Nature of Magnetism in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Ca</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>Co</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:math>

We find using local spin density approximation + Hubbard U band structure calculations that the novel one-dimensional cobaltate Ca3Co2O6 is not a ferromagnetic half-metal but a Mott insulator. Both the octahedral and the trigonal Co ions are formally trivalent, with the octahedral being in the low-spin and the trigonal in the high-spin state. The inclusion of the spin-orbit coupling leads to the occupation of the minority-spin d2 orbital for the unusually coordinated trigonal Co, producing a giant orbital moment (1.57 microB). It also results in an anomalously large magnetocrystalline anisotropy (of order 70 meV), elucidating why the magnetism is highly Ising-like. The role of the oxygen holes, carrying an induced magnetic moment of 0.13 microB per oxygen, for the exchange interactions is discussed.