Free Induction Decay
INCORRECT. Energy loss always occurs to the environment during a FID. Put another way: The envelope of an FID is always a T2* decay curve. (Even in a spin echo pulse sequence the FID follows a T2* envelope up until the first 180° pulse.) The FID does decay as the Mxy component of the net magnetisation vector decays away.
Dephasing of spins causes Mxy to decay away. The rotating frame is shown
CORRECT. In the rotating frame, the net magnetisation vector decays as spins lose phase coherence and begin to cancel each other out. They do this because they experience slightly different magnetic field strengths due to interaction between spins (via their own oscillating magnetic fields). Slightly different magnetic fields means slightly different precession (Larmor) frequencies. This causes some spins to "lag behind" the average, and some "get ahead" of the average. Eventually the spins point in arbitrary directions and the Mxy component of the net magnetisation vector is lost.
A free induction decay with a T2* envelope
This decaying, oscillating signal is the free induction decay.
In the laboratory frame (which is the frame of reference of any signal detection equipment), the oscillating signal from the oscillating magnetic field decays with an envelope which is described by the T2* time constant. The T2* time constant includes usual T2 related spin-spin interactions and additional loss of phase coherence due to imperfections in the external magnetic field, and magnetic susceptibility effects.
The FID is described mathematically by
Mxy(t) = Mxy(0)exp(-t/T2*)cos(ω0t) (laboratory frame).
This is just T2* decay, modified by an oscillation term. The signal is oscillating and decaying.
Although in examples it is clearer to depict a FID after a 90° pulse, a FID will occur after any angle rotation of the net magnetisation vector into the transverse plane. There will be an oscillating (precessing), decaying component of magnetisation generating a signal for us.
INCORRECT. The FID has nothing to do with RF excitation pulses (which rotate the net magnetisation vector away from alignment with the external magnetic field, ready for a signal measurement).