$\mu $SR studies of the extended kagome systems YBaCo$_{4}$O$_{7+\delta }$ ($\delta =$ 0 and 0.1)

We present a $\mu $SR study of the extended kagome systems YBaCo$_{4}$O$_{7+\delta }$ ($\delta =$ 0 and 0.1), which are made up of an alternating stacking of triangular and kagome layers. The parent material YBaCo$_{4}$O$_{7.0}$ undergoes a structural phase transition at 310 K, releasing geometrical frustration and thereby stabilizing an antiferromagnetically ordered state below T$_{N}=$ 106 K. The $\mu $SR spectra of YBaCo$_{4}$O$_{7.0}$ exhibit the loss of initial asymmetry and the development of a fast relaxation component below T$_{N}=$ 111 K. This indicates that the Co spins in the kagome planes remain in an inhomogeneous and dynamically fluctuating state down to 4 K, while the triangular spins order antiferromagnetically below T$_{N}$. The nonstoichiometric YBaCo$_{4}$O$_{7.1}$ compound with no magnetic ordering exhibits a disparate spin dynamics between the fast cooling (10 K/min) and slow cooling (1 K/min) procedures. While the fast-cooled $\mu $SR spectra show a simple exponential decay, the slow-cooled spectra are described with a sum of a simple exponential function and a stretched exponential function. These are in agreements with the occurrence of the phase separation between interstitial oxygen-rich and poor regions in the slow-cooling measurements.