Quasi-one-dimensional antiferromagnetism and multiferroicity in CuCrO$_4$*

The bulk magnetic properties of the new quasi-one-dimensional Heisenberg antiferromagnet, CuCrO$_4$, were characterized by magnetic susceptibility, heat capacity, optical spectroscopy, EPR and dielectric capacitance measurements and density functional evaluations of the intra- and interchain spin exchange interactions. We found type-II multiferroicity below the N\'{e}el temperature of 8.2(5)~K, arising from competing antiferromagnetic nearest-neighbor ($J_{\rm nn}$) and next-nearest-neighbor ($J_{\rm nnn}$) intra-chain spin exchange interactions. Experimental and theoretical results indicate that the ratio $J_{\rm nn}$/$J_{\rm nnn}$ is close to 2, putting CuCrO$_4$ in the vicinity of the Majumdar-Ghosh point. First low-temperature neutron powder diffraction data are consistent with a canted magnetic structure below $\sim$8 K.