The effect of quantum fluctuations on the ferromagnetic-helix transition in a Heisenberg tetragonal lattice with competing in-plane interactions

Perturbative treatments of quantum fluctuations in Heisenberg helimagnets starting from the classical approximation fail because for S to infinity the spin wave is well defined only for a fixed helix wavevector Q. Recently an exact T-matrix evaluation of the contribution to the ground-state energy from long-wavelength quantum fluctuations near the classical ferromagnetic-helix (F-H) transition line was performed in order to discuss the zero-temperature phase diagram in the j₂-J₃ plane, where j₂ (j₃) sets the scale of second (third) neighbour interactions in the basal plane. For the hexagonal lattice it was shown that quantum fluctuations could change from second to first order the F-H transition near the F-AF-H classical triple point, where AF denotes antiferromagnet. Here the authors give analogous calculations on a tetragonal lattice, which show unexpected lattice-dependent features. In addition to a behaviour similar to that found on the hexagonal lattice near the F-AF-H triple point, the change of the order of transition is found also on a semi-infinite part of the classical F-H phase boundary.