The many theoretical studies of the various magnetic, thermal and magnetoelastic properties for paramagnetic and ferromagnetic transition metals and alloys in the simple itinerant electron model are reviewed. The important amendments to the simple itinerant electron model or Stoner model of magnetism due to the spin wave excitations and spin fluctuations are explained.

https://iopscience.iop.org/article/10.1088/0034-4885/44/4/001/pdf

Itinerant electron magnetism

The electronic-structure theory of solids is presently dominated by density-functional methods which avoid calculations of the many-body wavefunction, and instead compute directly properties of the ground state. We argue that methods which determine the many-electron wavefunctions should receive particular attention in the future. A survey is given of our present knowledge of how to calculate these wavefunctions for a solid. The accuracy we envisage compares with the one obtainable for small molecules when applying quantum-chemical methods.

Wavefunction methods in electronic-structure theory of solids

A theory of the single-particle excitation spectrum is presented on the basis of the projection operator method combined with the many-body coherent-potential approximation (CPA). The theory describes the dynamics of the excitations by means of an energy-dependent Liouville operator accompanied by a coherent potential which is determined by the self-consistent CPA condition. It is shown that the present theory is essentially equivalent to the dynamical CPA and the dynamical mean-field theory. The Hubbard III approximation and the modified perturbation theory are rederived from the theory. A renormalized perturbation scheme for the Green function is developed on the basis of a general formula for the memory function. It interpolates between the weak- and strong-Coulomb interaction limits, and yields the metal-insulator transition for half-filled bands. Numerical calculations have been performed for the Gutzwiller-Hubbard model on a hypercubic lattice in infinite dimensions. The results show that the theory describes quantitatively the quasiparticle weight vs Coulomb interaction curve, yielding a reasonable critical Coulomb interaction for the metal-insulator transition. It produces the overall features of the excitation spectra and the momentum distributions for various Coulomb interaction strengths.

Coherent potential approximation and projection operators for interacting electrons

Recent progress in the theory of magnetism and electron correlations is reviewed to clarify the theories developed in the last decade and their mutual relations. A historical development of the theory of magnetism is outlined, and the dynamical coherent potential approximation (CPA) which completely takes account of the dynamical spin and charge fluctuations within the single-site approximation is introduced. Both the dynamical effects on various magnetic properties and the many-body band structure are shown to be explained on the same footing. It is shown that the dynamical CPA is equivalent to the other single-site theories of strongly correlated electrons: the many-body CPA, the dynamical mean-field theory (DMFT), and the projection operator method CPA (PM-CPA). These theories are elucidated with use of a common concept of effective medium or coherent potential. The effects of orbital degeneracy and the realistic calculation scheme are discussed with an emphasis on Hund’s rule coupling. Non-local theor...

Electron correlations and many-body techniques in magnetism

The coherent potential approximation (CPA) is a useful tool to describe the electron correlations as well as the effects of disorder on electrons. Among various theories of correlated electron systems, the many-body CPA, the dynamical CPA, and the dynamical mean-field theory have been investigated in great detail from the viewpoint of the CPA. It is demonstrated that these three theories are equivalent to each other, so that the theories of itinerant magnetism and those of the strongly correlated electron systems are unified within the single-site approximation. This explains why the N\'eel temperatures calculated by the dynamical mean-field theory agree well with the ones calculated by the classical and adiabatic versions of the dynamical CPA, the single-site spin-fluctuation theory, and the variational approach.

Many-body coherent potential approximation, dynamical coherent potential approximation, and dynamical mean-field theory

The electron correlation in disordered alloys is discussed in the Hubbard model. A single band model is assumed, and the t -approximation and the coherent potential approximation are used. It is shown that intra-atomic Coulomb interactions are screened by the effect of electron correlation and effective intra-atomic Coulomb interactions at atomic sites are introduced. As an example their numerical estimation is carried out for Pd–Rh alloys. The effective intra-atomic Coulomb interactions are found to be considerably dependent on the concentration of alloys. By taking into account the electron correlation a generalized transverse spin susceptibility for disordered alloys is also calculated.

A Theory of the Electron Correlation in Disordered Alloys

The volume paramagnetostriction of disordered alloys is calculated in the itinerant electron model. By assuming transfer energys and the number of d -electrons to vary with volume change, a general expression for the volume dependence of spin paramagnetic susceptibility is derived from the results for the spin paramagnetic susceptibility of a disordered binary alloy which is obtained in the coherent potential approximation and the t -approximation for the electron correlation. Numerical estimations of the spin paramagnetic susceptibility and its volume dependence are given for Pd–Rh, Ni–Rh and Pi–Ni alloys and a good agreement with experiments is obtained. It is found that a volume dependence of the transfer energy or the bandwidth has a main effect on the volume paramagnetostriction.

Calculation of Volume Paramagnetostriction for Pd-Rh, Ni-Rh and Pt-Ni Alloys

We propose a statistical approach to the Quark bag model. Considering a hadron as the many-body system of the Quark and self-interacting scalar fields, we calculate the thermo­ dynamical potential of the hadron in the one-loop approximation by the field theory at finite temperature and finite Quark density. We introduce the effective self-interactions between the Quark fields by the semi-classical method and estimate the surface energy of the bag and the spin-spin interaction energy. We apply our model to the calculations of the masses and other statical parameters of light hadrons.

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Statistical Quark Bag Model and Light Hadrons

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Phase Transition of Second Kind in Hadronic Matter

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Shigeru Hirooka

Papers

A Theory of the Electron Correlation in Disordered Alloys

Calculation of Volume Paramagnetostriction for Pd-Rh, Ni-Rh and Pt-Ni Alloys

Statistical Quark Bag Model and Light Hadrons

Phase Transition of Second Kind in Hadronic Matter

Hadron-Quark Phase Transition and Statistical Quark Bag Model