Abstract
The hysteresis loops and susceptibility of spin system with the crystal field have been studied within the framework of the effective-field theory with the differential technique. The effects of the external longitudinal magnetic field on the magnetization and susceptibility are discussed in detail. Numerical results are performed and analyzed for the cases of the honeycomb and square lattice. A number of interesting phenomena have been found due to the applied longitudinal magnetic field, such as, the shape of hysteresis loops and susceptibility are dependent on the longitudinal magnetic field and crystal field. The peak of susceptibility of the honeycomb lattice is bigger than that of the square lattice when the parameters are the same in the two systems.
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