Spin glass behavior in frustrated quantum spin system CuAl₂O₄ with a possible orbital liquid state

CuAl₂O₄ is a normal spinel oxide having quantum spin, S  =  1/2 for Cu²⁺. It is a rather unique feature that the Cu²⁺ ions of CuAl₂O₄ sit at a tetrahedral position, not like the usual octahedral position for many oxides. At low temperatures, it exhibits all the thermodynamic evidence of a quantum spin glass. For example, the polycrystalline CuAl₂O₄ shows a cusp centered at ~2 K in the low-field dc magnetization data and a clear frequency dependence in the ac magnetic susceptibility while it displays logarithmic relaxation behavior in a time dependence of the magnetization. At the same time, there is a peak at ~2.3 K in the heat capacity, which shifts towards a higher temperature with magnetic fields. On the other hand, there is no evidence of new superlattice peaks in the high-resolution neutron powder diffraction data when cooled from 40 to 0.4 K. This implies that there is no long-ranged magnetic order down to 0.4 K, thus confirming a spin glass-like ground state for CuAl₂O₄. Interestingly, there is no sign of structural distortion either although Cu²⁺ is a Jahn-Teller active ion. Thus, we claim that an orbital liquid state is the most likely ground state in CuAl₂O₄. Of further interest, it also exhibits a large frustration parameter, f  =  |θ _CW/T _m| ~ 67, one of the largest values reported for spinel oxides. Our observations suggest that CuAl₂O₄ should be a rare example of a frustrated quantum spin glass with a good candidate for an orbital liquid state.