Broken parity and a chiral ground state in the frustrated magnet CdCr2O4

We present a model describing the lattice distortion and incommensurate magnetic order in the spinel $\mathrm{Cd}{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$, a good realization of the Heisenberg ``pyrochlore'' antiferromagnet. The magnetic frustration is relieved through the spin-Peierls distortion of the lattice involving a phonon doublet with odd parity. The distortion stabilizes a collinear magnetic order with the propagation wave vector $\mathbf{q}=2\ensuremath{\pi}(0,0,1)$. The lack of inversion symmetry makes the crystal structure chiral. The handedness is transferred to magnetic order by the relativistic spin-orbit coupling: the collinear state is twisted into a long spiral with the spins in the $ac$ plane and $\mathbf{q}$ shifted to $2\ensuremath{\pi}(0,\ensuremath{\delta},1)$.