Crystal chemistry criteria of the existence of spin liquids on the kagome lattice

TL;DR

This paper analyzes the structural and magnetic properties of 25 antiferromagnetic kagome cuprates, identifying key criteria that influence the emergence of spin liquid states, especially focusing on the role of magnetic couplings and anisotropies.

Contribution

It introduces three crystal chemistry criteria for the existence of spin liquids on the kagome lattice, highlighting the importance of magnetic coupling duality and anisotropic interactions.

Findings

Duality of J3 couplings can suppress frustration in kagome AFM.

Herbertsmithite's spin liquid state is due to the rare elimination of J3 duality.

Presence of strong J1 couplings and magnetic isolation are crucial for spin liquids.

Abstract

The structural-magnetic models of 25 AFM kagome cuprates similar to herbertsmithite (ZnCu3(OH)6Cl2) - a perspective spin liquid - have been calculated and analyzed. Main correlations between the structure and magnetic properties of these compounds were revealed. It has been demonstrated that, in all AFM kagome cuprates, including herbertsmithite, there exists the competition between the exchange interaction and the antisymmetric anisotropic exchange one (the Dzyaloshinskii-Moriya interaction), as magnetic ions are not linked to the center of inversion in the kagome lattice. This competition is strengthened in all the kagome AFM, except herbertsmithite, by one more type of the anisotropy (duality) of the third in length J3 magnetic couplings (strong J3(J12) next-to-nearest-neighbor couplings in linear chains along the triangle edges and very weak FM or AFM J3(Jd) couplings along the hexagon diagonals). The above couplings are crystallographically identical, but are divided to two types of different in strength magnetic interactions. The existence of duality of J3 couplings originated from the structure of the kagome lattice itself. Only combined contributions of dual J3 couplings with anisotropic DM interactions are capable to suppress frustration of kagome AFM. It has been demonstrated that the possibility of elimination of such a duality in herbertsmithite, which made it a spin liquid, constitutes a rare lucky event in the kagome system. Three crystal chemistry criteria of the existence of spin liquids on the kagome lattice have been identified: first, the presence of frustrated kagome lattices with strong dominant antiferromagnetic nearest-neighbor J1 couplings competing only with each other in small triangles; second, magnetic isolation of these frustrated kagome lattices; and third, the absence of duality of the third in length J3 magnetic couplings.