Muon spin relaxation detection of the soft mode toward the exotic magnetic ground state in the bond-disordered quantum spin system IPA-Cu(Cl0.35Br0.65)3

The spin-gap system with a bond-disorder ${({\text{CH}}_{3})}_{2}{\text{CHNH}}_{3}\text{-Cu}{({\text{Cl}}_{x}{\text{Br}}_{1\ensuremath{-}x})}_{3}$ is reported by experiments on macroscopic quantities of the uniform susceptibility and the specific heat to show a magnetic order at low temperatures (when the value of $x$ is within the limited region between 0.44 and 0.87) and otherwise a gapped behavior. We have investigated microscopically the ground state of the sample with $x=0.35$ by muon spin relaxation $(\ensuremath{\mu}\text{SR})$ to observe that the frequency spectrum of the spin fluctuation tends to concentrate around zero energy as lowering temperatures. This behavior was interpreted as the soft mode toward the possible magnetic phase transition at absolute zero.