are coupled by nearest-neighbor exchange $J''$. Crystallographic $a$,$b$,$c$ axes are indicated.[]{data-label="fig: planar_lattice"}](planar_lattice.pdf){width="0.7\columnwidth"}

The relative smallness of the couplings other than $J$ suggests that one may perhaps fruitfully regard this Hamiltonian as one of Heisenberg spin chains along the $b$ axis defined by $J$, which are weakly coupled together by the remaining interactions.[@nersesyan1998; @bocquet2001] This point of view was validated in Refs. , where it was shown that much of the observed low energy ordering [*and*]{} the high energy inelastic neutron scattering data on [[Cs$_2$CuCl$_4$]{}]{} can be calculated starting from known exact results for 1d Heisenberg chains. Indeed, numerical approaches in Refs. showed that, due to frustration, the diagonal interaction may be as large as $J'/J < 0.7$ while still retaining approximate quasi-one-dimensionality.

While this approach has been quite successful for [[Cs$_2$CuCl$_4$]{}]{}, most notably in directly confronting data [*without any adjustable parameters*]{}, there remain some puzzling features in the experiments. One of the most striking ones is the drastic difference in the low temperature phase diagrams of the material in magnetic fields aligned along the three different principle axes of the crystal. Though some aspects of these differences were explained in Ref. , based upon the “standard” model in Eq. (\[eq:Hexpt\]), 