gyromagnetic

Gyromagnetic refers to the relationship between a system’s magnetic moment and its angular momentum. This relationship is quantified by the gyromagnetic ratio γ, sometimes called the magnetogyric ratio. For a given particle or composite system, the magnetic moment μ is proportional to its total angular momentum J, with μ = γ J. The ratio is a fundamental property that depends on the type of particle and, in composites, on electronic or nuclear contributions to the moment. Its units are radian per second per tesla (rad s−1 T−1), and its conventional frequency form γ/2π is often given in hertz per tesla (Hz T−1).

In quantum systems, γ is specific to the particle and can have a sign that indicates the direction of precession. For example, the electron has a negative gyromagnetic ratio, reflecting its negative charge, while the proton has a positive one. Common reference values (in frequency form) include γ/2π ≈ −28.0 GHz/T for the electron and γ/2π ≈ 42.58 MHz/T for the proton; other nuclei vary widely in their γ/2π values. These ratios determine how magnetic moments precess in an external magnetic field.

A central consequence of gyromagnetic behavior is the Larmor precession, with angular frequency ω = γ B and, for spectroscopy, the observable frequency f = γ B /(2π). This underpins techniques such as nuclear magnetic resonance (NMR), electron spin resonance (ESR), and magnetic resonance imaging (MRI), where resonance conditions reveal information about molecular structure and dynamics. Related phenomena include the Barnett and Einstein–de Haas effects, which connect magnetism to mechanical rotation through angular-momentum conservation, highlighting the broader scope of gyromagnetic interactions.