This chapter explores the microscopic origins of magnetism in matter, classifying materials into diamagnetic, paramagnetic, and ferromagnetic categories based on their response to external magnetic fields. It emphasizes that magnetism is fundamentally a quantum mechanical phenomenon, primarily arising from the orbital and spin magnetic moments of electrons. The concept of the Bohr magneton as the fundamental unit of magnetic moment is introduced. The chapter then presents the dynamics of a magnetic moment in a magnetic field, explaining Larmor precession and the subsequent relaxation processes that lead to the alignment of magnetic moments with an external field. This discussion highlights the principles behind Electron Spin Resonance (ESR) and Nuclear Magnetic Resonance (NMR), including their applications in fields like medical imaging (MRI). The macroscopic magnetic properties of materials are quantified by the magnetization vector ( \(\textbf{M}\) ), representing the average magnetic dipole moment per unit volume. A key development is the representation of a magnetized material by equivalent magnetization current densities (volume and surface currents), which contribute to the total magnetic field. This leads to the introduction of the magnetic excitation field ( \(\textbf{H}\) ), defined as \(\textbf{H}=\textbf{B}/\mu _{0} -\textbf{M}\) , which simplifies Ampére’s law in magnetic media by relating it directly to free currents. The chapter establishes the constitutive relations between \(\textbf{B}\) , \(\textbf{H}\) , and \(\textbf{M}\) , defining magnetic susceptibility ( \(\chi _m\) ) and magnetic permeability ( \(\mu \) ) for linear materials, and discussing the complex, nonlinear behavior of ferromagnets, including hysteresis and the distinction between soft and hard magnetic materials. Finally, the chapter outlines the boundary conditions for magnetic fields ( \(\textbf{B}\) and \(\textbf{H}\) ) at the interface between different magnetic media, demonstrating the continuity of the normal component of \(\textbf{B}\) and the discontinuity of the tangential component of \(\textbf{H}\) in the presence of surface currents. These principles provide a comprehensive framework for understanding and analyzing magnetic phenomena in various materials.

The Origin of Magnetism in Matter

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发表日期：

2025年

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Fabian Cadiz,
Arnaud Couairon

摘要

This chapter explores the microscopic origins of magnetism in matter, classifying materials into diamagnetic, paramagnetic, and ferromagnetic categories based on their response to external magnetic fields. It emphasizes that magnetism is fundamentally a quantum mechanical phenomenon, primarily arising from the orbital and spin magnetic moments of electrons. The concept of the Bohr magneton as the fundamental unit of magnetic moment is introduced. The chapter then presents the dynamics of a magnetic moment in a magnetic field, explaining Larmor precession and the subsequent relaxation processes that lead to the alignment of magnetic moments with an external field. This discussion highlights the principles behind Electron Spin Resonance (ESR) and Nuclear Magnetic Resonance (NMR), including their applications in fields like medical imaging (MRI). The macroscopic magnetic properties of materials are quantified by the magnetization vector ( \(\textbf{M}\) ), representing the average magnetic dipole moment per unit volume. A key development is the representation of a magnetized material by equivalent magnetization current densities (volume and surface currents), which contribute to the total magnetic field. This leads to the introduction of the magnetic excitation field ( \(\textbf{H}\) ), defined as \(\textbf{H}=\textbf{B}/\mu _{0} -\textbf{M}\) , which simplifies Ampére’s law in magnetic media by relating it directly to free currents. The chapter establishes the constitutive relations between \(\textbf{B}\) , \(\textbf{H}\) , and \(\textbf{M}\) , defining magnetic susceptibility ( \(\chi _m\) ) and magnetic permeability ( \(\mu \) ) for linear materials, and discussing the complex, nonlinear behavior of ferromagnets, including hysteresis and the distinction between soft and hard magnetic materials. Finally, the chapter outlines the boundary conditions for magnetic fields ( \(\textbf{B}\) and \(\textbf{H}\) ) at the interface between different magnetic media, demonstrating the continuity of the normal component of \(\textbf{B}\) and the discontinuity of the tangential component of \(\textbf{H}\) in the presence of surface currents. These principles provide a comprehensive framework for understanding and analyzing magnetic phenomena in various materials.