The discussion above describes relaxation of nuclear magnetization in the presence of a constant magnetic field B. This is called relaxation in the laboratory frame. 
Another technique, called relaxation in the rotating frame, is the relaxation of nuclear magnetization in the presence of the field B together with a time-dependent magnetic field B. The field B rotates in the plane perpendicular to B at the Larmor frequency of the nuclei in the B. The magnitude of B is typically much smaller than the magnitude of B. Under these circumstances the relaxation of the magnetization is similar to laboratory frame relaxation in a field B. The decay constant for the recovery of the magnetization component along B is called the spin-lattice relaxation time in the rotating frame and is denoted T. 
Relaxation in the rotating frame is useful because it provides information on slow motions of nuclei.