Structural, electronic and magnetic properties of MnxGa/Co2MnSi (x = 1, 3) bilayers

Directly coupled hard and soft ferromagnets were popularly used as the hybridized electrodes to enhance tunnel magnetoresistance (TMR) ratio in the perpendicular magnetic tunnel junction (pMTJ). In this paper, we employ the density functional theory (DFT) with general gradient approximation (GGA) to investigate the interfacial structure and magnetic behavior of tetragonal Heusler-type MnGa (MG)/L21-Co2MnSi (CMS) Heusler alloy bilayers with the MnGa being D022-MnGa alloy (Mn3Ga) and L10-MnGa alloy (MnGa). The MM-MS_B interface with the bridge (B) connection of MnMn termination (MM) of D022- and L10-MnGa layers to MnSi termination (MS) of CMS layers is found to be most stable in the energy point of view. Also, a strong antiferromagnetic coupling and relatively higher spin polarization can be observed in the MM-MS_B interface. Further, a remarkable potential difference to derive electrons to transfer from MG layer to CMS layer appears at the interface. These theoretical results indicate that the MG/CMS bilayers are promising candidates as coupled composites, and moreover, the D022-MG/CMS bilayer is better than L10-MG/CMS bilayer due to its larger spin polarization and built-in field at the interface.

Scientific REPORTS | (2018) 8:16530 | DOI: 10.1038/s41598-018-34881-y applied in hybridized electrode as interlayer because the MnGa alloys have a structure derived from Heusler alloys. The exchange coupling between Co-based Heusler alloys and D0 22 -MnGa films has been investigated experimentally [24][25][26] . Among several kinds of Co-based Heusler compounds, Co 2 MnSi was indeed identified to show the highest interfacial AFM coupling strength with D0 22 -MnGa. The pMTJ of L1 0 -MnGa-MgO with the Co 2 MnSi as an interlayer was demonstrated to a distinct TMR ratio of 65% at 10 K 27 . In such a coupled composite, the Co 2 MnSi as the high spin-polarized magnetic layer acts as spin-polarizer and the MnGa alloy as the hard PMA layer maintains the thermal stability. We aim to clarify the microscopic mechanism by analyzing the structural, electronic, magnetic properties of the MnGa/Co 2 MnSi composites with the MnGa being D0 22 -MnGa alloy (Mn 3 Ga) and L1 0 -MnGa alloy (MnGa) by employing the density functional calculations. Moreover, an in-depth understanding of the charge transfer process at the interface has also been performed with the help of the electrostatic potential energy, three-dimensional charge density difference, and Bader charge analysis.

Computaional Methods
For all MG/CMS interface models, spin polarized calculations based on the first-principles approach are executed by using the Vienna ab initio Simulation Package (VASP) under the density functional theory (DFT) framework. The electronic exchange and correlation effects are performed by generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) functional [28][29][30] , which has been widely used and confirmed to be suitable for the Heusler-like compounds 12,31,32 . The electronic wave function is expanded by the plane-wave basis sets of linear projector-augmental wave (PAW) model 33,34 , and the valence-electron configurations with Si (3s 2 3p 2 ), Mn (3d 5 4s 2 ), Co (3d 7 4s 2 ), and Ga (4s 2 4p 1 ) are adopted. The energy cutoff for plane-wave expansion is set to be 350 eV and both the energy convergence criteria of 10 −6 eV/atom and the tolerance for force convergence of 0.02 eV Å −1 have been adopted to obtain the optimized geometry configurations. The first Brillouin zone integration has been performed adopting Γ-centered 7 × 7 × 7 Monkhorst-Pack 35

Results and Discussion
Bulk property. The Heusler alloy with the chemical formula X 2 YZ possesses L2 1 structure (space group FM-3M) which consists of four interpenetrating fcc sublattices. X atoms are located at (0, 0, 0) and (1/2, 1/2, 1/2) site, Y atoms occupies (1/4, 1/4, 1/4) site, and Z atoms enter (3/4, 3/4, 3/4) site in Wyckoff positions. When X and Y are the same transition metal in L2 1 -X 2 YZ, it becomes D0 3 -X 3 Z. There are two different types for the three X atoms in the unit cell of X 3 Z: the first type includes two equivalent X atoms (named by X(A,C)), and they are surrounded by four X and four Z atoms in a tetrahedral coordination; the second type consists of one X atom (named by X(B)), and it is surrounded by eight X atoms in an octahedral coordination. The atomic positions in the unit cell of X 3 Z are (1/4, 1/4, 1/4) for X(A), (3/4, 3/4, 3/4) for X(C), (1/2, 1/2, 1/2) for X(B), and (0, 0, 0) for Z. The D0 22 structure of X 3 Z can be found by applying a tetragonal distortion to the D0 3 structure. In the D0 22 -type structure, the X atoms occupy two different positions: The first position X I with multiplicity 1, is located at the Wyckoff position 2b (0, 0, 1/2) and the second position X II with multiplicity 2, is at 4d (0, 1/2, 1/4). The Z atom is at the Wyckoff position 2a (0,0,0). The L1 0 -type structure is obtained by replacing the X atoms of the XZ layer in the D0 22 -type structure using the Z atom. The Co 2 MnSi has been found to be the L2 1 structure 18 . The Mn x Ga alloys have a quite complicated phase diagram with several magnetically ordered phases. The Mn 3 Ga was reported to exist in a face-centered-cubic structure and was predicted to be a half-metallic completely compensated ferrimagnet in the cubic D0 3 Heusler-type phase 38 . However, in experiments it turned out that the cubic phase of Mn 3 Ga is not stable when Mn 3 Ga is deposited on the substrates. Here we focus on two most interesting tetragonal phases with strong magnetism and high Curie temperature: L1 0 (space group P4/mmm) ordered thermodynamically ferromagnetic phase for 0.76 ≤ x ≤ 1.8 39 and D0 22 (space group I4/mmm) ordered ferrimagnetic phase for 2 ≤ x ≤ 3 5 . Especially, the structural models of the D0 3 -and D0 22 -Mn 3 Ga, and L1 0 -MnGa, together with L2 1 -CMS are shown in the top panel of Fig. 1. The magnetic and the electronic structures of isolated D0 3 -, L1 0 -MG and L2 1 -CMS bulks have been calculated using the PBE, PBEsol and LDA functionals. The obtained results, including the optimized lattice constant, formation energy, and atomic and total magnetic moments are presented in Tables 1 and 2, respectively. As shown in Table 1, the PBE produces the best agreement with available theoretical and experimental values 5,40-43 , while the PBEsol yields a slightly lower accuracy with comparison to the former. Comparing the formation energy of different ordered structures, we find that cubic D0 3 phase has higher formation energy than tetragonal D0 22 phase in the PBE and PBEsol functionals and therefore the D0 22 phase is more favourable than D0 3 phase for Mn 3 Ga alloy, which is supported by the experimental observation 5 . In contrast, the LDA formation energies is opposite for D0 3 -and D0 22 -MG bulks and the total magnetic moments give by the LDA are also fare from the experimental values. Thus, the PBE functional should be suitable for the further studies on the electronic and magnetic properties of the MG/CMS bilayers. It can also be seen that the Mn I and Mn II have opposite magnetic moment for D0 3 -and D0 22 -MG bulks, and moreover, D0 3 -MG bulk is fully compensated ferrimagnet due to the spin magnetic moments of Mn I atoms align antiparallelly to those of the Mn II atoms and the total magnet is equal to zero 44 , while D0 22 -MG bulk is partially compensated ferrimagnet due to the antiparallel spin magnetic moments of Mn I and Mn II atoms and its low saturation magnetization. The L1 0 -MG and L2 1 -CMS bulks are ferromagnets due to the atomic moments of Mn or Co are parallel to each other and they have nonzero net magnetization. In the bottom panel of Fig. 1, densities of states (DOS) of these bulks are shown at their equilibrium lattice constant. One can obtain the spin polarization (SP), which occupies a decisive position in the spintronic devices. The SP can be achieved by the following formula 45  contribution of majority-spin states and minority-spin states to the DOS at the Fermi level, respectively. The DOS of D0 3 -MG in Fig. 1(a) exhibits half-metallic properties, namely the minority-spin states have an energy gap near Fermi level, while the majority-spin states cross the Fermi level. In Fig. 1(b), the DOS of D0 22 -MG shows that the minority-spin state have a distinct valley at the Fermi level, reflecting high SP of 67%. The DOS of L1 0 -MG in Fig. 1(c) shows that both the majority-and minority-spin states cross the Fermi level, reflecting that L1 0 -MG is metallic with low SP of 25%. Similar to D0 3 -MG, the DOS of L2 1 -CMS in Fig. 1(d) also exhibits half-metallic characteristic and therefore 100% spin-polarization can be observed.    Fig. 3.
Here, we come to investigate the interfacial character of the MG/CMS bilayers in both interfacial ferromagnetic (FM) and antiferromagnetic (AFM) coupling. To examine the stability of various interface structures, we calculate the interface formation energy of each possible interface structure, which is defined as a function of the chemical potential of atoms under the thermodynamic equilibrium conditions: where E f represents the interface formation energy, A and G are the area of the supercell and the Gibbs free energy. N Co , N Ga , N Mn , and N Si represent the number of Co atom, Ga atom, Mn atom and Si atom in the system, respectively. μ Co , μ Ga , μ Mn , and μ Si represent the chemical potential of Co atom, Ga atom, Mn atom and Si atom, respectively. The calculated formation energies and in-plane lattice constants of all kinds of interface structures for the PBE and PBEsol functionals are presented in Table 3 for D0 22 -MG/CMS and L1 0 -MG/CMS bilayers. Slightly greater interface formation energies and the in-plane lattice constants are expected for the PBE functional as compared to the PBEsol functional for the same interface. However, the relative formation energies and lattice constants between AFM and FM states of all the interfaces are qualitatively same for the PBE and PBEsol functionals, and therefore only the PBE formation energies of all the interfaces are shown in Fig. 4(a) and (b) for D0 22 -MG/CMS and L1 0 -MG/CMS bilayers, respectively. The negative values of interface formation energy for all interfacial structures indicate that their synthesis are accompanied by the energy release and hence is likely to occur spontaneously during the epitaxy. All T-type interfaces possess comparatively high interface formation energy comparing to those of the corresponding B-type ones for both bilayers, indicating that the CMS is inclined to the connection with MG at B-type structure. By comparing the formation energy values of the systems in the FM and AFM configurations, we found that the most of interfaces have a lower energy in the case of AFM coupling, except for MM-CC_B and MG-CC_B for D0 22 -MG/CMS bilayer in Fig. 4(a) and MM-CC_B, GG-CC_B and GG-MS_T for L1 0 -MG/CMS bilayer in Fig. 4(b). Moreover, the AFM MM-MS_B is the most stable interface structure for both D0 22 -MG/CMS and L1 0 -MG/CMS bilayers since it has minimum formation energy in the D0 22 -and L1 0 -MG/ CMS bilayers. In AFM MM-MS_B interface with the lowest formation energy, the optimized in-plane lattice constants are 3.785 Å and 3.846 Å for D0 22     extremely similar behaviors to the corresponding bulk. Therefore, it can be deduced that interface effect has little influence on displacement of subinterface atom and even less on displacement of the next subinterface atom.
Magnetism behavior. The atom-resolved spin magnetic moments (AMMs) of the first five layers of AFM MM-MS_B interface are shown in Fig. 6 for D0 22 -MG/CMS and L1 0 -MG/CMS bilayers only for the PBE functional. It should be noted that the PBEsol and LDA functionals show slightly difference in atom-resolved spin magnetic moment as compared to the PBE functional, ant therefore the PBE moments is sufficient to account for the magnetic behavior of AFM MM-MS_B interface for the considered bilayers. The positive and negative oscillations of the magnetic moment curves on the MG side indicate that the magnetic moments are antiparallel. The magnitude of the positive and negative magnetic moments is not equal, reflecting that MG in the interfacial structure is ferrimagnetic. On the other side, the magnetic moment in the CMS side is always positive and the magnitude oscillates up and down due to the fact that the Co atomic magnetic moments in the CC atom layer are less than the Mn atomic magnetic moments in the MS atom layer, which indicates that the CMS still maintains the ferromagnet behavior of the bulk phase in the interface structure. Especially, the interfacial magnetic moments are opposite to each other indicating the AFM exchange coupling of the atomic magnetic moments at the MM-MS_B interface for both bilayers. In addition, the magnetic moment of Co atoms is significantly reduced at the interface affected by antiferromagnetic coupling. The magnetic moment of the interfacial atoms      Fig. 7(a) and (b), respectively. It can be clearly seen that the composites of MG/CMS bilayer show metal character due to the DOS cross the Fermi level in both spin channels, but both composites have the higher spin polarizations. As shown in Fig. 7(a), the SP of the D0 22 -MG/CMS bilayer is around 82%, higher than the 67% of D0 22 -MG bulk and lower than the 100% of CMS bulk, and as shown in Fig. 7(b), the SP of L1 0 -MG/CMS bilayer is around 54%, higher than the 25% of L1 0 -MG bulk and lower than the 100% of CMS bulk. Overall, D0 22 -MG/CMS bilayers is more worthy of research than L1 0 -MG/CMS bilayer due to the higher spin polarization. Next, we do a more detailed analysis of the electronic behavior in the interface. The density of states (DOS) and project density of states (PDOS) of the fist five layers are presented in Fig. 8(a) and (b) on the CMS sides and in Fig. 8(c) and (d) on the D0 22 -MG side for D0 22 -MG/CMS bilayer with AFM MM-MS_B interface, respectively. According to Fig. 8(a) and (b), on the CMS side, the odd number layers are MS ones, while the even number layers are CC ones. One can see that the half-metallicity of the MS layers have not been destroyed; there is a very robust band-gap in the minority-spin band, while the half-metallicity of the CC layers is completely destroyed due to some peaks mainly characterized by d-states emerge in the minority-spin gap of the second layer and such peaks declined in the fourth layer and even disappear in the sixth layer. Therefore, the SP and the values of total magnetic moment of CC layers are reduced compared to the bulk crystal. Since the crystal periodic field is truncated at the interface, the Mn-Co hybridization is reduced, resulting in the decrease of exchange splitting. As results, the Co d states move more towards the lower energy zone than Mn d states, leading to the reduction of the   Fig. 10. In the MG center layers, the spin polarization of the different atomic layers is not uniform. However, we should note that the closer the atomic layer is to the interface, the spin polarization become higher in the MG side. Moreover, the spin polarization of each layer on MG side are higher than that in their bulk. In the CMS side, although the spin polarization is declined, it still maintains a high value. Interestingly, the spin polarization of the CMS exhibits a  In the charge density differential part, the red region represents electron accumulation, and the blue region represents the electron consumption.
Scientific REPORTS | (2018) 8:16530 | DOI:10.1038/s41598-018-34881-y similar oscillatory behavior in the CMS side for both composites. The CMS interlayer is useful for improving the spin polarization of MG layer. Next, we will provide an in-depth understanding of the charge transfer process at the interface, the electrostatic potential energy along the c-axis, three-dimensional charge density difference, and Bader charge analysis of interface structure are performed and the calculated results are depicted in Fig. 11. The electrostatic potential energy has a slight mutation along the c axis of the supercell, since the work function of MG and CMS are not equal on both sides of the interface. Although the potential energy curve along the c-axis constantly oscillating, the average potential energy of MG is higher than the CMS, indicating that the electrons tend to be transferred from the MG side to the CMS side in the interface area. The average potential energy is slightly higher for the D0 22 -MG/CMS bilayer than that for the L1 0 -MG/CMS bilayer. It is an important issue for the mentioned case that by changing the external magnetic field, the electrostatic potentials are changed as well; so these interfaces can be good candidates for spin injection control in TMR and GMR devices. For three-dimensional charge density difference, the dissipation and accumulation of charge mainly occurs in the interface area. The electronic charge transfer from MG layer to CMS layer. The quantitative result of Bader analysis illustrates that the electron accumulation appears on the Mn atom of the first layer in the CMS interface for both composites, and the charge depletion mainly appears on the Mn atoms of the second layer for the D0 22 -MG/CMS bilayer, while such charge depletion mainly occurs on the Ga atoms of the second layer in the MG interface for the L1 0 -MG/CMS bilayer. Thus, the charge transfer from MG layer to CMS layer introduces the built-in electric field, which can produce a driving force to realize the electron injection in TMR and GMR devices.

Conclusion
The structural, electronic and magnetic properties of D0 22 and L1 0 bilayers are studied by employing the first-principles calculations based on density functional theory. The interface formation energy calculations show that all interface structures are stable in terms of theory, however the MM-MS_B interface with the bridge connection of MnMn termination (MM) of D0 22 -and L1 0 -MnGa layers to MnSi termination (MS) of CMS layers is most likely to be prepared in the growth. A strong antiferromagnetic coupling is observed in the MM-MS_B interface for the bilayers. The exchange coupling could completely change the magnetization direction of CMS layer from in-plane to perpendicular when the thickness of the CMS is less than the critical thickness. Further, the electronic structure calculations indicate that the spin polarizations of the MG layer and CMS layer are enhanced and reduced in the MS/CMS bilayers, respectively. However, the MS/CMS bilayers remain high spin polarization up to 82 and 54% for the D0 22 -and L1 0 -MG alloys, respectively. The potential energy, charge density difference, and Bader charge analysis show that the electrons are transferred from the MG layer to the CMS layer at the interface, which can produce a driving force to realize the electron injection from MG layer to CMS layer in TMR and GMR devices. Remarkably, compared to L1 0 -MG/CMS bilayer, the D0 22 -MG/CMS one is a more promising candidate as the composite electrode due to its larger spin polarization and built-in field at the interface.