$\mu $SR study of spin dynamics and phase transition of the two-dimensional tetramer-cuprate Na$_{5}$RbCu$_{4(}$AsO$_{4})_{4}$Cl$_{2}$

In an effort to explain the magnetic properties of such low-dimensional systems, $^{87}$Rb Nuclear Magnetic Resonance (NMR) experiments in a Na$_{5}$RbCu$_{4}$(AsO$_{4})$Cl$_{2}$ system were performed. This novel two-dimensional (2D) cuprate contains layers of coupled Cu$_{4}$O$_{4}$ tetramers. The spin exchange interactions are confined to 2D layers and the Cu are divalent, making the system a s=1/2 antiferromagnet. In zero applied magnetic field, it orders antiferromagnetically via a second-order phase transition at T$_{N}$=15(1) K. The ordered state was characterized by $^{87}$Rb NMR, and a non-collinear rather than collinear arrangement of spins was suggested. New structural phase transition(s) around 74 and 110 K were also evidenced. We present a \textit{$\mu $}SR study of this cuprate. The investigation of the spin dynamics (via the muon longitudinal relaxation rate $\lambda $(T) ) in the temperature range 2$<$T$<$300K in zero-field, with particular attention to the order parameter below T$_{N}$ and around structural phase transitions at T$\sim $74K and T$\sim $110K is shown.