Based on the technique of fragmentation-induced spin polarization combined with the β-ray detected NMR method, we have so far conducted a series of ground-state nuclear-moment measurements in a region of light neutron-rich nuclei at RIKEN and GANIL. The obtained experimental nuclear moments were useful to discuss, e.g., unknown ground-state spin parities, the effective spin g factor, the isospin dependence of effective charges, and island of inversion phenomena. In addition to the ground state, isomeric states of unstable nuclei have been also studied by means of the technique of fragmentation-induced spin alignment. Remarkably, we have recently developed a method to produce highly spin-aligned radioactive-isotope (RI) beams in a new scheme. The method was first examined at the RIKEN RI Beam Factory (RIBF) facility using the superconducting in-flight RI separator BigRIPS, the central instrument at the RI Beam Factory, where a highly spin-aligned isomeric 32mAl beam was successfully produced through the two-step projectile fragmentation reaction. These studies will be further enhanced by the upgrade of a fragment separator RIPS, a predecessor of BigRIPS, proposed as one of the RIBF phase-II programs.