Nature of Magnetism in ${\mathrm{Ca}}_3{\mathrm{Co}}_2{\mathrm{O}}_6$

We find using $\mathrm{\text{local spin density approximation}}+\mathrm{\text{Hubbard}}$ $\mathrm{U}$ band structure calculations that the novel one-dimensional cobaltate ${\mathrm{Ca}}_3{\mathrm{Co}}_2{\mathrm{O}}_6$ 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 $d_2$ orbital for the unusually coordinated trigonal Co, producing a giant orbital moment ($1.57{\mu }_B$). 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 $0.13{\mu }_B$ per oxygen, for the exchange interactions is discussed.

Figure 1

Density of states (DOS) of ${\mathrm{Ca}}_3{\mathrm{Co}}_2{\mathrm{O}}_6$ in the ferromagnetic half-metallic (FMHM) state from LSDA. The Fermi level is set at zero energy. (a) shows (from upper to lower panels) the total DOS, the ${\mathrm{Co}}_{\mathrm{oct}}$ $3d$, ${\mathrm{Co}}_{\mathrm{trig}}$ $3d$, and O $2p$ partial DOS. (b) shows the ${\mathrm{Co}}_{\mathrm{trig}}$ $3d$ orbitally resolved partial DOS. Solid (dashed) lines depict the spin-up (down) states.

Figure 2

Local crystal field energy diagram for: (left) ${\mathrm{Co}}_{\mathrm{oct}}$ and (right) ${\mathrm{Co}}_{\mathrm{trig}}$ without and with spin-orbit coupling.

Figure 3

Density of states (DOS) of ${\mathrm{Ca}}_3{\mathrm{Co}}_2{\mathrm{O}}_6$ in the ferromagnetic insulating (FMI) state from $\mathrm{LSDA}+\mathrm{U}+\mathrm{SOC}$.

Figure 4

$U$ dependence of the insulating gap (top panel), as well as of the spin and orbital contributions to the ${\mathrm{Co}}_{\mathrm{trig}}$ magnetic moment (bottom panel).