Structural,Electronic and Magnetic Properties of the GenEu(n=1-13)Clusters

JING Qun GE Gui-Xian CAO Hai-Bin HUANG Xu-Chu LIU Xiao-Yong YAN Hong-Xia

(Key Laboratory of Ecophysics and Department of Physics,Normal College,Shihezi University,Shihezi 832000,The Xinjiang Uygur Autonomous Region,P.R.China)

Structural,Electronic and Magnetic Properties of the GenEu(n=1-13)Clusters

JING Qun GE Gui-Xian CAO Hai-Bin*HUANG Xu-Chu LIU Xiao-Yong YAN Hong-Xia

(Key Laboratory of Ecophysics and Department of Physics,Normal College,Shihezi University,Shihezi 832000,The Xinjiang Uygur Autonomous Region,P.R.China)

The growth pattern and magnetic properties of the GenEu(n=1-13)clusters have been investigated using the density functional theory within the generalized gradient approximation.For all the ground state structures of the GenEu(n=1-13)clusters,Eu atom always prefers to cap on the surface of the germanium frame,which is different from the growth pattern of the SinEu cluster and other transition metal-doped semiconductor clusters.The total magnetic moments of the GenEu clusters have a constant value(7μB)except the GeEu cluster.The total magnetic moment of the GenEu clusters are mostly equal to the local magnetic moment of the 4f state of the Eu atom.Although charge transfer between Ge and Eu as well as hybridization among the 5d,6p,and 6s states of Eu atom can enhance the local magnetic moment of Eu,it does not enhance the total magnetic moment of the GenEu clusters.

Density functional theory;GenEu clusters;Growth pattern;Magnetic property

Recently,foreign atom-doped silicon and foreign atom-doped germanium clusters have been attracting a vast range of interest[1-14],as the silicon and germanium clusters may be employed not only as model systems for investigating localized effects in the condensed phase,but also as building blocks for developing new materials with tunable properties[1].And although the silicon and germanium are isovalent to the carbon element in the periodic table,the hollow cage structures are not the good candidates for their unstability[2].Various investigations[3-14]showed that the impurities encapsulated into the cage can enhance the stability of the host cluster and exhibit many novel properties.The geometry and electronic properties of GenFe clusters havebeen investigated by using the DFT computation[6].The average binding energies of the GenFe clusters are higher than those of the corresponding pure Genclusters,reflecting doping with a Fe atom can enhance the stability of germanium clusters.The geometry,electronic and magnetic properties of GenCo have been investigated by using the DFT computation[15].Addition of a Co atom enhances the stability of the host Genclusters.And for the GenCo clusters,starting from n=9,the Co atom completely falls into the Genframe and forms a cage.The highest occupied molecular orbital-lowest unoccupied molecular orbital(HOMOLUMO)gaps of the dopant clusters are smaller than those of the pure clusters,and the magnetic moment does not quench which isdark contrast to the previous results[5]with transition-metal-doped Sinclusters.Ni-doped[10],Zn-doped[13],Cu-doped[12],and W-doped[16]germanium clusters have been systematically investigated.Different growth patterns have been found between the firstrow and third-row transition metal(TM)atom-doped germanium clusters.For example,the stability of Ge10W in the form of a bicapped tetragonal antiprism is lower than that of its neighboring clusters,which is opposite to the corresponding results of Ge10doped with the first-row TM atoms(Cu,Ni,and Co).

Unlike the TM-atom doped silicon and germanium clusters, only a very limited work was reported on the rare earth(RE) doped silicon and germanium clusters.Recently,Luo et al.[17]investigated the structural and electronic properties of SinLu clusters by using the DFT computation.Zhao and co-workers[18]have investigated the structural,electronic,and magnetic properties of the SinEu clusters.They found that starting from the cluster size of n=12,the Eu atom of Si12Eu cluster completely fell into the center of the Si frame and formed a cage.The geometries and growth-pattern of SinYb clusters have been investigated by Han and co-workers[19-20].They found that Yb atom preferred to cap on the surface site of the silicon frame and no cagelike geometries were found up to n=13,which is different from the SinEu clusters.

On the other hand,it is interesting to investigate the magnetic properties of clusters.In cluster size,there are even more different properties from molecular or bulk materials.Many efforts have been paid to explain the interesting magnetic moment of the clusters.Ma et al.have studied the structures and magnetic properties of SinFe[5]and SinCo[7-8].In Ref.[5],they found the magnetic moments quenching after n≥9 for the SinFe clusters.They suggested that the charge transfer and the strong hybridization between Fe 4s,3d and Si 3s,3p states might be one major reason for the quenching of the magnetic moment of the Fe atom.The quenching of the magnetic moments was also found in other clusters such as SinNi[9],AgnTM(TM=Sc,Ti,V,Fe,Co, Ni)[21]and so on.Generally speaking,the quenching of magnetic moment for SinTM clusters was ascribed to hybridization between silicon′s sp states and d states of the endohedral TM atom.It is interesting to note that,although the germanium element is isovalent to the silicon element in the periodic table, the magnetic moments of the GenTM clusters are very different from those of the SinTM clusters.For example,the magnetic moment quenching is not found in the GenCo clusters[15].

Unlike the d electrons of the transition-metal(TM),the more localized f electrons of rare earth(RE)metal are to a large extent not responsible for bonding.In the latest experimental work, Bowen and co-workers[22]suggested that SinRE clusters,in which theREfelectronstoa large extent appeared not to interact significantlywiththesiliconcage,might retain their magnetic moments. They proposed that further support from theoretical calculations was needed to validate this speculation.Zhao et al.[18]have investigated the magnetic moments of the SinEu clusters by using the DFT computation.They found that the total magnetic moments of these clusters kept a fixed value(7μB)except for the SiEu and Si12Eu clusters.Then one should ask what will the structural, electronic,and magnetic properties of the GenEu clusters be?Do the properties of the GenEu like those of the SinEu clusters or not?It would be very interesting to investigate the growth patterns,the electronic and magnetic properties of the GenEu clusters.In order to answer these questions,we present the calculations on Eu doped germanium clusters GenEu.

1 Computational details

All calculations were performed using the spin-polarized density functional theory(DFT)implemented in the DMOL3package[23-24].In the electronic structure calculations,scalar relativistic pseudopotentials and double numerical basis set plus polarization(DNP)were chosen.The exchange-correlation interaction was treated within the generalized gradient approximation (GGA)using the PW91 functional[25].Self consistent field calculations were performed with a convergence criterion of 10-6hartree on the total energy.The density mixing criterion for charge and spin were 0.2 and 0.5,respectively.The direct inversion in an iterative subspace(DIIS)approach was used to speed up SCF convergence.In the geometry optimization,the converge thresholds were set to 10-5hartree for the energy change.No symmetry constraints were imposed on the structural geometry of the clusters during structural relaxation.The structures were optimized until the atomic forces were converged to be better than 0.02 hartree·nm-1.The on-site charges were evaluated via Mulliken population analysis.

For each initial geometry,all previous studies on the GenCo[15], SinEu[18]and other transition-metal doped semiconductor clusters were considered as guides,and as much as possible GenEu clusters were considered.For each of these clusters,the stability was reassured by calculating harmonic vibrational frequencies. If the unstable geometry with one imaginary frequency was found,a relaxation along the coordinates of the imaginary vibrational mode was rearranged until a true local minimum was finally reached.The search for the lowest-energy states of the clusters was performed keeping the total difference between spin-up and spin-down electrons fixed.For the GenEu clusters we considered values at least from 1μBto 9μB.In cases when total energy decreases with increasing spin,we consider increasing higher spin state until the energy minimum with respect to S is reached.

Similar method has been used to investigate the geometries, electronic and magnetic properties of SinEu[18].The accuracy is tested on clusters of Ge3,Ge4,Ge5and SiEu.As shown in Table 1,our calculations are in good agreement with earlier computation[18,26]and experiment[27]values.

2 Structures of the clusters

Using the computation scheme described in Section 1,we have explored a number of low-lying isomers and determined the lowest-energy structures for the GenEu clusters up to n=13.The obtained lowest-energy state structures are plotted in Fig.1.

Table 1 Comparison of our DFT results with experimental studies and other theoretical calculations for Ge3,Ge4,Ge5, and SiEu clusters

For the smallest GenEu(n≤3)clusters,the lowest-energy structuresare planar geometry.The bond length of the GeEu monomer is 0.291 nm.The lowest-energy structure of the Ge2Eu is an acute angle triangle with C2vsymmetry.The lowest-energy structure of the Ge3Eu cluster is a planar rhombus with C2vsymmetry.For the Ge4Eu cluster,the lowest-energy structure with Csis a distorted rhombus Ge4capped a Eu atom.The lowest-energy structure of the GenEu(n=1-4)clusters are similar to the lowest-energy structures of the GenCo[15]and SinEu[18]clusters.

Fig.1 The lowest-energy state structures of the GenEu(n=2-13)clustersThe dark and light balls represent the Ge and Eu atoms,respectively.

As seen in Fig.1,the most stable structure of the Ge5Eu cluster, which is different from the most stable geometry of the Si5Eu cluster[18],is a boatlike geometry with C1symmetry.In Ref.[18], the most stable structure of the Si5Eu cluster is the one in which a Eu atom adsorbed on a bipyramid of Si5.The ground state structure of the Ge6Eu cluster is a pentagonal bipyramid with C2vsymmetry,which is similar to the most stable structure of the Si6Eu cluster in Ref.[18].The most stable structure of the Ge7Eu cluster with Cssymmetry is a pentagonal bipyramid Ge7capped a Eu atom.The ground state structure of the Ge8Eu cluster with C1symmetry is a distorted octahedral Ge7Eu capped a Ge atom. As seen in Fig.1,the lowest-energy structure of the Ge9Eu cluster is a layer geometry with 1,5,4 atoms on each layer.The structure of the Ge9Eu cluster can be described as 1-5-4 layer structure.The lowest-energy structure of the Ge10Eu cluster is a distorted 1-5-4-1 layer structure;it can be seen as 1-5-4 layer Ge9Eu cluster capped one Ge atom.The most stable structure of the Ge11Eu cluster is the 1-4-4-1 layer Ge9Eu cluster capped two Ge atoms.The lowest energy structure of the Ge11Eu cluster is similar to the first low-lying structure of the Si11Eu cluster in Ref.[18].The lowest energy structures of the Ge12Eu and Ge13Eu clusters are 1-4-4-4 and 1-4-4-4-1 layer structures,respectively.

Noting that in the early investigation of the SinEu[18]cluster, starting from the cluster size n=12,the Eu atom of Si12Eu cluster completely falls into the center of the Si frame and forms a cage. Similar growth pattern can also be found in the GenCo[15],SinFe[5], and other transition-metal-doped semiconductor clusters[28].For example,for the GenCo clusters,starting from n=9,the Co atom of the Ge9Co cluster completely falls into the center of the Ge frame and forms a cage.Whereas similar growth pattern was not found in the GenEu clusters.For the lowest-energy structure of the GenEu cluster,the Eu atom always prefers to cap on the surface site of the germanium frame.It is interesting to note that similar growth pattern was also found in the SinYb clusters[19-20]. In Refs.[19-20],they found that Yb atom preferred to cap on the surface site of the silicon frame and no cagelike geometries were found up to n=13.

3 Size selectivity and electronic properties

In order to investigate the size selectivity and the electronic properties of the GenEu clusters,we have calculated Eb,the second-orderdifferenceofthetotalenergy(Δ2E),and the HOMOLUMO energy gaps.Eband Δ2E are defined as

where the E(GenEu),E(Gen+1Eu),E(Gen-1Eu),E(Eu),and E(Ge) denote the total energies of the GenEu,Gen+1Eu,Gen-1Eu,Eu,and Ge clusters,respectively.The calculated results of Eb,Δ2E,and the HOMO-LUMO energy gaps are plotted in Fig.2.

According to Fig.2,one can find that Ebof the GenEu clusters increases gradually as the size of n increasing;reflecting that the clusters can continue to gain energy during the growth process. Ebof the GenEu clusters gradually increases with the cluster size n rapidly up to n=5 and the size dependence becomes smooth at n=5-13.

In cluster physics,Δ2E is a sensitive quantity that can reflect the relative stability of the clusters.The curve of the Δ2E for the GenEu clusters is plotted in Fig.2.As seen in Fig.2,the peaks of the Δ2E localize at n=2,5,10,indicating these clusters are more stable than their neighboring clusters.

Fig.2 Size dependence of the second-order energy difference(Δ2E),the binding energy per atom(Eb)and the HOMO-LUMO energy gaps for the lowest-energy structures of GenEu clusters

As seen in Fig.2,the peaks of the HOMO-LUMO energy gaps localize at n=5,10,indicating these clusters may be more stable than their neighboring clusters.Noting that although the gaps of the GenEu clusters are smaller than those of the Genclusters(ca 2.0 eV[15]),almost all the gaps of the GenEu clusters are still larger than 1 eV except the Ge7Eu,and Ge12Eu clusters which are 0.79 and 0.94 eV,respectively.This is different from those of the GenCo clusters[15].In our earlier work[15],for the GenCo(n=1-13) clusters,almost all the gaps of the clusters are less than 1 eV. That is to say,unlike the GenCo clusters which are partially metallic,the electronic properties of the GenEu clusters should be similar to those of the Genclusters.

On the basis of the calculated results above,the GenEu clusters with n=5,10 show stronger stability than their neighboring clusters.The similar conclusion was also found in theoretical work of the GenCo cluster[15].

4 Magnetic properties

Based on the optimized geometries,the magnetic properties of GenEu clusters were obtained and the results are listed in Table 2.As shown in Table 2,the total magnetic moments(μtotal) oftheGenEuclusterskeepafixedvalue(7μB)exceptGeEucluster. Compared with the local spin magnetic moments of Eu atom (μEu),it clearly shows that μtotalis mainly from the Eu atom. Detailed analysis of the on-site atomic charges and local magnetic moments was performed to further understand the charge transfer and the magnetic properties of GenEu clusters. The magnetic moments of the Eu atom are mainly from the 4f state,following is the 5d state;the 6p and 6s states contribute little to the magnetic moment of Eu atom.Noting that the ground state electron configuration of Eu atom is[Xe]4f76s2.As seen in Table 2,the Q4fof Eu atoms in GenEu clusters are 6.991e-7.005e.Hence we can conclude that the 4f electrons of Eu atom in GenEu cluster do not interact with the germanium. Whereas there are still some charge transfer from the Ge atom to the Eu atom.As seen in Table 2,the charges of Eu atom in the GenEu clusters are 0.410e-0.747e.The charge transfer also occurs between the 5d,6p,and 6s states of Eu atom in the GenEu clusters.The charges of the 5d states of Eu atoms in the GenEu clusters are 0.361e-0.843e,the charges of the 6p states of Eu atoms in the GenEu clusters are 0.099e-0.156e,and the charges of the 6s states of Eu atoms are 0.345e-1.136e.One can find that the charge transfer between the Ge atom and Eu atom,and the hybridization between the 5d,6p,and 6s states of Eu atom make the local magnetic moment of Eu atom as much as 7.148μB-7.267μB.But the local magnetic moment of the 4f state of the Eu atom in the GenEu cluster is mainly equal to the total magnetic moment of the GenEu cluster.In other words,although the charge transfer enhances the local moment of the Eu atom,it can also enhance the local moment of the Ge atom.So the charge transfer does not help to enhance the total magnetic moment of the GenEu clusters.

Table 2 Charges and the spin magnetic moments of the GenEu clusters

5 Conclusions

First-principles calculations have been performed to study the growth patterns,the electronic and magnetic properties of the GenEu clusters.All the results are summarized in the following:

(1)For the ground state structures of the GenEu(n=1-13) clusters,the Eu atom always prefers to cap on the surface of the germanium frame,which is different from the growth patterns of the SinEu cluster and other transition-metal-doped-semiconductor clusters.

(2)According to the results of Δ2E and HOMO-LUMO energy gap,the GenEu clusters with n=5,10 are more stable than their neighbors.

(3)The total magnetic moments of the GenEu clusters keep a fixed value(7μB)except the GeEu cluster.The total magnetic moments of the GenEu clusters are mainly equal to the local magnetic moment of the 4f state of the Eu atom.Although the charge transfer from the Ge atom to the Eu atom and the hybridization between the 5d,6p,and 6s states of Eu atom can enhance the local magnetic moment of Eu atom,it can not help to enhance the total magnetic moment of the GenEu clusters.

Acknowledgments: Thanks very much to Dr.ZHAI Feng-Xiao of Shanghai Institute of Optics and Fine Mechanics and Dr.GUO Ling-Ju of Institute of Solid State Physics for their help and useful discussion. This work was done under the School of Physics and Electronics of Henan University.Thanks very much for their help.

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GenEu(n=1-13)團(tuán)簇的結(jié)構(gòu)、電子及磁性質(zhì)

井 群 葛桂賢 曹海賓*黃旭初 劉效勇 閆紅霞

(石河子大學(xué)師范學(xué)院物理系,生態(tài)物理重點(diǎn)實(shí)驗(yàn)室,新疆石河子 832000)

利用密度泛函理論在廣義梯度近似下研究了GenEu(n=1-13)團(tuán)簇的生長(zhǎng)模式和磁性.結(jié)果表明:對(duì)于GenEu(n=1-13)團(tuán)簇的基態(tài)結(jié)構(gòu)而言,沒有Eu原子陷入籠中.這和SinEu以及其它過渡金屬摻雜半導(dǎo)體團(tuán)簇的生長(zhǎng)模式不同.除GeEu團(tuán)簇外,GenEu(n=2-13)團(tuán)簇的磁矩均為7μB.團(tuán)簇的總磁矩與Eu原子的4f軌道磁矩基本相等.Ge、Eu原子間的電荷轉(zhuǎn)移以及Eu原子的5d、6p和6s間的軌道雜化可以增強(qiáng)Eu原子的局域磁矩,卻不能增強(qiáng)團(tuán)簇總磁矩.

密度泛函理論; GenEu團(tuán)簇; 生長(zhǎng)模式; 磁性

O641 been investigated by using the DFT computation[6].The average binding energies of the GenFe clusters are higher than those of the corresponding pure Genclusters,reflecting doping with a Fe atom can enhance the stability of germanium clusters.The geometry,electronic and magnetic properties of GenCo have been investigated by using the DFT computation[15].Addition of a Co atom enhances the stability of the host Genclusters.And for the GenCo clusters,starting from n=9,the Co atom completely falls into the Genframe and forms a cage.The highest occupied molecular orbital-lowest unoccupied molecular orbital(HOMOLUMO)gaps of the dopant clusters are smaller than those of the pure clusters,and the magnetic moment does not quench which is

Received:May 12,2010;Revised:July 8,2010;Published on Web:July 20,2010.

*Corresponding author.Email:caohb@shzu.edu.cn;Tel:+86-993-2315965

?Editorial office of Acta Physico-Chimica Sinica