  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 N\'eel 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.
