Thermal Hall effect in a phonon-glass Ba\(_3\)CuSb\(_2\)O\(_9\)

A distinct thermal Hall signal is observed in a quantum spin liquid candidate Ba\(_3\)CuSb\(_2\)O\(_9\). The transverse thermal conduction shows a power-law temperature dependence below 40 K where a spin gap opens. We suggest that, through the very low longitudinal thermal conductivity and the thermal Hall signals, a phonon Hall effect is induced by strong phonon scatterings by orphan Cu\(^{2+}\) spins formed in random domains of Cu\(^{2+}\)-Sb\(^{5+}\) dumbbells.