The Magnetism of Li doped La$_{2}$CuO$_4$: the antiferromagnetic spin-shard state

TL;DR

This paper investigates how lithium doping in La$_{2}$CuO$_4$ leads to a unique antiferromagnetic shard state due to hole localization and clustering, differing significantly from strontium doping effects.

Contribution

It introduces the concept of a spin-shard state in Li-doped La$_{2}$CuO$_4$, explaining magnetic and electric properties through hole localization and cluster formation.

Findings

Holes in Li-doped La$_{2}$CuO$_4$ are always localized.

A critical doping level $x_c\,\approx 0.03$ causes antiferromagnetic fragmentation.

The spin-shard state describes the magnetic and electric behavior of the material.

Abstract

We study the dynamics of a single hole in Li and Sr doped La$_{2}$CuO$_4$ and its extension to a finite hole concentration. We compare the physics of La$_{2-x}$Sr$_x$CuO$_4$ and La$_{2}$Cu$_{1-x}$Li$_x$O$_4$ and explain why these systems are remarkably different. We demonstrate that holes in La$_{2}$Cu$_{1-x}$Li$_x$O$_4$ are always localized and that there is a critical concentration, $x_c\approx 0.03$, above which the holes break the global antiferromagnetic state into an array of weakly coupled antiferromagnetic clusters (antiferromagnetic shards). We show that the spin-shard state provides a description of the magnetic and electric properties of La$_{2}$Cu$_{1-x}$Li$_x$O$_4$. Two experiments that can test our theory are proposed.