Abstract
We investigated the structural, electronic, magnetic, and phonon properties of ${\mathrm{Pu}}_{3}M$, where $M$ = Al, Ga, In, and Tl, using first-principles calculations with the spin-orbit coupling taken into consideration. All four compounds are found to contain transverse phonons along [011] and [111] that remarkably soften at the boundaries of the first Brillouin zone, corresponding to the $\mathrm{M}$ and $\mathrm{R}$ points. Through detailed analyses of the vibrational modes and bond strengths, we reveal that all four types of $M$ atoms have softer bonding with neighboring Pu than Pu-Pu bond, which accounts for the phonon softening and may shed light on the $\ensuremath{\delta}$-stabilization of Pu by trivalent metal doping. In addition, we find that, due to the missing $p\text{\ensuremath{-}}d$ hybridization, ${\mathrm{Pu}}_{3}\mathrm{Al}$ behaves quite differently from the other three ${\mathrm{Pu}}_{3}M$ compounds. For example, ${\mathrm{Pu}}_{3}\mathrm{Al}$ has an unexpected equilibrium volume and high-frequency disentangled optical branches of phonons.
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