Quadrupole Excitations in hysteresis loops of magnetic NanoCluster Fe₈

Experiments show several steps in hysteresis loops of high spin nanocluster $Fe_8$. It is thought that these steps are due to thermally assisted resonant tunneling between different quanta spin states. Up to now, in calculatiing it, only dipole excitations were considered. Because of the symmetry and the power of spin operators in Hamiltonian, we think that other multipole excitation must be considered too. In this paper we consider both dipole and quadrupole excitations in Hamiltonian and then quantum resonant tunneling phenomena are obtained numerically. As we can show in these figures, this phenomenon is different in these two conditions and the second condition is nearly to the fact.