Temperature-dependent magnetocrystalline anisotropy of rare earth/transition metal permanent magnets from first principles: The light $R{\mathrm{Co}}_5 (R=\mathrm{Y}, \text{La-Gd})$ intermetallics

Computational design of more efficient rare earth/transition metal (RE-TM) permanent magnets requires accurately calculating the magnetocrystalline anisotropy (MCA) at finite temperature, since this property places an upper bound on the coercivity. Here, we present a first-principles methodology to calculate the MCA of RE-TM magnets which fully accounts for the effects of temperature on the underlying electrons. The itinerant electron TM magnetism is described within the disordered local moment picture, and the localized RE-$4f$ magnetism is described within crystal field theory. We use our model, which is free of adjustable parameters, to calculate the MCA of the $R{\mathrm{Co}}_5 (R=\mathrm{Y}, \text{La-Gd})$ magnet family for temperatures 0–600 K. We correctly find a huge uniaxial anisotropy for ${\mathrm{SmCo}}_5$ ($21.3\text{MJ}{\text{m}}^{-3}$ at 300 K) and two finite temperature spin reorientation transitions for ${\mathrm{NdCo}}_5$. The calculations also demonstrate dramatic valency effects in ${\mathrm{CeCo}}_5$ and ${\mathrm{PrCo}}_5$. Our calculations provide quantitative, first-principles insight into several decades of RE-TM experimental studies.

Figure 1

Preferred orientation of RE-$4f$ charge clouds (with magnetic moments indicated by arrows) for Nd and Sm in the ${R\mathrm{Co}}_5$ crystal field, shown on the contour plot. The Co and RE atoms are shaded in gray and purple, respectively. Repulsive (attractive) corresponds to high (low) potential energy.

Figure 2

Experimental anisotropy constants ${\kappa }_1$ (and ${\kappa }_2$ for ${\mathrm{NdCo}}_5$) [30] of ${R\mathrm{Co}}_5$, compared to the current calculations.

Figure 3

Evolution of the easy magnetization direction $\alpha$ in ${\mathrm{NdCo}}_5$, as reported experimentally [31] and calculated here.

Figure 4

Comparison of experimental and calculated anisotropy constants for ${\mathrm{CeCo}}_5$ and ${\mathrm{PrCo}}_5$. Values are shown for both itinerant and localized (RE in $3+$ state) $4f$ electrons, with the ground state predicted by the LSIC calculations shown in the darker color.