Correlation-driven phonon renormalization and the equation of state of 𝛾-cerium

Cerium is one of the strangest metals in the periodic table. Cool it down or squeeze it, and it can suddenly collapse by about 15% in volume — then warm it back up and it swells out again, all without ever changing its crystal structure. Physicists have puzzled over this behaviour for decades, because it comes down to the collective quantum behaviour of the metal’s electrons, which conventional theories struggle to capture.

In this work, we tackled a piece of the puzzle that had been largely overlooked: the role of atomic vibrations. Every solid is constantly jiggling, and those vibrations carry energy that helps decide which form of a material is stable. We combined a state-of-the-art method for treating cerium’s tricky electrons (dynamical mean-field theory) with a calculation of how the atoms vibrate — and, crucially, allowed the two to influence each other.

The surprise was that the electrons reshape the vibrations in a counterintuitive way. Where the simpler theory predicts the vibrations should soften as the metal expands, the fuller treatment shows certain vibrations actually stiffen instead. Once this feedback is included, our prediction for cerium’s size falls almost exactly on the experimental value — something that had eluded simpler approaches.

Beyond cerium itself, the method offers a general recipe for predicting the stability of a whole family of complex materials — including the lanthanides and actinides relevant to magnets, nuclear fuels, and energy technologies — where the interplay between electrons and atomic vibrations matters.

The work was a collaboration between TYC members at King’s College London, and University of Cambridge, the Slovak Academy of Sciences, UCLouvain, TU Wien, and FZU – the Institute of Physics of the Czech Academy of Sciences. 

https://journals.aps.org/prb/abstract/10.1103/zm4r-vs8j#s2

Authors: Yao Wei, Siyu Chen, Evgeny Plekhanov, Ivan Štich, Cedric Weber, and Jan M. Tomczak