Intrinsic coercivity induced by valence fluctuations in Ce(Co${1-x}$Cu$x)5$ permanent magnet

In rare-earth permanent magnets, magnetization and Curie temperature are mainly dominated by 3$d$-electrons of Fe-group elements, and magnetic anisotropy at low temperatures arises mostly from 4$f$-electrons, typically as an outcome from the combination of the crystal field effect and the spin-orbit interaction (SOI).
Here we propose enhancement of an intrinsic coercivity due to the valence fluctuation derived from the 4$f$-electrons in Ce-based rare-earth magnets [1]. Valence-fluctuations combined with SOI bring an effective magnetic anisotropy driven by kinetic energy in the hybridization of delocalized 4$f$-electrons and conduction electrons. This kinetic-energy-driven anisotropy has an order of magnitude stronger energy scale than the magnetic anisotropy driven by potential energy of well localized 4$f$-electrons in the crystal fields. The relatively strong coupling between 4$f$-3$d$ electrons make such kinetic-energy driven anisotropy robust against high temperatures. This mechanism of intrinsic magnetic anisotropy is not only scientifically intriguing but also promising for application to permanent magnets.
We employed Ce(Co$_{1-x}$Cu$_x$)$_5$ as an inter-valence Ce-based permanent magnets. It crystalizes in the hexagonal CaCu$_5$ structure, which is one of the most fundamental building blocks of rare-earth permanent magnets. CeCo$_5$ and CeCu$_5$ are prototypical rare-earth ferromagnet with mixed valence state [2] and heavy fermion antiferromagnet with robust trivalent Ce [3], respectively. The Curie temperature is reduced by Cu substitutions, and reaches to zero at $x \sim$ 0.6 [4]. The change of valence state of Ce is also suggested at $x$ ~ 0.5 [4].
Magnetization curves of Ce(Co$_{1-x}$Cu$_x$)$_5$ $(0 \leq x \leq 0.7)$ were measured at various temperatures. The coercive force $H_c$ = 9 kOe at 300 K reaches 24.6 kOe at 1.9 K for Ce(Co$_{0.7}$Cu$_{0.3})_5$. A remarkable enhancement of intrinsic coercivity was observed in intermediate concentration of $x$ = 0.3 and 0.4 compared to the other ranges of $x$. Concomitantly, the coercivity at $x$ = 0.3 and 0.4 persists to higher temperatures. It indicates an intrinsic coercivity emerged on inter-valence Ce-based permanent magnets.

[1] H. Shishido $et$ $al$., arXiv:2103.10202.
[2] J. H. Wernick and S. Geller, Acta. Cryst. 12, 662 (1959): K. Strant $et$ $al$., J. Appl. Phys. 38, 1001 (1967).
[3] E. Bauer $et$ $al$., J. Magn. Magn. Mater. 63-64, 37 (1987).
[4] D. Girodin $et$ $al$., J. Less Common Metals 110, 149 (1985).