$mu$SR studies of the frustrated quasi-2d square-lattice spin system Cu(Cl,Br)La(Nb,Ta)$_{2}$O$_{7}$: evolution from spin-gap to antiferromagnetic state

We report muon spin relaxation ($mu$SR) and magnetic susceptibility measurements on Cu(Cl,Br)La(Nb,Ta)$_{2}$O$_{7}$, which demonstrate: (a) the absence of static magnetism in (CuCl)LaNb$_{2}$O$_{7}$ down to 15 mK confirming a spin-gapped ground state; (b) phase separation between partial volumes with a spin-gap and static magnetism in (CuCl)La(Nb,Ta)$_{2}$O$_{7}$; (c) history-dependent magnetization in the (Nb,Ta) and (Cl,Br) substitution systems; (d) a uniform long-range collinear antiferromagnetic state in (CuBr)LaNb$_{2}$O$_{7}$; and (e) a decrease of Neel temperature with decreasing Br concentration $x$ in Cu(Cl$_{1-x}$Br$_{x}$)LaNb$_{2}$O$_{7}$ with no change in the ordered Cu moment size for $0.33 leq x leq 1$. Together with several other $mu$SR studies of quantum phase transitions in geometrically-frustrated spin systems, the present results reveal that the evolution from a spin-gap to a magnetically ordered state is often associated with phase separation and/or a first order phase transition.