Ab-initio study of electronic and magnetic properties of CoIrMnZ (Z = Al, Si, Ga, Ge) Heusler alloys

Journal Pre-proofs Research articles Ab-initio study of electronic and magnetic properties of CoIrMnZ (Z=Al, Si, Ga, Ge) Heusler alloys Tufan Roy, Masahito Tsujikawa, Takuro Kanemura, Masafumi Shirai PII: DOI: Reference:

S0304-8853(19)33071-9 https://doi.org/10.1016/j.jmmm.2019.166092 MAGMA 166092

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Journal of Magnetism and Magnetic Materials

Received Date: Accepted Date:

3 September 2019 1 November 2019

Please cite this article as: T. Roy, M. Tsujikawa, T. Kanemura, M. Shirai, Ab-initio study of electronic and magnetic properties of CoIrMnZ (Z=Al, Si, Ga, Ge) Heusler alloys, Journal of Magnetism and Magnetic Materials (2019), doi: https://doi.org/10.1016/j.jmmm.2019.166092

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© 2019 Published by Elsevier B.V.

Ab-initio study of electronic and magnetic properties of CoIrMnZ (Z=Al, Si, Ga, Ge) Heusler alloys Tufan Roy1a , Masahito Tsujikawa1,2 , Takuro Kanemura1 , Masafumi Shirai1,2,3 1

Research Institute of Electrical Communication, Tohoku University, Sendai 980-8579, Japan

2

Center for Spintronics Research Network (CSRN), Tohoku University, Sendai 980-8579, Japan and

3

Center for Science and Innovation in Spintronics (CSIS),

Core Research Cluster (CRC), Tohoku University, Sendai 980-8577, Japan

Abstract Using first principles calculations based on density functional theory, we study electronic and magnetic properties of CoIrMnZ (Z=Al, Si, Ga, Ge) Heusler systems. Based on the electronic structure calculations, CoIrMnSi and CoIrMnGe are predicted to be half-metallic. For the studied systems, the ground state magnetic configurations are found to be ferromagnetic with magnetic moment consistent with the Slater-Pauling rule. The calculated ferromagnetic transition temperatures are much higher than the room temperature for all the cases. The effect of spin orbit coupling has been discussed on the electronic structure for all the systems studied here. Furthermore, we construct junctions with MgO along (001) direction. The MnZ terminations are found to be energetically more favourable compared to the CoIr terminations. After discussing the tunnelling conductance, we find that CoIrMnSi/MgO/CoIrMnSi could be a promising magnetic tunnelling junction (MTJ) candidate. Keywords: Density functional theory, Heusler alloys, Half-metallic, Density of states

a

Electronic mail: [email protected]

1

I.

INTRODUCTION

Heusler alloys are drawing considerable attention to the researchers because of its promising technological application during last few decades. There is a family of Heusler alloys which undergo a structural transition from a high temperature phase with higher symmetry to a phase of lower symmetry upon cooling, known as martensite transition. This family of Heusler alloys may find their application in devices like sensors, antenna etc. Ni2 MnGa is known to be the prototype Heusler alloys in this category.1 There is an another group of Heusler alloys which are found to be metallic for one spin channel and insulator for the other spin channel, known to be half-metallic ferromagnet (Figure 1(a)). Many of the Co-based Heusler alloys belong to this category and they are also known for the robustness of high spin polarization against atomic disorder.2–6 Besides high spin polarization, Co-based Heusler alloys are reported to have high Curie temperature (TC )7 , all of these features make them one of the promising candidates in spintronics application. One major technology, where half-metallic Co-based Heusler alloys are widely used is magnetic tunnelling junctions (MTJ). Many experimental studies have been carried out with amorphous AlOx as barrier and Co-based Heusler alloys as ferromagnet.8 Later on, half-metallic Heusler alloy, Co2 MnSi, with crystalline MgO as an insulating barrier has received keen interest of the researchers both from experiments and theoretical studies point of view.9–15 It has been observed that in case of single crystalline barrier like MgO, the presence of spin polarized ∆1 band of Co2 MnSi plays a crucial role in coherent tunnelling probability for one spin direction, hence results a large tunnelling magnetoresistance (TMR) ratio.11 The importance of the spin polarized ∆1 band in enhancing the tunnelling probability has been well discussed in literature.16 So, it can be of immense interest to predict materials with spin polarized ∆1 band with high TC as its possible application in MTJ. Apart from the application, the Heusler alloys are also well-known to have wide diversity in terms of their electronic structure. Recently, there has been a growing interest to discover spin-gapless semiconductor (SGS) type of Heusler alloys both from the experiment and first principles based calculations.17–23 An ideal SGS should have a band gap in one spin channel and a band gap of zero width for the other spin channel, at the E F . Figure 1 shows the schematic diagram of density of states (DOS) of (a) Half-metallic ferromagnet 2

(b) Spin-gapless semiconductor. Based on the first principles calculations, Gao et al have reported DO3 type binary SGS Heusler alloy Cr3 Al.24 Some of the equiatomic quaternary Heusler alloys (QHAs) are already reported to have this kind of electronic structure, namely, CoFeMnSi, CoFeCrGa etc.18,19,25,26

FIG. 1: (Color online)Schematic density of states (DOS) of (a) Half-metallic ferromagnet (b) Spin gapless semiconductor.

The number and the nature of valence electrons are known to play a crucial role in determining the electronic properties and magnetism of these systems.28,29 It is argued that the Heusler alloys with 26 or 28 valence electrons are likely to be spin-gapless semiconductor.23 Miura et al have also suggested that if the number of valence electrons (Nv ) ≥ 28.0, it is possible to obtain spin polarized majority ∆1 band.11 Still the date, Co2 MnZ (Z=sp element) materials have been extensively studied. Recently, Benkabou et al have studied the electronic and magnetic properties of CoRhMnZ (Z = Al, Ga, Ge and Si) systems which are predicted to be half-metallic.30 But, to the best of our knowledge the equiatomic QSHAs, CoIrMnZ (Z = Al, Ga, Ge and Si) systems have not been probed, whereas Ir is isoelectronic to both Co and Rh atom. Apart from this, lattice mismatch between Co2 MnSi and MgO for 45◦ in plane rotation has been reported to be around 5%,11 thus replacement of one Co atom by Ir atom may reduce the lattice mismatch, as Ir is a 5d element. These reasons motivate us to study the CoIr-based Heusler alloys. In the present manuscript, we study the electronic and magnetic properties of bulk CoIrMnZ (Z=Al, Si, Ga, Ge) Heusler systems, where CoIrMnAl and CoIrMnGa have twenty eight 3

valence electrons and the other set i.e. CoIrMnSi and CoIrMnGe have twenty nine valence electrons. Later on, we focus on the CoIrMnZ/MgO junction.

II.

METHOD

Geometry optimization of bulk structures has been carried out using Vienna Ab Initio Simulation Package (VASP)31 which has been used in combination with the projector augmented wave (PAW) method32 and the generalized gradient approximation (GGA) for the exchange-correlation (XC) functional.33 We have used an energy cutoff of 500 eV for the planewaves. The final energies have been calculated with a k-mesh of 16×16×16 for the cubic case and a comparable number of k-points have been used for the tetragonal case. The energy and the force tolerance for our calculations were 10 µeV and 10 meV/˚ A, respectively. We find that in all the cases, the systems obtain optimized structure when the internal pressure becomes less than 0.02 kbar. With the optimized geometry of the bulk material, we form CoIrMnZ/MgO junction with eleven layers of CoIrMnZ and five that of MgO, with both CoIr termination and MnZ termination. Figure 2 shows the structure of junction with MnZ termination. Then we relaxed the geometry of the junction along the c axis while in plane lattice parameters were fixed to that of the respective bulk Heusler systems. It is worth mentioning that the in plane lattice parameter in case of junction √ corresponds to a/ 2, where a is the optimized lattice parameter of bulk CoIrMnZ. For the geometry optimization of the junction along c-axis we use k-mesh of dimension 10×10×1. A denser k-mesh of dimension 16×16×2 has been used for the further calculations of electronic structure and magnetic property of the heterojunction.

FIG. 2: (Color online)Heterojunction of CoIrMnZ and MgO, with MnZ termination.

We employ the Green’s function based spin-polarized relativistic Korringa-Kohn-Rostoker method (SPR-KKR) as implemented in the SPR-KKR programme package34 in order to calculate Heisenberg exchange coupling constant within a real space approach as proposed 4

by Liechenstein et al.35 Thereafter, we calculate TC under mean field approximation for the bulk systems. Full potential method has been used for the self-consistent-field (SCF) calculations. Also, here we use GGA for the exchange correlation potential. We use 917 irreducible k-points for the Brillouin zone integration and further an angular expansion upto lmax = 3 has been used for each atom. For the calculation of conductance, we use the code Quantum ESPRESSO36 using the method as suggested by Choi and Ihm.37 PW91 GGA has been used for the exchange correlation functional.38 A k-mesh of dimension 12×12×1 has been used here. The cutoff energy for the wave function and the charge density is set to 50 and 500 Ry. Further detail of the calculational method of conductance can be found in the Ref-10 and 11.

III.

1.

RESULTS AND DISCUSSION

Bulk phase

The Heusler alloys studied here possess F¯43m crystal structure in their bulk configuration. It consists of four interpenetrating face-centered-cubic (fcc) sub-lattices with origin at the fractional positions, (0.0, 0.0, 0.0), (0.5, 0.5, 0.5), (0.25, 0.25, 0.25), and (0.75, 0.75, 0.75). In the supplemental materials39 , we have considered different possible configurations of these CoIrMnZ systems, where the sub-lattices are occupied by the different atoms as described in literature.40 After comparing the total energies of each cases, we find that in the lowest energy structure, the above-mentioned sub lattices are occupied by Co, Ir, Mn, and Z atoms, respectively. In Table 1, we report the optimized lattice parameters of these systems. We find that the systems with 3p atoms (i.e. Al or Si) as a Z-element have shorter lattice parameter compared to the systems with 4p atoms (i.e. Ga or Ge). This observation can be related to the larger atomic radii of 4p elements compared to the 3p elements. Furthermore, to confirm the cubic ground states, we apply the tetragonal distortion, keeping the volume constant as that of the optimized F¯43m structure (Figure 3). The presence of the global minimum at c/a = 1 assures the stability of the cubic phase for all of these studied systems, here. Figure 4 shows the atom resolved and spin polarized density of states (DOS) for CoIrMnAl (left panels) and CoIrMnGa (right panels). In inset, of the top panels of Figure 4, we present 5

140

E (meV/atom)

120 CoIrMnAl CoIrMnGa CoIrMnSi CoIrMnGe

100 80 60 40 20 0 0.9

1.0

1.1

1.2

1.3

1.4

c/a

FIG. 3: (Color online) Energy difference (E) between the tetragonal and cubic structure of CoIrMnZ systems as a function of ratio of lattice constants c and a. The energies have been normalized with respect to the energy of cubic structures.

the DOS at the vicinity of E F . It is to be noted that in case of the transition metal elements, the main contribution to the DOS near Fermi level originates from the d-orbital. So, in case of the Co, Ir, and, Mn we show only the contribution arising from d-orbitals in their respective DOS. It is observed that in case of the majority spin channel of CoIrMnAl, there is an abrupt decrease of the DOS (0.05 states/atom) at Fermi level (E F ), hence forms a pseudo gap of almost zero width. In the later part of the discussion (Figure 7), we will show that one electronic band crosses the Fermi level along the Γ- X direction, hence gives rise to the minute DOS at the E F of majority spin channel. Detail analysis shows that this band has ∆5 symmetry. On the other hand, a bandgap of around 0.9 eV is observed in the minority spin channel, though there is a negligible DOS at the E F (0.03 states/atom), which is found to originate mainly from Co 3d orbitals, and very slight contribution to that come from Ir and Mn atoms. From the DOS of CoIrMnAl, we observe a pseuogap at E F in the majority spin channel and a finite band gap in the minority spin channel. Hence, it could be called as a spin-gapless semiconductor, with gapless majority spin channel and nearly semiconducting minority spin channel. In case of CoIrMnGa, the pseudo gap in the majority DOS is located just below the E F (-0.05 eV), resulting a considerable DOS at E F . Nevertheless, a band gap of around 0.9 eV 6

DOS (states/eV f.u.)

10 5 0 -5 -10 4 2 0 -2 -4 2 0 -2 4 2 0 -2 -4

CoIrMnAl

5 0 -5 -0.10.0 0.1

5 0 -5 -0.1 0.0 0.1

Co-d

Co-d

Ir-d

Ir-d

Mn-d

Mn-d

Al

0.2 0.0 -0.2 -6 -4 -2

CoIrMnGa

0

2

Ga

-6 -4 -2

0

2

Energy (eV)

FIG. 4: (Color online) The left and right panels represent the spin polarized and atom resolved density of states (DOS) of CoIrMnAl and CoIrMnGa, respectively. The Fermi level is at 0 eV.

is still visible in the minority spin channel of CoIrMnGa. In this case also there is a presence of negligibly small DOS at the E F . Similar to CoIrMnAl system, it originates mainly from Co atom. In Figure 5, we present the DOS of CoIrMnSi (left panels) and CoIrMnGe (right panels). Both the systems are perfectly half-metallic with 100% spin polarization at the E F . For CoIrMnSi the band gap in the minority spin channel is about 0.7 eV whereas for CoIrMnGe it is about 0.45 eV. In case of CoIrMnSi the E F lies at the middle of the band gap for the minority spin channel. For both the cases of CoIrMnSi and CoIrMnGe, the pseudo gap at or around E F vanishes in the majority spin channel which was observed in case of the CoIrMnAl or CoIrMnGa. In figure 6, we compare the total DOS of the each system between ’with the effects of spin orbit coupling (SOC)’ and ’without the effects of SOC’. We find that there is almost 7

DOS (states/eV f.u.)

10 5 0 -5 -10 4 2 0 -2 -4 2 1 0 -1 -2 4 2 0 -2 -4 0.4 0.2 0.0 -0.2 -0.4 -6 -4 -2

CoIrMnSi

CoIrMnGe

Co-d

Co-d

Ir-d

Ir-d

Mn-d

Mn-d

Ge

Si

0

2

-6 -4 -2

0

2

Energy (eV)

FIG. 5: (Color online) The left and right panels represent the spin polarized and atom resolved density of states (DOS) of CoIrMnSi and CoIrMnGe, respectively. The Fermi level is at 0 eV.

no change in electronic structure of these systems after the inclusion of SOC, which allows us to carry forward our study further without considering SOC. In the later part of this work, we discuss about the spin transport properties of the selected CoIrMnZ/MgO junction along the (001) direction. Figure 7 depicts the majority spin band dispersion of all the CoIrMnZ systems along (001) direction i.e. Γ-X direction. However, we present the band structure of both the majority and minority spin along the various high symmetry direction of the Brillouin zone in Figure S1 of the supplemental material. From Figure 7 it is observed that for all these systems, there are two conduction bands closed to the E F . We mark the ∆1 band, while the other one is ∆5 band. For CoIrMnAl and CoIrMnGa, ∆5 band crosses the E F upto about -0.35 eV, and ∆1 band remains unoccupied. Whereas for rest of these systems, i.e. for CoIrMnSi and CoIrMnGe, ∆5 band crosses the E F upto about -1.00 eV, and ∆1 band crosses the E F ( about -0.5 eV). 8

DOS (states/eV f.u.)

12

10

10

(a) CoIrMnAl

(b) CoIrMnGa

5

8

5

0 -0.5 0.0 0.5

Without SOC With SOC

0 -0.5 0.0 0.5

4 0 12

(c) CoIrMnSi

(d) CoIrMnGe

8 4 0 -6

-4

-2

0

2 -6 -4 Energy (eV)

-2

0

2

FIG. 6: (Color online) Comparison of total DOS with and without the effects of SOC: (a) CoIrMnAl, (b)CoIrMnGa, (c)CoIrMnSi and, (d)CoIrMnGe, respectively. The Fermi level is at 0 eV. Table 1. Calculated lattice parameters, magnetic moments and Curie temperatures of CoIrMnZ.a Material

a

µtotal µCo µIr µM n µZ

TC

(˚ A) (µB ) (µB ) (µB ) (µB ) (µB ) (K) CoIrMnAl 5.905 4.03 0.95 0.16 2.95 -0.02 584 CoIrMnSi 5.860 5.00 1.32 0.32 3.29 0.00 1020 CoIrMnGa 5.931 4.09 0.97 0.14 3.00 -0.07 517 CoIrMnGe 5.964 5.00 1.31 0.29 3.32 -0.01 956 Co2 MnSi 5.630 5.00 1.02

–

5.65b 5.00c a

2.99 -0.03 1204 985b

Comparison with experiments or previous calculations, wherever data are available b

Ref.41 (experimental result) c Ref.7 (theoretical result)

This can be attributed to presence of an extra valence electrons in the cases of CoIrMnSi and CoIrMnGe (twenty nine valence electron system) compared to the other two systems, CoIrMnAl and CoIrMnGa (twenty eight valence electrons system). In the later part of the discussion we will discuss about the role of these two bands in the spin transport properties. 9

FIG. 7: (Color online) Band structure of: (a) CoIrMnAl, (b)CoIrMnGa, (c)CoIrMnSi and, (d)CoIrMnGe, respectively along Γ-X direction for the majority spin electrons. The Fermi level is at 0 eV.

In Table 1, we summarize our calculated total and partial magnetic moments and lattice parameters. We include the result corresponding to well-known material Co2 MnSi for the sake of comparison of its properties with our predicted materials CoIrMnZ. We find that, CoIrMnAl and CoIrMnGa are found to possess total magnetic moment close to 4 µB whereas CoIrMnSi and CoIrMnGe have the total magnetic moments exactly 5 µB , which are consistent with the Slater-Pauling rule. A slight deviation from the integer moment for CoIrMnAl and CoIrMnGa can be attributed to the presence of small DOS at E F in the minority spin channel. For all these systems the magnetic moment is mainly confined to the Mn atoms because of its larger exchange splitting compared to other magnetic atoms. The magnetic moment of Co atoms are significantly higher than Ir for all these systems in spite of having same number of valence electrons. This observation may be attributed to the fact that 5d orbitals are of more delocallized nature compared to that of 3d orbitals. For Co2 MnSi, the 10

calculated magnetic moment is consistent with the earlier report.7 In Table 1, we also present the Tc , calculated from the Heisenberg exchange coupling constant as already has been carried out in literature.42 TC of CoIrMnSi and CoIrMnGe are reasonably higher than that of CoIrMnAl and CoIrMnGa. In literature, the role of sp electrons in mediating the magnetic exchange interactions between the magnetic atoms have been well reported.29,43 Here, it is found that the first indirect Mn-Mn exchange coupling constant is negative for the CoIrMnAl and CoIrMnGa, but as we add an sp electron to the system i.e. the cases for CoIrMnSi and CoIrMnGe, the Mn-Mn exchange interaction becomes positive. It makes ferromagnetic interaction more dominant, hence results a higher TC in the cases of CoIrMnSi and CoIrMnGe. In case of Co2 MnSi, our calculated TC is higher than the experimental values available in literature. It has been already reported that there is an overestimation of the TC under mean field approximation.44–46 Because in mean field approximation, the spin fluctuations have been neglected and magnetic moments are considered to be more rigid.

2.

Junction with MgO

We observed in the previous section that the CoIrMnAl and CoIrMnGa are isoelectronic systems and have similarity in terms of their electronic structure and magnetic properties. Similarly, CoIrMnSi and CoIrMnGe systems are also closed in terms of their electronic and magnetic properties. Therefore, in the discussion of the Heusler alloy/MgO heterojunctions, we limit our study within two systems, which are CoIrMnAl/MgO and CoIrMnSi/MgO systems. Firstly, we focus on the electronic structure of CoIrMnAl/MgO and CoIrMnSi/MgO junctions. We have considered three positions of MgO interface layer with respect to CoIrMnZ terminating atoms. In the considered three cases, terminating atoms of CoIrMnZ are placed on top of the (a) O atoms (O top); (b) Mg atoms (Mg top); (c) hollow of the MgO (001) surface, for both the CoIr termination and MnZ termination. The total energy of each case with respect to their respective O top case has been summarized for both the MnZ and CoIr terminations, in Table 2s and Table 3s of the supplemental material.39 We find that, the interfaces with O-top configurations is energetically favourable for both types of termination. In Table 2 we summarize ∆Ecoh , which is the cohesive energy of the respective systems with CoIr termination with respect to its MnZ termination in their 11

30 (a)

20 10

DOS (states/ev f.u.)

0 -10 -20 -30 30 20

(b)

10 0 -10 -20 -30 -6

-4

-2

0

2

Energy (eV) FIG. 8: (Color online) Spin polarized DOS of the junctions: (a) CoIrMnAl/MgO and, (b) CoIrMnSi/MgO. The Fermi level is at 0 eV. respective O top configuration. First we calculate the cohesive energy of each termination using the following formula: Ecoh = Etot −

X

ni Ei

(1)

i

where Etot is the total energy of the junctions (CoIr terminated or MnZ terminated), ni is the number of each elements and Ei is the energy of the particular element in their corresponding bulk configuration. Furthermore, we calculate ∆Ecoh as the cohesive energy of the CoIr termination case with respect to its MnZ termination case, for the respective cases, i.e., CoIr M nZ ∆Ecoh = Ecoh − Ecoh

(2)

Hence, the positive values of the ∆Ecoh in both the cases indicate that MnZ termination is energetically more favourable compared to the CoIr termination. This result is in well 12

Local DOS at EF (states/eV atom)

(a)

0.4

Mn Al Co

0.0 Ir Mg O

-0.4 -15

-10

-5

0

5 (b)

0.4

Mn Si

0.0 Co Ir Mg O

-0.4 -15

-10

-5

0

5

10

Distance from interface (Å)

FIG. 9: (Color online) The local density of states at the E F , corresponding to each atoms are plotted as function of distance from the interface for (a) CoIrMnAl/MgO and, (b) CoIrMnSi/MgO heterojunctions. Up-arrow indicates majority spin and down-arrow indicates minority spin. Table 2. Cohesive energy, total magnetic moment, spin polarization and the interfacial lattice mismatch between respective Heusler systems and MgO are listed here. Material ∆Ecoh

Total

Spin

∆a/a

(eV) moment (µB ) polarization (%) (%) CoIrMnAl 2.36

26.00

100

0.81

CoIrMnSi 0.53

28.69

46

1.6

agreement with the previous findings by Miura et al., as they reported MnSi terminations to be more energetically favourable over Co termination case in case of Co2 MnSi/MgO junctions.11 It has been observed that the magnetic moment for CoIrMnAl/MgO junction is equal to 26.00 µB whereas for CoIrMnSi/MgO junction the total magnetic moment is 28.69 µB which is far from the integer value. The deviation of moment from the integer value in the latter case has a direct consequence on the spin polarization of the junctions, as we can find from the Table 2 for the CoIrMnAl/MgO junction, the spin polarization is 100% whereas 13

for the other one, spin polarization reduces to the 46% at the E F . It is worth-mentioning that the interfacial lattice mismatch is in the order of 1% for both the cases. Figure 8(a) and 8(b) show the spin-polarized DOS of CoIrMnAl/MgO and CoIrMnSi/MgO interfaces, respectively. In both the cases, the majority spin channel has metallic electronic structure whereas there is a presence of the band gap in the minority spin channel for CoIrMnAl/MgO system. But in case of the CoIrMnSi/MgO junction, the half-metallicity has been lost at the E F . Figure 9(a) and 9(b) represent the local DOS of majority and minority spin of individual atoms at the E F , as a function of distance from the interface for CoIrMnAl/MgO and CoIrMnSi/MgO junctions, respectively. We observe that there are no interfacial states in case of minority spin channel of CoIrMnAl/MgO heterojunction which gives rise to 100% spin polarization at the interface. On the other hand in case of CoIrMnSi/MgO junction the interfacial states appear in the minority spin channel.

4

(a)

2

DOS (states/ev atom)

0 -2

Bulk Mn Interfacial Mn

-4 4 (b)

2 0 -2 -6

-4

-2

0

2

Energy (eV)

FIG. 10: (Color online) Spin polarized DOS of the interfacial Mn and bulk Mn atom: (a) CoIrMnAl/MgO and, (b) CoIrMnSi/MgO. The Fermi level is at 0 eV.

In Figure 10 (a) and 10 (b), we present the local DOS of interfacial Mn atom and bulk Mn atom for CoIrMnAl/MgO and CoIrMnSi/MgO heterojunctions. In both the cases, for 14

2 (a)

DOS (states/eV atom)

1 0 -1

Mn-3(dyz+dzx) CoIrMnSi Mn-3(dyz+dzx) CoIrMnAl

-2 0.2 (b)

0.1 0.0 -0.1 -0.2 -6

Si-pz Al-pz

-4

-2 0 Energy (eV)

2

FIG. 11: (Color online) Spin polarized DOS of interfacial: (a) Mn-3(dyz +dzx ), and (b) Si-pz and Al-pz for CoIrMnSi/MgO and CoIrMnAl/MgO junctions. The Fermi level is at 0 eV.

the interfacial Mn atom, DOS of the occupied energy levels are shifted towards the higher binding energy side with respect to the E F which leads more localization of interfacial Mn moment compared to moment of the bulk Mn atom. We observe that for the case of CoIrMnAl/MgO junction the magnetic moment of the interfacial Mn atom is 3.60 µB and for bulk Mn atom the magnetic moment is 2.99 µB . In case of the CoIrMnSi/MgO heterojuction the values of the interacial and bulk Mn moments are 3.78 µB and 3.26 µB , respectively. It has been argued that the enhancement of magnetic moment in case of interfacial Mn atom is because of the charge transfer from the minority spin to majority spin states.11 We find that there is a peak (around -0.05 eV) at the minority spin channel of interfacial Mn atom (Figure 10) in case of CoIrMnSi/MgO which reduces the spin polarization at E F . An in depth analysis shows that (Figure 11), this peak corresponds to Mn-3dyz and Mn3dzx and a significant contribution to it comes from interfacial Si-pz states, which effectively reduces the spin polarization. But in case of CoIrMnAl/MgO, as we observe from figure 11 (b), there are no states available near E F at the minority spin channel of Al. To understand the reason behind the appearance of Si states at the interface, the nature of chemical bonding 15

FIG. 12: (Color online) Band structure of CoIrMnSi/MgO junction for the minority spin channel. The Fermi level is at 0 eV.

at the interface should be discussed. We find that in the case of CoIrMnSi/MgO interface the Mn-O distance is 2.23 ˚ A, while the Si-O distance is 2.97 ˚ A. As a result of this, Si atom moves away from the junction towards the subinterfacial layer, and only Mn atom makes bonding with the O atom. Whereas in the case of CoIrMnAl/MgO junction, the Mn-O and Al-O distances remain almost same, 2.21 ˚ Aand 2.15 ˚ A. This allows to have stronger bonding between Al-O, unlike the Si-O case. In Figure S2 of the supplemental material,39 we compare the DOS of Al and Si atoms both from the interfacial and bulk region of the CoIrMnAl/MgO and CoIrMnSi/MgO systems. Because of the weak bonding with O atom, the DOS of the interfacial Si atoms are shifted towards the lower binding energy side (around E F ) compared to the bulk Si atom of the CoIrMnSi/MgO heterojunction. These appeared states from Si atom make hybridization with neighbouring subinterfacial Co atom and Ir atom and interfacial Mn atom, which results in loss of half-metallicity in the case of CoIrMnSi/MgO. On the other hand, there are no states in case of interfacial Al at the E F in the minority spin channel of CoIrMnAl/MgO junction. Figure 12 depicts the band structure of the CoIrMnSi/MgO heterojunction for the minority spin channel, to have a better understanding about the origin and symmetry of 16

interafacial states appearing at E F . There are two minority spin bands which cross the E F . One of these bands (marked by arrow) originates mainly from the interfacial Mn atom which has ∆5 symmetry. The other band crossing the E F is found to have ∆1 symmetry, but it originates mainly from subinterfacial Co and Ir atoms, with a contribution from interfacial Si atom. As Co and Ir atoms appear at the subinterfacial layer and Si-O distance is significantly large as mentioned earlier, so this ∆1 band may not play a crucial role in the transport of minority spin through the MgO barrier. Figure 13 and Figure 14 represent the in plane wave vector dependence of majority spin transmittance at the E F for CoIrMnAl/MgO/CoIrMnAl(001) and CoIrMnSi/MgO/CoIrMnSi(001) in parallel magnetization. It is to be observed that for CoIrMnAl/MgO/CoIrMnAl, there are spikes like structure at the two dimensional Brillouin zone, which originates from ∆5 conduction channel, as we observed in the band structure of bulk CoIrMnAl (Figure 7) that in the majority spin channel, only ∆5 band crosses the E F . In case of CoIrMnSi/MgO/CoIrMnSi, the transmittance peak is found to be broad in nature and it caves around (kx , ky )= (0, 0) and some spikes are also visible at some other (kx , ky ) points of the Brillouin zone. This kind of structure of the transmittance peak can be attributed to the transmittance through both ∆1 and ∆5 channel. As we observed in the band structure of bulk CoIrMnSi that both the ∆1 and ∆5 bands crosses the Fermi level. However, the contribution of ∆5 band to the transmittance can be reduced by increasing number of MgO layers as it decays much faster compared to the ∆1 band in insulating barrier.47 It is also to be noted that in parallel magnetization, majority spin conductance of CoIrMnSi/MgO/CoIrMnSi junction is much larger (5.341 × 10−3 G0 , G0 is the e2 /h unit) compared to that of CoIrMnAl/MgO/CoIrMnAl (3.4401 × 10−5 G0 ), owing to the presence of spin polarized ∆1 band in case of the former one.

IV.

CONCLUSION

From first principles-based calculations, we study the electronic and magnetic properties of CoIrMnZ (Z=Al, Si, Ga, Ge) Heusler alloys in their bulk forms. We predict CoIrMnAl as a novel ferromagnetic Heusler alloy which has a signature of electronic structure closed to a spin-gapless semiconductor. The inclusion of SOC have negligible effects on the electronic structure of all the studied Heusler alloys here. CoIrMnSi and CoIrMnGe are found to have 17

0.00010

0.000064

0.00005

T

0.000056 0.000048 0.000040

0.00000

0.000032 0.000024 0.000016

−0.00005 0.000008 0.5 0.000000

−0.5

0.0

ky

0.0

kx

0.5 −0.5

FIG. 13: (Color online) Transmittance (T) in CoIrMnAl/MgO/CoIrMnAl(001) as a function of in plane wave vectors kx and ky at E F in parallel magnetization of majority spin electrons.

0.0015 0.00150 0.00135 0.0010

T

0.00120 0.00105 0.00090

0.0005

0.00075 0.00060 0.00045

0.0000 0.5

0.00030 0.00015 0.00000

−0.5

0.0

ky

0.0

kx

0.5 −0.5

FIG. 14: (Color online) Transmittance (T) in CoIrMnSi/MgO/CoIrMnSi(001) as a function of in plane wave vectors kx and ky at E F in parallel magnetization of majority spin electrons. spin polarized ∆1 band along Γ-X direction. Our calculation shows that all these systems possess TC above room temperature and it is predicted to be highest for CoIrMnSi (1020 K). We show that the interfaces with the MnZ terminations are energetically favourable over the CoIr terminations for the CoIrMnAl/MgO and CoIrMnSi/MgO heterojunctions. The interafcial lattice mismatch is found to be around 1% for both the cases. More importantly, 18

CoIrMnSi/MgO/CoIrMnSi shows a high majority spin tunnelling conductance in the parallel magnetization owing to the presence of spin polarized ∆1 band.

V.

ACKNOWLEDGEMENTS

The authors are grateful to S. Mizukami, A. Hirohata, T. Tsuchiya, and T. Ichinose for valuable discussion. TR also thanks A. Chakrabarti and T. Kanomata for their valuable suggestions. This work was partially supported by JST CREST (No. JPMJCR17J5) and JSPS Core-to-Core Program ”New-Concept Spintronics Devices”.

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