Order-by-disorder effects in antiferromagnets on face-centered cubic lattice

•“order by disorder” phenomenon.•$1/S$-expansion.•Antiferromagnet on the FCC.•magnon dynamics.

We discuss the role of quantum fluctuations in Heisenberg antiferromagnets on face-centered cubic lattice with small dipolar interaction in which the next-nearest-neighbor exchange coupling dominates over the nearest-neighbor one. It is well known that a collinear magnetic structure which contains (111) ferromagnetic planes arranged antiferromagnetically along one of the space diagonals of the cube is stabilized in this model via order-by-disorder mechanism. On the mean-field level, the dipolar interaction forces spin to lie within (111) planes. By considering 1/S1/S corrections to the ground state energy, we demonstrate that quantum fluctuations lead to an anisotropy within (111) planes favoring three equivalent directions for the staggered magnetization (e.g., [112¯], [12¯1], and [2¯11] directions for (111) plane). Such in-plane anisotropy was obtained experimentally in related materials MnO, α-MnS, α  -MnSe, EuTe, and EuSe. We find that the order-by-disorder mechanism can contribute significantly to the value of the in-plane anisotropy in EuTe. Magnon spectrum is also derived in the first order in 1/S1/S.