The origin of both the Ising chain magnetism and ferroelectricity in Ca3CoMnO6 is studied by ab initio electronic structure calculations and x-ray absorption spectroscopy. We find that Ca3CoMnO6 has the alternate trigonal prismatic Co 2+ and octahedral Mn 4+ sites in the spin chain. Both the Co 2+ and Mn 4+ are in the high spin state. In addition, the Co 2+ has a huge orbital moment of 1.7 µB which is responsible for the significant Ising magnetism. The centrosymmetric crystal structure known so far is calculated to be unstable with respect to exchange striction in the experimentally observed ↑↑↓↓ antiferromagnetic structure for the Ising chain. The calculated inequivalence of the Co-Mn distances accounts for the ferroelectricity.PACS numbers: 78.70.Dm, 71.27.+a Among a variety of multiferroic materials discovered so far [1,2], ferroelectric Ising chain magnet Ca 3 CoMnO 6 is quite unique, because the ferroelectricity (FE) is driven by exchange striction in a collinear Ising spin chain consisting of the charge ordered transition-metal ions [3]. The spin chain has the alternate trigonal prismatic and octahedral sites [3,4]. Special ↑↑↓↓ antiferromagnetic (AF) structure is detected in Ca 3 CoMnO 6 below T N ≈13 K by neutron diffraction. However, the measured magnetic moment of 0.66 µ B /Co and 1.93 µ B /Mn is much smaller than the expected one of the normal high-spin (HS) Co 2+ (S=3/2) and Mn 4+ (S=3/2). This led Choi et al. to a conclusion that the Co 2+ is (surprisingly) in a low-spin (LS) state [3]. In contrast, the effective magnetic moment of µ eff =5.8-6.0 µ B per formula unit (f.u.), extracted from magnetic susceptibility measurements above T N [4,5], suggests that both Co 2+ and Mn 4+ are in a HS state. Thus there is an apparent controversy between those data, and the problem concerning the spin state of, in particular, Co 2+ ions seems to be still unsolved. Another important question is to understand the nature of the Ising magnetism and of the resulting exchange striction, which are apparently crucial for the appearance of FE in Ca 3 CoMnO 6 . To this end, we carried out ab initio electronic structure calculations and x-ray absorption spectroscopy (XAS). We address the important issues including the Co/Mn site preference, their charge/spin/orbital states, the origin of the Ising magnetism, and the exchange striction.Our ab initio calculations were performed by using the full-potential augmented plane waves plus local orbital method (Wien2k code) [6]. We took the experimental centrosymmetric structure data of the rhombohedral lattice (R-3c) which has in a hexagonal setting the lattice constant a=9.1314Å and c=10.5817Å [4,7]. The calculations were done for different magnetic structures (↑↓↑↓, ↑↑↓↓, ↑↓↓↓, and ↑↑↑↑ orderings in the Co-Mn-CoMn chains). To study the exchange striction effect, we investigated the effect of internal atomic relaxation allowing the inversion symmetry to be broken in the ↑↑↓↓ spin chain, as discussed below. The muffin-tin sphere radii are chosen to be 2.4, 2.1 and 1.4 Bohr for ...