# Combinatorial exploration of quantum spin liquid candidates in the herbertsmithite material family

## TL;DR

This study systematically explores structurally related kagome lattice compounds using first-principles calculations to identify promising quantum spin liquid candidates among herbertsmithite-like materials.

## Contribution

It introduces a combinatorial first-principles approach to evaluate and predict new quantum spin liquid candidates within the herbertsmithite material family.

## Key findings

- Identified several compounds with favorable structural and thermodynamic properties for quantum spin liquids.
- Assessed synthesis feasibility through convex hull calculations.
- Evaluated disorder and distortion likelihood in candidate materials.

## Abstract

Geometric frustration of magnetic ions can lead to a quantum spin liquid ground state where long range magnetic order is avoided despite strong exchange interactions. The physical realization of quantum spin liquids comprises a major unresolved area of contemporary materials science. One prominent magnetically-frustrated structure is the kagome lattice. The naturally occurring minerals herbertsmithite [ZnCu$_3$(OH)$_6$Cl$_2$] and Zn-substituted barlowite [ZnCu$_3$(OH)$_6$BrF] both feature perfect kagome layers of spin-$1/2$ copper ions and display experimental signatures consistent with a quantum spin liquid state at low temperatures. To investigate other possible candidates within this material family, we perform a systematic first-principles combinatorial exploration of structurally related compounds [$A$Cu$_3$(OH)$_6B_2$ and $A$Cu$_3$(OH)$_6BC$] by substituting non-magnetic divalent cations ($A$) and halide anions ($B$, $C$). After optimizing such structures using density functional theory, we compare various structural and thermodynamic parameters to determine which compounds are most likely to favor a quantum spin liquid state. Convex hull calculations using binary compounds are performed to determine feasibility of synthesis. We also estimate the likelihood of interlayer substitutional disorder and spontaneous distortions of the kagome layers. After considering all of these factors as a whole, we select several promising candidate materials that we believe deserve further attention.