  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 ($\theta_{CW}$) 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 ($\chi = M/\mu_0H$) 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, $M(T,\mu_0H)$ and $C_m(T,\mu_0H)/T$ 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 $P(J)
\propto J^{-\gamma}$ ($J$ 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 $\chi$ and
$C_m(T,\mu_0H)/T$ as a whole. Thus, our comprehensive experimental and
theoretical analysis provides evidence for the stabilization of the RSS state
in a three-dimensional lattice.
