Next Article in Journal
Photo-Fenton like Catalyst System: Activated Carbon/CoFe2O4 Nanocomposite for Reactive Dye Removal from Textile Wastewater
Next Article in Special Issue
Electronic, Optical, Mechanical and Lattice Dynamical Properties of MgBi2O6: A First-Principles Study
Previous Article in Journal
Highly Controlled Integration of Graphene Oxide into PAN Nanofiber Membranes
Previous Article in Special Issue
Theoretical Investigations on the Mechanical, Magneto-Electronic Properties and Half-Metallic Characteristics of ZrRhTiZ (Z = Al, Ga) Quaternary Heusler Compounds
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Applied Sciences
Volume 9
Issue 5
10.3390/app9050964
applsci-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Phase Stability and Magnetic Properties of Mn3Z (Z = Al, Ga, In, Tl, Ge, Sn, Pb) Heusler Alloys

by
Haopeng Zhang
1,
Wenbin Liu
1,
Tingting Lin
1,2,
Wenhong Wang
3 and
Guodong Liu
1,*
1
School of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 400044, China
2
Institute of Materials Science, Technische Universtät Darmstadt, 64287 Darmstadt, Germany
3
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(5), 964; https://doi.org/10.3390/app9050964
Submission received: 20 November 2018 / Revised: 4 December 2018 / Accepted: 5 December 2018 / Published: 7 March 2019
(This article belongs to the Special Issue Recent Advances in Novel Materials for Future Spintronics)
Browse Figures
Versions Notes

Abstract

:
The structural stability and magnetic properties of the cubic and tetragonal phases of Mn3Z (Z = Ga, In, Tl, Ge, Sn, Pb) Heusler alloys are studied by using first-principles calculations. It is found that with the increasing of the atomic radius of Z atom, the more stable phase varies from the cubic to the tetragonal structure. With increasing tetragonal distortion, the magnetic moments of Mn (A/C and B) atoms change in a regular way, which can be traced back to the change of the relative distance and the covalent hybridization between the atoms.

1. Introduction

Tetragonal Heusler compounds have been receiving huge attention in recent years due to their potential applications in spintronic [1,2,3,4,5] and magnetoelectronic devices [6,7,8,9], such as ultrahigh density spintronic devices [9,10,11,12,13], spin-transfer torque (STT) [9,10,11,12,13,14,15,16] and permanent hard magnets [17,18]. Among the tetragonal Heusler compounds, Mn3-based Heusler compounds exhibit very interesting properties. The previous theoretical and experimental studies [4,16,19,20,21,22] show that the tetragonal (DO22) phase of Mn3Ga compound is ferrimagnetic at room temperature and shows a unique combination of magnetic and electronic properties, including low magnetization, high uniaxial anisotropy, high spin polarization, and high Curie temperature. Because of these interesting properties, this material is believed to have potential for nanometer-sized spin transfer torque (STT) -based nonvolatile memories [4,16,23]. The first-principles calculations reveal that Mn3Z (Z = Ga, Sn and Ge) type Heusler compounds can have three different structural phases, where each phase exhibits different magnetic properties [24]. There are also some other reports about the phase stability and the magnetic properties for these systems [25,26,27,28], but the relation between the phase stability and the magnetic properties of Mn3Z tetragonal Heusler alloys has not been investigated in detail.
In this paper, the relation between the phase stability, magnetic properties, the covalent hybridization effect, and the relative position between atoms of Mn3Z (Z = Al, Ga, In, Tl, Si, Ge, Sn, Pb) Heusler alloys has been investigated by using the first-principles calculations. It is found that the atomic radius of Z atoms and the level of distortion have great effects on the degree of the covalent hybridization between atoms in Mn3Z system, which plays an important role in the phase stability and the magnetic properties of Mn3Z Heusler compounds.

2. Calculation Details

The calculations of total energy, electronic structure, and magnetic moments were performed by the Cambridge Serial Total Energy Package (CASTEP) code based on the pseudopotential method with a plane-wave basis set [29]. The exchange and correlation effects were treated using the local density approximation (LDA) [30]. The plane wave basis set cut-off was 500 eV for all of the cases, and 182 k-points were employed in the irreducible Brillouin zone. The convergence tolerance for the calculations was selected as the difference in the total energy within the 1 × 10−6 eV/atom. These parameters ensure good convergences for the total energy.

3. Results and Discussion

Heusler alloys crystallize in a highly-ordered cubic structure, and have a stoichiometric composition of X2YZ, where X and Y are transition-metal elements, and Z is a main group element. Generally, the Heusler structure can be considered as four interpenetrating f.c.c lattices along the space diagonal, in which the transition metal atoms occupy the A (0, 0, 0), B (0.25, 0.25, 0.25) and C (0.5, 0.5, 0.5) Wyckoff positions, respectively. The main group element occupies the D (0.75, 0.75, 0.75) position. The tetragonal Heusler alloys can be considered as tetragonal distortions of the cubic phase along the z direction, and the c/a ratio can be used to quantify the amount of tetragonal distortion [9,31,32]. For tetragonal Mn3Z (Z = Al, Ga, In Tl, Si, Ge, Sn, Pb) alloys, the Mn(A), Mn(B), Mn(C) and Z atoms occupy the (0, 0, 0), (0.25, 0.25, 0.25), (0.5, 0.5, 0.5) and (0.75, 0.75, 0.75) Wyckoff positions, respectively.
As a typical example, we first present the results of Mn3Ga alloy. Figure 1 shows the total energy as a function of c/a (ΔEtotal-c/a curve) for Mn3Ga alloy. The total energy of the cubic phase is set as the zero point. The lattice constant of the cubic phase is obtained by minimizing the total energy and is 5.66 Å. The unit cell volume is the same as that of cubic phase, and is fixed when the tetragonal distortion is considered. From Figure 1, it can be seen that there are two local energy minima on the ΔEtotal-c/a curve, i.e., a shallow one is at c/a = 1.35 and a deeper one at c/a = 1. The latter is energetically favorable. Between the two energy minima, there is an energy barrier at c/a = 1.15. The lower and upper insets show the corresponding crystal structures, band structures, and densities of states (DOS) for the cubic (c/a = 1) and distorted (c/a = 1.35) cases. From the band structures, we can see that the cubic phase (c/a = 1) of Mn3Ga is close to the half-metal, with a high degree of spin polarization. But in the tetragonal phase (c/a = 1.35), the band structure is completely different from the cubic one, and it can also be seen that the spin polarization declines rapidly at the Fermi level from the density of states patterns. This is mainly due to the fact that cubic symmetry is reduced after the tetragonal distortion.
Comparing the work reported by Delin Zhang et al. [31] with that by Claudia Felser et al. [33], it can be noted that the difference of volume can have a large impact on the ΔEtotal-c/a curves. Therefore, we performed a series of investigations on the tetragonal distortion with different volumes to further understand the relation between the volume and the ΔEtotal-c/a curves for Mn3Ga alloy. In Figure 2a, we show the ΔEtotal-c/a curves of Mn3Ga alloy with different volumes (v = 17.0 nm3, 18.0 nm3, 19.0 nm3, 20.0 nm3, 21.0 nm3, 22.0 nm3), which correspond to the different lattice constants in the cubic phase. It can be seen that the shape of the ΔEtotal-c/a curves varies with the change of the volume. There are two local energy minima in the ΔEtotal-c/a curves for all the Mn3Ga alloys with different volumes. For V = 17.0 nm3 and 18.0 nm3, the total energy of cubic phase is lower than that of the tetragonal phase, which indicates that the cubic phase is more stable than the tetragonal phase. As the volume expands to higher level than 19.0 nm3, the total energy of the tetragonal phase becomes lower than the cubic phase. At same time, the energy barrier from the cubic phase to the tetragonal phase gradually decreases with the increasing volume, and finally, disappears at V = 21.0 nm3. This indicates that the tetragonal phase becomes a more stable phase with the expanding volume, and it becomes easier to transform from the cubic phase to the tetragonal phase. So, from the ΔEtotal-c/a curves with different volume of Mn3Ga, it is clear that a very small change of the volume can lead to a great change of the shape of the ΔEtotal-c/a curves. In other word, the phase stability of Mn3Ga Heusler alloys is very sensitive to the change of the volume. For the Mn3Ga systems, we can adjust the volume to achieve the alloys with different structures as well as possible martensitic transformations.
A good way to adjust the volume is to dope similar elements into the matrix. Therefore, next, we extend the research scope to all the other Mn3Z (Z = Al, In, Tl, Si, Ge, Sn, Pb) alloys. We perform systematical investigations on ΔEtotal-c/a curves for these alloys under their respective equilibrium cell volumes, which are achieved by their equilibrium lattice constant in the cubic structure. The equilibrium lattice constants in the cubic structure are 5.6 Å, 5.95 Å, 6.01 Å, 5.53 Å, 5.61 Å, 5.87 Å, and 6.01 Å for Mn3Z (Z = Al, In, Tl, Si, Ge, Sn, Pb) alloys respectively. Their ΔEtotal-c/a curves are shown in Figure 2b. For a clear analogy, the ΔEtotal-c/a curve of Mn3Ga is also replotted in Figure 2b, in which one can see that, similar to Mn3Ga alloy, there are two local energy minima in the ΔEtotal-c/a curves for all the other Mn3Z alloys. One energy minimum is at c/a = 1 (cubic phase), and the other is at c/a = 1.35 (tetragonal phase), except for Mn3Ge, where it is at c/a = 1.4. From Figure 2b, we can observe that when Z is cognate element, the ΔEtotal of the tetragonal phase at c/a = 1.35 (for Mn3Ge at c/a = 1.4) decreases gradually with the increase of atomic number. It is also clear that the smaller the atomic number, the smaller the volume of compound. The cubic phase is more stable than the tetragonal phase for the compounds with a small volume, such as Mn3Al, Mn3Ga, Mn3Si, and Mn3Ge. And the tetragonal phase is more stable in energy for the compounds with bigger atomic number, such as Mn3In, Mn3Tl, Mn3Sn and Mn3Pb.
The energy barrier between the two local energy minima is crucial to the occurrence of martensitic transformation (or reverse transformation) from the cubic (tetragonal) to tetragonal (cubic) phase. When the energy barrier is higher than the driving forces of phase transformation, the compound is stable in one of two local energy minima, and the martensitic transformation can not occur in the compound. Conversely, when the energy barrier is lower than the driving force of phase transformation, martensitic transformation may occur in the compound. In addition, from Figure 2b, it can be found that when the Z atom varies from Al to Tl (Si to Pb), the energy barrier exhibits a maximum at Mn3Ga (Mn3Sn) for ΔEtotal, and the local energy minimum of tetragonal phase changes from positive to negative value with the increasing atomic number.
All the above results imply that the atomic radius of the main group element Z has a great influence on the volume. We can mix different Z elements to obtain Mn3Z alloys with the different volumes and stable phases. It should be noted that a thermoelastic martensitic transformation from cubic to tetragonal phase may also occur in the Mn3Z alloys, since the energy barrier can be flexibly regulated by the mixture of different Z elements. So, the Mn3Z alloys have the potential to be developed into a series of magnetic shape memory alloys originating from thermoelastic martensitic transformation.
It is well known that with the increase of the distance between the main group Z atom and the nearest neighbor Mn(A) and Mn(C), the hybridization strength of the p-d orbitals between Z and Mn(A/C) atoms is weakened [34]. Before we start to analyze the magnetic properties, we perform an investigation on the change of the relative position of the atoms in Mn3Z alloys during the tetragonal distortion. As shown in Figure 3a, the distance between Z and Mn(B) and the distance between Mn(A) and Mn(C) along the c axis increase linearly with the increase of the c/a ratio in the process of tetragonal distortion, while the distance between Z and Mn(B) and the distance between Mn(A) and Mn(C) along the a or b axis decreases linearly with the increase of the c/a ratio. Figure 3b show the changing curve of the distance between two nearest-neighbor atoms with the change of c/a ratio. It is clear that the distance of between two nearest neighbor atoms decreases first, and then increases with the increase of the c/a ratio and get a minimum at c/a = 1.
Next, we will compare and analyze the atomic magnetic moments for the Mn3Ga alloy with different volumes, and all the other Mn3Z alloys with the equilibrium volume, which are shown in Figure 4 and Figure 5. As we know, with the increase of the lattice constant, the distance between atoms increases, which leads to the weakening of covalent hybridization between atoms. The weakened covalent hybridization will result in an increase of atomic magnetic moments in the Heusler alloys [35,36]. When we compress the lattice along the c-axis (c/a < 1), we see that the dependence of the magnetic moment of Mn(A/C) on c/a ratio shows three different tendency ranges with the change of the volume for Mn3Ga alloy, as shown in Figure 4a. (1) When the volume is small (V = 17 nm3), the magnetic moment of Mn(A/C) atom shows a sharp decrease with the increase of c/a. (2) When the volume is in the range of 18 nm3~20 nm3, the magnetic moment of Mn(A/C) almost remains constant with the increase of c/a, which indicates that the moment is very stable against the compressive strain along the c-axis. (3) When the volume is higher than 21 nm3, the magnetic moment of Mn(A/C) increases slowly with the increase of c/a.
The three different changing trends of the Mn(A/C) moment are due to the change of covalent hybridization between these atoms with the changing tetragonal distortion ratio [37]. There are three kinds of possible covalent hybridizations, i.e., between Ga and Mn(A/C), between Mn(A) and Mn(C) along c axis and between Mn(A/C) and Mn(B), which compete to determine the atomic magnetic moments. When c/a < 1, with the increase of the c/a ratio, the following occurs: (1) The distance between Ga and Mn(A/C) decreases, which leads to the strengthened p-d orbital covalent hybridization between Ga and Mn(A/C). Thus, the magnetic moment of Mn(A/C) decreases with the increase of c/a ratio. (2) The distance between Mn(A) and Mn(C) along the c axis increases, and the d-d orbital covalent hybridization between them was weakened. So, the magnetic moment of Mn(A/C) increases. (3) The distance between Mn(A/C) and Mn(B), namely, the distance between two nearest neighbor atoms, decreases and the d-d covalent hybridization is strengthened. Thus, the magnetic moments of Mn(A/C) and Mn(B) show a decrease trend. According to the above phenomena, it can be observed that when the volume is small (v = 17 nm3), the d-d orbital covalent hybridization between Mn(A) and Mn(C) atoms plays a dominant role to lead to a sharp decrease of the magnetic moment of Mn(A/C) with the increase of c/a. When the volume is greater than 21 nm3, the p-d orbital covalent hybridization between Ga and Mn(A/C) and the d-d orbital covalent hybridization between Mn(A/C) and Mn(B) atoms are the main contributors. As for the cases of 18~20 nm3, which have moderate distances among atoms, the p-d orbital covalent hybridization between Ga and Mn(A/C), the d-d orbital covalent hybridization between Mn(A) and Mn(C) atoms, and the d-d orbital covalent hybridization between Mn(A/C) and Mn(B) atoms counteract each other. Thus, the magnetic moment of Mn(A/C) remains almost unchanged with the increase of c/a.
From Figure 4a, it can also be seen that when c/a > 1, the moment of Mn(A/C) first increases and then generates a downward trend. We might consider the case of c/a < 1 to understand the situation. Firstly, with the increase of c/a ratio, the distance between Mn(A/C) and Ga (also Mn(B)) increases. So, the p-d (d-d) covalent hybridization decreases and the moment of Mn(A/C) increases. Secondly, the distance between Mn(A) and Mn(C) atoms along c axis increases. Thus, the d-d covalent hybridization was weakened and the magnetic moments of Mn(A/C) increase. Thirdly, with the increase of c/a ratio, the distance between the Mn(A) and Mn(C) along the a or b axis decreases, which leads to the strengthened of d-d covalent hybridization between them and a decrease of the Mn(A/C) moment. So, we can know that the Mn(A/C) magnetic moment increases first, and then decreases with the increase of c/a, which may be attributed to the change of covalent hybridization originating from the change of interatomic distance. Furthermore, with the increase of volume, the position of the inflection point to go down gradually shifts to the right. This is because Mn3Ga alloy with larger volume needs a larger degree of distortion (a larger c/a ratio) to make the distance between Mn(A) and Mn(C) along the a or b axes sufficiently small to achieve the same strength of d-d orbital covalent hybridization.
The magnetic moment of Mn(B) as a function of c/a ratio is plotted in Figure 4b for Mn3Ga alloys with different volumes. In the process of tetragonal distortion, the distance between Ga and Mn(B) atoms along the c axis gradually increases, and the p-d orbital covalent hybridization between these atoms gradually weakens, which makes the Mn(B) moment continue to increase. At the same time, the distance between Ga and Mn(B) atom along the a or b axis gradually decreases with the increase of c/a ratio. So, the p-d orbital covalent hybridization between these atoms gradually strengthens and the Mn(B) moment decreases. Thus, we can also understand this changing behavior of the magnetic moment of Mn(B).
Furthermore, from Figure 4b, we can see that the interatomic distance effects on the covalent hybridization counteract each other when c/a ratio is small for Mn3Ga alloys with V = 17.0~21.0 nm3. And the magnetic moment of Mn(B) moment is essentially unchanged. But when c/a ratio increases to about 1.2, the p-d orbital covalent hybridization between Ga and Mn(B) atoms along the c axis plays a major role, and the magnetic moment of Mn(B) has an upward trend. When the volume increases to 22.0 nm3, the distance between atoms is quite large, and the covalent hybridization becomes weaker. As c/a is in the range of 0.85–1, the p-d orbital covalent hybridization between Ga and Mn(B) atoms along the a or c axis and the d-d covalent hybridization between Mn(A/C) and Mn(B) are the main contributors, and the magnetic moment of Mn(B) has a downward trend. For the case of c/a > 1, both the p-d orbital covalent hybridization between Ga and Mn(B) along the c axis and the d-d covalent hybridization between Mn(A/C) and Mn(B) make the magnetic moment of Mn(B) show an upward trend.
We can see that the magnetic moments of Mn(A/C) and Mn(B) as functions of c/a ratio are very similar to Mn3Ga alloy for all the other Mn3Z (Z = Al, In, Tl, Si, Ge, Sn, Pb) alloys, as shown in Figure 5. As different main group elements have different atomic radii, the distance between atoms can be tuned by changing the main group element in Mn3Z which is similar to that in Mn3Ga alloy with different volume.

4. Conclusions

In summary, the structural and magnetic properties of tetragonal Heusler alloys Mn3Z (Z = Ga, In, Tl, Ge, Sn, Pb) have been systemically investigated by the first-principles calculations. The calculations indicate that the stability of the system is very sensitive to changes of volume. And the volume can be tuned by changing the main group element in Mn3Z alloys. The p-d and d-d covalent hybridization play very important roles during the tetragonal distortion, and have great influence on the atomic magnetic moments in Mn3Z alloys.

Author Contributions

Conceptualization, G.L. and H.Z.; methodology, H.Z.; formal analysis, G.L., H.Z. and W.W.; investigation, H.Z., W.L. and T.L.; writing—original draft preparation, H.Z.

Funding

This work was supported by the Program for Leading Talents in Science and Technology Innovation of Chongqing City (No. CSTCKJCXLJRC19) and Natural Science Foundation of Tianjin City (No. 16JCYBJC17200).

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Wollmann, L.; Fecher, G.H.; Chadov, S.; Felser, C. A scheme for spin-selective electron localization in Mn3Ga Heusler material. J. Phys. D Appl. Phys. 2015, 48, 164004. [Google Scholar] [CrossRef]
  2. Wu, H.K.F.; Sudoh, I.; Xu, R.H.; Si, W.S.; Vaz, C.A.F.; Kim, J.; Vallejo-Fernandez, G.; Hirohata, A. Large exchange bias induced by polycrystalline Mn3Ga antiferromagnetic films with controlled layer thickness. J. Phys. D Appl. Phys. 2018, 51, 215003. [Google Scholar] [CrossRef]
  3. Wu, F.; Mizukami, S.; Watanabe, D.; Sajitha, E.P.; Naganuma, H.; Oogane, M.; Ando, Y.; Miyazaki, T. Structural and Magnetic Properties of Perpendicular Magnetized MnGa Epitaxial Films. IEEE Trans. Magn. 2010, 46, 1863–1865. [Google Scholar] [CrossRef]
  4. Winterlik, J.; Balke, B.; Fecher, G.H.; Felser, C. Structural, electronic, and magnetic properties of tetragonal Mn3−xGa: Experiments and first-principles calculations. Phys. Rev. B 2008, 77, 054406. [Google Scholar] [CrossRef]
  5. Feng, W.W.; Thiet, D.V.; Dung, D.D.; Shin, Y.; Cho, S. Substrate-modified ferrimagnetism in MnGa films. J. Appl. Phys. 2010, 108, 113903. [Google Scholar] [CrossRef]
  6. Niida, H.; Hori, T.; Onodera, H.; Yamaguchi, Y.; Nakagawa, Y. Magnetization and coercivity of Mn3−δGa alloys with a D022-type structure. J. Appl. Phys. 1996, 79, 5946–5948. [Google Scholar] [CrossRef]
  7. Elm, M.T.; Hara, S. Transport Properties of Hybrids with Ferromagnetic MnAs Nanoclusters and Their Potential for New Magnetoelectronic Devices. Adv. Mater. 2014, 26, 8079–8095. [Google Scholar] [CrossRef]
  8. Ma, Q.L.; Kubota, T.; Mizukami, S.; Zhang, X.M.; Naganuma, H.; Oogane, M.; Ando, Y.; Miyazaki, T. Interface tailoring effect on magnetic properties and their utilization in MnGa-based perpendicular magnetic tunnel junctions. Phys. Rev. B 2013, 87, 184426. [Google Scholar] [CrossRef]
  9. Winterlik, J.; Chadov, S.; Gupta, A.; Alijani, V.; Gasi, T.; Filsinger, K.; Balke, B.; Fecher, G.H.; Jenkins, C.A.; Casper, F.; et al. Design Scheme of New Tetragonal Heusler Compounds for Spin-Transfer Torque Applications and its Experimental Realization. Adv. Mater. 2012, 24, 6283–6287. [Google Scholar] [CrossRef] [Green Version]
  10. Gutierrez-Perez, R.M.; Holguın-Momaca, J.T.; Elizalde-Galindo, J.T.; Espinosa-Maga~na, F.; Olive-Mendez, S.F. Giant magnetization on Mn3Ga ultra-thin films grown by magnetron sputtering on SiO2/Si(001). J. Appl. Phys. 2015, 117, 123902. [Google Scholar] [CrossRef]
  11. Baltz, V.; Manchon, A.; Tsoi, M.; Moriyama, T.; Ono, T.; Tserkovnyak, Y. Antiferromagnetic spintronics. Rev. Mod. Phys. 2018, 90, 015005. [Google Scholar] [CrossRef] [Green Version]
  12. Kurt, H.; Baadji, N.; Rode, K.; Venkatesan, M.; Stamenov, P.; Sanvito, S.; Coey, J.M.D. Magnetic and electronic properties of D022-Mn3Ge (001) films. Appl. Phys. Lett. 2012, 101, 132410. [Google Scholar] [CrossRef]
  13. Wu, F.; Sajitha, E.P.; Mizukami, S.; Watanabe, D.; Miyazaki, T.; Naganuma, H.; Oogane, M.; Ando, Y. Electrical transport properties of perpendicular magnetized Mn-Ga epitaxial films. Appl. Phys. Lett. 2010, 96, 042505. [Google Scholar] [CrossRef]
  14. Sugihara, A.; Suzuki, K.Z.; Miyazaki, T.; Mizukami, S. Magnetic properties of ultrathin tetragonal Heusler D022-Mn3Ge perpendicular-magnetized films. J. Appl. Phys. 2015, 117, 17B511. [Google Scholar] [CrossRef]
  15. Bai, Z.Q.; Cai, Y.Q.; Shen, L.; Yang, M.; Ko, V.; Han, G.C.; Feng, Y.P. Magnetic and transport properties of Mn3−xGa/MgO/Mn3−xGa magnetic tunnel junctions: A first-principles study. Appl. Phys. Lett. 2012, 100, 022408. [Google Scholar] [CrossRef]
  16. Balke, B.; Fecher, G.H.; Winterlik, J.; Felser, C. Mn3Ga, a compensated ferrimagnet with high Curie temperature and low magnetic moment for spin torque transfer applications. Appl. Phys. Lett. 2007, 90, 152504. [Google Scholar] [CrossRef]
  17. Zhu, L.J.; Nie, S.H.; Meng, K.K.; Pan, D.; Zhao, J.H.; Zheng, H.Z. Multifunctional L10-Mn1.5Ga Films with Ultrahigh Coercivity, Giant Perpendicular Magnetocrystalline Anisotropy and Large Magnetic Energy Product. Adv. Mater. 2012, 24, 4547–4551. [Google Scholar] [CrossRef]
  18. Zhu, L.J.; Pan, D.; Nie, S.H.; Lu, J.; Zhao, J.H. Tailoring magnetism of multifunctional MnxGa films with giant perpendicular anisotropy. Appl. Phys. Lett. 2013, 102, 132403. [Google Scholar] [CrossRef]
  19. Kurt, H.; Rode, K.; Venkatesan, M.; Stamenov, P.; Coey, J.M.D. High spin polarization in epitaxial films of ferrimagnetic Mn3Ga. Phys. Rev. B 2011, 83, 020405. [Google Scholar] [CrossRef]
  20. Chadov, S.; Souza, S.W.D.; Wollmann, L.; Kiss, J.; Fecher, G.H.; Felser, C. Chemical disorder as an engineering tool for spin polarization in Mn3Ga-based Heusler systems. Phys. Rev. B 2015, 91, 094203. [Google Scholar] [CrossRef]
  21. Khmelevskyi, S.; Shick, A.B.; Mohn, P. Prospect for tunneling anisotropic magneto-resistance in ferrimagnets: Spin-orbit coupling effects in Mn3Ge and Mn3Ga. Appl. Phys. Lett. 2016, 109, 222402. [Google Scholar] [CrossRef]
  22. You, Y.R.; Xu, G.Z.; Hu, F.; Gong, Y.Y.; Liu, E.; Peng, G.; Xu, F. Designing magnetic compensated states in tetragonal Mn3Ge-based Heusler alloys. J. Magn. Magn. Mater. 2017, 429, 40–44. [Google Scholar] [CrossRef]
  23. Jeong, J.; Ferrante, Y.; Faleev, S.V.; Samant, M.G.; Felser, C.; Parkin, S.S.P. Termination layer compensated tunnelling magnetoresistance in ferrimagnetic Heusler compounds with high perpendicular magnetic anisotropy. Nat. Commun. 2016, 7, 10276. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  24. Zhang, D.L.; Yan, B.H.; Wu, S.C.; Kübler, J.; Kreiner, G.; Parkin, S.S.P.; Felser, C. First-principles study of the structural stability of cubic, tetragonal and hexagonal phases in Mn3Z (Z = Ga, Sn and Ge) Heusler compounds. J. Phys. Condens. Matter. 2013, 25, 206006. [Google Scholar] [CrossRef] [PubMed]
  25. Yun, W.S.; Cha, G.B.; Kim, I.G.; Rhim, S.H.; Hong, S.C. Strong perpendicular magnetocrystalline anisotropy of bulk and the (001) surface of DO22 Mn3Ga: A density functional study. J. Phys. Condens. Matter 2012, 24, 416003. [Google Scholar] [CrossRef] [PubMed]
  26. Minakuchi, K.; Umetsu, R.Y.; Ishida, K.; Kainuma, R. Phase equilibria in the Mn-rich portion of Mn–Ga binary system. J. Alloys Compd. 2012, 537, 332–337. [Google Scholar] [CrossRef]
  27. Cable, J.W.; Wakabayashi, N.; Radhakrishna, P. Magnetic excitations in the triangular antiferromagnets Mn3Sn and Mn3Ge. Phys. Rev. B 1993, 48, 6159–6166. [Google Scholar] [CrossRef]
  28. Sung, N.H.; Ronning, F.; Thompson, J.D.; Bauer, E.D. Magnetic phase dependence of the anomalous Hall effect in Mn3Sn single crystals. Appl. Phys. Lett. 2018, 112, 132406. [Google Scholar] [CrossRef]
  29. Segall, M.D.; Lindan, P.J.D.; Probert, M.J.; Pickard, C.J.; Hasnip, P.J.; Clark, S.J.; Payne, M.C. First-principles simulation: Ideas, illustrations and the CASTEP code. J. Phys. Condens. Matter. 2002, 14, 2717–2744. [Google Scholar] [CrossRef]
  30. Vosko, S.H.; Wilk, L.; Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis. Can. J. Phys. 1980, 58, 1200–1211. [Google Scholar] [CrossRef]
  31. Ye, M.; Kimura, A.; Miura, Y.; Shirai, M.; Cui, Y.T.; Shimada, K.; Namatame, H.; Taniguchi, M.; Ueda, S.; Kobayashi, K.; et al. Role of Electronic Structure in the Martensitic Phase Transition of Ni2Mn1+xSn1−x Studied by Hard-X-Ray Photoelectron Spectroscopy and Ab Initio Calculation. Phys. Rev. Lett. 2010, 104, 176401. [Google Scholar] [CrossRef] [PubMed]
  32. Siewert, M.; Gruner, M.E.; Dannenberg, A.; Chakrabarti, A.; Herper, H.C.; Wuttig, M.; Barman, S.R.; Singh, S.; Al-Zubi, A.; Hickel, T.; et al. Designing shape-memory Heusler alloys from first-principles. Appl. Phys. Lett. 2011, 99, 191904. [Google Scholar] [CrossRef]
  33. Felser, C.; Alijani, V.; Winterlik, J.; Chadov, S.; Nayak, A.K. Tetragonal Heusler Compounds for Spintronics. IEEE Trans. Magn. 2013, 49, 682–685. [Google Scholar] [CrossRef]
  34. Liu, G.D.; Dai, X.F.; Liu, H.Y.; Chen, J.L.; Li, Y.X.; Xiao, G.; Wu, G.H. Mn2CoZ (Z = Al, Ga, In, Si, Ge, Sn, Sb) compounds: Structural, electronic, and magnetic properties. Phys. Rev. B 2008, 77, 014424. [Google Scholar] [CrossRef]
  35. Li, G.J.; Liu, E.K.; Zhang, H.G.; Zhang, Y.J.; Xu, G.Z.; Luo, H.Z.; Zhang, H.W.; Wang, W.H.; Wu, G.H. Role of covalent hybridization in the martensitic structure and magnetic properties of shape-memory alloys: The case of Ni50Mn5+xGa35−xCu10. Appl. Phys. Lett. 2013, 102, 062407. [Google Scholar] [CrossRef]
  36. Zhang, Y.J.; Wang, W.H.; Zhang, H.G.; Liu, E.K.; Ma, R.S.; Wu, G.H. Structure and magnetic properties of Fe2NiZ (Z = Al, Ga, Si and Ge) Heusler alloys. Physica B 2013, 420, 86–89. [Google Scholar] [CrossRef]
  37. Liu, E.K.; Wang, W.H.; Feng, L.; Zhu, W.; Li, G.J.; Chen, J.L.; Zhang, H.W.; Wu, G.H.; Jiang, C.B.; Xu, H.B.; et al. Stable magnetostructural coupling with tunable magnetoresponsive effects in hexagonal ferromagnets. Nat. Commun. 2012, 3, 873. [Google Scholar] [CrossRef] [PubMed] [Green Version]
Applsci 09 00964 g001 550
Figure 1. Total energy difference (per formula unit) relative to the cubic phase as a function of c/a for Mn3Ga alloy (ΔEtotal = Etotal(c/a) − Etotal(c/a = 1). The lower insets show the corresponding crystal structures and the upper insets show the band structures and densities of states for the cubic (c/a = 1) and distorted (c/a = 1.35) phases.
Figure 1. Total energy difference (per formula unit) relative to the cubic phase as a function of c/a for Mn3Ga alloy (ΔEtotal = Etotal(c/a) − Etotal(c/a = 1). The lower insets show the corresponding crystal structures and the upper insets show the band structures and densities of states for the cubic (c/a = 1) and distorted (c/a = 1.35) phases.
Applsci 09 00964 g001
Applsci 09 00964 g002 550
Figure 2. (a) Total energy as functions of c/a ratio for Mn3Ga alloy with different volume (V = 17.0 nm3, 18.0 nm3, 19.0 nm3, 20.0 nm3, 21.0 nm3, 22.0 nm3). (b) Total energy difference (per formula unit) relative to the cubic phase as a function of c/a for Mn3Z (Z = Al, Ga, In, Tl) and (c) for Mn3Z (Z = Ge, Sn, Pb) alloys.
Figure 2. (a) Total energy as functions of c/a ratio for Mn3Ga alloy with different volume (V = 17.0 nm3, 18.0 nm3, 19.0 nm3, 20.0 nm3, 21.0 nm3, 22.0 nm3). (b) Total energy difference (per formula unit) relative to the cubic phase as a function of c/a for Mn3Z (Z = Al, Ga, In, Tl) and (c) for Mn3Z (Z = Ge, Sn, Pb) alloys.
Applsci 09 00964 g002
Applsci 09 00964 g003 550
Figure 3. The change of interatomic distance in the process of tetragonal distortion for Mn3Ga alloy (the lattice constant of cubic structure is 5.65 Å): (a) The red circle represents the distance between Ga and Mn(B) and the distance between Mn(A) and Mn(C) along c axis. The blue triangle represents the distance between Ga and Mn(B) and the distance between Mn(A) and Mn(C) along a or b axis. (b) The changing curve of the distance between two nearest neighbor atoms with the change of c/a. The thick lines between the atoms in the inset indicate the corresponding interatomic distance).
Figure 3. The change of interatomic distance in the process of tetragonal distortion for Mn3Ga alloy (the lattice constant of cubic structure is 5.65 Å): (a) The red circle represents the distance between Ga and Mn(B) and the distance between Mn(A) and Mn(C) along c axis. The blue triangle represents the distance between Ga and Mn(B) and the distance between Mn(A) and Mn(C) along a or b axis. (b) The changing curve of the distance between two nearest neighbor atoms with the change of c/a. The thick lines between the atoms in the inset indicate the corresponding interatomic distance).
Applsci 09 00964 g003
Applsci 09 00964 g004 550
Figure 4. The atomic magnetic moments of Mn(A/C) (a) and Mn(B) (b) as functions of c/a ratio for Mn3Ga alloy with different lattice constants.
Figure 4. The atomic magnetic moments of Mn(A/C) (a) and Mn(B) (b) as functions of c/a ratio for Mn3Ga alloy with different lattice constants.
Applsci 09 00964 g004
Applsci 09 00964 g005 550
Figure 5. The atomic magnetic moments of Mn(A/C) (a,b) and Mn(B) (c,d) as functions of c/a ratio for Mn3Z (Z = Al, Ga, In, Tl, Si, Ge, Sn, Pb) alloys.
Figure 5. The atomic magnetic moments of Mn(A/C) (a,b) and Mn(B) (c,d) as functions of c/a ratio for Mn3Z (Z = Al, Ga, In, Tl, Si, Ge, Sn, Pb) alloys.
Applsci 09 00964 g005

Share and Cite

MDPI and ACS Style

Zhang, H.; Liu, W.; Lin, T.; Wang, W.; Liu, G. Phase Stability and Magnetic Properties of Mn3Z (Z = Al, Ga, In, Tl, Ge, Sn, Pb) Heusler Alloys. Appl. Sci. 2019, 9, 964. https://doi.org/10.3390/app9050964

AMA Style

Zhang H, Liu W, Lin T, Wang W, Liu G. Phase Stability and Magnetic Properties of Mn3Z (Z = Al, Ga, In, Tl, Ge, Sn, Pb) Heusler Alloys. Applied Sciences. 2019; 9(5):964. https://doi.org/10.3390/app9050964

Chicago/Turabian Style

Zhang, Haopeng, Wenbin Liu, Tingting Lin, Wenhong Wang, and Guodong Liu. 2019. "Phase Stability and Magnetic Properties of Mn3Z (Z = Al, Ga, In, Tl, Ge, Sn, Pb) Heusler Alloys" Applied Sciences 9, no. 5: 964. https://doi.org/10.3390/app9050964

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop