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Register a new userDensity Functional Methods for the Magnetism of Transition Metals: SCAN in Relation to Other Functionals
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We report tests of various density functionals for ferromagnetic, Fe, Co and Ni with a focus on characterizing the behavior of the so-called strongly constrained and appropriately normed (SCAN) functional. It is found that SCAN is closer in behavior to functionals that yield localized behavior, such as hybrid functionals, than other semilocal functionals that are tested. The results are understood in terms of a tendency to differentiate orbitals, favoring integer occupation, which is necessary for a correct description of atomic systems, but inappropriate for the open shell metallic ferromagnetic metals studied here.
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Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities stemming from the generalized Pauli principle, the many-body wave-function can be written explicitly in terms of the natural occupation numbers and natural orbitals. This leads to an expression for the two-particle density matrix and therefore for the correlation energy functional. This functional was then tested for a three-electron Hubbard model where it showed excellent performance both in the weak and strong correlation regimes.
A novel approach to electronic correlations and magnetism of crystals based on realistic electronic structure calculations is reviewed. In its simplest form it is a combination of the ``local density approximation (LDA) and the dynamical mean field theory (DMFT) approaches. Using numerically exact QMC solution to the effective DMFT multi-orbital quantum-impurity problem, a successful description of electronic structure and finite temperature magnetism of transition metals has been achieved. We discuss a simplified perturbation LDA+DMFT scheme which combines the T-matrix and fluctuation-exchange approximation (TM-FLEX). We end with a discussion of cluster generalization of the non-local DMFT scheme and its applications to the magnetism and superconductivity of high-Tc superconductors.
We present an ab initio quantum theory of the finite temperature magnetism of iron and nickel. A recently developed technique which combines dynamical mean-field theory with realistic electronic structure methods, successfully describes the many-body features of the one electron spectra and the observed magnetic moments below and above the Curie temperature.
We find that the recently developed self consistent and appropriately normed (SCAN) meta-generalized gradient approximation, which has been found to provide highly accurate results for many materials, is, however, not able to describe the stability and properties of phases of Fe important for steel. This is due to an overestimated tendency towards magnetism and exaggeration of magnetic energies, which we also find in other transition metals.
In this document, I present a personal view on the heavy-fermion problem, within a phenomenological approach guided by experiments. This review presents a set of historical works which established the ground bases of the thematic during the last decades. An exhaustive and systematic approach is privileged. After a general presentation in Chapter 2, the properties of heavy-fermion paramagnets, antiferromagnets, and ferromagnets are considered in Chapters 3, 4, and 5, respectively. Chapters 6 and 7 are dedicated to two specific compounds, URu$_2$Si$_2$ for which a hidden-order phase constitutes a more-than-thirty-years-old unsolved mystery, and UTe$_2$, where multiple superconducting phases have been discovered in the last two years. Experiments performed using a panel of techniques ranging from microscopic (neutron scattering, NMR, etc.) to thermodynamic (specific heat, magnetization, etc.) and transport (electrical resistivity, etc.) probes, under extreme conditions of low temperatures, intense magnetic fields and high pressures, are reviewed. They show that magnetism plays a central role in the quantum critical properties of heavy-fermion systems. An emphasis is given to the intersite magnetic fluctuations, presented as the driving force for a heavy Fermi liquid, precursor of quantum magnetic criticality ending in magnetically-ordered phases. They are also suspected to drive an unconventional mechanism for superconductivity, which develops in the vicinity of quantum magnetic phase transitions induced under pressure or magnetic field. The appearance of magnetic fluctuations and ultimately magnetic order in heavy-fermion compounds occurs in a nearly-integer-valence regime, in which $f$ electrons have a dual itinerant-localized character. Fermi-surface and valence studies, which give complementary information about this duality, are also considered.
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