Abstract Magnetic anomalies caused by crossing of the lowest-lying energy levels (crossover) of Tm 3+ ion in the magnetic field along the tetragonal axis of a TmPO 4 single-crystal near 30 T are investigated experimentally and theoretically. Measurements of the differential magnetic susceptibility dM=dH by the compensated pick-up coil method with different rates of up-and down-sweep of the magnetic field from 2 K to about 19 K have allowed studying temperature variations of width and shape of the dM=dH peak and hysteresis phenomena associated with relaxation processes. The influence of the misorientation effect and hyperfine coupling on the character of anomalies are explored. Comparison of experimental and theoretical data suggests a cooling of a sample, accompanied by an increase of spin-lattice relaxation times, when approaching the crossover in pulsed regime.
