# Quantum spin liquid and magnetic order in a two-dimensional non-symmorphic lattice: considering the distorted Kagome lattice of Volborthite

## TL;DR

This paper investigates quantum spin liquids and magnetic orders in a non-symmorphic lattice model inspired by Volborthite, revealing potential phases and signatures relevant for experimental detection.

## Contribution

It classifies possible spin liquid and magnetic phases in a non-symmorphic lattice using PSG and Schwinger boson methods, specific to Volborthite's anisotropic structure.

## Key findings

- Quantum spin liquids connect to incommensurate spiral order.
- Spin liquids exhibit symmetry fractionalization signatures.
- Magnetic phases include incommensurate spiral and commensurate spin density wave.

## Abstract

The Kagome-lattice-based material, Volborthite, $\mathrm{Cu_3 V_2 O_7 (OH)_2 \cdot 2 H_2 O}$, has been considered as a promising platform for discovery of unusual quantum ground states due to the frustrated nature of spin interactions. Here we explore possible quantum spin liquid and magnetically ordered phases in a two-dimensional non-symmorphic lattice described by $p2gg$ layer space group, which is consistent with the spatial anisotropy of the spin model derived from density functional theory (DFT) for Volborthite. Using the projective symmetry group (PSG) analysis and Schwinger boson mean field theory, we classify possible spin liquid phases with bosonic spinons and investigate magnetically ordered phases connected to such states. It is shown, in general, that only translationally invariant mean field states are allowed in two-dimensional non-symmorphic lattices, which simplifies the classification considerably. The mean field phase diagram of the DFT-derived spin model is studied and it is found that possible quantum spin liquid phases are connected to two types of magnetically ordered phases, a coplanar incommensurate $(q,0)$ spiral order as the ground state and a closely competing coplanar commensurate $(\pi,\pi)$ spin density wave order. In addition, periodicity enhancement of the two-spinon continuum, a signature of symmetry fractionalization, is found in the spin liquid phases connected to the $(\pi,\pi)$ spin density wave order. We discuss relevance of these results to recent and future experiments on Volborthite.