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 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 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. Disciplines Physics | Quantum Physics Comments 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. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/345 Three-dimensional ordering in bct antiferromagnets due to quantum disorder T. Yildirim University of Maryland, College Park, Maryland 20742; National Institute of Standards and Technology, Gaithersburg, Maryland 20899; and Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104 A. B. Harris Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104; Theoretical Physics, Oxford University, Oxford, OX2 3NP, United Kingdom; and School of Physics and Astronomy, Raymond and Beverly Sackler Institute of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel E. F. Shender Department of Physics, University of California, Berkeley, California 94720 and Institute of Nuclear Physics, St. Petersburg, Russia ~Received 11 August 1995! 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-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' 2 /(JS), 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 s i (i51,2, . . . M ) to the staggered moment of the planes. Our result for the zero-point energy ~for M.2! up to the sixth order in j5J' /J is E~$si%!5E11CEG~j 6/S!F22s1s322sM22sM12( i51 M22 sisi1223( i51 M23 sisi11si12si13G, where C.0 and E1 are constants independent of the s’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 s-dependent contribution at order j/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, s-dependent terms first appear at order 1/S and these also favor antiferromagnetic coupling of alternate planes.