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We report the signatures of dynamic spin fluctuations in the layeredhoneycomb Li$_3$Cu$_2$SbO$_6$ compound, with a 3$d$ S = 1/2 $d^9$ Cu$^{2+}$configuration, through muon spin rotation and relaxation ($\mu$SR) and neutronscattering studies. Our zero-field (ZF) and longitudinal-field (LF)-$\mu$SRresults demonstrate the slowing down of the Cu$^{2+}$ spin fluctuations below4.0 K. The saturation of the ZF relaxation rate at low temperature, togetherwith its weak dependence on the longitudinal field between 0 and 3.2 kG,indicates the presence of dynamic spin fluctuations persisting even at 80 mKwithout static order. Neutron scattering study reveals the gaped magneticexcitations with three modes at 7.7, 13.5 and 33 meV. Our DFT calculationsreveal that the next nearest neighbors (NNN) AFM exchange ($J_{AFM}$ = 31 meV)is stronger than the NN FM exchange ($J_{FM}$ = -21 meV) indicating theimportance of the orbital degrees of freedom. Our results suggest that thephysics of Li$_3$Cu$_2$SbO$_6$ can be explained by an alternating AFM chainrather than the honeycomb lattice.

Dynamic Spin Fluctuations in the Frustrated Spin Chain Compound Li$_3$Cu$_2$SbO$_6$