Magnetism in parent iron chalcogenides: quantum fluctuations select plaquette order.

We analyze magnetic order in Fe chalcogenide Fe(1+y)Te, the parent compound of the high-temperature superconductor Fe(1+y)Te(1-x)Se(x). Experiments show that magnetic order in this material contains components with momentum Q(1)=(π/2,π/2) and Q(2)=(π/2,-π/2) in the Fe only Brillouin zone. The actual spin order depends on the interplay between these two components. Previous works assumed that the ordered state has a single Q (either Q(1) or Q(2)). In such a state, spins form double stripes along one of the diagonals breaking the rotational C(4) symmetry. We show that quantum fluctuations actually select another order-a double Q plaquette state with equal weight of Q(1) and Q(2) components, which preserves C(4) symmetry. We argue that the order in Fe(1+y)Te is determined by the competition between quantum fluctuations and magnetoelastic coupling.