Larmor precession

In physics, Larmor precession (named after Joseph Larmor) is the precession of the magnetic moments of electrons, atomic nuclei, and atoms about an external magnetic field. The magnetic field exerts a torque on the magnetic moment,

${\vec {\Gamma }}={\vec {\mu }}\times {\vec {B}}=\gamma {\vec {J}}\times {\vec {B}}$

where ${\vec {\Gamma }}$ is the torque, ${\vec {\mu }}$ is the magnetic dipole moment, ${\vec {J}}$ is the angular momentum vector, ${\vec {B}}$ is the external magnetic field, $\times$ is the cross product, and $\ \gamma$ is the gyromagnetic ratio which gives the proportionality constant between the magnetic moment and the angular momentum. The angular momentum vector ${\vec {J}}$ precesses about the external field axis with an angular frequency known as the Larmor frequency,

$\omega =-\gamma B$

where $\omega$ is the angular frequency, $\gamma ={\frac {-eg}{2m}}$ is the gyromagnetic ratio, and $B$ is the magnitude of the magnetic field and $g$ is the g-factor (normally 1, except for in quantum physics).

A famous 1935 paper published by Lev Landau and Evgeny Lifshitz predicted the existence of ferromagnetic resonance of the Larmor precession, which was verified experimentally and independently by J. H. E. Griffiths (UK) and E. K. Zavoiskij (USSR) in 1946.

Larmor precession is important in nuclear magnetic resonance, electron paramagnetic resonance and muon spin resonance.

See also

• Rabi cycle
• Georgia State University HyperPhysics page on Larmor Frequency