Interplay between Jahn-Teller instability, uniaxial magnetism, and ferroelectricity inCa3CoMnO6

${\text{Ca}}_3{\text{CoMnO}}_6$ is composed of ${\text{CoMnO}}_6$ chains made up of face-sharing ${\text{CoO}}_6$ trigonal prisms and ${\text{MnO}}_6$ octahedra. The structural, magnetic, and ferroelectric properties of this compound were investigated on the basis of density-functional theory calculations. ${\text{Ca}}_3{\text{CoMnO}}_6$ is found to undergo a Jahn-Teller distortion associated with the ${\text{CoO}}_6$ trigonal prisms containing high-spin ${\text{Co}}^{2+}$ $\left(d^7\right)$ ions, which removes the ${\text{C}}_3$ rotational symmetry and hence uniaxial magnetism. However, the Jahn-Teller distortion is not strong enough to fully quench the orbital moment of the high-spin ${\text{Co}}^{2+}$ ions thereby leading to an electronic state with substantial magnetic anisotropy. The Jahn-Teller distorted ${\text{Ca}}_3{\text{CoMnO}}_6$ in the magnetic ground state with up-up-down-down spin arrangement is predicted to have electric polarizations much greater than experimentally observed. Implications of the discrepancy between theory and experiment were discussed.