Proximate quantum spin liquid state in the frustrated HoInCu$_4$ metal

TL;DR

This study reveals that HoInCu4 exhibits a proximate quantum spin liquid state characterized by partial magnetic order and persistent spin dynamics, highlighting the role of frustration in stabilizing such exotic states in metallic systems.

Contribution

First experimental evidence of a proximate quantum spin liquid state in a frustrated metallic compound, supported by muon-spin relaxation and neutron results.

Findings

HoInCu4 shows only 30% static magnetic order below T_N.

70% of Ho-moments exhibit dynamic correlations down to 0.3 K.

Presence of quantum critical fluctuations near T_N.

Abstract

We conducted a comprehensive and comparative muon-spin relaxation and rotation ($\mu$SR) investigation on two fcc-lattice metallic compounds, HoCdCu$_4$ ($T_\mathrm{N}\approx 8$ K) and HoInCu$_4$ ($T_\mathrm{N}\approx 0.76$ K), to elucidate the nature of their magnetic ground states and the role of frustration in stabilizing them. Our $\mu$SR results reveal that, in contrast to HoCdCu$_4$, strong magnetic frustration exists in HoInCu$_4$. Notably, in HoInCu$_{4}$, only 30% of the Ho-moments participate in the static magnetic ordering below $T_\mathrm{N}$, while the remaining 70% of the Ho-moments exhibit dynamic correlations and persistent spin dynamics down to 0.3 K, resembling a quantum spin-liquid (QSL) behavior. By contrast, in HoCdCu$_{4}$, all the Ho-moments contribute to the magnetic order below $T_\mathrm{N}$. Furthermore, in HoInCu$_{4}$, the temperature dependence of the relaxation rate indicates the presence of quantum critical fluctuations in the paramagnetic state near $T_\mathrm{N}$, suggesting the proximity to a quantum critical point (QCP). These observations suggest that the ground state of HoInCu$_{4}$ is a proximate quantum spin liquid (PQSL), a state that has not been reported before in frustrated metallic systems. Our $\mu$SR findings are further corroborated by recent inelastic neutron results on HoInCu$_4$, which show similarities to other insulating PQSL candidates, thus reinforcing our conclusions.