Frustration and quantum fluctuations in Heisenberg fcc antiferromagnets

Abstract

We consider the quantum Heisenberg antiferromagnet on a face-centered-cubic lattice in which J, the secondneighbor (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 ith 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 ΔE Q eff =−1/ 2Q∑ 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. Disciplines Physics | Quantum Physics CommentsAt 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. We consider the quantum Heisenberg antiferromagnet on a face-centered-cubic lattice in which J, the second-neighbor ͑intrasublattice͒ exchange constant, dominates JЈ, the first-neighbor ͑intersublattice͒ exchange constant. It is shown that the continuous degeneracy of the classical ground state with four decoupled ͑in a mean-field sense͒ simple cubic antiferromagnetic sublattices is removed so that at second order in JЈ/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 /JϭC 0 ϩC 4 1 2 3 4 (JЈ/J) 4 ϩO(JЈ/J) 5 , where i specifies the phase of the ith collinear sublattice, C 0 depends on JЈ/J but not on the 's, and C 4 is a positive constant. Thus the ground state is one in which the product of the 's is Ϫ1. This state, known as the second kind of type A, is stable in the range ͉JЈ͉Ͻ2͉J͉ 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 ⌬E Q eff ϭϪ 1 2 Q͚ 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 ...

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