Electronic and magnetic properties of light rare-earth cubic Laves compounds derived from x-ray magnetic circular dichroism

This work presents electronic and magnetic properties of selected members in the cubic Laves phase series ${\mathrm{Nd}}_{1\ensuremath{-}x}{\mathrm{Pr}}_{x}\mathrm{CoNi}$ (0 $\ensuremath{\le} x \ensuremath{\le}$ 1) and ${\mathrm{Ce}}_{0.25}{\mathrm{Pr}}_{0.75}\mathrm{CoNi}$, together with the corresponding binary compositions (${\mathrm{NdCo}}_{2}, {\mathrm{NdNi}}_{2}, {\mathrm{PrCo}}_{2}, {\mathrm{PrNi}}_{2}, {\mathrm{CeCo}}_{2}, {\mathrm{CeNi}}_{2}$), using soft x-ray absorption spectroscopy, x-ray magnetic circular dichroism (XMCD), density-functional theory, and crystal field multiplet calculations. All transition-metal moments saturate below 1 T, while the rare-earth moments do not saturate even at 5 T, consistent with van Vleck paramagnetic contributions and crystal field suppression. While the sum rules are widely used to extract element-specific magnetic moments from XMCD, we show that for $3d$ transition metals, their application requires accurate estimates of the number of unoccupied $3d$ states. We observe a finite magnetic moment on Ni, challenging the common assumption of its nonmagnetic character in Laves phases. The orbital magnetic moments were determined using the spin rules, while the spin moments were estimated from single-ion values from multiplet calculations, due to the invalidity of the spin sum rule for light rare-earth elements. The magnetic moments of Nd and Pr are found to be suppressed relative to their free-ion values, with multiplet theory indicating that this is due to crystal field effects. Our results confirm that Nd and Pr maintain localized $4{f}^{3}$ and $4{f}^{2}$ configurations, respectively, and that their element-specific magnetic moments are robust to rare-earth substitution. Ce, on the other hand, exhibits a tuneable mixed-valent ground state with both magnetic $4{f}^{1}$ and nonmagnetic $4{f}^{0}$ components. The relative fraction of these states varies with the electronegativity of the surrounding $3d$ transition metals, revealing a pathway to tune Ce magnetism via composition. This work establishes a framework for accurately interpreting XMCD in light rare-earth-based intermetallics and provides insight for designing light rare-earth-based magnetocaloric materials.