Origin of magnetic anisotropy in doped ${\mathbf{Ce}}_2{\mathbf{Co}}_{17}$ alloys

Magnetocrystalline anisotropy (MCA) in doped ${\mathrm{Ce}}_2{\mathrm{Co}}_{17}$ and other competing structures was investigated using density functional theory. We confirmed that the MCA contribution from dumbbell Co sites is very negative. Replacing Co dumbbell atoms with a pair of Fe or Mn atoms greatly enhance the uniaxial anisotropy, which agrees quantitatively with experiment, and this enhancement arises from electronic-structure features near the Fermi level, mostly associated with dumbbell sites. With Co dumbbell atoms replaced by other elements, the variation of anisotropy is generally a collective effect and contributions from other sublattices may change significantly. Moreover, we found that Zr doping promotes the formation of 1-5 structure that exhibits a large uniaxial anisotropy, such that Zr is the most effective element to enhance MCA in this system.

Figure 1

Experimental anisotropy fields $H_{\text{A}}$ in ${\mathrm{Ce}}_2{T}_x{\mathrm{Co}}_{17-x}$ with $T=\mathrm{Al}$ [6, 7], Si [6, 8], Ga [6, 9], Zr [10], Hf [10], V [5], Cr [5], Mn [5, 11], Fe [5], and Cu [5].

Figure 2

Schematic crystal structures of (a) ${\mathrm{CeCo}}_5$, (b) hexagonal $H-{\mathrm{Ce}}_2{\mathrm{Co}}_{17}$, and (c) rhombohedral $R-{\mathrm{Ce}}_2{\mathrm{Co}}_{17}$. Ce atoms are indicated with large (yellow or magenta colored) spheres. Co atoms are denoted by Wyckoff sites. Dumbbell (red) sites are denoted in $H-{\mathrm{Ce}}_2{\mathrm{Co}}_{17}$ ($4f$ sites) and in $R-{\mathrm{Ce}}_2{\mathrm{Co}}_{17}$ ($6c$ sites), and indicated further by arrows and label. We use larger cells for ${\mathrm{CeCo}}_5$ and $R-{\mathrm{Ce}}_2{\mathrm{Co}}_{17}$ to compare with $H-{\mathrm{Ce}}_2{\mathrm{Co}}_{17}$.

Figure 3

Magnetic anisotropy in ${\mathrm{Ce}}_2{T}_2{\mathrm{Co}}_{15}$ and ${\mathrm{Ce}}_{0.66}{T}_{0.33}{\mathrm{Co}}_5$ with $T=\mathrm{Ti}$, V, Cr, Mn, Fe, Co, Ni, Cu, Zr, and Hf. In ${\mathrm{Ce}}_2{T}_2{\mathrm{Co}}_{15}, T$ atoms occupy the dumbbell sublattice. The ${\mathrm{Ce}}_{0.66}{T}_{0.33}{\mathrm{Co}}_5$ structure was obtained by replacing the pair of dumbbell Co atoms in the original ${\mathrm{Ce}}_2{\mathrm{Co}}_{17}$ with a single $T$ atom. $K$ values derived from experimental $H_{\text{A}}$ measurements [5, 11] by using $K=\frac{1}{2}{\mu }_0{M}_{\text{s}}{H}_{\text{A}}$ are also shown.

Figure 4

Anisotropy of the scaled onsite SOC energy $K_{\text{so}}$ in ${\mathrm{Ce}}_2{T}_2{\mathrm{Co}}_{15}$ and its contributions from the dumbbell sublattice $T$($6c$) and the rest sublattices.

Figure 5

(a) Site-resolved anisotropy of the onsite SOC energy $K_{\text{so}}$ and (b) orbital-resolved $K_{\text{so}}(6c$) in ${\mathrm{Ce}}_2{\mathrm{Co}}_{17-x}{T}_x$ with $T=\mathrm{Co}$, Fe, and Mn.

Figure 6

The scalar-relativistic partial density of states projected on the $3d$ states of $T$ sites in $R–{\mathrm{Ce}}_2{T}_2{\mathrm{Co}}_{15}$ with $T=\mathrm{Co}$, Fe, and Mn. $T$ atoms occupy the dumbbell ($6c$) sites.