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 stabilizes a collinear magnetic order with the propagation wave vector q=2π(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 2π(0,δ,1).