Anisotropy and orbital moment in Sm-Co permanent magnets

Structural and magnetic properties of iron-free and iron-substituted $\mathrm{SmC}{\mathrm{o}}_5$ have been investigated theoretically and experimentally. The nanocrystalline ribbons of ${\mathrm{SmCo}}_{5-x}{\mathrm{Fe}}_x\left(0\le x\le 2\right)$, which were produced by rapid solidification, crystallize in the hexagonal $\mathrm{CaC}{\mathrm{u}}_5$ structure for $x\le 0.75$. Small Fe additions $\left(x=0.25\right)$ substantially improve the coercivity, from 0.45 to 2.70 T, which we interpret as combined intrinsic and extrinsic effect. Most of our findings are consistent with past samarium-cobalt research, but some are at odds with findings that have seemingly been well established through decades of rare-earth transition-metal research. In particular, our local spin-density approximation with Hubbard parameter calculations indicate that the electronic structure of the Sm atoms violates Hund's rules and that the orbital moment is strongly quenched. Possible reasons for the apparent disagreement between theory and experiment are discussed. We explicitly determine the dependence of the Sm $4f$ charge distribution, arguing that an accurate density-functional description of $\mathrm{SmC}{\mathrm{o}}_5$ is a challenge to future research.

Figure 1

Unit cell of the hexagonal intermetallic $\mathrm{SmC}{\mathrm{o}}_5$.

Figure 2

XRD analysis of $\mathrm{SmC}{\mathrm{o}}_{5-x}\mathrm{F}{\mathrm{e}}_x$: (a) patterns for $x=0$, 0.25, 0.5, 0.75, and 2 compared with the prototype $\mathrm{CaC}{\mathrm{u}}_5$ structure (vertical lines), (b) expanded view showing peak shift towards lower angles due to Fe addition (vertical dotted lines), and (c) $\mathrm{SmC}{\mathrm{o}}_3\mathrm{F}{\mathrm{e}}_2$ showing mixture of $\mathrm{SmC}{\mathrm{o}}_5$ (vertical solid lines) and $\mathrm{S}{\mathrm{m}}_2\mathrm{C}{\mathrm{o}}_{17}$ (vertical dotted lines).

Figure 3

Hysteresis loops: (a) comparison of $\mathrm{SmC}{\mathrm{o}}_5$ and $\mathrm{SmC}{\mathrm{o}}_{4.75}\mathrm{F}{\mathrm{e}}_{0.25}$ and (b) two-phase loop $\mathrm{SmC}{\mathrm{o}}_3\mathrm{F}{\mathrm{e}}_2$ exhibiting a hard-soft two-phase characteristic.

Figure 4

Coercivity $H_{\mathrm{c}}$ and magnetization (polarization $J_{\mathrm{s}})$ of $\mathrm{SmC}{\mathrm{o}}_{5-x}\mathrm{F}{\mathrm{e}}_x$ as a function of Fe content.

Figure 5

Theoretically calculated magnetocrystalline anisotropies and formation energies of $\mathrm{SmC}{\mathrm{o}}_{5-x}\mathrm{F}{\mathrm{e}}_x$ as a function of Fe content.

Figure 6

Total spin moment and orbital moment of Sm-atom (inset figure) of $\mathrm{SmC}{\mathrm{o}}_{5-x}\mathrm{F}{\mathrm{e}}_x$ as a function of Fe content. The spin moment is opposite in sign with the Sm-$4f$ orbital moment as expected from Hund's rule.

Figure 7

Quenching, charge distribution, and anisotropy (schematic): (a) charge distribution in terms of Stevens coefficients, (b) rare-earth moment in the hard direction, (c) effect of crystal field on the charge distribution for the easy direction, and (d) effect of crystal field on the charge distribution in a hard direction. Bluish regions denote the negative charges of the $\mathrm{S}{\mathrm{m}}^{3+}$ ion (center) and of the Co ligands (small circles).

Figure 8

Charge density ρ as calculated by DFT: (a) easy direction and (b) hard direction. The charge density has ranged from 0 to $1\mathrm{e}/{\AA }^3$.