Abstract
The crystal and magnetic structures of the $S=\frac{3}{2}$ antiferromagnet $\ensuremath{\beta}{\text{-CaCr}}_{2}{\text{O}}_{4}$ have been investigated by means of specific heat, magnetization, muon relaxation, and neutron powder diffraction between 300 and 1.5 K. In this compound, in which the unusual topology of the ${\text{Cr}}^{3+}$ magnetic lattice can be described as a network of triangular ``zigzag'' ladders with legs parallel to $c$, a complex antiferromagnetic ordering with an incommensurate propagation vector $\mathbf{k}=(0,0,q)$ ($q\ensuremath{\sim}0.477$ at 1.5 K) is evidenced below ${T}_{\text{N}}=21\text{ }\text{K}$. This complex magnetic ordering can be described as a honeycomblike arrangement of cycloids, running along $c$, and presenting a unique pattern of staggered chirality. To understand the experimental observation of this staggered chirality, we propose to use antisymmetric Dzyaloshinskii-Moriya terms in the exchange Hamiltonian.
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