# Tomonaga-Luttinger spin liquid in the spin-1/2 inequilateral diamond-chain compound K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$

## TL;DR

This study identifies K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$ as a realization of a Tomonaga-Luttinger spin liquid, exhibiting one-dimensional quantum spin behavior with no long-range order down to very low temperatures.

## Contribution

It provides experimental evidence of Tomonaga-Luttinger spin liquid behavior in an inequilateral diamond-chain compound through neutron scattering and muon spectroscopy.

## Key findings

- Observation of spinon continuum and spin-singlet excitations
- No long-range magnetic order down to 90 mK
- Agreement with theoretical dimer-monomer model

## Abstract

K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$ is a highly one-dimensional spin-1/2 inequilateral diamond-chain antiferromagnet. Spinon continuum and spin-singlet dimer excitations are observed in the inelastic neutron scattering spectra, which is in excellent agreement with a theoretical prediction: a dimer-monomer composite structure, where the dimer is caused by strong antiferromagnetic (AFM) coupling and the monomer forms an almost isolated quantum AFM chain controlling low-energy excitations. Moreover, muon spin rotation/relaxation spectroscopy shows no long-range ordering down to 90~mK, which is roughly three orders of magnitude lower than the exchange interaction of the quantum AFM chain. K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$ is, thus, regarded as a compound that exhibits a Tomonaga-Luttinger spin liquid behavior at low temperatures close to the ground state.