刘 俊 张 博 陈 立 陈培达 董会宁 郑瑞伦

(1重庆邮电大学数理学院,重庆400065; 2重庆邮电大学通信学院,重庆400065; 3西南大学物理科学与技术学院,重庆400715)

几种纤锌矿相半金属铁磁体磁学性能的第一原理研究

刘 俊1,*张 博2陈 立1陈培达1董会宁1郑瑞伦3

(1重庆邮电大学数理学院,重庆400065;2重庆邮电大学通信学院,重庆400065;3西南大学物理科学与技术学院,重庆400715)

通过基于密度泛函理论的第一原理计算,优化了纤锌矿结构的化合物TmZn15S16(Tm=V,Cr,Mn)的几何结构,并研究了它们的磁学性能.结果表明:TmZn15S16均为典型的半金属铁磁体,它们的超胞磁矩分别为3.0099µB,3.9977µB和5.0092µB;这些磁矩主要来源于被掺入的过渡元素;CrZn15S16的半金属特性比VZn15S16和MnZn15S16更稳定;这些半金属铁磁体的半金属带隙均比较宽,表明它们可能具有较高的居里温度; TmZn15S16中杂质过渡离子的电子结构分别为V:eg2↑t12g↑,Cr:eg2↑t22g↑和Mn:eg2↑t32g↑.

半金属性;磁学性质;超胞磁矩;居里温度;电子结构

1 Introduction

Half-metallic ferromagnets(HMFs)have attracted increasing interest since one of their two spin channels is metallic and the other is semiconducting or insulating,1-6leading to complete spin polarization(±100%)at the Fermi level.HMFs are very important spintronic materials based on their application prospects in the following cases.Firstly,the increasing importance has been attached to magnetoresistance materials since the giant magnetoresistance effect(GMR)was found in 1988.7-10Many magnetoresistance devices such as magnetoresistance random access memory(MRAM)and read-write magnetic-head of computers had been invented.11,12However,only the transmission of the spins of electrons is considered in the traditional magnetoresistance materials.In fact,electrons have the charges and the spins,and the spins may be also transmitted in HMFs.Therefore,the transmission of spins and charges may be simultaneously controlled in HMFs so that HMFs have better application prospects than traditional magnetoresistance materials in spintronics.1,12Secondly,the realization of spintronic semiconductor devices requires highly spin-polarized current injected from magnetic electrodes to them.4,11,12HMFs have ±100%spin polarization,and their resistivity matches well with that of semiconductors,so they are the best magnetic electrode materials of spin semiconductors.4,11,12Recently,much attention has been paid to transition-metal doped or pure zinc blende semiconductor-type HMFs,such as CrAs,CrSb,and doped ZnTe.12-18Some of them have been found to have halfmetallicity experimentally.12-17Little attention has been paid to wurtzite HMFs yet.In this paper,some transition-metal doped wurtzite HMFs were predicted and their magnetic properties were investigated based on the density functional theory.

2 Technicality

Wurtzite ZnS is a typical kind of semiconductor,whose experimental crystal constants of 1×1×1 supercell are a=b=0.382 nm and c=0.626 nm.19To achieve the realistic experimental dopant concentration(10%-30%),a periodic 2×2×2 supercell of ZnS consisting of 16 Zn-ions and 16 S-ions was used.Then one Zn-ion was supposed to be substituted by one transition-metal(Tm)ion,so the dopant concentration was 6.75% (atomic fraction).The doped supercell was shown in Fig.1, where the‘Tm’indicated the V-,Cr-,and Mn-ions,respectively,corresponding to the VZn15S16,CrZn15S16,and MnZn15S16supercell.

Their space groups are all P63MC.The optimization of geometrical structures and calculations of magnetic properties were performed by using the‘VASP code’based on the density functional theory.The wave function was expanded with the plane-wave pseudo-potentials,and the exchange correlation function was the Perdew-Burke-Ernzerhof functional(PBE)of three nonlocal gradient-corrected exchange-correlation functionals(GGA).The cutoff energy was 500 eV and a gamma centered 4×4×4 k-mesh was used for the first Brillouin zone. The cell parameters and the atomic positions of all structures were optimized until all components of the residual forces were less than-0.01 eV·nm-1.The self-consistent energy was set to 10-5eV.

Fig.1 Supercells of TmZn15S16(Tm=V,Cr,Mn)

In order to confirm our calculations,the geometrical structures of wurtzite ZnS,CrAs,and CrTe were optimized and compared with experimental or calculated values of others. Our calculated lattice constants of CrAs(a=b=0.403 nm,c= 0.654 nm)and CrTe(a=b=0.447 nm,c=0.725 nm)basically accord with those of CrAs(a=b=0.400 nm,c=0.653 nm)and those of CrTe(a=b=0.446 nm,c=0.723 nm)calculated by Xie20and Zhang21et al.,respectively.Furthermore,the relative differences of the calculated crystal constants of ZnS(a=b=0.393 nm,c=0.647 nm)with the experimental values(a=b=0.382 nm,c=0.626 nm)are only 2.88%and 3.35%,19respectively. This shows that our calculations basically accord with experimental values.On the other hand,the crystal constants of Zn0.442Fe0.558S are a=b=0.384 nm,c=0.630 nm,which are near to a=b=0.382 nm,c=0.626 nm of ZnS experimentally.22In this paper,V-,Cr-,and Mn-elements are on the same line with Zn element in the Period Table of elements and the dopant concentration is very low(only 6.75%)so that they cause little influence on the crystal constants.For comparison,the crystal constants of VZn15S16,CrZn15S16,and MnZn15S16supercells are all selected as a=b=0.786 nm,c=1.294 nm,which are the same as those of Zn16S16.

3 Results and discussion

3.1 Total density of state of wurtzite TmZn15S16

Total spin-polarized densities of states(TDOS)of wurtzite TmZn15S16(Tm=V,Cr,Mn)are shown in Fig.2,where the solid and the dashed lines show the TDOS of up-spin and down-spin sub-bands,respectively.The TDOS of TmZn15S16are also calculated by GGA+U,respectively.Through comparing the TDOS by GGA with those calculated by GGA+U,we find that they are very similar to each other.It means that these materials are all possibly half-metallic materials.The TDOS whose energy is from-15.0 to-8.8 eV(aTDOS)are not plotted,confined by the size of these plots.From Fig.2,the spin polarization of TmZn15S16at the Fermi level is all 100%,so they are all potential half-metallic ferromagnets. Furthermore, VZn15S16, CrZn15S16,and MnZn15S16have similar TDOS when their energies are much lower than the Fermi level.For instance,their up-spin and down-spin TDOS whose energy is from-15.0 to-6.5 eV are almost axially symmetrical with the axial line showing DOS=0,so they cause no influence on the magnetic properties of TmZn15S16.The possible reason is that V-,Cr-, and Mn-ions have similar isolated atomic orbital structures and these orbitals are shielded by outer electrons.However,the up-spin and down-spin TDOS near the Fermi level are evidently not axially symmetrical,which cause main contribution to their magnetic properties.On the other hand,the Fermi levels of TmZn15S16relatively move toward lower energy when the dopants vary from V to Mn.The reason is perhaps that intra-ionic interaction including the coulomb repulsion and exchange interaction is stronger if supercells have more electrons.Among these materials,VZn15S16have the least electrons,but Mn-Zn15S16have the most electrons.Stronger intra-atomic interaction results in huger separation of their down-spin sub-bands and pushes the Fermi levels to move toward the lower energy. This results in the spin-flip gap or half-metallic gap 1.35 eV of CrZn15S16,defined as the minimum absolute values of the Efvand Efc,are evidently larger than 0.51 and 0.78 eV of VZn15S16and MnZn15S16,shown in Fig.2.Here,the Efvindicates the energy distance from the maximum energy of the semiconducting valence sub-bands to the Fermi level of the metallic sub-bands, and the Efcindicates the energy distance from the Fermi level of the metallic sub-bands to the minimum energy of semiconducting conduction sub-bands.Therefore,the half-metallicity of CrZn15S16is more stable than VZn15S16and MnZn15S16.

Fig.2 Spin-polarized total density of states(TDOS)of TmZn15S16(Tm=V,Cr,Mn) These TDOS lay in five energy areas.For VZn15S16,as an example,TDOS includeaTDOS（below the-8.8 eV,being not plotted here）,bTDOS(from-8.8 to-7.8 eV), cTDOS(from-6.5 to-1.9 eV),dTDOS(through the Fermi level),andeTDOS(above the Fermi level),respectively

The spin gaps of VZn15S16,CrZn15S16,and MnZn15S16,defined as the energy distance from the maximum energy of semiconducting valence sub-bands to the minimum energy of the semiconducting conduction sub-bands,are 3.85,2.73,and 2.14 eV, respectively.They are all larger than 2.0 eV.These calculated spin gaps by GGA are generally much less than experimental values due to the correlation effect of excitation electrons being underestimated.23This shows that the spin gaps of these HMFs are wide,and then they have high Curie temperature possibly.This is very important for the application of magnetic materials.It is also shown in Fig.2 that the up-spin TDOS of VZn15S16and CrZn15S16at the Fermi level are much larger than those of MnZn15S16.Furthermore,the TDOS curves of VZn15S16and CrZn15S16at the Fermi levels slope more gently than those of MnZn15S16.This shows that there are more conduction electrons in VZn15S16and CrZn15S16than that in MnZn15S16,so the conductivities of VZn15S16and CrZn15S16are possibly higher than that of MnZn15S16.On the other hand,MnZn15S16have some up-spin holes since the energy maximum of its up-spin conduction sub-bands is a little higher than the Fermi level. However,VZn15S16and CrZn15S16have no up-spin holes near the Fermi level.Therefore,the conductivities of VZn15S16and CrZn15S16come mainly from its conduction electrons,but that of MnZn15S16arises from both its conduction electrons and holes.

3.2 Local density of state of wurtzite TmZn15S16

The spin-polarized local densities of states(LDOS)of TmZn15S16are shown in Fig.3.Curves above and below the line indicating DOS=0 show the DOS of up-spin and down-spin sub-bands,respectively.The LDOS of Tm-ions,including the DOS of s-,p-,and d-orbitals are plotted,and only the total DOS of one Zn-ion and one S-ion are plotted since the magnetic properties of HMFs come mainly from Tm-ions.From Fig.3,theaTDOS of VZn15S16come mainly from S-3s orbitals. Similarly,those of CrZn15S16and MnZn15S16are also mainly from S-3s orbitals.These orbitals are localized in their S-ions since their energies are much lower than the Fermi level.The TDOS of VZn15S16from-8.8 to-7.8 eV(bTDOS)come mainly from Zn-3d orbitals.The TDOS of VZn15S16from-6.5 to-1.9 eV(cTDOS)come mainly from S-3p,V-3d and Zn-4s orbitals.The TDOS at the Fermi level(dTDOS)comes mainly from V-3d spin-up orbitals.The energy of spin-down orbitals is evidently higher than the Fermi level.This shows that there is strong crystal field,resulting in the split of spin-up and spin-down 3d-orbitals.cTDOS anddTDOS of CrZn15S16and Mn-Zn15S16both have similar properties similar to VZn15S16.However,the Fermi level of CrZn15S16and MnZn15S16are nearer to the spin-down valence sub-bands.The main reason is that the crystal field in CrZn15S16and MnZn15S16is stronger than that in VZn15S16.Then the stronger crystal field will pull the Fermi level to the lower energy.

The above discussions are also supported by the orbitals of TmZn15S16near the Fermi level shown in the Fig.4.Only the up-spin orbitals are given in Fig.4 since there are no down-spin orbitals near the Fermi level for TmZn15S16.From Fig.4,the orbitals are mainly from the Tm-ions(Tm=V,Cr,Mn),and partially S-ions around them.This shows that the magnetic moments and half-metallicity come mainly from Tm-ions and partially from their ligands.On the other hand,both Zn-ions and their ligands of CrZn15S16and MnZn15S16have no spin-up orbitals near the Fermi level,but S-ions around Zn-ions of VZn15S16have some.This shows that the conductivity of VZn15S16is possibly larger than those of CrZn15S16and TmZn15S16.

Fig.3 Spin-polarized local density of states(LDOS)of TmZn15S16These LDOS lay in five energy areas,corresponding to the energy areas ofaTDOS,bTDOS,cTDOS,dTDOS,andeTDOS in Fig.2.

The ionic magnetic moments of the TmZn15S16supercells are calculated in detail and are given in Table 1 to know well their magnetic properties.They include the magnetic moments of s-, p-,d-orbitals and total magnetic moments(Ms,Mp,Md,Mtin Table 1).In Table 1,ions having the same magnetic moment distribution are put in the same row and the subscripts show the places of ions.From Table 1,the ionic magnetic moments of one V-ion,one Cr-ion and one Mn-ion in VZn15S16,CrZn15S16and MnZn15S16are 2.9929µB,4.0202µB,and 4.7556µB,respectively,which are much higher than those of Zn-and S-ions. This shows that Tm-ions give main contribution to the half-metallicity and supercell magnetic moments of TmZn15S16,and there is strong crystal field between the Tm-ions and S-ions. On the other hand,adding up all ionic magnetic moments of the TmZn15S16supercells,we can get that the supercell magnetic moments ofVZn15S16,CrZn15S16,and MnZn15S16are 3.0099µB,3.9977µB,and 5.0092μB,respectively.They are almost equal to the integral magnetic moments 3.0000µB, 4.0000µB,and 5.0000μB,respectively.Having integer supercell magnetic moments is one of important characters of half-metallic ferromagnets(HMFs).This shows that VZn15S16,CrZn15S16, and MnZn15S16are all HMFs potentially,which accord with those results from both Fig.2 and Fig.3.

Fig.4 Up-spin orbitals of some ions of TmZn15S16 (Tm=V,Cr,Mn)near the Fermi level

From the ligand field theory,23-25there are four S-ligands around one Tm-ion(Tm=V,Cr,Mn),and then one Tm-ion and its ligands form the tetrahedral coordinate compound(ML4). There is strong tetrahedral crystal field in ML4,which results in 3d-orbitals of Tm-ions being split into bonding orbitals containing two egand three t2g-orbitals with lower energy,and their corresponding anti-bonding orbitals containing two eg*and three t2g*-orbitals with higher energy.Furthermore,the energy of the eg-orbitals is lower than that of the t2g-orbitals.One V-ion has three 3d-electrons which enter into two eg-orbitals and one t2g-orbital in parallel,respectively,based on the lowest energy principle.Therefore,the electronic structures of V-ions are V eg2↑t2g1↑.One isolated Cr-ion has five 3d-electrons,but one of them enters into 4s-orbital and conforms paired electronswith the 4s-electron in the compound CrZn15S16.Therefore,the Cr-ion has four 3d-electrons and they enter into two eg-orbitals and two t2g-orbitals in parallel,respectively,so the electronic structures of Cr-ions are Cr eg2↑t2g2↑.Similarly,five 3d-electrons of a Mn-ion enter into two eg-orbitals and three t2g-orbitals in parallel,so the electronic structures of Mn-ions are Mn eg2↑t2g3↑.From the electronic structures of V-,Cr-,and Mn-ions,the supercellmagnetic moments ofVZn15S16, CrZn15S16,and MnZn15S16are 3.0000µB, 4.0000µB, and 5.0000µB,respectively,which agree well with those in Table 1.

Table 1 Calculated ionic magnetic moments and supercell magnetic moments of TmZn15S16(Tm=V,Cr,Mn)

4 Conclusions

In summary,we have explored the structural,electric,and magnetic properties of TmZn15S16(Tm=V,Cr,Mn)by performing the first-principles calculations within the GGA-PBE for the exchange-correlation functional.TmZn15S16are typical half-metallic ferromagnets.The supercell magnetic moments of VZn15S16,CrZn15S16,and MnZn15S16are 3.0099µB,3.9977µB, and 5.0092µB,respectively,which arise mainly from Tm-ions. The half-metallicity of CrZn15S16is more stable than those of VZn15S16and MnZn15S16.They all have possibly high Curie temperatures,then the wide application prospects.The electronic structures of V-,Cr-,and Mn-ions are eg2↑t2g1↑,eg2↑t2g2↑,and eg2↑t2g3↑,respectively.

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January 12,2011;Revised:March 29,2011;Published on Web:May 30,2011.

First-Principles Investigation of Magnetic Properties of Several Wurtzite Half-Metallic Ferromagnets

LIU Jun1,*ZHANG Bo2CHEN Li1CHEN Pei-Da1DONG Hui-Ning1ZHENG Rui-Lun3
(1College of Mathematics and Physics,Chongqing University of Posts and Telecommunications,Chongqing 400065,P.R.China;2College of Communications and Information Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,P.R.China;3School of Physical Science and Technology,Southwest University,Chongqing 400715,P.R.China)

By performing first-principles calculations based on the density functional theory we optimized the geometric structures of TmZn15S16(Tm=V,Cr,Mn)and determined their magnetic properties.TmZn15S16are typical half-metallic ferromagnets.The supercell magnetic moments of VZn15S16,CrZn15S16,and MnZn15S16are 3.0099µB,3.9977µB,and 5.0092µB,respectively,and these arise mainly from the Tm ions. The half-metallicity of CrZn15S16is more stable than that of VZn15S16and MnZn15S16.These half-metallic ferromagnets have wide spin gaps.Therefore,high Curie temperatures are possible.The electronic structures of the V,Cr,and Mn ions are eg2↑t12g↑,eg2↑t22g↑,and eg2↑t32g↑,respectively.

Half-metallicity;Magnetic property;Supercell magnetic moment;Curie temperature; Electronic structure

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∗Corresponding author.Email:liujun@cqupt.edu.cn,phyv51@nus.edu.sg;Tel:+86-23-62471346.

The project was supported by the Chongqing Natural Science Foundation,China(CSTC2009BB4083,CSTC2010BB4405),and Doctoral Foundation of Chongqing University of Posts and Telecommunications,China(A2008-63).

重庆市自然科学基金（CSTC2010BB4405,CSTC2009BB4083)和重庆邮电大学博士启动基金(A2008-63)资助项目