spins precess in the same sense on all chains within a plane. For fields along $a$, however, this sense alternates between successive vertical layers, owing to the staggering of $D$. Within a single layer, cone states for fields along other axes are identical to this one after a global spin rotation.[]{data-label="fig:cone-state"}](conea_gray.pdf){width="0.95\columnwidth"}

![A single layer of the AF state, illustrated for a field along the $b$ axis. The spins lie in a plane spanned by the $b$ axis and a second axis within the $a-c$ plane but at a non-zero angle to both the $a$ and $c$ axes. The component of the spin normal to $b$ is antiparallel on successive even (or odd) chains, so that the patten has period $\Delta y=4$ along the $c$ axis. This corresponds to a doubled cystallographic unit cell in this direction.[]{data-label="fig:af-state"}](afb_gray.pdf){width="0.95\columnwidth"}

![A single layer of the IC state, illustrated for a field along the $c$ axis. Circles with arrows indicate the sense of precession of the spins, as one moves along the $x$ axis. This is most easily seen intuitively by comparing every other spin, which compensates for the natural staggering due to the underlying Néel correlations of the 1d chains. Note that in the 