What is a Free Induction Decay?

In magnetic resonance, free induction decay (or FID) is the temporal profile of induction of sample placed in the magnetic field in the absence of external radio-frequency (in NMR or microwave frequency in EPR) irradiation after some irradiation has been applied and then interrupted.

Also, spectrocopists often refer to FID as a recording of the actual FID signal sampled in time. FID is almost never sampled directly as larmor precession frequecies of nuclear and electron are too high to be sampled that way.

Oscillations in the recorded FID’s occur at frequencies equal the difference between the larmor frequency and the radio- (or microwave) frequencies of the applied pulses.

In their famous NMR analyzer experiments of 1946, Bloch, Purcell, and colleagues employed a continuous wave (CW) technique using a fixed frequency RF field (B1) while the main magnetic field (Bo) was swept through resonance. They observed transient fluctuations in coil voltage referred to as “resonance absorption” by Purcell and the “nuclear induction signal” by Bloch.

Two years later, Bloembergen, Purcell, and Pound noted that immediately after the system had passed through resonance, small oscillations appeared on either side of the main absorption tracing that were named the “wiggles”.

About the same time, Erwin Hahn, a graduate student at the University of Illinois at Urbana, was investigating pulsed NMR techniques. In pulsed methods the main magnetic field is held constant while an RF-field at the Larmor frequency is pulsed on and off. Immediately after the RF pulse Hahn observed a transient oscillation he recognized was equivalent to Bloembergen’s “wiggles”. Hahn called this signal the “nuclear induction decay” or “free induction,” which today is commonly referred to as the free induction decay (FID).
As described in a previous Q&A the nuclear induction signal arises as the net magnetization (M) vector precesses around the z-axis (the direction of Bo). The transverse components of M generate a current in the receiver coil based on the Faraday-Lenz Law of electromagnetism. The signal is a sine wave oscillating at the Larmor frequency (ωo).
Free induction decay (FID)
The NMR signal, however, does not persist forever. The initially coherent transverse components of M dephase as a result of both magnetic field inhomogeneities and intrinsic T2 mechanisms, incorporated in the concept of T2*-decay. The resulting signal is the FID, a damped sine wave of the following form

[sin ωot ] e-t/T2*

Although it is convenient to think about an FID arising from the action of a 90° pulse, an FID will be created by an RF pulse of any flip angle because some component of longitudinal magnetization is always tipped into the transverse plane. (The only theoretical exception to this rule might be a 180° pulse, which in principle should only invert the longitudinal magnetization and not generate any transverse components. In practice, however, all 180° pulses are imperfect, and therefore always produce FID signals.)

The FID is just one of four basic types of NMR signals produced in different ways.