NMR and mu-SR study on the critical phenomena in the Bose-glass phase with Tc=0

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(CH_3)_2CHNH_3Cu(Cl_xBr_<1-x>)_3 abbreviated IPACu(Cl_xBr_<1-x>)_3 is a mixed system of spin-gap compounds IPACuCl_3 and IPACuBr_3. This mixed system is reported by macroscopic measurements to show a magnetic order when the value of x is between the quantum critical points(QCPs) 0.44 and 0.87. We have investigated microscopically the ground state of the samples x=0.40, 0.45 and 0.50 which are located near the QCP of xc=0.44, by Muon Spin Relaxation(μSR) and NMR measurements. For x=0.40, mSR measurements in zero and longitudinal fields have shown that the spin fluctuation shows a significant slowing down with decreasing temperature, although the magnetic order does not appear down to T=15 mK, indicating that the ground state is an exotic one rather than a gapped one. For x=0.45 and 0.50, mSR and NMR measurements do not show any magnetic order at low temperatures, indicating that the QCP is larger than the reported value of x_c=0.44.