Origin of Ising magnetism in Ca$_3$Co$_2$O$_6$ unveiled by orbital imaging

The one-dimensional cobaltate Ca$_3$Co$_2$O$_6$ is an intriguing material having an unconventional magnetic structure, displaying quantum tunneling phenomena in its magnetization. Using a newly developed experimental method, $s$-core-level non-resonant inelastic x-ray scattering ($s$-NIXS), we were able to image the atomic Co 3$d$ orbital that is responsible for the Ising magnetism in this system. We can directly observe that corrections to the commonly accepted ideal prismatic trigonal crystal field scheme occur in Ca$_3$Co$_2$O$_6$, and it is the complex $d_2$ orbital occupied by the sixth electron at the high-spin Co$^{3+}_\text{trig}$ ($d^6$) sites that generates the Ising-like behavior. The ability to directly relate the orbital occupation with the local crystal structure is essential to model the magnetic properties of this system