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 CdCr2O4, 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 stablizes a collinear magnetic order with the propagation wavevector q=2\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 q shifted to 2\pi(0,\delta,1). 
Gia-Wei Chern, C. J. Fennie, and O. Tchernyshyov