Paramagnetism in the kagome compounds (Zn,Mg,Cd)Cu$_{3}$(OH)$_{6}$Cl$_{2}$

TL;DR

This study combines theoretical and computational methods to explore the magnetic properties of kagome lattice compounds, revealing how pressure and composition influence their transition between ordered and disordered magnetic phases.

Contribution

It introduces a combined pseudofermion functional renormalization-group and extit{ab initio} approach to analyze and predict magnetic phase behavior in kagome compounds.

Findings

Kapellasite and haydeeite are near phase boundaries, sensitive to modifications.

Pressure and composition variations can induce transitions between magnetic phases.

The compounds can be tuned into a paramagnetic regime through external parameters.

Abstract

Frustrated magnetism on the kagome lattice has been a fertile ground for rich and fascinating physics, ranging from experimental evidence of a spin liquid to theoretical predictions of exotic superconductivity. Among experimentally realized spin-$\frac{1}{2}$ kagome magnets, herbertsmithite, kapellasite, and haydeeite [(Zn,Mg)Cu$_{3}$(OH)$_{6}$Cl$_{2}$] are all well described by a three-parameter Heisenberg model, but they exhibit distinctly different physics. We address the problem using a pseudofermion functional renormalization-group approach and analyze the low-energy physics in the experimentally accessible parameter range. Our analysis places kapellasite and haydeeite near the boundaries between magnetically ordered and disordered phases, implying that slight modifications could dramatically affect their magnetic properties. Inspired by this, we perform \textit{ab initio} density functional theory calculations of (Zn,Mg,Cd)Cu$_{3}$ (OH)$_{6}$Cl$_{2}$ at various pressures. Our results suggest that by varying pressure and composition one can traverse a paramagnetic regime between different magnetically ordered phases.