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

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 spins to lie within (111) planes. By considering 1/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., $[11\overline{2}]$, $[1\overline{2}1]$, and $[\overline{2}11]$ 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/S.