Nonexistence of the s − f volume-collapse transition in solid gadolinium at pressure

Gadolinium has long been believed to undergo a high-pressure phase transition with a volume collapse around 5%. Theoretical explanations have focused on the idea of electrons transferring from the extended $s$-orbital to the compact $f$-orbital. However, experimental measurement has been unable to detect any associated change in the magnetic properties of the $f$-electrons [Fabbris et al., Phys. Rev. B 88, 245103 (2013)]. Here we resolve this discrepancy by showing that there is no significant volume collapse, beyond what is typical in high-pressure phase transformations. We present density functional theory calculations of solid gadolinium under high pressure using a range of methods, and revisit the experimental situation using x-ray diffraction (XRD). The standard lanthanide pressure-transformation sequence involving different stackings of close-packed planes $hcp\ensuremath{\rightarrow}9R\ensuremath{\rightarrow}\mathit{dhcp}\ensuremath{\rightarrow}\mathit{fcc}\ensuremath{\rightarrow}\mathit{d}\ensuremath{-}\mathit{fcc}$ is reproduced. The so-called ``volume-collapsed'' high-pressure phase is shown to be an unusual stacking of close-packed planes, with $\mathit{Fddd}$ symmetry and a density change of less than 2%. The distorted fcc (d-fcc) structure is revealed to arise as a consequence of antiferromagnetism. The theoretical results are shown to be remarkably robust to various treatments of the $f$-electrons. The key result is that there is no XRD evidence for volume collapse in gadolinium. The sequence of phase transitions is well described by standard density functional theory. There is no need for special treatment of the $f$-electrons or evidence of $f$-electron bonding. Noting that in previous spectroscopic evidence there is no change in the $f$-electrons we conclude that high-pressure gadolinium has no complicated $f$-electron physics such as Mott-Hubbard, Kondo, or valence transitions.