The mechanism of magnetostructural transition in Heusler alloy Co2V1.5Ga0.5

Journal Pre-proofs The mechanism of magnetostructural transition in Heusler alloy Co2V1.5Ga0.5 Obaidallah A. Algethami, Q.Q. Zhang, J.G. Tan, X.T. Wang, Z.H. Liu, X.Q. Ma PII: DOI: Reference:

S0304-8853(19)33011-2 https://doi.org/10.1016/j.jmmm.2019.166252 MAGMA 166252

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Journal of Magnetism and Magnetic Materials

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28 August 2019 23 October 2019 29 November 2019

Please cite this article as: O.A. Algethami, Q.Q. Zhang, J.G. Tan, X.T. Wang, Z.H. Liu, X.Q. Ma, The mechanism of magnetostructural transition in Heusler alloy Co2V1.5Ga0.5, Journal of Magnetism and Magnetic Materials (2019), doi: https://doi.org/10.1016/j.jmmm.2019.166252

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The mechanism of magnetostructural transition in Heusler alloy Co2V1.5Ga0.5

Obaidallah A. Algethami1, 2, Q. Q. Zhang1, J. G. Tan1, X. T. Wang3, Z. H. Liu1,, X. Q. Ma1 1Department

of Physics, University of Science and Technology Beijing, Beijing 100083, China

2Physics

Department, Faculty of Science, Al-Baha University, Albaha, Kingdom of Saudi Arabia

3School

of Physical Science and Technology, Southwest University, Chongqing 400715, China

Abstract Recently, magnetic field induced low magnetization tetragonal martensite to high magnetization cubic austenite transformation has been realized in Heusler alloy Co50V34Ga16 (Applied Physics Letters 112, 211903 (2018)). In this paper, first-principles calculations have been performed on Heusler alloy Co2V1.5Ga0.5 to reveal the mechanism for magnetostructural transition. It has been found that the alloy prefers to crystallize into ferromagnetic L21 type structure at austenite, with Co atoms tending to occupy the Wyckoff sites A (0, 0, 0) and C (0.5, 0.5, 0.5), V atoms occupying at site B (0.25, 0.25, 0.25), Ga and the extra V atoms entering D (0.75, 0.75, 0.75) site. Moments of Co and V atoms parallel to each other and a total formula moment of 2.95 B is achieved. A potential of tetragonal distortion from ferromagnetic cubic structure to non-magnetic tetragonal structure has been predicted from the view of energetically favorable state. The stability



[email protected] (Z. H. Liu);

of tetragonal Co2V1.5Ga0.5 is further confirmed by the phonon spectrum. The peaks of dx2-y2 and dz2 states for Co and V(D) 3d states near the Fermi level for the cubic structure split at the tetragonal structure, implying the structural transition is mainly attributed to the band Jahn-Teller effect. The hybridization between the Co 3d states and the 3d states of V at D site plays an important role in the martensitic transformation. A volume contraction of 1.3% is obtained accompanying with the magnetostructural transition. Keywords: Magnetostructural transformation; Heusler alloy; Band Jahn-Teller effect; Electronic structure.

1. Introduction Ferromagnetic shape memory alloys (FSMAs) have been extensively studied because they have brought enormous potential applications in the field of magnetic sensors, magnetic refrigeration and magnetic actuators due to their diverse excellent properties, i.e. magnetic-field-induced strains[1], Hall effect[2–4], magnetoresistance[5], magnetic-field-induced structural transition[6], magnetic entropy change[7],and exchange bias[8]. A lot of FSMAs have been discovered to be multi-functional intermetallic Heusler compounds, such as Ni2MnGa[9], Ni2MnAl[10], Ni-Mn-In(Sn, Sb)[11], Fe-Mn-Ga[12], Co-Ni-Al(Ga)[13,14], Co2Cr(Ga, Si)[15], Co-V-Ga[16]. Conventional stoichiometric Heusler alloys have a chemical formula of X2YZ, where X and Y represent the transition-metal elements, Z is the main-group elements. It can be considered to be comprised of four face-centered cubic (fcc) sublattices which can be represented by four Wyckoff sites A (0 0 0), B (0.25 0.25 0.25), C (0.5 0.5 0.5) and D (0.75 0.75 0.75). Atoms X, Y will occupy A, B and C sites, while D site will be taken by element Z. There are two major variants of Heusler

alloys. One is L21-type (also called Cu2MnAl-type) Heusler alloy with a space group of Fm-3m (No. 225) which possesses an atomic configuration of X-Y-X-Z; and the other is Xa-type Heusler alloy (Hg2CuTi-type) with a space group of F-43m (No. 216) and an atomic configuration of X-X-Y-Z. The former one generally appears in the case of the valence electrons of X is larger than Y, and the latter one is in the opposite case[17–19]. This is called the conventional site preference rule of Heusler alloys. However, the atomic site occupation sometimes does not obey this rule[20,21]. Co-based Heusler alloys have received a lot of attention for their half-metallic behavior and potential applications in spintronic devices. Except for this, it is reported that Co-based Heusler alloys also possess the martensitic transformation, i.e. Co-Ni-Al(Ga)[22], Co2Cr(Ga, Si)[15], Co2V(Ga, Si)[23], Co-V-Al[24], Co-V-Si[25]. Recently, a martensitic transformation over a wide temperature range from 250 K to 500 K was confirmed to transform from cubic L21 parent phase to the D022 tetragonal martensite phase in the off-stoichiometric Heusler alloy Co-V-Ga by Xu et al[16]. They also indicated that the magnetization of martensite for Co50V35Ga15 alloy changes almost linearly with magnetic field, showing paramagnetic behavior

[16].

Compared with

NiMn-based Heusler alloys, Co based shape memory alloys usually have good ductility. However, cubic Co2Cr(Ga, Si), Co2V(Ga, Si), Co-V-Si, Co-V-Ga usually have low Curie temperature, which makes the martensitic transformation of these alloys is difficult to control by external magnetic field. Through tailoring the composition, Liu et al. realized a metamagnetic martensitic transformation from low-magnetization martensite to high magnetization austenitic phase in Co50V34Ga16[26]. However, the mechanism behind the magnetostructural transformation of Co-V-Ga has not been discussed yet. In this work, first-principles calculations were performed on

Co2V1.5Ga0.5, and this composition is close to Co50V35Ga15 and Co50V34Ga16. A magnetostructural transformation from ferromagnetic cubic structure to non-magnetic tetragonal structure has been predicted. The site preference, electronic structures and tetragonal distortion are discussed in detail, which can help us to understand the mechanism of the magnetostructural transition.

2. Theoretical computational methods The calculations are performed through Vienna ab initio simulation package (VASP)[27] using the plane-wave pseudo-potential method in the framework of density functional theory[28,29]. The exchange-correlation energy is determined by Perdew-Wang generalized-gradient approximation (GGA)[30], and a cut-off energy of 500 eV is used for the plane wave basis set. The k-mesh grid of 171717 and 15×15×13 for cubic structure and tetragonal structure over the first Brillouin zone are generated by Monkhorst–Pack method[31], respectively. The convergence criterion for the calculations is selected as the total energy difference within 10-6 eV/atom. Note that, all calculations are carried out in a 16-atom conventional cell. The phonon energy calculation of Co2V1.5Ga0.5 was performed in NanoAcademic Device Calculator (Nanodcal) code by using the

linear-response density function perturbation theory (DFPT)[32]. A plane-wave cut-off energy of 80 Hartree was used for the calculations. The unit cell considered in this calculation contains 16 atoms. The 16-atom cubic austenite and martensite Co8V6Ga2 structures are shown in Fig. 1. The lattice optimization of Co2V1.5Ga0.5 are performed considering both L21 and Xa structure. Figure 1(a) and (b) show the atomic occupation of cubic L21 and Xa structure which are Co-V-Co-Ga/V and Co-Co-V-Ga/V, respectively. Figure 1(c) and (d) present the related tetragonal atomic configuration of L21 and Xa Co2V1.5Ga0.5. Along with the lattice optimization,

magnetic configuration is also taken into consideration where the neighboring Co atoms possess a ferromagnetic (FM), antiferromagnetic (AFM) and non-magnetic (NM), respectively. AFM indicates the anti-parallel alignment of spin moments between the neighboring Co-V atoms, the parallel case is FM, and NM means the non-spin polarization state.

Figure 1 Schematic of atomic occupations for cubic L21-type (a), cubic Xa-type (b), tetragonal L21-type (c)and tetragonal Xa-type (d) Co2V1.5Ga0.5 alloy.

3. Results and discussion The lattice optimization of Co2V1.5Ga0.5 is performed on both L21 and Xa structures. Figure 2 presents the optimization results of total energy (E) as a function of lattice constants. It is noted

that L21 structure is more stable than Xa structure because the L21 structure always possesses a smaller energy than the Xa structure if they have the same magnetic configuration. For L21 structure, the FM spin alignment turns out to be the most energy favorable ground state since it has the lowest energy (see Fig. 2), and the equilibrium lattice constant is 5.79 Å. It was reported that Co2VGa has a lattice constant of 5.779 Å[33], which is slightly smaller than that of Co2V1.5Ga0.5. The increase of lattice constant of Co2V1.5Ga0.5 is mainly due to that the larger V atoms partially replace the smaller Ga atoms in Co2VGa.

-6083.3 -6083.4

Energy (eV/f.u.)

-6083.5

L21 FM

Xa FM

L21 AFM

Xa AFM

L21 NM

Xa NM

-6083.6 -6083.7 -6083.8 -6083.9 -6084.0 -6084.1 -6084.2 -6084.3

5.65 5.70 5.75 5.80 5.85 5.90 5.95

Lattice constant a (Å)

Figure 2. Total energy E as a function of the cubic lattice constant of Co2V1.5Ga0.5 with different atomic (both L21 and Xa types) and magnetic (AFM, FM and NM) configurations.

To further get an insight into the mechanism of the martensitic transformation of Co2V1.5Ga0.5, total energy calculations of tetragonal distortion with different magnetic configurations are carried out based on the L21 structure. The distortions take place along c-axis assuming that the volume for equilibrium state does not change, which is usually adopted in many other FSMAs[34,35].

Figure 3 shows the total energy difference(ΔE) between tetragonal distorted structure and cubic structure (ΔE =Etot(c/a) –Etot(c/a=1)) as a function of c/a ratio for FM, AFM and NM magnetic configurations. In this graph, the energy of equilibrium FM state with L21-type structure is chosen to be the zero-point energy. Two clear minima are achieved in all three ΔE curves. One is the global minimum appearing at c/a > 1(c/a = 1.29), and another one is the local minimum which is observed at c/a = 1 for FM state and c/a < 1 for AFM, NM states. It is worth noting that when the distortion ratio c/a is in the range from 0.85 to 1.12, ΔE curve for FM state has a big difference with those of AFM and NM magnetic configurations. FM state has the lowest energy among the three magnetic states in this c/a region. It is suggested again that the FM with L21-type is more stable than the other two magnetic states of cubic Co2V1.5Ga0.5. However, when the distortion further increases, the energy differences between three magnetic states shrink and the three curves almost overlap to each other. It should be pointed out that when the distortion is large enough (c/a ≤ 0.85 and c/a ≥1.12, circled out in Fig. 3), the system always automatically finds that NM state is the most stable state no matter what kind of magnetic configuration is set before the calculation. Therefore, it suggests that the stable tetragonal structure presents NM magnetic configuration. That is to say that Co2V1.5Ga0.5 alloy tends to transform from FM cubic structure to NM tetragonal structure, exhibiting a magnetostructural transformation. Hence a field induced metamagnetization transformation from NM tetragonal structure to FM cubic structure may be realized in this system. There is a little difference between our theoretical calculation and the experimental result of Co50V34Ga16. In their experiments, the martensite is low magnetization state with a small magnetization of 10 Am2/kg [26], while our calculation result indicates it is NM state. Our calculation supposes that the alloy is in highly ordered state. Actually, atomic antisite

usually happens in preparing Heusler alloys in experiment[36,37]. So the magnetization difference between our calculation and the experiment is probably due to the atomic disorder induced during the preparation process. It should be noted that Xu et. al have found that the tetragonal martensite for Co50V35Ga15 shows paramagnetic property

[16],

which is almost in agreement with our

calculation.

0.6

L21 FM L21 AFM

E (eV/f.u.)

0.4

L21 NM 0.2

0.0

-0.2 0.8

1.0

1.2

1.4

1.6

c/a ratio

Figure 3 the total energy differences (ΔE) between tetragonal distorted phase and cubic phase (ΔE=Etot(c/a) – Etot(c/a=1)) as a function of c/a ratio for Co2V1.5Ga0.5. The zero point is corresponding to the energy of equilibrium state of FM L21 structure.

Both total and partial spin polarized density of states (DOS) of Co2V1.5Ga0.5 are calculated considering NM and FM magnetic configurations to clarify the mechanism of the magnetostructural transformation. Fig. 4 (a), (b) and (c) shows the total and partial DOS of NM, FM L21-type and NM tetragonal Co2V1.5Ga0.5, respectively. In the NM cubic structure, there is a pseudogap from -1 to -0.5 eV at the energy lower than Fermi level Ef. A strong localized peak at Ef is observed which is mainly contributed by the Co dx2-y2 and dz2 states (eg states) and V 3d states.

Furthermore, the width of this peak contributed by V atoms is much wider than that of Co atoms. Since Ef situated in a high peak of DOS, this gives rise to that NM cubic structure is not the energetically stable configuration. Therefore, a spin polarization would happen to decrease the system energy. For the spin-resolved FM situation, as shown in Fig. 4(b), in the spin up state, the Co and V-3d states shifted towards lower energy states, while in the spin down state, the Co and V-3d states shifted to the higher energy state with respect to the NM state. Since the existence of a pseudogap about from -1 to -0.5 eV in NM states, the exchange splitting results in a band gap at Ef. While in spin up direction, because the localized peak is as wide as 2 eV, the downshifting of DOS still makes the Fermi level situate at the peak tails of Co dx2-y2 and dz2 states and the peaks of V(D) dx2-y2 and dz2 band, not falling into the valley of DOS. It indicates that FM cubic Co2V1.5Ga0.5 still has a potential of distortion to enhance the structure stabilization. It can be also seen that Co 3d states has a larger exchange splitting than V 3d states, which makes two Co atoms carry a large moment of 1.96 B. V atoms at B and D sites have a smaller contribution to the total magnetic moment, and they are 0.54 and 0.46 B, respectively. A total magnetic moment of 2.95

B for cubic structure is obtained. (a) NM cubic

15 Total 12 9 6 3 0 1.5 Co-d

5

Intensity (a.u.)

(c) NM tetragonal 12 Total 9 6 3 0 1.5 Co-d

Total

0 -10 1 Co-d

1.0

0

0.5 0.0 3 V(B)-d

dxy dyz

2

dz

1

dx -y

2

2

dxz

2

0 2 V(D)-d 1

0.1

(b) FM cubic

-5

1.0

0 0.2

10

Ga-p

py pz px

0.0 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Energy (eV)

-1 3 V(B)-d 2 1 0 -1 1.5 1.0 V(D)-d 0.5 0.0 -0.5 -1.0 0.1 Ga-p

0.5

dxy

dz

dyz

dx -y

dxz

2

2

2

0.0 1.5 V(B)-d

dxy

1.0

dz

dyz

0.5

dx -y

2

2

2

dxz

0.0 2 V(D)-d 1 0 0.2 Ga-p 0.1

0.0

-0.1 0.0 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Energy (eV)

Energy (eV)

Figure 4 Total and partial DOS for NM cubic (a), FM cubic (b), and NM tetragonal(c/a>1) (c) Co2V1.5Ga0.5 alloy.

The total and partial DOS of tetragonal Co2V1.5Ga0.5 are shown in Fig. 4 (c). Because the system always finds the most stable NM state automatically, the three DOS curves almost overlapped to each other, so only NM DOS curves for tetragonal Co2V1.5Ga0.5 are presented. It is noticed that the DOS peaks at Ef in FM cubic structure change to DOS valleys in tetragonal structure. This is caused by the splitting of the peaks for V(D) and Co dx2-y2 and dz2 bands near Ef revealed for FM cubic Co2V1.5Ga0.5 under the effect of crystal field. The total energy is relaxed by the splitting of these peaks and the system becomes more stable after tetragonal distortion, suggesting that a band Jahn-Teller effect is expected to be responsible for this structural transition. It can be seen that V(D) dz2 states move towards high energy state and dx2-y2 states mainly lies below Ef for the tetragonal structure. Simultaneously, the tetragonal structure of Co 3d states shift towards the Ef in the spin up direction compared with cubic structure. These can be attributed to the hybridization between Co 3d states and 3d states of V(D) atoms, as evident by a hybridization peak at ~-0.12 eV and 0.12 eV in spin-up direction for FM cubic state, which causes the splitting of the peaks near Ef, leading to the reduction of energy at Ef.

Figure 5 The calculated phonon energy of NM tetragonal Co2V1.5Ga0.5

The stability of NM tetragonal Co2V1.5Ga0.5 can be further confirmed by the phonon spectrum, as shown in Fig. 5. No virtual frequency can be observed, which guarantees the stability of the tetragonal state. For most of the Heusler alloys, volume change is not taken a consideration during the calculation. However, some of them do need to take it into account since volume change did really happen upon the martensitic transformation, such as there is a volume change of -2.54% in MnNiCoTi[38], -1.31% in Ni41Co9Mn40Sn10[39] and -2.4% in Ni50Mn37Sn13[11]. Liu et al. have reported that there is a relative length change of 0.2% in ploycrystalline Co50V34Ga16[26]. Therefore, it is necessary to test the effect of cell volume on the total energy of Co2V1.5Ga0.5. We carried out the volume change step by step manually based on the equilibrium cell volume of cubic

Co2V1.5Ga0.5. In every step, a curve like Fig. 3 was obtained to acquire the lowest energy in corresponding cell volume. Figure 6 shows the energy difference(ΔE) and the c/a ratio as the function of the tetragonal cell volume change, where ΔE is the energy difference between volume change and the equilibrium cell volume of FM cubic L21 type Co2V1.5Ga0.5. The volume change in the calculation is ranged from -2.0% to +2.0%. A clear valley is observed in ΔE curve when the volume contracts, implying that a suitable shrink of cell volume can further reduce the total energy of system and the opposite case takes place as the cell volume expanses. The system achieved the lowest energy as the volume change reached -1.3%, which is ~5 meV/f. u. lower than the non-volume change distortion, confirming that there is a volume change during the martensitic transformation. Meanwhile, no matter how big the volume changes, the c/a ratio for achieving the lowest energy at the corresponding cell volume stays almost the same, 1.30.

1.50

E c/a ratio

30 25

1.45 1.40

15 10

1.35

5

1.30

c/a ratio

E (meV/f.u.)

20

0 1.25

-5 -10

-2

-1

0

1

2

1.20

Volume change (%)

Figure 6 Variation of total energy difference (ΔE) and c/a ratio as a function of cell volume change. The zero point of ΔE was set as the total energy of tetragonal state without volume change.

4. Conclusion

In this work, the phase stability, tetragonal distortion and electronic structure of Co2V1.5Ga0.5 were discussed. The first-principles calculations predict that magnetostructural transformation from FM cubic to NM tetragonal structure tends to occur in Co2V1.5Ga0.5 since the ground state energy of NM tetragonal structure is much smaller than that for FM cubic structure and the corresponding c/a ratio of the tetragonal phase is 1.3. Furthermore, Theoretical calculation revealed that the martensitic transformation in Co2V1.5Ga0.5 is driven by band-Jahn Teller effect. There is a strong hybridization between the Co 3d states and V(D) 3d states, which causes the splitting of the peaks of dx2-y2 and dz2 states for Co and V(D) near the Fermi level for the cubic structure. Accompanying with the magnetostructural transition, a volume contraction of 1.3% is obtained.

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Highlights

 Transition from FM cubicNM tetragonal structure is confirmed by ab initio method.  The mechanism behind the magnetostructural transformation of Co-V-Ga is discussed.  The structural transition is attributed to the band Jahn-Teller effect.  The Co d and V(D) d hybridization plays a crucial role in martensitic transformation.

Conflict of Interests

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work. There are no conflict of interests of our manuscript entitled “The mechanism of magnetostructural transition in Heusler alloy Co2V1.5Ga0.5”.

Zhuhong Liu

Department of Physics University of Science and Technology Beijing