Can Frustration Preserve a Quasi-Two-Dimensional Spin Fluid?

TL;DR

This paper demonstrates that geometric frustration does not maintain a quasi-two-dimensional spin fluid due to quantum-mechanical couplings arising from order from disorder and magnon pair tunneling, even in classical XY models.

Contribution

It reveals that frustration cannot prevent interlayer coupling in quantum spin systems, highlighting the role of quantum tunneling mechanisms like magnon pair tunneling.

Findings

Quantum tunneling induces interlayer coupling despite frustration.

Biquadratic spin coupling can be as large as in-plane coupling.

Classical XY models can form sliding phases, but quantum effects destabilize them.

Abstract

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 anti-ferromagnet, spin layers innevitably 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 a biquadratic spin coupling between layers, and for quantum spins, these coupling terms are as large as the inplane coupling. 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.