Structural And Magnetic Properties Of Praseodymium Clusters: A Density Functional Theory Investigation

The development of hard magnetic nanoparticles and the study of magnetic properties are a hotspot in the field of nanostructured materials and a good carrier for deep understanding of basic magnetic problems.When the scale of the magnetic nanoparticles is reduced to the atomic level,the excellent magnetic properties of the particles will be more obvious under the action of the quantum size effect and the surface effect.Rare earth atoms due to the lack of 4f orbit to make it have a large spin magnetic moment and orbital magnetic moment,while strong local and spin-orbit coupling effect of 4f electrons will make rare earth atoms strong magnetic anisotropy characteristics.Therefore,in-depth study of rare earth nanoclusters can help to develop new optoelect ronic materials,and should be high-density magnetic storage records,spin electronics and chemical catalysis and other high-tech materials.In recent years,the structural,magnetic and electronic structures of rare earth clusters have been studied in this paper.The magnetic moments,ionization potentials and vibrational spectra of Pr,Tb,Tm,Dy and other atomic clusters are measured.The relationship between cluster size and these physical properties is obtained.Subsequent theoretical calculations also validate and explain some experimental results.Unfortunately,the existing theoretical work does not take into account the contribution of the orbital moment of the system,and conventional density functional theory has a well-known defect in the processing of 4f electron rare earth systems.In particular,the magnetic anisotropy in rare earth clusters can show no correlation,whereas magnetic anisotropy is a key factor in whether magnetic nanoparticles can act as magnetic recording materials.In this paper,the GGA and GGA + U methods in the framework of density functional theory(DFT)are used to study the structural evolution of rare earth metal Prn(n = 2-16)clusters in close relationship with the recent experimental study.The spin magnetic moment,the orbital magnetic moment,the magnetic anisotropy,the electronic structure and other related properties.On the basis of explaining the experimental phenomena and revealing its connotation,some novel physical properties are found.The concrete contents and conclusions are as follows:(1)Using the GGA and GGA + U calculations of spin polarization,it is found that the Pr clusters are characterized by the immobilized structure of the icosahedral bodies,in which the Pr13 clusters have typical structural features of icosahedral structures with high stability.The structure of rare earth clusters is similar to that of the main ferromagnetic transition metal clusters.The f orbital mainly derived from rare earth atoms is partially filled with the same transition metal atoms as d atoms.(Ie,GGA + U),although the repulsion between the atoms is enhanced and the bond length of the cluster is slightly elongated,the binding energy is reduced but does not change the cluster Structural morphology and the order of the energy of each isomer.The second energy difference and binding energy shows that the stability of Pr clusters at the size of 4,8,13 is higher than that of the nearest neighbor,suggesting that these dimensions are magic number.(2)GGA calculations show that the Pr atoms in different clusters have a spin magnetic moment of 2.20-4.16 ?B/atom,and the U value has little effect on the local spin of the system atoms,with only a slight increase of 0.1-0.5 ?B/atom;At the same time as GGA + U,it is found that at the time of n = 6,the GGA + U is a ferroelectric arrangement.The cluster starts to change from the ferromagnetic sequence to the antiferromagnetic sequence,indicating that GGA + U can induce the spin coupling between Pr atoms.Considering the experimental results show that the magnetic moments of the cluster show obvious oscillatory behavior with the change of the size.The two theoretical values are compared with the experimental changes.The GGA + U treatment method is more reliable than the GGA method.Revealing the magnetic coupling has a crucial role.(3)Considering the spin-orbit coupling effect(SOC),it is found that the effect of SOC on the spin-magnetic moments of the remaining size clusters is small except that the spin moments of n = 7,15 are greatly improved.Compared with GGA + SOC and GGA + U + SOC,it is found that the effect of U value on the spin magnetic moment of each atom is weak,and the GGA + SOC + U method improves the atomic magnetic moment well.Part of the size of the experimental measurements,but the qualitative evolution of the trend and the experiment is better.The GGA calculation shows that the mean value of the orbital magnetic moment of the Pr cluster is 1.06-2.77 ?B/atom.After calculating the GGA + U,the mean value of the orbital magnetic moment is 1.26-6.87 ?B/atom,which indicates that the U value exclusion potential makes the distribution of f electrons in the sub-orbit.In summary,the average orbital magnetic moments obtained by the two methods have the same oscillatory trend as the average spin magnetic moments,and the atomic moments of the atomic orbital in a single cluster have similar oscillatory behavior to the spin magnetic moments,The orbital coupling effect exists not only between clusters but also inside the cluster.(4)The GGA + U + SOC method improves the orbital moment of the atom to a certain extent,indicating that the larger orbital magnetic moment of the Pr cluster will make the system exhibit large magnetic anisotropy.GGA + SOC calculation found that the magnetic anisotropy range is from 1.0-7.7 meV/atom,and n = 7,13 when the magnetic anisotropy can be the largest;plus U,the magnetic anisotropy can be raised to 3.6-60 MeV/atom,in the size of n = 4,6,12,15 than the size of the adjacent anisotropy larger.It is found that the easy axis of the small-sized praseodymium clusters is always parallel to the plane of the number of atoms,that is,the in-plane magnetization,and the hard axis is always perpendicular to the plane of the number of atoms,that is,However,the U value changes the magnetization axis of some clusters.(5)From the HOMO-LUMO energy gap,we observe that the energy gaps under the two computational methods appear oscillating,similar to the energy gap of the transition metal cluster,and the GGA + U method has a larger energy gap,indicating that the GGA + U has a certain effect on the electronic structure.For this reason,we study the sub-wave density of Pr10 and Pr13 clusters and find that GGA + U has more spin splitting than GGA.The U value causes f electrons to shift to s or d electrons,resulting in increased magnetic moments.