Spin Liquid State in the 3D Frustrated Antiferromagnet PbCuTe_{2}O_{6}: NMR and Muon Spin Relaxation Studies.

PbCuTe_{2}O_{6} is a rare example of a spin liquid candidate featuring a three-dimensional magnetic lattice. Strong geometric frustration arises from the dominant antiferromagnetic interaction that generates a hyperkagome network of Cu^{2+} ions although additional interactions enhance the magnetic lattice connectivity. Through a combination of magnetization measurements and local probe investigations by NMR and muon spin relaxation down to 20 mK, we provide robust evidence for the absence of magnetic freezing in the ground state. The local spin susceptibility probed by the NMR shift hardly deviates from the macroscopic one down to 1 K pointing to a homogeneous magnetic system with a low defect concentration. The saturation of the NMR shift and the sublinear power law temperature (T) evolution of the 1/T_{1} NMR relaxation rate at low T point to a nonsinglet ground state favoring a gapless fermionic description of the magnetic excitations. Below 1 K a pronounced slowing down of the spin dynamics is witnessed, which may signal a reconstruction of spinon Fermi surface. Nonetheless, the compound remains in a fluctuating spin liquid state down to the lowest temperature of the present investigation.