Perpendicular magnetic anisotropy in nearly fully compensated ferrimagnetic Heusler alloy Mn0.75Co1.25VIn: An ab initio study

Perpendicular magnetic anisotropy in nearly fully compensated ferrimagnetic Heusler alloy Mn0.75Co1.25VIn: An ab initio study

Accepted Manuscript Research articles Perpendicular magnetic anisotropy in nearly fully compensated ferrimagnetic Heusler alloy Mn0.75Co1.25VIn: An ab...

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Accepted Manuscript Research articles Perpendicular magnetic anisotropy in nearly fully compensated ferrimagnetic Heusler alloy Mn0.75Co1.25VIn: An ab initio study Muthui Zipporah, Musembi Robinson, Mwabora Julius, Kashyap Arti PII: DOI: Reference:

S0304-8853(17)31056-9 http://dx.doi.org/10.1016/j.jmmm.2017.06.102 MAGMA 62898

To appear in:

Journal of Magnetism and Magnetic Materials

Received Date: Revised Date: Accepted Date:

29 March 2017 30 May 2017 24 June 2017

Please cite this article as: M. Zipporah, M. Robinson, M. Julius, K. Arti, Perpendicular magnetic anisotropy in nearly fully compensated ferrimagnetic Heusler alloy Mn0.75Co1.25VIn: An ab initio study, Journal of Magnetism and Magnetic Materials (2017), doi: http://dx.doi.org/10.1016/j.jmmm.2017.06.102

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Perpendicular magnetic anisotropy in nearly fully compensated ferrimagnetic Heusler alloy Mn0.75Co1.25VIn: An ab initio study Muthui Zipporah1, 2, Musembi Robinson1, Mwabora Julius1, and Kashyap Arti2 a) 1

2

Department of Physics, University of Nairobi, P.O.Box 30197, 00100, Nairobi, Kenya School of Basic Sciences, Indian Institute of Technology, Mandi, Himachal Pradesh, 175005, India

ABSTRACT

First principles calculations are reported on perpendicular magnetic anisotropy (PMA) in nearly fully compensated ferrimagnetic Heusler compound Mn0.75Co1.25VIn. The structural, electronic and magnetic properties of Mn2-xCoxVIn Heusler compounds (x = 0.0, 0.25, 0.50, 0.75, 1.0, 1.25, and 1.75) have been investigated using Density Functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP). The Perdew Burke Ernzerhof parametrization of the generalized gradient approximation (GGA) was used to treat the exchange and correlation in the system. The crystal structure of the compounds with x = 0.75, 1.00 and 1.25 are found to be tetragonally distorted. While the former exhibits inplane magnetocrystalline anisotropy (IMA) energy of 0.035 meV, the latter two exhibit perpendicular magnetocrystalline anisotropy (PMA) energy of 11.700 meV and 96.800 meV respectively. Additionally, the magnetic moments for x = 0.75 and 1.25 are found to be~ 0.5 µB/f.u. while for x = 1.00, it is found to be ~ 0 µB/f.u., in agreement with the Slater Pauling rule for half metallic systems. Through Co replacement of Mn in Mn2VIn which is not half metallic at the optimized volume, a composition whose crystal structure is tetragonally distorted is found, which is not only a highly spin polarized nearly fully compensated ferrimagnet but also exhibits PMA.

INTRODUCTION Half metallic ferrimagnetism is one of the properties possessed by some X2YZ Heusler compounds, which is preferred over half metallic ferromagnetism in magneto electronic applications. This is due to the small total magnetic moments in these systems which are not affected by external magnetic fields and do not give rise to strong stray fields, while leading to (

a) Electronic mail to [email protected] .ac.in (b) All the authors contributed equally to this work. ( c) This research was performed while Muthui Z. was at IIT, Mandi, Himachal Pradesh, 175005, India

smaller energy consumption in devices[1][2][3][4]. The spin magnetic moments of the transition metal atoms, X and Y in these systems are anti parallel, which is common in X2YZ (X=Mn) Heusler compounds such as Mn2CoGa and Mn2VAl, with the latter having been shown to be stable in the L21 phase [4][5]. This desirable property if present in a material can be exploited in the constantly growing field of antiferromagnetic spintronics [6]. It has been created in materials through various techniques such as doping of diluted magnetic semiconductors or inclusion of defects in Cr pnictides [4]. This is interesting and quite significant for practical applications because materials can be prepared for spintronics devices with strong ferromagnetic, weak ferromagnetic or nonmagnetic properties coupled with high spin polarization by adjusting the compositions of the atoms [4][7]. Heusler systems allow the formation of substitutional series of single sites resulting in tailoring of magnetic properties and tuning of the spin polarization [8][9]. By means of first principles electronic structure calculations, fully compensated ferrimagnets have been designed this way by doping Mn2VAl and Mn2VSi with Co [4]. Özdoğan et al., have achieved half metallic ferrimagnetism in Co2MnZ (Z = Al, Ga, Si, Ge, Sn) Heusler compounds by creating Mn antisites at the Co sites [10]. The impurity Mn atoms couple antiferromagnetically with the Co and Mn atoms at the perfect sites without destroying the half metallic character of the original compounds [10]. Cr2CoGa, which is made of magnetic constituents but is a half metallic fully compensated ferrimagnet also known as a half metallic antiferromagnet has been successfully grown using molecular beam epitaxy [6]. A change in the total number of valence electrons has been shown both experimentally and by first principle investigations to shift the Fermi level within the half metallic gap[11][12][13][14]. This has been experimentally observed in Co2FeAl0.5Si0.5 and Co2Fe1−xCrxSi in which a high Tunneling Magneto Resitance (TMR) of 175% and increase in spin polarization respectively were attributed to the central positioning of the Fermi level [15]. In Co2CrGa and Co2TiGa, substitution with Fe and Mn, respectively, for the Y element, increased the stability of the L21 structure as well as the half metallic gap [16][17] and Co2FeAl0.5Si0.5 has been found to have a larger effective spin polarization as compared to the stoichiometric compound Co2FeSi. A TMR of 16% at room temperature and 26.5% at 5K were found in Co2Cr0.6Fe0.4Al thin films [18], while Fe doping in Co2MnSn was found to increase the spin polarization measured by Andreev reflection technique. 2

Fermi level tuning by doping has been used to decrease the phase transition temperature in Heusler compounds having Al as the Z element which often exhibit a B2 (CsCl) type of disorder as evidenced by X-ray diffraction (XRD) measurements[19]. Doping with Si in Co2FeAl, forming the Co2FeAl1-xSix series, results in the formation of CoFeAlSi, which is a stable ordered half metallic ferromagnet used in Magnetic Tunneling Junctions (MTJ’s) [19]. The same observation was made for Co2MnAl1-xSix and both compounds are predicted to have stable half metallicity as well as high spin polarization [19]. The effect of the Z element on the structure of Heusler compounds was demonstrated in an investigation of the structural properties of Mn2YZ series, in which Z = In and Sn resulted in tetragonally distorted structures which had a directional preference of magnetization [8]. In the Mn3-xCoxGa series, tetragonal highly spin polarized compositions were predicted [9]. The resulting structures are examples of the tetragonal derivatives of Heusler structure obtained by elongation or compression of the cell axes of the cubic parent phase [20]. We have carried out Co substitution on Mn site in Mn2VIn with the aim of increasing the spin polarization and to tune the Fermi level to fall within the resulting half metallic gap, as well as to provide yet another alternative material in the field of antiferromagnetic spintronics. COMPUTATIONAL DETAILS The electronic structure calculations of stoichiometric and off- stoichiometric Mn2-xCoxVIn Heusler compounds, where x = 0.0, 0.25, 0.50, 0.75, 1.0, 1.25, and 1.75, were carried out using the density functional theory (DFT) as implemented in VASP which uses plane waves and projector augmented plane wave (PAW) approach. The plane wave basis set cut off energy was set at 430 eV. Self consistent calculations were performed employing the Perdew Burke Enzerhof parameterization of the generalized gradient approximation (PBE-GGA) exchange and correlation (XC) potentials. A conventional 1×1×1 cell of 16 atoms in the L21 cubic structure, space group Fm3m, space group no. 225, with wyckoff positions 8c, 4b and 4a occupied by Mn, V and In respectively, was generated to simulate the various doping concentrations. The Co addition was carried out by gradually replacing the Mn atoms by the Co atoms in the optimized Mn2VIn unit cell. Replacing one Mn atom by one Co atom resulted in x = 0.25 configuration, similarly by substituting two Mn atoms with two Co atoms, x = 0.5 configuration is achieved and 3

so on. The resulting input L21 crystal structures after Co substitution are shown in Fig. 1 for all configurations. Before studying the electronic and magnetic properties of the compounds, full relaxation of the internal atomic coordinates was carried out. The k-space integration was carried out using the linear tetrahedron method with Blöchl corrections. A ᴦ centered 21 × 21 × 21 kpoint Mornkhorst-Pack mesh was used as the base for the integration and the energy convergence criterion was set to 10-8 eV, while the charge convergence was also monitored along with it. The magneto crystalline anisotropy energy (MCAE) was taken as the energy difference between states with magnetization pointing along the z axis and the x axis, that is, EMCAE = E (100) – E (001).

Fig.1: L21 structures in which Mn (Co) occupies the 8 equivalent 8c (¼, ¼, ¼) sites, while V and In occupy the 4b (½, ½. ½) and 4 a (0, 0, 0) sites respectively. Co atoms substitute Mn atoms gradually. The structures corresponding to x = 0.25 - 1.75 are shown from (a) to (g), RESULTS AND DISCUSSIONS In this section, the electronic structure is discussed alongside the crystal structure and eventually, the magnetic properties of each configuration are discussed.

Electronic and Structural Properties Mn2VIn has a very low spin polarization of 15.38% at the optimized lattice constant of 6.25 Å as shown in Fig. 2. At this lattice constant, there is hardly any hybridization between the Mn and V states, which occur at different energy regions, resulting in a metallic band structure. Mn d states exhibit an exchange splitting of around 1.5 eV, which leads to localized spin moments at the Mn 4

site due to a near exclusion of spin down electrons from the Mn site as explained by Galanakis et al. [21]. Several Co substitutions of Mn were carried out in Mn2VIn thereby resulting in compositions Mn2-xCoxVIn for x ranging from 0.25 to 1.75 in steps of 0.25. This leads to the contraction of the lattice as the atomic size of Co is smaller than that of Mn. Deka et al. made a similar observation in their study of the (Mn1-xCox)2VAl series [22].

Fig.2: Total density of states (TDOS) and atom resolved Partial density of states (PDOS) for Mn2VIn Compositions of x = 0.25 and 0.5 resulted in total density of states (TDOS) in which both spin channels were heavily conducting, as shown in Fig.3 (a) and (b), hence no half metallic gap.

Fig.3: Total density of states plots (TDOS) for (a) Mn1.75Co0.25VIn and (b) Mn1.5Co0.5VIn. Inset in each figure is the corresponding structure showing the impurity Co atom in Mn sites 5

Both compounds maintained the cubic structure on full relaxation, resulting in lattice constants of 6.189 Å and 6.165Å for Mn1.75Co0.25VIn and Mn1.5Co0.25VIn respectively. In both cases, the minority states are enhanced by the addition of Co 3 d states leading to spin polarizations of 17.87% and 14.70% for x = 0.25 and 0.5 respectively. However, at these lattice constants, hybridization of the d states leading to the formation of a half metallic gap does not occur. While the spin polarization in the x = 0.25 concentration increases in comparison to Mn2VIn, that of x = 0.5 concentration reduces. This is attributed to the higher contraction of the lattice resulting in the increase of d states near the Fermi level for both the minority and majority spin channels at the higher Co concentration, as seen in Fig. 3 (b). For x = 0.75, 1 and 1.25 Co concentrations, the fully relaxed structures result in a tetragonal distortion of the L21 structure with a slight elongation of the c parameter with respect to the a=b parameter. The tetragonal distortions increase with Co concentration, resulting in c/a ratios of 1.0023, 1.0108 and 1.0110 for Mn1.25Co1.75VIn, MnCoVIn and Mn0.75Co1.25VIn respectively. The tetragonal distortion has been attributed in previous studies, to the occurrence of density of state peaks at the Fermi level known as the Van Hove singularity, which triggers a tetragonal distortion in order to minimize the energy of the system. This is often accompanied by the destruction of the half metallic gap, as d states are pulled towards the Fermi level resulting in reduced spin polarizations in the resulting tetragonally distorted systems [8]. The electronic structure for MnCoVIn corresponding to x = 1 shown in Fig. 4, is highly spin polarized at 64.95%, with the emergence of a half metallic gap in the spin up states, and the Fermi level closer to the conduction band. This is as a result of the reduced lattice constant of the fully relaxed structure at a = b = 6.003, c = 6.068, at which hybridization takes place. The spin polarization is however less than expected due to the balance between the lattice constant and the tetragonal distortion in the system. While the tetragonal distortion in Mn0.75Co1.25VIn is higher, the lattice is more contracted, which allows for more effective hybridization, resulting in a higher spin polarization. On the other hand, the distortion in Mn1.25Co1.75VIn is less and does not result in a high reduction in the spin polarization. The resulting densities of states for x = 0.75 and 1.25 are highly spin polarized at 74.29% and 82.15% respectively. 6

Fig.4: Total density of states plot (TDOS) for MnCoVIn. Inset is the corresponding structure showing the impurity Co atoms in Mn sites This is depicted in Fig.5 (a) and (b). The lattice constants for Mn1.25Co0.75VIn and Mn0.75Co1.25VIn relaxed structures are a = b = 6.028 Å, c = 6.042 Å and a = b = 5.989 Å, c = 6.055Å respectively.

Fig.5: Total density of states plots (TDOS) for (a) Mn1.25Co0.75VIn and (b) Mn0.75Co1.25VIn. Inset in each figure is the corresponding structure showing the impurity Co atom in Mn sites Interestingly, while the half metallic gap is in the spin up states for the Mn rich variant, it is switched to the spin down states in the Co rich variant. This is a property that can be exploited in design of spintronic devices, such as those requiring the tunneling spin polarization to be parallel

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to the magnetization, and for the other to be opposite as described in a study on ferrimagnetic Heusler materials [23]. The Fermi level remained in the half metallic gap in the spin down states of Mn0.5Co1.5VIn which maintained a cubic structure with a = 6.011Å having a spin polarization of 92.70% while in cubic Mn0.25Co1.75VIn, having a = 6.003Å, the Fermi level fell almost at the center of the half metallic gap in the spin down states, with a resulting spin polarization of 93.6% as shown in Fig.6 (a) and (b). Further substitution of Mn by Co tunes the Fermi level to fall within the gap in Mn0.25Co1.75VIn. The location of the Fermi level almost at the center of the gap as well as a stable density of majority states, devoid of Van Hove singularity, points to the stability of the half metallic gap in this composition.

Figure 6: Total density of states plots (TDOS) for (a) Mn0.5Co1.5VIn and (b) Mn0.25Co1.75VIn. Inset in each figure is the corresponding structure showing the impurity Co atom in Mn sites The lattice parameters of all the fully relaxed structures are recorded in Table 1 together with the corresponding spin polarizations. In Fig. 7, the atom resolved partial densities of states highlighting the contributions of the states of each atom to the electronic structure of Mn0.25Co1.75VIn are shown. It is evident that the TDOS of Mn0.25Co1.75VIn shown in Fig. 6 (b) has an overwhelming Co and V character near the Fermi energy level whereas the In contribution is almost negligible. The Mn d states, though of a relatively less spectral weight, are also available for hybridization within a region of 1 eV from the Fermi level.

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Notable is the contribution of the majority V d orbitals which have a significant weight that hybridize with the majority Co d states in the same region near the Fermi level contributing to the increased majority states in the TDOS as well as the Co and V states above the Fermi level for the minority states resulting in a half metallic gap. From the results of the electronic structure, it emerges that Co and V states hybridize in a manner favorable to the formation of a half metallic electronic structure. A similar hybridization is reported in literature as well as from our earlier work on Co2VIn which would correspond to x = 2 in this study, resulting in much higher spin polarization and half metallicity [24][25]. A further investigation of the structure of Mn0.25Co1.75VIn revealed that it is more stable in the regular L21 Cu2MnAl structure than the inverse Heusler Hg2CuTi structure.

Fig. 7: Partial density of states (PDOS) for Mn0.25Co1.75VIn Magnetic Properties Just like the electronic properties, the magnetic moments of the elements in the resulting compositions on Co substitution were found to have a great dependence on whether hybridization is possible at the lattice constants of the relaxed structures as well as on the crystal structures of the unit cells. Generally, for lattice constants > 6.1 Å, there is localization of magnetic moments, with Mn having a magnetic moment of ~ 3µ B. 9

Table 1 highlights the atom resolved magnetic moments in the unit cells as well as their corresponding lattice constants and the resulting spin polarizations. A general observation is made that there is a parallel alignment of Co and V spin moments in all the Co substituted compositions. Additionally, for all structures having a < 6.1 Å, the Slater Pauling rule for predicting the total magnetic moments of half metallic Heusler compounds is obeyed. Table 1: The calculated results for spin polarization and atom resolved magnetic moments at the lattice constants of the relaxed structures of various Mn2-xCoxVIn compositions

Mn2-xCoxVIn Mn2VIn Mn1.75Co0.25VIn Mn1.5Co0.5VIn Mn1.25Co0.75VIn MnCoVIn Mn0.75Co1.25VIn Mn0.5Co1.5VIn Mn0.25Co1.75VIn

Unit cell parameters (Å) a = 6.250 a = 6.189 a = 6.165 a = b = 6.028 c =6.042 a = b = 6.003 c=6.068 a = b = 5.989 c =6.055 a = 6.011 a = 6.003

-0.059 -0.049 -0.048 -0.015

Total µB /f.u. 3.980 2.683 2.213 0.493

Slater Pauling µ B /f.u. 2.0 1.5 1 0.5

Spin pol. % 15.380 17.870 14.700 74.290

-0.839

-0.008

0.020

0

64.950

0.751

0.628

-0.015

0.536

0.5

82.146

0.849 0.897

0.504 0.327

-0.022 -0.047

1.023 1.543

1 1.5

92.700 93.600

Mn (µ B)

Co (µ B)

V (µ B)

In (µ B)

3.009 2.767 2.714 1.651

-1.161 -0.454 -0.698

-1.979 -1.820 -1.583 -1.035

1.518

-0.691

-1.355 -1.465 -1.231

This is true for Mn1.25Co0.75VIn, MnCoVIn, Mn0.75Co1.25VIn, Mn0.5Co1.5VIn and Mn0.25Co1.75VIn. In all these compositions, the Mn magnetic moment is anti parallel to the Co and V moments. Tetragonal distortions resulted in three cases, right at the middle of the substituted variants for x = 0.75, 1.00 and 1.25. In these three, there were vanishing total magnetic moments, and were therefore nearly antiferromagnetic. In fact, MnCoVIn is as good as anti ferromagnetic, with the small total magnetic moment value of 0.02 µ B /f.u being as a result of the slight distortion of the structure. The tetragonal distortions in Mn1.25Co1.75VIn, MnCoVIn and Mn0.75Co1.25VIn, triggered an investigation of magnetic anisotropy energy which is of great significance to technological application. Similar to the distorted bulk Mn2VIn, the Manganese rich variant Mn1.25Co0.75VIn has an in plane magnetic anisotropy (IMA) of 0.035 meV, while perpendicular magnetic 10

anisotropy energy (PMA) of 96.8 meV and 11.700 meV was established to be present in the Mn0.75Co1.25VIn and MnCoVIn bulk systems. This trend is as expected as magnetocrystalline anisotropy increases with the c/a ratios. The great significance of this finding is that this effect if present in the bulk material, it is expected to be much higher in thin films and interfaces which are technologically more relevant, where spin orbit effects become significant at reduced dimensions enhancing PMA. CONCLUSION Mn2VIn has demonstrated the flexibility and versatility of Heusler compounds, in which the Mn0.75Co1.25VIn composition has exhibited technologically relevant properties such as high spin polarization, near fully compensated ferrimagnetism due to a vanishing magnetic moment, tetragonal distortion as well as PMA resulting from the introduction of Co atoms in the Mn site. It is noteworthy that the spin polarization increased in very low concentrations of impurity Co atoms. Mn0.25Co1.75VIn, which has a composition closer to Co2VIn than to Mn2VIn exhibited the highest spin polarization amongst all the compositions. In addition, the site substitution and Fermi level tuning in Mn2-xCoxVIn has demonstrated the usefulness of the technique in achieving materials with higher spin polarization and has provided a route to decreasing the magnetic moments resulting in near antiferromagnetic coupling in the tetragonally distorted structures introducing new systems that may be used as candidates for spin valves and magnetic tunnel junction applications as well as in devices in which half metallic fully compensated ferromagnetic materials are desirable. We believe that our calculations will motivate the experimentalists to synthesize these new materials with technologically desirable properties. ACKNOWLEDGEMENTS Muthui Z. acknowledges the assistance of OWSD fellowship, IIT-Mandi, India and DAAD for a Ph.D scholarship at the University of Nairobi. REFERENCES [1] N. Xing, H. Li, J. Dong, R. Long, and C. Zhang, “First-principle prediction of half-metallic ferrimagnetism of the Heusler alloys Mn2CoZ (Z = Al, Ga, Si, Ge) with a high-ordered structure,” Comput. Mater. Sci., vol. 42, no. 4, pp. 600–605, Jun. 2008. [2] K. Özdogan, I. Galanakis, E. Şaşioglu, and B. Aktaş, “Search for half-metallic ferrimagnetism in Vbased Heusler alloys Mn 2 VZ (Z = Al, Ga, In, Si, Ge, Sn),” J. Phys. Condens. Matter, vol. 18, no. 10, p. 2905, 2006.

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[22] B. Deka, A. Srinivasan, R. K. Singh, B. S. D. C. S. Varaprasad, Y. K. Takahashi, and K. Hono, “Effect of Co substitution for Mn on spin polarization and magnetic properties of ferrimagnetic Mn2VAl,” J. Alloys Compd., vol. 662, pp. 510–515, 2016. [23] J. Jeong, Y. Ferrante, S. V. Faleev, M. G. Samant, C. Felser, and S. S. P. Parkin, “Termination layer compensated tunnelling magnetoresistance in ferrimagnetic Heusler compounds with high perpendicular magnetic anisotropy,” Nat. Commun., vol. 7, Jan. 2016. [24] M. Zipporah, R. Pathak, M. Robinson, J. Mwabora, R. Skomski, and A. Kashyap, “First-principle investigation of structural, electronic and magnetic properties of Co2VIn and CoVIn Heusler compounds,” AIP Adv., vol. 7, no. 5, p. 055705, Jan. 2017. [25] S. Khenchoul, A. Guibadj, B. Lagoun, A. Chadli, and S. Maabed, “First-Principles Prediction of Structural, Magnetic, Electronic, and Elastic Properties of Full-Heusler Compounds Co2YIn (Y = Ti, V),” J. Supercond. Nov. Magn., vol. 29, no. 9, pp. 2225–2233, Sep. 2016.

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Highlights     

Site substitution for Mn with Co is carried out in Mn2VIn to create a half metallic gap. Near antiferromagnetism emerges in Mn1.25Co0.75VIn, Mn0.75Co1.25VIn and MnCoVIn with magnetic moments of ~ 0.5 µB/f.u , for the former two and ~ 0 µB/f.u for the latter. Tetragonal distortions to the cubic L21 structure are observed in Mn1.25Co0.75VIn, Mn0.75Co1.25VIn and MnCoVIn. Perpendicular magnetic anisotropy observed in Mn0.75Co1.25VIn and MnCoVIn and inplane magnetic anisotropy in Mn1.25Co0.75VIn Electronic structure of Mn0.25Co1.75VIn is highly spin polarized, with a spin polarization of 93.6%.