Vector chiral spin liquid phase in absence of geometrical frustration

Making use of detailed classical Monte Carlo simulations, we study the critical properties of a two dimensional planar spin model on a square lattice composed by weakly interacting helimagnetic chains. We find a large temperature window where the vector chirality order parameter, <k_{jk}>=<S_j x S_k>, the key quantity in multiferroic systems, takes nonzero value in absence of long-range order or quasi-long-range order, so that, our model is the first example where, at finite temperatures, a vector chiral spin liquid phase in absence of geometrical frustration is explicitly reported. We also show that the strength of interchain interaction is fundamental in order to obtain the vector chiral spin liquid phase. The relevance of our results for three-dimensional models is also discussed.