Simulations Of Exchange Bias In The Ferromagnetic/Antiferromagnetic Composite Nanostructures With Various Morphologies

Recently, magnetic materials of nanostructures have gained high interest from both fundamental and application research, stemming partially from the applications in high-density magnetic storage media and biomedicine. For the former, the most challenge is to beat the superparamagnetism at finite temperatures, which causes thermal destabilization of the nano-scale recording units. It is found that exchange bias in composite nanostructures may be the core technology to solve this issue. Motivated by recent experimental findings, exchange bias in the nanostructures with various morphologies, including core-matrix, core-shell, alloy-like, and nanopillar, is studied by performing a modified Monte Carlo method, based on the classical Heisenberg model.In the present paper, the standard Monte Carlo simulation is modified. We not only consider the thermal fluctuations of all spins along the arbitrary directions, but also calculate the energy of each spin at any time in order to clarify whether there are the energy barriers during the reversal of spin. The acceptation probability in the standard Monte Carlo simulation is dependent on the energy difference between the new and initial states. Whereas in this paper the acceptation probability is determined by the energy difference between the saddle point and the initial state, as long as the rotation of spin needs to straddle the energy barriers. After the modification, the Monte Carlo simulation has proved useful for the systems with finite anisotropies.Firstly, exchange bias in the system with core-matrix morphology is studied in the present paper. Exchange bias field may be positive at low temperature after cooling in strong fields when the ferromagnetic/antiferromagnetic interfacial coupling is antiferromagnetic. Moreover, positive exchange bias field appears more easily for weak antiferromagnetic interfacial couplings. Coercivity is almost independent of cooling field and its behavior is symmetric about zero interfacial coupling. Variation of field-cooling direction only determines the mapping value of magnetization in the field-measuring direction, while the change of field-measuring direction even may change the magnetization reversal mechanisms. Furthermore, with the increase of exchange coupling in the antiferromagnet, the antiferromagnetic order is more stable and thus the surplus magnetization of antiferromagnet at the ferromagnetic/antiferromagnetic interface decreases. Finally, exchange bias field is suppressed. In addition, exchange bias field increases monotonously towards the negative direction with the increase of antiferromagnetic anisotropy at low temperature after cooling in weak fields, while for strong cooling fields exchange bias field increases towards the negative direction initially and then changes its sign, finally, increases towards the positive direction and levels off. The phenomena are interpreted by analyzing the energy competition among exchange coupling, especially at the ferromagnetic/antiferromagnetic interface, antiferromagnetic anisotropy, and external magnetic field in the processes of cooling and magnetizing. Finally, it is found that exchange bias field and coercivity may change due to the change of distribution and number of ferromagnetic and antiferromagnetic spins, but their main trends affected by other factors are not changed when the magnetisms of the core and the matrix are exchanged.Secondly, exchange bias in the system with antiferromagnetic core-ferromagnetic shell morphology is studied in the present paper. The results indicate that effects of temperature, interfacial coupling, size, defects in antiferromagnetic core, and training on exchange bias are all consistent well with the experimental findings. When we study the exchange bias in the egg-shaped nanoparticles, dependence of exchange bias on cooling field as well as size and position of antiferromagnetic core reflects the fact that besides the antiferromagnetic core, another pinning source, namely, the hard ferromagnetic particle surface, exists to affect exchange bias. Because of this extra effect, the results obtained from this model are quite distinct from those obtained in the systems with conventional morphologies.Moreover, exchange bias in the system with "alloy-like" morphology is studied in the present paper. Because "alloy-like" morphology is one of the commonest and most available morphologies. It is found that the blocking temperature of exchange bias decreases monotonously with the increase of cooling field. However, with the increase of ferromagnetic component ratio, the blocking temperature changes little firstly, and then decreases obviously, finally becomes zero. Some discrete error bars emerge for large ratios of ferromagnetic component due to the superparamagnetic or agglomerate behavior of the small antiferromagnets. Exchange bias in such alloy-like systems also depends strongly on the morphology of ferromagnetic/antiferromagnetic interface. When the orientations of easy axes of spins at the interface are uniform, exchange bias field is not only about ten times larger than that for the case of the random orientations, but the linear relation between exchange bias field and magnetization vertical shift is also valid at low temperature after cooling in strong fields. Whereas coercivity exhibits three distinct kinds of trends with cooling fields, and the behavior is also dependent on the morphology at the ferromagnetic/antiferromagnetic interface. On the other hand, for the case of the random orientations, the behavior of exchange bias field becomes complex while coercivity has a peak as the ratio of ferromagnetic to antiferromagnetic component is1:1. Distinct trends of two coercive fields at both branches in the hysteresis loops are used to interpret the results directly, implying that exchange bias is not only dependent on interfacial coupling and cooling field, but also depends on external magnetic field direction during magnetizing strongly.Finally, exchange bias in the system with nanopillar morphology is studied in the present paper. At low temperature after field cooling, an oscillatory exchange bias is observed with excised length and angle of inclination, respectively. However, the behaviors of coercivity exhibit a monotonous decrease with excision but also an oscillation with tilt. The phenomena are intriguing and corroborated by means of the microscopic spin configurations and the magnetization reversal mechanisms in the hysteresis loops. Occurrence of oscillatory exchange bias is mainly because of the shape inducement in the nanopillar, which results in the energy fluctuations of interfacial coupling and the nonuniformities of domain distribution.In summary, a modified Monte Carlo method is used to study the exchange bias in the ferromagnetic/antiferromagnetic composite nanostructures with various morphologies. By means of calculating magnetization, microscopic spin configurations and energy distributions, hysteresis loops, and others, we have shed new light on the microscopic origin of exchange bias in the nanostructures with various morphologies.