## Department of Physics Papers

#### 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 *J ^{2}*

_{⊥}

*/(J*, where

^{2}S)*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}}) =

*E*

_{1}+

*CE*

_{G}(j^{6}/

*S*)[-2σ

_{1}σ

_{3}-2σ

_{M−2}σ

_{M}+2∑

_{i =1}

^{M-2}σ

_{i}σ

_{i+2}-3∑

_{i=1}

^{M-3}σ

_{i}σ

_{i+1}σ

_{i+2}σ

_{i+3}],

where *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*<

*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.

#### 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

**Date Posted:** 12 August 2015

This document has been peer reviewed.

## 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.