Monte Carlo Simulation On The Magnetic Properties Of A Honeycomb Monolayer Film

Because of its important value in practice, we use Monte Carlo (MC) simulation to study the magnetic properties of a planar honeycomb (hexagonal) magnetic monolayer film. The investigation is based on the present situation both at home and abroad. Both an Ising model and a transverse Ising model are adopted according to the real status. The difference of the Ising model from conventional one is that we consider not only the nearest-neighbors' pair-spin interactions but also the nearest-neighbors'four-spin interactions on the honeycomb lattice. We investigate the properties of spontaneous magnetization, technical magnetization and the anisotropy of magnetization behavior of the systems in order. The result presents:(1)The property of spontaneous magnetization of the system is affected not only by temperature and 2-spin interaction but also by 4-spin interaction. So we divided the system to ferromagnetism, ferrimagnetism and anti-ferromagnetism according the magnitude of 4-spin interactions. At super low temperature, the 4-spin interaction affects the energy, the magnetization and the critical temperature of the system. The critical temperature is as a monotonously increase function of 4-spin interaction. The results of simulation are identical with the exact one used analytical method in qualitatively. It expresses that Monte Carlo simulation is an effective method.(2)When the systems are forced by a longitudinal external field, there is a first-order magnetic phase transition for the ferromagnetism or ferrimagnetism. And the critical temperatures are dependent on the magnitude of 4-spin interaction and longitudinal external magnetic field. However, the property of anti-ferromagnetism is far from those. When the longitudinal external field is higher, it shows the first-order magnetic phase transition and reentry phenomenon. While the external field is lower, there is a second-order magnetic phase transition. In the region of low temperatures, the curves of magnetization are affected obviously by 4-spin interaction. The greater the 4-spin interaction, the faster the magnetization reaches its saturation magnetization. Also the values of magnetic entropy of various systems are affected by 4-spin interaction obviously, under little external field. The values of magnetic entropy change are negative for ferromagnetism and ferrimagnetism. And the negative magnetic entropy change have maximum at their critical points. It indicates the maximum of isothermal exothermal appear at the critical points. Furthermore, it is observed an abnormal phenomenon for anti-ferromagnetism that the values of magnetic entropy change may be positive, in the region of low temperatures. The behavior that excitation-endothermic is the result of frustration which produced from the competitive of various interactions. It shows the 4-spin interaction plays an important role in it.(3)The magnetization behavior of magnetic system is dependent on the 4-spin interaction, when it is forced by both the longitudinal magnetic field (Z direction) that parallel to the spins of conventional Ising model external and transverse external magnetic field (X direction) which vertical to Z direction. We obtained the curves of magnetization for various magnetic systems in longitudinal direction and in transverse direction, respectively. They express that it is easer that the system arrives saturation magnetization on Z axis then on X axis for both ferromagnetism and ferrimagnetism. Furthermore, the curve of magnetization of anti-ferromagnetism on Z direction is not same as it on X direction. They show Z axis is the easy axis and X axis is the hard axis for all of them. It shows the magnetization behavior of anti-ferromagnetism is not as paramagnetism which is isotropy. The result express that the interaction between spins have obviously affection to the magnetic anisotropy.