Three-Dimensional Ordering in bct Antiferromagnets Due to Quantum Disorder

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Yildirim, Taner
Harris, A. Brooks
Shender, Eugene F

Quantum effects on magnetic ordering in body-centered-tetragonal antiferromagnets with only nearest-neighbor 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-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 J2⊥/(J2S), 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 σi (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 in j=J⊥/J is E({σi}) =E1+CEG(j6/S)[-2σ1σ3-2σM−2σM+2∑i =1M-2σiσi+2-3∑i=1M-3σiσi+1σi+2σi+3], where C>0 and E1 are constants independent of the σ’s, and EG is the classical ground-state energy. (Here sums from i to j when j<i are interpreted to be zero.) Surprisingly, there is no σ-dependent contribution at order j4/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 j4, σ-dependent terms first appear at order 1/S3 and these also favor antiferromagnetic coupling of alternate planes.

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Physical Review B
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<p>At 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.</p>
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