Using 1/S expansion, we discuss the magnon spectrum of Heisenberg antiferromagnet (AF) on a simple cubic lattice with small dipolar interaction at small temperature T ≪ TN , where TN is the Neel temperature. Similar to 3D and 2D ferromagnets, quantum and thermal fluctuations renormalize greatly the bare gapless spectrum leading to a gap ∆ ∼ ω0, where ω0 is the characteristic dipolar energy. This gap is accompanied by anisotropic corrections to the free energy which make the cube edges easy directions for the staggered magnetization (dipolar anisotropy). In accordance with previous results, we find that dipolar forces split the magnon spectrum into two branches. This splitting makes possible two types of processes which lead to a considerable enhance of the damping compared to the Heisenberg AF: a magnon decay into two other magnons and a confluence of two magnons. It is found that magnons are well defined quasiparticles in quantum AF. We demonstrate however that a small fraction of long-wavelength magnons can be overdamped in AFs with S ≫ 1 and in quantum AFs with a single-ion anisotropy competing with the dipolar anisotropy. Particular materials are pointed out which can be suitable for experimental observation of this long-wavelength magnons breakdown that contradicts expectation of the quasiparticle concept.
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., [112], [121], and [211] 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.
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