Disorder-driven coexistence of distinct dynamical states in frustrated Sr${}_3$CuNb${}_2$O${}_9$: a microscopic $\mu$SR and ${}^{93}$Nb NMR study

Abstract

Despite recent progress in identifying the exotic random singlet (RS) state in disordered frustrated magnets as a distinct correlated phase, three-dimensional (3D) realizations remain scarce. Sr${}_3$CuNb${}_2$O${}_9$ was proposed to be one of such 3D frustrated systems with magnetic site disorder hosting an RS ground state. Here, we report a detailed microscopic investigation of Sr${}_3$CuNb${}_2$O${}_9$ employing muon spin relaxation ($\mu$SR) and ${}^{93}$Nb nuclear magnetic resonance (NMR) techniques. The $\mu$SR zero-field relaxation rate reveals a power-law divergence of the relaxation rate as a function of temperature. Also, a power-law divergence is present in the relaxation rate as a function of applied longitudinal field, consistent with the formation of an RS phase. The ${}^{93}$Nb NMR spectra unambiguously resolve two components with distinct local magnetic environments, whose nature is further elucidated through spin-lattice relaxation measurements analyzed via an inverse Laplace transform (ILT) of the nuclear magnetization recovery. The relaxation-rate distribution obtained from ILT reveals two well-separated channels: a fast component, $(1/T_1{)}_{\mathrm{fast}}$, and a slow component, $(1/T_1{)}_{\mathrm{slow}}$. Both components follow distinct power-law temperature dependences ($T^{\alpha }$), with $\alpha =0.6$ and $1.1$ for the fast and slow channels, respectively. The combined spectral and relaxation data demonstrate that the fast channel qualitatively represents an RS-like state, whereas the slow channel exhibits quantum spin liquid (QSL) like behavior, thereby establishing the microscopic coexistence of RS and QSL-like phases in Sr${}_3$CuNb${}_2$O${}_9$.

8 pages, 3 figures