Symmetry-Dependent Transport Properties of γ-Graphyne-based Molecular Magnetic Tunnel Junctions

Yishun Yang,Min Zhou,＊,Yanxia Xing,＊

1 Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement,Ministry of Education,Beijing Institute of Technology,Beijing 100081,China.

2 Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems,Beijing Institute of Technology,Beijing 100081,China.

Abstract:The molecular magnetic tunnel junction(MMTJ)with high tunnel magnetoresistance(TMR)is an important component for devices such as computers and electronic storage.With the rapid development of the modern electronics industry,the decrease of device size and the increase of area density,it is important to improve TMR technology.In addition,the computing process faces huge challenges.As the size of electronic devices decreases,small changes may cause completely different transmission characteristics,therefore the minute details of the device must be carefully controlled.In this paper,in order to find large TMR values and explore the role of symmetry on spin-polarized transport properties,γ-graphyne nanodots(γ-GYND)coupled between ferromagnetic(FM)metallic zigzag graphene nanoribbon(ZGNR)electrodes were used.Depending on the widths of the ZGNR and two types of contact positions between the ZGNR and γ-graphyne nanodots(γ-GYND),eight ZGNR/γ-GYND/ZGNR MMTJs with different symmetries were constructed.By using Keldysh non-equilibrium Green’s function(NEGF)and density functional theory(DFT),the I-V curve,the spin-injection efficiency(SIE)and TMR of MMTJs were calculated.We found that the transport properties of these MMTJs differed substantially.For absolute symmetric MMTJs,due to the wave functions corresponding to the band structure near the Fermi energy having different parity,the electron transport between the wave functions with different parity is prohibited,so we can see that the spin-down current is always zero.This implies that these absolutely symmetrical structures have 100% spin injection efficiency over a wide range of bias voltages.In addition,the calculation results also show that these absolutely symmetric structures also have large TMR at low bias,up to 3.7 × 105,indicating that these devices have a large magnetoresistance effect and high magnetic field sensitivity,which can be used in the read head of computer hard disks,MRAM,and various magnetic sensors.However,for these asymmetric MMTJs,since there is no limitation of the wave function parity of the left and right electrodes,the spin-up current and spin-down current fluctuated as the bias voltage increased,so perfect SIE does not appear.In addition,the calculation results showed that the TMR of asymmetric MMTJs were four orders of magnitude smaller than with symmetric MMTJs.Thus the symmetry of MMTJs has a great influence on the spin-polarized transport properties of the device.These absolutely symmetrical MMTJs have spin-polarized transport properties that are far superior to other MMTJs.This is conducive to the manufacture of spin filters,rectifiers,and various magnetic sensors.Finally,these excellent characteristics can be explained by the transmission coefficient,local density of states(LDOS)and band structure.

Key Words:Non-equilibrium Green’s function;Density functional theory;Zigzag graphene nanoribbon;γ-Graphyne nanodot;Spin injection efficiency;Tunneling magnetoresistance;Spin-polarized transport property

1 Introduction

Spintronics have been in the focus of intensive research as the next-generation technology1.Low-dimensional materials with unusual properties and fascinating prospects provide a novel platform for the innovative design of spintronics devices2-5.Among them,zigzag graphene nanoribbon(ZGNR)has attracted enormous attention for its unique electronic and magnetic properties6-16.The symmetry with respect to the middle plane between the two edges of ZGNR has great influence on the transport properties under bias voltage9.For the ZGNR with symmetric edges,the spin-up and spin-down currents are filtered unidirectionally in the presence of opposite bias voltages,resulting in the double spin injection efficiency(DSIE).However,the spin currents of asymmetric ZGNR are proportional to the bias voltage,DSIE will not occur17.

Based on the discovery of graphene,two-dimensional(2D)carbon allotropes have attracted wide attention,especially 2D graphyne18-22.Unlike graphene,graphyne has both sp and sp2hybrid carbon bonds23,24.The sp hybrid carbon bonds destroy the original honeycomb lattice of graphene,resulting in four different geometries of graphyne:α-graphyne,β-graphyne,γgraphyne and 6,6,12-graphyne25,26.The four different structures have 100%,66.67%,33.33% and 41.67% percentage of alkyne linkages,respectively.Besides,α-graphyne,β-graphyne and γgraphyne have hexagonal symmetries like graphene27,whereas 6,6,12-graphyne has rectangular symmetry28,29.Although there are some differences in these structures,their properties have certain similarities.For instance,the properties of twodimensional α-graphyne and 6,6,12-graphyne are the most similar to those of graphene.They have metal conductance,and armchair nanoribbons are non-magnetic semiconductors,zigzag nanoribbons have an anti-ferromagnetic(AFM)ground state,and the transport properties are also related to the symmetry of structures30-32.However,there are also some inconsistencies,such as the β-graphyne nanoribbon has no edge state and the transport property is independent of the symmetry of the structures33.The γ-graphyne and γ-graphyne nanoribbon both have semiconducting properties34.

In this paper,by sandwiching semiconductor γ-graphyne nanodot(γ-GYND)between two ferromagnetic ZGNR electrodes,we construct eight molecular magnetic tunnel junctions(MMTJ)with different symmetries depending on the width of ZGNR and different coupling positions between ZGNR and γ-GYND,as shown in Fig.1.Then we calculate the spindependent transport properties using non-equilibrium Green's function formalism combined with density functional theory(NEGF-DFT).The graphene ribbon with even carbon chains have specific band structure symmetry.For the central coupling cases(Fig.1a,c),the absolute mirror symmetry makes the extra restriction that brings very different transport current for the different spin and different ferromagnetism.So,the absolute symmetric structures have the spin polarization and GMR ratio are far superior to other structures,such as 100% spin injection efficiency in a wide range of bias voltage and the tunneling magnetoresistance(TMR)can reach to 105.When the coupling position of MMTJs is off the center of ferromagnetic ZGNR electrodes(Fig.1e-h),the SIE changes with the bias voltage and the maximum TMR is only three order of magnitude at the zero bias.All in all,the results show that the MMTJs with the mirror symmetry about the middle plane of two edges of ZGNR electrode have excellent spin transport properties and are promising spintronics devices.

Fig.1 Schematic diagram of ZGNR/γ-GYND/ZGNR MMTJs.

2 Models and computational method

Previous studies have shown that ZGNR has a spontaneous magnetic moment,the total magnetic moment is zero in antiferromagnetic(AFM)ZGNR,and the total magnetic moment is non-zero in ferromagnetic(FM)ZGNR.In this paper,only FM ZGNR is considered in order to study the spin transport properties of the device.The external electric field or magnetic field can control the spin direction of the left(right)electrode.If the spin direction at two electrodes point is in the same or opposite direction,then the ZGNR electrodes would show the parallel(P)or anti-parallel(AP)spin configuration.We sandwich γ-GYND between two ZGNR electrodes.Depending on the width of ZGNR and the difference of coupling position,several MMTJs are shown in Fig.1,namely(a)4C,(b)5C,(c)6C,(d)7C,(e)4E,(f)5E,(g)6E and(h)7E.All the MMTJs are symmetric to the middle plane of z-direction.For the 4C,5C,6C and 7C,the coupling position locate at the center or near the center of ZGNR electrodes.The 4C and 6C have the mirror symmetries with respect to the x-direction because the 4-ZGNR and 6-ZGNR are symmetric about the middle plane between the two edges of ZGNR.As for the 5C and 7C,the coupling position are slightly off the center of 5-ZGNR and 7-ZGNR to keep identical coupling forms(pentagon coupling)between ZGNR and γ-GYND35.Different from the 4C 5C 6C and 7C,the coupling positions of 4E 5E 6E and 7E locate at the edge of ZGNR,and the ZGNR electrodes and γ-GYND maintain the pentagon coupling.All the dangling bonds of carbon atoms are saturated by hydrogen atoms.The MMTJs consist of three regions:left electrode,central scattering region and right electrode.By switching the directions of magnetic fields applied on the two ZGNR electrodes to be parallel or antiparallel,we have the parallel configuration(PC)and antiparallel configuration(APC),respectively(see the red arrow and the black arrow in Fig.1).

The spin-dependent transport properties of MMTJs are calculated by using the NEGF-DFT implemented in the NANODCAL software package36,37.The Hamiltonian and electronic structure of the device are determined by the DFT,the NEGF determines the non-equilibrium quantum statistics of the device38,39.In our calculation,the wave functions are expanded using the double-ζ polarized atomic orbital basis and the exchange-correlation is treated at the level of local spin density approximation40-43.Atomic cores are defined by the standard norm-conserving nonlocal pseudo-potentials44.In selfconsistence Hamiltonian calculations,the convergence criteria of Hamiltonian matrix is set to 10-4eV.The electron transport is along the z-direction and a large vacuum region of 15 Å(1 Å=0.1 nm)is included in the x and y directions to avoid interactions between periodic images.The spin-dependent current is calculated from the Landauer-Büttiker formula:

where σ=↑,↓ represents spin-up and spin-down,µLand µRrepresent the electrochemical potential of the left and right electrodes.Tσ(E)is the transmission spectrum:

where Grand Gaare the retarded and advanced Green’s functions of the system;ΓL/Ris the linewidth function used to describe the coupling between the left(right)lead and scattering region.

The spin-injection efficiency(SIE)is defined as

The tunneling magnetoresistance(TMR)is defined as:

3 Results and discussion

Fig.2 Spin-polarized I-V curves of centre-coupled MMTJs.

Fig.3 Spin-polarized I-V curves of edge-coupled MMTJs.

Fig.4 SIE and TMR versus bias for the MMTJs.

Then when the coupling position locates at the edge of ZGNR,as shown in Figs.3a-d,the trends of spin-polarized currents are almost the same regardless of the widths of the ZGNR.From these spin-polarized I-V curves,we can conclude that all these MMTJs show semiconducting behaviors.Within the critical bias voltage Vc,the spin-polarized currents are zero.When the bias voltage exceeds Vc,all the spin-polarized currents are generated with the increasing of bias voltage,we cannot get pure I↑or I↓at the calculated range of bias voltage.In addition,we also find an interesting phenomenon.For different spin configurations,the same spin-polarized currents have similar trend,which indicates that when the coupling position locates at the edge of ZGNR,the different spin configurations have no effect on the transport properties.Therefore,the symmetry of the MMTJ has a great influence on the transport properties of electrons.

We also calculate the SIE of all the MMTJs in the PC and APC with the center or near center contact and edge contact as shown in Fig.4a,b and d,e,respectively.The SIE measures the degree of spin polarization,so a large and stable SIE is desirable for MMTJs.We can see that the 4C and 6C have large and stable SIE both in the PC and APC.When the coupling position locates at the edge of ferromagnetic ZGNR electrodes,the SIE changes irregularly with the increasing of bias voltage.But especially we find an interesting SIE phenomenon for the PC of 7C,see the blue circle in Fig.4a.At low bias,7C also has a large SIE.This is because the electrode band structure has no restrictions on electron transport for the PC,so as the width of the ZGNR increases,this structure approaches a pseudo-symmetry,leading to a large SIE similar to 6C.But with the increase of bias voltage,this pseudo-symmetry is recognized,so the SIE starts to decrease again under high bias voltage.In addition,we show TMR in Fig.4c,f.From Fig.4c,the 4C and 6C have large TMR at lower bias voltage,and the largest TMR can reach up to 105.For the 5C and 7C,although the maximum TMR is three order of magnitude smaller than the 4C and 6C,the TMR of 7C is larger than the TMR of 5C,which means that when the odd width of ZGNR continues to increase,maybe the TMR magnitude of the asymmetric MMTJ will reach the magnitude of TMR of absolute symmetric MMTJ.In Fig.4f,when the coupling position locates at the edge of the ZGNR,the maximum TMR of all MMTJs is only about one order of magnitude.Overall,the MMTJs with symmetry(4C and 6C)have perfect spin transport properties,such as large TMR and stable 100% SIE,which is very important for the application of spintronic device.

Fig.5 Zero bias transmission coefficient versus electron energy.

Fig.6 Transmission coefficient versus electron energy of 4C and 6C at different bias voltages.

To further confirm this physical mechanism,we show the band structure and partial density of states(PDOS)of left and right electrodes of APC for 6C at different bias voltages,as shown in Fig.7.From Fig.7 we can see that there are two subbands around the Fermi level for the same spin current and they meet at the Kza=π(a=2.46 Å)point in the Brillouin zone.Generally,we call these two subbands as bonding π and antibonding π*band,and it is found that the Bloch function of π(π*)subband is antisymmetric(symmetric)under the σ mirror operation which is the midplane between two edges.In addition,due to the S orbit in these MMTJs we constructed has very small contribution(almost zero)to electron transport,so only the PDOS of the P orbit are shown in Fig.7.We find that at large PDOS,π subband and π*subband become flat gradually,indicating that there is a very high density of electronic states in the flat band.Fig.7a,b shows the band structures of left and right electrodes at the equilibrium state.We find the down-spin π*subband of left electrode overlaps with the down-spin π subband of right electrodes near the Fermi level.Since the π and π*subbands have opposite parity under σ mirror plane,the downspin electron transmission between them is prohibited,resulting in the transmission gap(see green dotted line in Fig.5).The upspin transmission can be analyzed similarly.When the bias increase to 0.4 and 0.8 V,within the bias windows,the downspin π*subband of left electrode overlaps with the down-spin π subband of right electrodes,however the up-spin π*subband and π subband of left electrode overlaps with the up-spin two subbands of right electrodes,so the down-spin electron transmission is still forbidden,resulting in perfect SIE values.This analysis can apply to all symmetrical structures.Similarly,it can also be used to explain all asymmetric structures with respect to the x-direction.For asymmetric structures,the band structures of the electrodes are similar to the symmetrical structures.However,the π(π*)subband has no definite parity due to the absence of the σ mirror plane,resulting in π*(π)subband of left electrode to π(π*)subband of right electrodes has no parity limit.This is the reason that the asymmetric structures not have a stable SIE value.

Fig.7 Band structures and partial density of states(PDOS)of left and right FM electrodes of APC for 6C at different bias voltages.

Fig.8 Local density of state(LDOS)of PC for 6C at zero bias.

4 Conclusions

In summary,depending on the widths of ferromagnetic ZGNR electrodes and the coupling positions between the ZGNR and γ-GYND,we construct MMTJs with different symmetries,namely 4C,5C,6C,7C,4E,5E,6E,7E.By NEGF-DFT,the I-V curve,transmission coefficient,SIE and TMR of the MMTJs are calculated.The results show that only the 4C and 6C have large and stable SIE in a wide range of external bias and can reach a giant TMR up to105at low bias voltage.However,for 5C,7C,4E,5E,6E,7E,we cannot obtain pure spin currents,and the maximum TMR is four order of magnitude smaller than the TMR of 4C and 6C.As we all know,TMR and SIE are important phenomena in MMTJ.Large SIE and TMR can provide higher sensitivity for practical applications.Therefore,for absolutely symmetrical MMTJs(4C,6C)with high SIE and TMR,whether this MMTJ is used as a magnetic random access memory or various types of sensors,it has unparalleled advantages.