Three-dimensional ordering in bct antiferromagnets due to quantum disorder

Abstract

Quantum effects on magnetic ordering in body-centered-tetragonal antiferromagnets with only nearestneighbor interactions are studied in detail using interacting spin-wave theory. The model consists of M noninteracting (in a mean-field sense) antiferromagnetic planes which together form a body-centeredtetragonal structure. We obtain the leading quantum correction of order 1/S from the zero-point energy for a system of M planes whose staggered moments have arbitrary orientations. The infinite degeneracy of the ground-state manifold of this system is partially removed by collinear ordering in view of effects previously calculated by Shender at relative order J 2 ⊥ /(J 2 S), where J, the antiferromagnetic in-plane exchange interaction, is assumed to dominate J ⊥ , the out-of-plane interaction which can be of either sign. We study the complete removal of the remaining degeneracy of the collinear spin structures by assigning an arbitrary sign σ i (i=1,2,...M) to the staggered moment of the planes. Our result for the zero-point energy (for M>2) up to the sixth order inwhere C>0 and E 1 are constants independent of the σ's, and E G is the classical ground-state energy. (Here sums from i to j when j<<em>i are interpreted to be zero.) Surprisingly, there is no σ-dependent contribution at order j 4 /S. This result shows that for M>4 second-neighboring planes are antiferromagnetically coupled in the ground state and thus the three-dimensional spin structure cannot be described by a single wave vector, as is often assumed. At order j 4 , σ-dependent terms first appear at order 1/S 3 and these also favor antiferromagnetic coupling of alternate planes. Disciplines Physics | Quantum Physics CommentsAt the time of publication, author A. Brooks Harris was also affiliated with Oxford University and Tel Aviv University. Currently, he is a faculty member in the Physics Department at the University of Pennsylvania. Quantum effects on magnetic ordering in body-centered-tetragonal antiferromagnets with only nearestneighbor interactions are studied in detail using interacting spin-wave theory. The model consists of M noninteracting ͑in a mean-field sense͒ antiferromagnetic planes which together form a body-centered-tetragonal structure. We obtain the leading quantum correction of order 1/S from the zero-point energy for a system of M planes whose staggered moments have arbitrary orientations. The infinite degeneracy of the ground-state manifold of this system is partially removed by collinear ordering in view of effects previously calculated by Shender at relative order J Ќ 2 /(J 2 S), where J, the antiferromagnetic in-plane exchange interaction, is assumed to dominate J Ќ , the out-of-plane interaction which can be of either sign. We study the complete removal of the remaining degeneracy of the collinear spin structures by assigning an arbitrary sign i (iϭ1,2, . . . M ) to the staggered moment of the planes. Our result for the zero-point energy ͑for M Ͼ2͒ up to the sixth order in jϭJ Ќ /J iswhere CϾ0 and E 1 are constants indep...

Chapter 199 Neutron scattering studies of lanthanide magnetic ordering

“…In addition, magnetic ordering of Cu and, therefore, the Nd−Cu coupling, are observed in as-grown samples, while they disappear when the excess oxygen is removed. As mentioned earlier, the linear exchange interaction between Cu layers cancels due to the bct symmetry, and the actual spin structure is then a result of a delicate balance of superexchange, spin-orbit, and Coulomb exchange interactions (Yildirim et al 1994(Yildirim et al , 1996. In the absence of the R ions, quantum fluctuations would be expected to yield the collinear magnetic structure (Yildirim 1999) and this may indeed be the case for the Sr 2 CuO 2 Cl 2 material ).…”

“…The nearest-neighbor exchange interaction J S i ·S j between layers, on the other hand, is seen to cancel due to the body-centered tetragonal (bct) symmetry, further rendering the net Cu spin interactions 2D in nature. Hence the three-dimensional magnetic structure that is actually realized must be stabilized by higher-order interactions (Yildirim et al 1996), as we will discuss shortly. The detailed spin structure, which entails assigning a spin direction to each site, turns out to contain an ambiguity; there are two possible descriptions (figs.…”

Frustration and quantum fluctuations in Heisenberg fcc antiferromagnets

“…As we shall see, the degeneracy between type A and type B structures is removed when the effects of quantum fluctuations are included to higher order in JЈ/J. For this type of calculation the formalism introduced previously 10 is convenient. We also point out that in real systems there may be mechanisms other than quantum fluctuations which could remove the degeneracy between the collinear states.…”

“…Subsequently many examples of groundstate selection via quantum fluctuations have been analyzed. [6][7][8][9][10] This phenomenon is the analog of ordering by disorder due to thermal fluctuations, a concept discussed by Villain et al 11 for Ising systems and then extended to vector spin systems by Henley. 12,5 The same effect can be realized by configurational fluctuations associated with random substitution in alloys.…”

“…III we use linearized spin-wave theory to calculate the quantum corrections at first order in 1/S due to the zero-point motion. To analyze this complicated expression we follow our previous work 10 and expand the zero-point energy in powers of JЈ/J to get the effective interaction between sublattices. These interactions lead to the structure experimentally determined for MnO.…”