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) exchan ge constant, dominates J', the first-neighbor (intersublattice) exchan ge constant. It is shown that the continuous degeneracy of the classic al ground state with four decoupled (in a mean-field sense) simple cub ic antiferromagnetic sublattices is removed so that at second order in J'/J the spins are collinear. Here we study the degeneracy between th e 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 sig ma(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 s tate, 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 th at the main effect of the zero-point fluctuations is at small wave vec tor and call be well modeled by an effective biquadratic interaction o f 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-ener gy modes to have a nonzero energy of order J' root S. We also study th e dependence of the zero-point spin reduction on J'/J and the sublatti ce magnetization on temperature. The resulting experimental consequenc es are discussed.