ScholarlyCommons

Title

Three-Dimensional Ordering in bct Antiferromagnets Due to Quantum Disorder

Author(s)

Taner Yildirim, University of PennsylvaniaFollow
A. Brooks Harris, University of PennsylvaniaFollow
Eugene F. Shender

Document Type

Journal Article

Date of this Version

3-1-1996

Publication Source

Physical Review B

Volume

53

Issue

10

Start Page

6455

Last Page

6476

DOI

10.1103/PhysRevB.53.6455

Abstract

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 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 in j=J_⊥/J is E({σ_i}) =E₁+CE_G(j⁶/S)[-2σ₁σ₃-2σ_M−2σ_M+2∑_{i =1}^M-2σ_iσ_i+2-3∑_i=1^M-3σ_iσ_i+1σ_i+2σ_i+3],

where C>0 and E₁ are constants independent of the σ’s, and E_G 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.

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.

Recommended Citation

Yildirim, T., Harris, A., & Shender, E. F. (1996). Three-Dimensional Ordering in bct Antiferromagnets Due to Quantum Disorder. Physical Review B, 53 (10), 6455-6476. http://dx.doi.org/10.1103/PhysRevB.53.6455