Fluctuations and correlations in a frustrated S=1/2 square lattice with competing ferromagnetic and antiferromagnetic interactions: a muSR study

Zero and longitudinal field $\mu$SR measurements in Pb$_2$VO(PO$_4$)$_2$ and BaCdVO(PO$_4$)$_2$, two prototypes of the frustrated $S=1/2$ square lattice model with competing ferromagnetic and antiferromagnetic interactions, are presented. Both systems are observed to undergo a phase transition to a long-range magnetic order at $T_N\simeq 3.46$ K, for Pb$_2$VO(PO$_4$)$_2$, and at $T_N\simeq 0.99$ K, for BaCdVO(PO$_4$)$_2$. In Pb$_2$VO(PO$_4$)$_2$ both the temperature dependence of the order parameter and the longitudinal relaxation rate above $T_N$ are consistent with a two-dimensional XY model. On the other hand, for BaCdVO(PO$_4$)$_2$, which lies very close to the magnetically disordered region of the phase diagram where a bond-nematic order was predicted, a peculiar logarithmic increase of the relaxation is observed above $T_N$. In both systems a rather broad distribution of internal fields at the muon sites is noticed below $T_N$. The origin of this distribution is discussed in the light of the $\mu$SR experiments already performed on $S=1/2$ frustrated antiferromagnets on a square lattice.