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The spin-lattice relaxation rate $T_1^{-1}$ of $^1$H-NMR has been measured in(CH$_3$)$_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x}$)$_3$ with $x=0$ and 0.35, in order toinvestigate the microscopic magnetism of systems. Previous macroscopicmagnetization and specific heat measurements suggested that these two exist ina singlet-dimer phase. The temperature dependence of $T_1^{-1}$ in an $x=0$system decreased exponentially toward zero, indicating microscopic evidence ofthe gapped singlet ground state, which is consistent with the macroscopicexperiments. At the same time, in the $x=0.35$ system, $T_1^{-1}$ showed asharp peak structure at around 7.5 K though no splitting of $^1$H-NMR spectraindicative of the magnetic ordering was observed. We discuss the observed sharppeak structure in the $x=0.35$ system with the soft mode toward the exoticmagnetic ground state suggested by the recent $\mu$SR experiments.

$^1$H-NMR Spin-Lattice Relaxation Rate of IPACu(Cl$_{x}$Br$_{1-x}$)$_3$ with $x=0$ and 0.35