Failure of geometric frustration to preserve a quasi-two-dimensional spin fluid

Using spin-wave theory, we show that geometric frustration fails to preserve a two-dimensional spin fluid. Even though frustration can remove the interlayer coupling in the ground state of a classical antiferromagnet, spin layers inevitably develop a quantum-mechanical coupling via the mechanism of order from disorder. We show how the order from disorder coupling mechanism can be viewed as a result of magnon pair tunneling, a process closely analogous to pair tunneling in the Josephson effect. In the spin system, the Josephson coupling manifests itself as a biquadratic spin coupling between layers, and for quantum spins, these coupling terms become comparable with the in-plane coupling terms. An alternative mechanism for decoupling spin layers occurs in classical XY models in which decoupled sliding phases of spin fluid can form in certain finely tuned conditions. Unfortunately, these finely tuned situations appear equally susceptible to the strong-coupling effects of quantum tunneling, forcing us to conclude that, in general, geometric frustration cannot preserve a two-dimensional spin fluid.