Quantum and classical phases of the pyrochlore Heisenberg model with competing interactions

We investigate the Heisenberg model on the pyrochlore lattice for a generic spin-S in the presence of nearest-neighbor J1 and second-nearest-neighbor J2 interactions. Employing the pseudofermion functional renormalization group method we find, for S=1/2 and S=1, an extended quantum spin liquid phase centred around J2=0. At J2=0, the paramagnetic character of this phase is found to be robust against the introduction of breathing anisotropy. The J1-J2 model is shown to host seven different classical magnetic orders, which are also found in the low-spin regime, with no new magnetic orders being stabilized by quantum fluctuations. As a ``material application'', we investigate the low-temperature physics of NaCaNi2F7, a recently synthesized S=1 quantum spin liquid candidate material. Using density functional theory, we find that the compound is well described by a J1-J2 (both antiferromagnetic) Heisenberg model, with J2/J1=0.02, which securely places it deep inside the putative quantum spin liquid phase. A PFFRG analysis of the model Hamiltonian of NaCaNi2F7 reveals paramagnetic behavior down to a temperature of at least T=|\Theta_{\rm CW}|/100, in agreement with the experimental findings, and pointing to a first potential realization of a S=1 quantum spin liquid in three dimensions.