Effect of disorder on a pressure-induced $z=1$ magnetic quantum phase transition

TL;DR

This study investigates how bond disorder affects the pressure-induced quantum phase transition in a magnetic system, revealing inhomogeneous ordering and potential Griffiths phase formation at certain disorder levels.

Contribution

It provides experimental evidence on the impact of bond disorder on a pressure-induced quantum critical point in a specific quantum spin system.

Findings

Disorder causes inhomogeneous magnetic order above 1% concentration.

Critical pressure increases with Br-substitution.

Possible formation of a quantum Griffiths phase at higher disorder.

Abstract

Pressure-induced ordering close to a $z=1$ quantum critical point is studied in the presence of bond disorder in the quantum spin system (C$_4$H$_{12}$N$_2$)Cu$_2$(Cl$_{1-x}$Br$_{x}$)$_6$ (PHCX) by means of muon-spin rotation and relaxation. As for the pure system (C$_4$H$_{12}$N$_2$)Cu$_2$Cl$_6$, pressure allows PHCX with small levels of disorder ($x\leq 7.5\%$) to be driven through a quantum critical point separating a low-pressure quantum paramagnetic phase from magnetic order at high pressures. However, the pressure-induced ordered state is highly inhomogeneous for disorder concentrations $x>1\%$. This behavior might be related to the formation of a quantum Griffiths phase above a critical disorder concentration $7.5\%<x_{\rm c}<15\%$. Br-substitution increases the critical pressure and suppresses critical temperatures and ordered moment sizes.