We investigate the stability of the spiral spin liquid phase in ${\mathrm{MnSc}}_2{\mathrm{S}}_4$ 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 ${\mathrm{MnSc}}_2{\mathrm{S}}_4$, featuring second $\left(J_2\right)$ and third $\left(J_3\right)$ neighbor Heisenberg interactions on the diamond lattice that are considerably larger than previously assumed. We argue that the combination of strong $J_2$ and $J_3$ 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 $J_3$ 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 ${\mathrm{MnSc}}_2{\mathrm{S}}_4$.

• Received 7 February 2018
• Revised 25 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.064427