When only the static magnetic field (B) is turned on, the spin will precess around it with Larmor frequency ν and the corresponding angular frequency is ω.
According to mechanics, the equation of motion of the spin J is:
where μ is the magnetic moment.
g is g-factor, which is dimensionless and reflecting the environmental effect on the spin.
Solving gives the angular frequency (Larmor frequency) with the magnetic field pointing on z-axis:
The minus sign is necessary. It reflects that the J is rotating in left-hand when the thumb is pointing as the H field.
when turned on the rotating magnetic field (B), with angular frequency ω. In the rotating frame of the rotating field, the equation of motion is:
or
if , the static field is cancelled, and the spin now precesses around H with angular frequency Rabi frequency
Since the rotating field is perpendicular to the static field, the spin in rotating frame is now able to flip between up and down.
By sweeping ω, one can obtain a maximum flipping and determine the magnetic moment.