$\mathrm{<ruby><rb>\alpha </rb><rt>あるふぁ</rt></ruby>}$-CaCr${}_2$O${}_4$ is a distorted triangular antiferromagnet. The magnetic Cr${}^{3+}$ ions, which have spin-3$/$2 and interact with their nearest neighbors via Heisenberg direct exchange interactions, develop long-range magnetic order below $T_N=42.6$ K. Powder and single-crystal neutron diffraction reveal a helical magnetic structure with ordering wave vector $\mathbf{k}=(0,\sim 1/3,0)$ and angles close to ${120}^{\circ }$ between neighboring spins. Spherical neutron polarimetry unambiguously proves that the spins lie in the $ac$ plane perpendicular to $\mathbf{k}$. The magnetic structure is therefore that expected for an ideal triangular antiferromagnet where all nearest-neighbor interactions are equal, in spite of the fact that $\mathrm{<ruby><rb>\alpha </rb><rt>あるふぁ</rt></ruby>}$-CaCr${}_2$O${}_4$ is distorted with two inequivalent Cr${}^{3+}$ ions and four different nearest-neighbor interactions. By simulating the magnetic order as a function of these four interactions, it is found that the special pattern of interactions in $\mathrm{<ruby><rb>\alpha </rb><rt>あるふぁ</rt></ruby>}$-CaCr${}_2$O${}_4$ stabilizes ${120}^{\circ }$ helical order for a large range of exchange interactions.

• Received 16 February 2011

DOI:https://doi.org/10.1103/PhysRevB.84.054452