A quantum model for the magnetic multi-valued recording

We have proposed a quantum model for the magnetic multi-valued recording in this paper. The hysteresis loops of the two-dimensional systems with randomly distributed magnetic atoms have been studied by the quantum theory developed previously. The method has been proved to be exact in this case. We find that the single-ion anisotropies and the densities of the magnetic atoms are mainly responsible for the hysterisis loops. Only if the magnetic atoms contained by the systems are of different (not uniform) anistropies and their density is low, there may be more sharp steps in the hysteresis loops. Such materials can be used as the recording media for the so-called magnetic multi-valued recording. Our result explained the experimental results qualitativly.