M <sub> 13 </ Sub> @ Au <sub> 20 </ Sub> (m = Fe, Ti), Geometric Structure And Magnetic Properties Of Computing Research

The geometric and magnetic properties of M₁₃and M₁₃@Au₂₀clusters have been studied using the generalized gradient approximation(GGA)based on the density functional theory (DFT).To the Fe₁₃and Fe₁₃@Au₂₀cluster,It is showed that in the lowest-energy state,the total magnetic moment of Fe₁₃cluster is 44μ_B,and the average magnetic moment of surface Fe atoms is 3.45μ_B,while the core atom possesses 2.6μ_B magnetic moment.Thus,there are ferromagnetic interactions between the Fe atoms in the cluster.The energy curve with the different magnetic moments shows that there is another local minimum at total spin 34μ_B,and the average magnetic moment of surface Fe atoms is 2.99μ_B,while the core atom possesses the -1.88μ_B magnetic moment.Therefore,there are antiferromagnetic interactions between the central Fe atom and the outer 12 Fe atoms.After putting Fe₁₃cluster into Au₂₀cage,the total magnetic moment of the most stable Fe₁₃@Au₂₀cluster decrease to 38μ_B,in which the magnetic moment of center Fe atom is 2.76μ_B,the respective average magnetic moment of inner 12 Fe and Au atoms are 2.87μ_B and 0.04μ_B.So there are ferromagnetic interactions between the 20 Au and the inner 13 clusters.Similar to Fe₁₃,there is another local minimum of the spin 28μ_B,in which the magnetic moment of center Fe atom is 2.48μ_B,the respective average magnetic moments of inner 12 Fe and Au atoms are 2.21μ_B and -0.04μ_B.Thus there are antiferromagnetic interactions between the 20 Au and the inner 12 Fe atoms,while,the central Fe atom interacts ferromagnetically with the 12 Fe atoms.For Tia3 cluster,when total magnetic moment is 6μ_B,the energy is the lowest,in which the core and the surface Ti atoms possesse 0.12 and 0.49μ_B(average)magnetic moment.So the Ti atoms show ferromagnetically order.After putting Ti₁₃cluster into Au₂₀cage,the total magnetic moment of the lowest-energy Ti₁₃@Au₂₀cluster is 4μ_B magnetic moment,in which the average magnetic moment of Au atoms is 0.04μ_B,while the average magnetic moments of surface 12 Ti atoms and center atom are 0.28μ_B and -0.22μ_B.Thus,there are ferromagnetic interactions between the 20 Au and 12 Ti atoms,and there are antiferromagnetic interactions between the central and the 12 Ti atoms...