Magnetic anisotropy and orbital angular momentum in the orbital ferrimagnet ${\mathrm{CoMnO}}_3$

We investigated the temperature dependence of the saturation magnetization $M_S\left(T\right)$ and magnetic anisotropy constant $K_u\left(T\right)$ of ${\mathrm{CoMnO}}_3$ with an ilmenite structure, which is known as an orbital ferrimagnet. Because of strong antiferromagnetic coupling between the ${\mathrm{Co}}^{2+}$ spin $(d^7\text{:}S=3/2)$ and ${\mathrm{Mn}}^{4+}$ spin $(d^3\text{:}S=3/2)$ in ${\mathrm{CoMnO}}_3$, the net magnetic moment is considered to originate only from the orbital angular momentum [(OAM); $\langle L\rangle \approx 1]$ of ${\mathrm{Co}}^{2+}$. Experimental results for ${\mathrm{CoMnO}}_3$ epitaxial films clearly show that $K_u\left(T\right)$ is proportional to $M_S\left(T\right)$ for a wide temperature range up to the transition temperature, suggesting that $K_u\left(T\right)$ is proportional to $\langle L\rangle$. An electron theory based on the cluster model for $K_u$ and the OAM of ${\mathrm{Co}}^{2+}$ at 0 K also indicates that $K_u$ is proportional to the OAM and to the orbital angular anisotropy of ${\mathrm{Co}}^{2+}$.

Figure 1

Temperature dependence of $M-H$ loops of a CMO film. $M_S$ values were determined by the total magnetic moment divided by the intrinsic volume, excluding the dead layer thickness.

Figure 2

The temperature dependence of the film from Ref. [21] and Eq. (2).

Figure 3

Temperature dependence of the magnetotorque curve of the film.

Figure 4

The temperature dependence of $M_S(=\langle L\rangle$) versus the $K_u$ plot.

Figure 5

The relation between the $t_{2g}$ orbital and ${\lambda }_c$. Lines of the same color represent the same orbit, open symbols denote the $\mathit{M}\parallel c$ axis, and closed symbols denote the $\mathit{M}\parallel ab$ plane.

Figure 6

The relations between ${\lambda }_c$ versus (a) $L_x,L_z$, and (b) $\mathrm{\Delta }L$ of both cations. (c) The relation between ${\lambda }_c$ versus $\mathrm{\Delta }E$. (d) The relation between $\mathrm{\Delta }L$ and $\mathrm{\Delta }E$ of ${\mathrm{Co}}^{2+}$, and the inset shows $L_x$ versus $\mathrm{\Delta }E$.