Nuclear spins experience forces in the presence of a magnetic field gradient. The forces cause the spin-up and spin-down nuclei to move in opposite directions, resulting in a flow of longitudinal magnetization. The effect can generate local longitudinal spin magnetization though it does not involve transitions (flipping) of spins. This phenomenon, spin sorting, competes with real spin-lattice relaxation and is generally not observable when T 1 is short. We present our calculations of the longitudinal magnetization of diffusing spins with long T 1 in magnetic field gradients. We show that the longitudinal spin magnetization due to spin sorting can be dominant at short times in such a system. Experimental confirmation is provided by observation of sorting-induced negative spin magnetization in 3 He gas. We show how this phenomenon can potentially be used to generate nuclear magnetizations larger than thermal equilibrium.