Frustration and quantum fluctuations in Heisenberg fcc antiferromagnets

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)sigma(1)sigma(2)sigma(3)sigma(4)(J'/J)(4) + O(J'/J)(5), where sigma(1) specifies the phase of the i th collinear sublattice, Co depends on J'/J but not on the a's, and C-4 is a positive constant. Thus the ground state is one in which the product of the sigma'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 call be well modeled by an effective biquadratic interaction of the form Delta E-Q(eff) = - 1/2 Q Sigma(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' root 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.