A complete theory for the magnetism of an ideal gas of electrons

TL;DR

This paper develops a comprehensive theoretical framework unifying Pauli paramagnetism, Landau diamagnetism, and de Haas-van Alphen effects for an ideal electron gas across all temperatures and magnetic field strengths, including new asymptotic series expansions.

Contribution

It presents a unified theory that extends previous models and describes the crossover and saturation phenomena in electron gas magnetism.

Findings

Unified description of magnetic effects in electron gas

Crossover from de Haas-van Alphen oscillations to saturation

New asymptotic series for low-temperature properties

Abstract

We have explored Pauli paramagnetism, Landau diamagnetism and de Haas-van Alphen effect in a single framework, and unified these three effects for all temperatures as well as for all strengths of magnetic field. Our result goes beyond Pauli-Landau result on the magnetism of the 3-D ideal gas of electrons, and is able to describe crossover of the de Haas-van Alphen oscillation to the saturation of magnetization. We also have obtained a novel asymptotic series expansion for the low temperature properties of the system.