## Department of Physics Papers

#### Document Type

Journal Article

#### Date of this Version

8-1-1998

#### Publication Source

Physical Review B

#### Volume

58

#### Issue

6

#### Start Page

3144

#### Last Page

3159

#### DOI

10.1103/PhysRevB.58.3144

#### Abstract

We consider the quantum Heisenberg antiferromagnet on a face-centered-cubic lattice in which *J*, the second-neighbor (intrasublattice) exchange constant, dominates *J′*, the first-neighbor (intersublattice) exchange constant. It is shown that the continuous degeneracy of the classical ground state with four decoupled (in a mean-field sense) simple cubic antiferromagnetic sublattices is removed so that at second order in *J′/J* the spins are collinear. Here we study the degeneracy between the two inequivalent collinear structures by analyzing the contribution to the spin-wave zero-point energy which is of the form *H*_{eff}/*J*=*C*_{0}+*C*_{4}σ_{1}σ_{2}σ_{3}σ_{4}(*J′/J*)^{4}+O(*J′/J*)^{5}, where σ_{i} specifies the phase of the *i*th collinear sublattice, *C*_{0} depends on *J′/J* but not on the σ’s, and *C*_{4} is a positive constant. Thus the ground state is one in which the product of the σ’s is −1. This state, known as the *second kind of type A*, is stable in the range |*J′*|<2|*J*| for large *S*. Using interacting spin-wave theory, it is shown that the main effect of the zero-point fluctuations is at small wave vector and can be well modeled by an effective biquadratic interaction of the form Δ*E*_{Q}^{eff}=−1/2*Q*∑_{i,j}[S(*i*)⋅S(*j*)]^{2}/*S*^{3}. This interaction opens a spin gap by causing the extra classical zero-energy modes to have a nonzero energy of order *J′*√*S*. We also study the dependence of the zero-point spin reduction on *J′/J* and the sublattice magnetization on temperature. The resulting experimental consequences are discussed.

#### Recommended Citation

Yildirim, T.,
Harris, A.,
&
Shender, E. F.
(1998).
Frustration and Quantum Fluctuations in Heisenberg fcc Antiferromagnets.
*Physical Review B,*
*58*
(6),
3144-3159.
http://dx.doi.org/10.1103/PhysRevB.58.3144

**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 Tel Aviv University, Tel Aviv, Israel. Currently, he is a faculty member in the Physics Department at the University of Pennsylvania.