The ground state of the quasi-one-dimensional system with bond-disorder (CH3)2CHNH3Cu(ClxBr1-x)3 with x = 0, 0.25 and 0.3 has been investigated by muSR. The Fourier spectrum of electron spin fluctuation in x =0.25 and 0.3 obtained by LF-muSR techniqu
e shows that there exists a soft-mode toward a possible phase transition to an exotic phase such as Bose-glass. In gapped system with x = 0, the Fourier spectrum is totally different from the other two, indicating the existence of the quantum critical point at a finite x between 0 and 0.25.
The high-field ground state of the competing-spin-chain compound Cs2Cu2Mo3O12 with the ferromagnetic first-nearest-neighbor J1=-93 K and the antiferromagnetic second-nearest-neighbor J2 = +33 K was investigated by 133Cs-NMR. A divergence of T1-1 and
a peak-splitting in spectra were observed at TN = 1.85 K, indicating the existence of a field-induced long range magnetic order. In the paramagnetic region above 4 K, T1-1 showed a power-law temperature dependence T2K-1. The exponent K was strongly field-dependent, suggesting the possibility of the spin-nematic Tomonaga Luttinger Liquid state.
