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We report muon spin relaxation ($\mu$SR) and magnetic susceptibilitymeasurements on Cu(Cl,Br)La(Nb,Ta)$_{2}$O$_{7}$, which demonstrate: (a) theabsence of static magnetism in (CuCl)LaNb$_{2}$O$_{7}$ down to 15 mK confirminga spin-gapped ground state; (b) phase separation between partial volumes with aspin-gap and static magnetism in (CuCl)La(Nb,Ta)$_{2}$O$_{7}$; (c)history-dependent magnetization in the (Nb,Ta) and (Cl,Br) substitutionsystems; (d) a uniform long-range collinear antiferromagnetic state in(CuBr)LaNb$_{2}$O$_{7}$; and (e) a decrease of N\'eel temperature withdecreasing Br concentration $x$ in Cu(Cl$_{1-x}$Br$_{x}$)LaNb$_{2}$O$_{7}$ withno change in the ordered Cu moment size for $0.33 \leq x \leq 1$. Together withseveral other $\mu$SR studies of quantum phase transitions ingeometrically-frustrated spin systems, the present results reveal that theevolution from a spin-gap to a magnetically ordered state is often associatedwith phase separation and/or a first order phase transition.

physical review. b, condensed matter and materials physics

$\mu$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