distorted SKL compound mentioned in [Morita & Tohyama, J. Phys. Soc. Japan 87, 043704 (2018)]. We have studied its spin$-1/2$ $J_{1}$-$J_{2}$ phase diagram with an unrestricted Schwinger boson mean-field theory (SBMFT). We show that, in addition of agreeing with previous studies, three original phases appear: two incommensurate orders and a topological quantum spin liquid with weak nematicity. The topological order is characterized by fluxes on specific gauge-invariant quantities and the phase is stable under anisotropic perturbations relevant for experiments. Finally, we provide dynamical structure factors of the reported phases that could be observed in inelastic neutron scattering.
Highlights
The search for novel topological phases is one of the most active fields in condensed-matter physics, often accompanied by the emergence of fractionalized excitations [1,2,3,4,5]
The topological order is characterized by fluxes on specific gaugeinvariant quantities and the phase is stable under anisotropic perturbations relevant for experiments
Defining the parameter x = J2/J1 > 0, we show that for small and large values, our Schwinger boson mean-field theory (SBMFT) is consistent with the plaquette and ferrimagnetic phases reported in Ref. [23]
Summary
The search for novel topological phases is one of the most active fields in condensed-matter physics, often accompanied by the emergence of fractionalized excitations [1,2,3,4,5]. The ground state (GS) of the quantum kagome antiferromagnet, made of corner-sharing triangles, is still under debate as to whether it is a gapless Dirac spin liquid [6,7,8,9,10,11], a gapped Z2 spin liquid [12,13,14], or something else [8,11] In this context, it is appealing to step away from the cumbersome kagome problem and to consider an alternate, and potentially just as rich, network of this elementary brick of frustration. While the kagome lattice supports only the smallest loops of six sites, the SKL is paved with two types of small loops of lengths 4 and 8 On one hand, this asymmetry suggests a more localized quantum entanglement, and a possibly more tractable treatment. To make contact with materials, we discuss the robustness of the TNSL under further anisotropy [17] and provide inelastic neutron scattering signatures of the reported phases
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