Evidence of random spin-singlet state in a three-dimensional quantum spin liquid candidate Sr$_3$CuNb$_2$O$_9$

Abstract

Disorder is ubiquitous in any quantum many-body system and is usually considered to be an obstacle to the elucidation of the underlying physics of complex systems, but its presence can often introduce exotic phases of matter that cannot generally be realized in a clean system. We report here a detailed experimental and theoretical study of magnetic properties of highly disordered Sr$_3$CuNb$_2$O$_9$ material which exhibits random site mixing between Cu and Nb. The magnetic moments (Cu$^{2+}$) are arranged in a quasi-cubic (three-dimensional) manner, leading to a high degree of frustration with a Curie-Weiss temperature ($θ_{CW}$) of about -60 K without any long-range magnetic ordering down to 466 mK. These observations suggest that Sr$_3$CuNb$_2$O$_9$ is a candidate for a quantum spin liquid. More interestingly, the susceptibility ($χ= M/μ_0H$) and the $C_m/T$ ($C_m$ is the magnetic part of the heat capacity) follow a power-law behavior with decreasing temperature. In addition, $M(T,μ_0H)$ and $C_m(T,μ_0H)/T$ show scaling relationships over a wide temperature and field range. This unusual behavior with respect to the conventional behavior of a QSL can be discussed qualitatively as the coexistence of a disorder-induced random spin singlet (RSS) state and a QSL state. A quantitative description has been given by numerical calculations considering a power-law probability distribution $P(J) \propto J^{-γ}$ ($J$ is the exchange interaction) of random spin singlets. The parameters extracted from the numerical calculations are in excellent agreement with the experimental data. Furthermore, the analytical results are also consistent with the power-law and scaling behavior of $χ$ and $C_m(T,μ_0H)/T$ as a whole. Thus, our comprehensive experimental and theoretical analysis provides evidence for the stabilization of the RSS state in a three-dimensional lattice.