Magnetic Ordering in the Frustrated Heisenberg Chain System CuCl$_2$

We report a detailed examination the magnetic structure of anhydrous cupric chloride CuCl$_2$ carried out by powder neutron diffraction, magnetic susceptibility and specific heat measurements as well as an evaluation of the spin exchange interactions by first principles density functional theory (DFT) calculations. Anhydrous CuCl$_2$ shows one dimensional antiferromagnetic behavior and long range antiferromagnetic ordering below a N$\acute{\rm e}$el temperature of 23.9 K. Neutron powder and single crystal diffraction reveal that, below 23.9 K, CuCl$_2$ undergoes a phase transition into an incommensurate magnetic structure (propagation vector (1,0.2257,0.5) with a spin-spiral propagating along $b$ and the moments confined in the $bc$ crystallographic plane. Our DFT calculations show that the spin-spiral results from competing ferromagnetic nearest neighbor and antiferromagnetic next-nearest neighbor spin-exchange interaction along the spin chains. Implications for possible multiferroic behavior of CuCl$_2$ are discussed.