The Theoretical Study Of Spin-orbital Coupling Effect And Construction Of Magnetic Superatom Based On 13-atom Transition Metal Clusters

Due to their unfilled d electronic structure,the transition metal clusters show magic magnetic properties,and are extensively noticed owing to their potential applications in magnetic information storage materials and electronic spin devices field.Since the relative high stabilities of 13-atom culsters,they always have high occurrences in time-of-flight mass spectrometry experiments and attract more and more interestsMn13 cluster shows local minimum magnetic moment in Stern-Gerlach experiment,which has been verified by many theoretical studies.Resulted from its antiferromagnetic coupling of spin moment in Mn13 cluster,it shows 3 μB of total magnetic moment which is far smaller than the spin moment of isolated Mn atom.How to change the coupling style to increase the magnetic moment of Mn13 cluster is a hot topicAs the main ingredient of classical magnetic storage material,the ferromagnetic elements of Fe,Co,and Ni are widely studied.With the improvement of experimental magnetic measurement on transition metal clusters,especially X-ray magnetic circular dichroism spectroscopy,which can gives access to the intrinsic spin and orbital magnetic moments of isolated clusters,the theoretical studies on orbital moment and magnetic anisotropy can be proceed based on experimental results successfully.It will improve the practical applications of transition metal clusters in high density magnetic information storage materials by tuning their magnetic anisotropic energy of them as we willThe spin moments of modified Mn13 clusters as well as spin-orbital coupling effect and magnetic anisotropies of 13-atom Fe-Pt,Co-Pt and Ni-Pt alloy clusters are systematically investigated by means of density functional method.The main contents and results are as follows.1.The magnetic properties of TM@Mn12@Au20(TM=Fe,Co,Ni,Ru,Rh,Pd and Pt)clustersThe ternary three-shell icosahedral clusters of TM@Mn12@Au20(TM=Fe,Co,Ni,Ru,Rh,Pd,and Pt)are constructed by substituting center atom by Fe,Co,Ni,Ru,Rh,Pd,and Pt accompanying with coating with Au20 cage.Then a systematical density functional study was performed.The geometry optimizations and energy calculations of TM@Mn12@Au20(TM=Fe,Co,Ni,Ru,Rh,Pd and Pt)clusters are also done for comparison.The embedding energy shows that it is easy to embed TM@Mn12 to the Au20 cage.Compared with that of Mn13 cluster,the magnetic moments of TM@Mn12@Au20(TM=Fe,Co,Ru,Rh,Pd and Pt)are all increased,and the total magnetic moment of Fe@Mn12@Au20 cluster is enhanced most,which is up to 51 μB.We analyzed the reason by calculating the average atomic distances of TM-Mn,Mn-Mn and Mn-Au.The result shows that coating with Au20 cage is largely increases the average atomic distances which is helpful to transform antiferromagnetic coupling between spin moments of Mn13 to ferromagnetic coupling,and finally enhances the total moment2.Spin-orbit coupling effect on structural and magnetic properties of ConRh13-n(n=0-13)clustersThe structural and magnetic properties of ConRh13-n(n=0-13)clusters are studied by density functional method with(GGA+U+SOC)and without spin-orbital coupling(GGA+U)respectively.The geometries of ConRh13-n clusters exhibit a transition from DSC,then ICO,finally to HBL with the number of Co atoms n increases.The inclusion of spin-orbital coupling in calculation does not change the geometries of clusters.For n=1-9,the total spin moments of clusters turn to be a constant of 21 μB,which is attributed to the similar geometries of clusters and similar valence electron configurations of Co with Rh atom Spin-orbital interaction recovers orbital moment and its anisotropy by removing crystal field effect in calculation.In SOC calculations,we obtained the orbital moments which are 7-13%to spin moments and high anisotropies of orbital moments are found in CoRh12 and Co11Rh2 clusters.The low symmetry and strength of bonding are responsible for the high anisotropy by analyzing the bonding character in HOMO and LUMO.When n increases to 7 and above,the obvious noncollinearity between spin and orbital moments result in decrease of total magnetic moments.Due to size reduction,the 13-atom Co-Rh clusters have a greater average atomic MAE than the Co-Rh nanoparticles with 300-400 atoms.Large MAEs are found in Co4Rh9(C1),Co5Rh8 and Co9Rh4 clusters,verifying that the MAE is mainly determined by crystal symmetry and atomic composition.The dz2-dyz interaction contributes the most to MAE of Co3Rh10 cluster.3.The spin-orbital coupling effect and magnetic anisotropic energy of 13-atom Fe-Pt、Co-Pt、Ni-Pt alloy clustersThe calculations with spin-orbital coupling of FenPt13-n、ConPt13-n and Ni,Pt13-n(n=0-13)clusters show that the average atomic spin moments are enhanced by doping with Pt atom;the anisotropies of orbital moments in 13-atom Fe-Pt clusters are the largest among the three kinds of alloy clusters,especially for n=1,2,8 and 9,correspondingly,Fe2Pt11,FegPts and Fe9Pt4 clusters have relative higher MAE than neighbors.While the corresponding relationship does not appear in Co-Pt and Ni-Pt systems;Fe-Pt alloy clusters has relative higher magnetic anisotropic energy than the other two system and FegPts cluster has the largest magnetic anisotropic energy among all the clusters;the easy-magnetization axis can be concluded as x and the magnetic anisotropic energy is 29.21 meV which comes from the energy difference between magnetization direction x and z;the main contribution to magnetic anisotropic energy in FegPts cluster comes from the interaction of dxy-dx2-y2 and dxz-dz2 in Pt atoms.