Re: How does radio wave absorbtion work in MRI?

Wonderful Question! NMR is what I got my PhD in.
The short answer to your question is : "both and neither".

There are two ways to do NMR:
1) Continuous wave (not done much anymore), in which a low power RF continuous signal is applied to the nuclei. This causes them to precess away from their desired alignment, and a small RF signal is emitted (90 degrees out of phase with the stimulus signal) which can be detected. This can go on forever if the stimulus is small enough; the energy being pumped in is, through a variety of mechanisms, eventually turned into heat (microwatts).

2) Pulsed, where a high power (10KW) short (10uSec) RF pulse is applied to the sample. This causes most of the nuclei to precess in phase, and induces an EMF in a receiver coil. The received signal gradually decays, again with a variety of mechanisms, and so the EMF drops off. Then you put another pulse in, and the process starts all over. The energy pumped in is, of course, eventually transformed into heat. By the way, this is how MRI imagers work.

There are two times associated with either technique:
T1, called spin-lattice relaxation time, in which the nuclear spins gradually realign themselves with the applied magnetic field.
T2, called spin-spin relaxation time, in which the nuclear spins are still precessing, but get out of phase with each other so that the EMF signal decays.
T2 can be shorter than T1, but never longer; the individual magnetic moments can get out of phase with each other but still be misaligned with the main magnetic field, at which point T1 mechanisms take over.

I hope that this answers your question. For a good introductory reference, try C. P. Schlichter, Nuclear Magnetic Relaxation.

Thanks again!