We investigate the stability of the spiral spin liquid phase in MnSc2S4 against thermal and quantum fluctuations as well as against perturbing effects of longer-range interactions. Employing ab initio density functional theory (DFT) calculations we propose a realistic Hamiltonian for MnSc2S4, featuring second (J2) and third (J3) neighbor Heisenberg interactions on the diamond lattice that are considerably larger than previously assumed. We argue that the combination of strong J2 and J3 couplings reproduces the correct magnetic Bragg peak position measured experimentally. Calculating the spin-structure factor within the pseudofermion functional-renormalization group technique, we find that close to the magnetic phase transition the sizable J3 couplings induce a strong spiral selection effect, in agreement with experiments. With increasing temperature the spiral selection becomes weaker such that in a window around three to five times the ordering temperature an approximate spiral spin liquid is realized in MnSc2S4
