Characterisation of the quantum helix in Heisenberg models

Unexpected features in helimagnets are produced by quantum fluctuations. On hexagonal and tetragonal lattices with competing in-phase interactions up to third-nearest neighbours, the zero-temperature phase diagram, obtained in the classical approximation, is strongly affected by quantum effects in the neighbourhood of the triple point where ferromagnetic, antiferromagnetic, and helical phases coexist. The ferromagnetic configuration turns out to be unstable against long-wavelength quantum fluctuations, allowing a novel helix of quantum origin to have its onset and the corresponding ferro-helix phase transitions to become first order. This result has been obtained by an exact evaluation of the ground-state energy within Q⁴ contributions. However, the value of the helic wavevector Q cannot be obtained by such a calculation. Here the authors give this wavevector as a function of the Hamiltonian parameters by evaluating at leading order in 1/S the Q⁶ contributions to the ground-state energy. Their result is consistent with the assumption that the quantum helix wavevector is small.