Most solids are rather incompressible. That is, when squeezed, their volume changes only a little, even if a structural phase transition takes place during the process. By contrast, several Lanthanides exhibit phase transitions under pressure characterized by abnormally large volume changes (14% for Cerium and 9% for Praseodymium). The physical mechanisms responsible for these transitions have been debated since discovery of the Cerium phenomenon over 50 years ago. Currently, there are two main viable conjectures: The first is a ``Mott'' transition in which the 4f electrons are insulating and magnetic at low pressure (large volume) but then become delocalized at high pressure (low volume) when the atomic overlap is increased. The second is a ``Kondo volume collapse'' in which the key feature is a screening of the 4f moments by the valence electrons arising from a rapid change in the 4f--valence electron coupling. In both cases the strongly correlated nature of the 4f electrons is fundamentally implicated.
These theories are at a somewhat unsatisfactory stage. They rely strongly on mean field analysis which can be shown to be qualitatively incorrect at strong electron--electron interaction strength, or they treat a simplified ``impurity model'' which has a single f electron site interacting with a conduction sea. We published a comprehensive review of the central experimental and theoretical issues.
We first improved on existing calculations by studying the three dimensional periodic Anderson model with QMC. Our approach treats the interactions exactly, and also considers a lattice of many f sites, directly addressing two important defects in past analysis. We found that the cross--over to the Kondo singlet regime, where the f electron moments are screened by the conduction electrons, is remarkably sharp at low temperatures, and that the behavior of magnetic correlations is consistently reflected in both the thermodynamics and the density of states. The abruptness of the transition suggests that energy changes associated with the screening of local moments by conduction electrons might be sufficient to drive large volume changes in systems like Cerium.
Next we moved away from such model Hamiltonians and treated Cerium itself within the LDA+DMFT approach. That is, the correct Cerium band structure was fed into an approximation in which the many body correlations are treated with a frequency dependent self-energy (but no momentum dependence). This many body problem was solved with Quantum Monte Carlo. We found that within the correct volume range for the alpha-gamma transition the spectral function develops a Kondo resonance, the local moment undergoes a rapid evolution (but remains well formed on the alpha side of the transition), and that the volume dependence of the energy exhibits a dramatic broadening consistent with the development of a double well structure (which at present we cannot resolve within our error bars).
Finally, we have been interacting closely with a diamond anvil cell group at Lawrence Livermore National Laboratory to examine experimental and theoretical signatures of the changes in the degree of electron correlation with pressure. We have studied transition metal monoxides (MnO), rare earths (Gd), and lithium nitride. As with Cerium, some of the key questions concern the interplay between metal-insulator transitions and the behavior of the magnetic moment. In MnO we showed that a sharp change in the moment coincides with the onset of metalization. However, the situation is a good deal more complex than would be described by a single band Hubbard model. Indeed, the key ingredient seems to be how the relative magnitudes of the crystal field and exchange energies evolve with pressure.
A. McMahan, C. Huscroft, R.T. Scalettar, and E.L. Pollock,
``Volume Collapse transitions in the rare earth metals,''
J. of Computer-Aided Materials Design 5, 131 (1998).
[87.] Carey Huscroft, A.K. McMahan, and R.T. Scalettar,
``Magnetic and Thermodynamic Properties of the Three-Dimensional Periodic Anderson Hamiltonian,''
Phys. Rev. Lett. 82, 2342 (1999).
K. Held, C. Huscroft, R.T. Scalettar, and A.K. McMahan,
"Similarities between the Hubbard and Periodic Anderson Models at Finite Temperatures",
Phys. Rev. Lett. 85, 373 (2000).
[112.] K. Held, A.K. McMahan, and R.T. Scalettar,
``The Cerium Volume Collapse: Results from the LDA+DMFT Approach,''
Phys. Rev. Lett. 87, 276404 (2001).
[114.] K. Held, I.A. Nekrasov, G. Keller, V. Eyert, N. Blumer, A.K.
McMahan, R.T. Scalettar,
T. Pruschke, V.I. Anisimov, and D. Vollhardt,
``The LDA+DMFT Approach to Materials with Strong Electronic Correlations,''
Proceedings of the Winter School on ``Quantum Simulations of Complex Many-Body Systems:
From Theory to Algorithms", eds. J. Grotendorst, D. Marx and A. Muramatsu,
NIC Series Volume 10 (NIC Directors, Forschungszentrum Julich), 175-209 (2002).
[120.] A. K. McMahan, K. Held, and R. T. Scalettar,
"Thermodynamic and spectral properties of compressed Ce calculated by the merger of the
local density approximation and dynamical mean field theory,"
Phys. Rev. B67, 075108 (2003).
[128.] K. Held, I.A. Nekrasov, G. Keller, V. Eyert, N. Blumer, A.K.
McMahan, R.T. Scalettar, Th. Pruschke,
V.I. Anisimov, and D. Vollhardt, Psi-k Newsletter 56, April, 65-103 (2003).
``Realistic investigations of correlated electron systems with LDA+DMFT'',
Psi-k Newsletter 56, April, 65-103 (2003).
[136.] C.S. Yoo, B. Maddox, J.H.P. Klepeis, V. Iota, W. Evans, A.
McMahan, M. Hu, P. Chow,
M. Somayazulu, D. Hausermann, R.T. Scalettar, and W.E. Pickett,
"First-order Isostructural Mott transition in highly-compressed MnO,"
Phys. Rev. Lett. 94, 115502 (2005).
[146.] A. Lazicki, B. Maddox, W. Evans, C.S. Yoo, A.K. McMahan,
W.E. Pickett, R.T. Scalettar,
M.Y. Hu, and P. Chow,
"New cubic phase of lithium nitride to 200 GPa,"
Phys. Rev. Lett. 95, 165503 (2005).
[153.] Deepa Kasinathan, J. Kunes, A. Lazicki, H. Rosner, C.-S. Yoo,
and W.E. Pickett,
"Singular Kohn Anomaly Surfaces and Superconductivity in Compressed Lithium,"
Phys. Rev. Lett. 96, 047004 (2006).
[157.] B.R. Maddox, A. Lazicki, C.S. Yoo, V. Iota, M. Chen, A. McMahan,
M.Y. Hu, P. Chow,
R.T. Scalettar, and W.E. Pickett,
"4f Delocalization in Gd: Inelastic X-Ray Scattering at Ultrahigh Pressure,"
Phys. Rev. Lett. 96, 215701 (2006).
[161.] B.R. Maddox, C.S. Yoo, D. Kasinathan, W.E. Pickett, and R.T.
"High Pressure Study of Half-Metallic CrO2,"
Phys. Rev. B73, 144111 (2006).
[171.] J. Kunes, A.V. Lukoyanov, V.I. Anisimov, R.T. Scalettar,
Collapse of Magnetic Moment drives the Mott Transition in MnO,
Nature Materials 7, 198 (2008).
A.K. McMahan, R.T. Scalettar, and M. Jarrell,
"The screening of $4f$ moments and delocalization in the compressed light rare earths,"
submitted to Phys. Rev. B.