Quantum Spin Liquids in Frustrated Spin-1 Diamond Antiferromagnets

Motivated by the recent synthesis of the spin-1 A-site spinel NiRh_{2}O_{4}, we investigate the classical to quantum crossover of a frustrated J_{1}-J_{2} Heisenberg model on the diamond lattice upon varying the spin length S. Applying a recently developed pseudospin functional renormalization group approach for arbitrary spin-S magnets, we find that systems with S≥3/2 reside in the classical regime, where the low-temperature physics is dominated by the formation of coplanar spirals and a thermal (order-by-disorder) transition. For smaller local moments S=1 or S=1/2, we find that the system evades a thermal ordering transition and forms a quantum spiral spin liquid where the fluctuations are restricted to characteristic momentum-space surfaces. For the tetragonal phase of NiRh_{2}O_{4}, a modified J_{1}-J_{2}^{-}-J_{2}^{⊥} exchange model is found to favor a conventionally ordered Néel state (for arbitrary spin S), even in the presence of a strong local single-ion spin anisotropy, and it requires additional sources of frustration to explain the experimentally observed absence of a thermal ordering transition.