The Larmor precession frequency is the rate of precession of a spin packet under the influence of a magnetic field. The frequency of an RF signal, which will cause a change in the nucleus spin energy level, is given by the Larmor equation. The frequency is determined by the gyro magnetic ratio of atoms and the strength of the magnetic field. The gyromagnetic ratio is different for each nucleus of different atoms.
The stronger the magnetic field, the higher the precessional frequency. If an RF pulse at the Larmor frequency is applied to the nucleus of an atom, the protons will alter their alignment from the direction of the main magnetic field to the direction opposite the main magnetic field. As the proton tries to realign with the main magnetic field, it will emit energy at the Larmor frequency. By varying the magnetic field across the body with a magnetic field gradient, the corresponding variation of the Larmor frequency can be used to encode the position. For protons (hydrogen nuclei), the Larmor frequency is 42.58 MHz/Tesla.

See also Larmor Equation.

(AFP) Adiabatic fast passage is a NMR technique of producing rotation of the macroscopic magnetization vector by shifting the frequency of RF energy pulses (or the strength of the magnetic field) through resonance (the Larmor frequency) in a time short compared to the relaxation times. Particularly used for inversion of the spins between high and low energy states with an excess of spins in the higher energy level. A continuous wave NMR technique used in e.g., MR spectroscopy.

[B₁] A conventional symbol for the radio frequency field strength (another symbol historically used, is H1). In MRI, B1 labels the field produced by the radio frequency coil.
The B1 field is often conceived of two vectors rotating in opposite directions, usually in a plane transverse to B0. At the Larmor frequency, the vector rotating in the same direction as the precessing spins will interact strongly with the spins.

Bound spins. Protons in water, bound caused hydration at macromolecules. Bound spins have no defined Larmor frequency and are not visible in the image.

(ESR) Electron spin resonance is a spectroscopic technique to identify paramagnetic substances. This magnetic resonance phenomenon investigates the nature of the bonding within molecules by identifying unpaired electrons, e.g. in free radicals and their interaction with their immediate surroundings. The Larmor frequency are much higher than corresponding NMR frequencies in the same static magnetic field.
Nuclei with an odd number of neutrons and/or protons, because of their spin, react like tiny magnets and can be lined up in an applied magnetic field. Energy applied by alternating radio frequency radiation is absorbed when its frequency coincides with that of precession of the electron magnets. The spectrum of radiation absorbed as the field changes gives information valuable in chemistry, biology, and medicine since over 50 years.