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

Abstract:

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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I. INTRODUCTION 

Frustrated spin systems have attracted a great deal of interest in recent years.1 In many of them, classical ground state has a degeneracy which can be lifted by quantum or thermal fluctuations who thereby select and stabilize an ordered state. This is the so-called “order by disorder” phenomenon.2–4 One of such spin systems is the Heisenberg antiferromagnet (AF) on face-centered cubic (fcc) lattice in which the next-nearest-neighbor AF exchange coupling (i.e., that along the cube edge) dominates over the nearest-neighbor one.5 Although this model describes a number of prototypical AFs (e.g., MnO), some open problems remain in this field. AF on fcc lattice can be viewed as four interpenetrating AF cubic sublattices (see Fig. 1(a)).5,6 Any spin from a sublattice locates at zero molecular field of spins from three other sublattices. As a result, staggered magnetizations of these sublattices can be oriented arbitrary relative to each other that leads to an infinite ground state degeneracy. However, quantum fluctuations make staggered magnetizations of all sublattices parallel to each other.5 Besides, among two possible collinear arrangements, they select that presented in Fig. 1(b) which is referred to in the literature as AF structure of the second kind, type A (fluctuations make unfavorable type B structure).5,6 This AF structure contains (111) ferromagnetic (FM) planes arranged antiferromagnetically along one of h111i directions. As soon as [111], [¯111], [1¯11], and [11¯1] directions are equivalent, there are four equivalent spin arrangements of this type which are described by vectors of the magnetic structure k0 = (π, π, π), (π, 0, 0), (0, π, 0), and (0, 0, π) (hereafter we set to unity the cube edge length). This symmetry breaking by fluctuations is naturally accompanied by appearance of gaps induced by fluctuations in some magnon branches (not all the magnon branches acquire gaps because the continuous symmetry remains related to a rotation of all spins by any angle about any axis).5 It can be shown also that the selection of collinear spin structures can be described phenomenologically on the mean-field level by introducing to the Hamiltonian a biquadratic interaction between spins from different sublattices having the form −Q(SiSj ) 2 , where Q > 0.5,7