# Topological Nematic Spin Liquid on the Square-Kagome Lattice

## TL;DR

This paper investigates the ground states of the square-kagome lattice, revealing a topological nematic quantum spin liquid phase with unique properties, supported by mean-field theory and dynamical structure factor calculations.

## Contribution

It introduces a new topological nematic quantum spin liquid phase in the square-kagome lattice and characterizes its stability and experimental signatures.

## Key findings

- Discovery of a topological nematic quantum spin liquid phase.
- Identification of incommensurate magnetic orders.
- Provision of dynamical structure factors for experimental detection.

## 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.