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Influence of Fe-doping on magnetic structure and martensitic transformation in NiMnIn and NiMnSb alloys
Intermetallics xxx (xxxx) xxx–xxx
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Influence of Fe-doping on magnetic structure and martensitic transformation in NieMneIn and NieMneSb alloys Yuexing Ma, Hongyue Hao, Xiaotong Liu, Hongzhi Luo∗, Fanbin Meng, Heyan Liu School of Materials Science and Engineering, Hebei University of Technology, Tianjin, 300130, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: A. Magnetic alloys B. Magnetic properties Electronic structure Martensitic transformation E. Ab-initio calculations
Influence of Fe substitution for Ni on the magnetic properties and martensitic transformation was investigated theoretically in Heusler alloys Ni2Mn1.5Z0.5 (Z = In, Sb). Fe-doping does not change the general magnetic structure of Ni2Mn1.5Z0.5. In both Ni2Mn15In0.5 and Ni1.75Fe0.25Mn1.5In0.5 the austenitic phase is ferromagnetic and martensitic phase is antiferromagnetic, which leads to the large ΔM observed experimentally. But in Ni2Mn1.5Sb0.5 and Ni1.75Fe0.25Mn1.5Sb0.5, the antiferromagnetic state is stable in both austenite and martensite. This difference is mainly related to the different atomic radii of In and Sb, which change the distance between Mn (B) and Mn (D). Parallel or antiparallel coupled Mn moments determine the magnetic properties of these alloys. But the partial moment of Fe is large and its direction reverses after martensitic transformation, which makes it a possible way to adjust the magnetic properties of MSMAs. Calculation also suggests that the substitution of Fe for Ni can lower the martensitic transition driving force and lead to the decrease of phase transition temperature. These results agree well with preceding experimental results and make reasonable explanation for them.
1. Introduction Magnetic shape memory alloys (MSMAs) have received more and more attention for their various applications in magnetic refrigeration and actuator. Since the first MSMA Ni2MnGa was reported [1,2], different series of alloys like NieMneZ (In, Sn, Sb), MneNieGa, Ni2FeGa, CoeNieGa(Al) and FeeMneGa were also synthesized [3–10]. Among them, NieMneZ (In, Sn, Sb) alloys are particularly interesting for the valuable properties like magnetic field induced martensitic transformation (MFIMT), large magnetocaloric effect and exchange-bias effect in them [4,11–13]. These properties are associated with the structural and magnetic transition between austenite and martensite. Therefore, NieMneZ alloys are regarded as promising candidates for multifunctional applications. A large ΔM is quite preferable for MFIMT, which means a ferromagnetic-antiferromagnetic (FM-AFM) or ferromangetic-paramagnetic (FM-PM) transition during the structural transformation (here AFM refers to the antiparallel coupling between Mn moments) [4,14]. To realize this, doping other main group or transition metal elements to Heusler alloys is a common method. According to literature, Co is the first choice as the doping elements in NieMneZ alloys. The substitution of Co for Mn or Ni can help to stabilize the FM state in austenitic NieMneZ while retain AFM state in martensite [15,16]. Till now, there
∗
are few reports on the similar effect of other transition metal elements. Quite recently, Ref. [17] reported that Fe substitution for Ni in Ni50Mn39Sn11 can enhance ferromagnetism in austenitic state. If so, the effect of Fe doping can be of great value in MSMAs and worth further investigation. Meanwhile, the mechanical property is significantly improved with Fe doping. This is meaningful for industrial applications, for the brittleness is a big problem in Heusler type MSMAs. The substitution of Fe for Mn or main group elements has also been performed in other NieMneZ alloys and its influence on the magnetic properties and phase transition temperature has been discussed experimentally [18–20]. Recently, Lobo et al. synthesized Ni2MnIn1-xFex alloys and investigated the influence of Fe substitution for In on their structure, phase transition and magnetic properties [21]. But till now, the detailed mechanism of Fe-doping on the phase transformation, magnetic structure of NieMneZ alloys has not been thoroughly studied. As we know, these properties are related to the electronic structures of the alloys, then first-principles calculation can be a useful way to discuss the physical nature in these MSMAs. In this paper, the electronic structure, magnetic properties of Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) have been calculated. The influence of Fe doping on phase transformation temperature and magnetic structure was explained and compared with experimental results in literature. This work can help to understand the phase
Corresponding author. E-mail address: [email protected] (H. Luo).
http://dx.doi.org/10.1016/j.intermet.2017.10.003 Received 8 September 2017; Received in revised form 5 October 2017; Accepted 6 October 2017 0966-9795/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Ma, Y., Intermetallics (2017), http://dx.doi.org/10.1016/j.intermet.2017.10.003
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magnetic structures of Ni2Mn1.5In0.5 and Ni2Mn1.5Sb0.5 are different. In Ni2Mn1.5In0.5, a crossover between the FM and AFM curves is observed, when the lattice constant is smaller than 5.96 Å, AFM state is lower in energy, but above 5.96 Å, FM state energy decreases rapidly and reaches ground state at 6.00 Å. Then in Ni2Mn1.5In0.5 the FM state is more stable. However, it should be noticed that no obvious ferromagnetic character was observed in the experimental curves of Ni2Mn1.5In0.5 [21,27]. We think one possible reason for this difference may be related to the atomic ordering. The calculation is based on a simple ordered structure with supercell approach. But in experimental sample, the case is rather complicated. In NieMneIn, with decreasing In content, the sample may become partly disordered [28], then the next nearest neighbor Mn in calculation may become nearest neighbor, this can change the distance between Mn and have influence on the magnetic properties of Ni2Mn1.5In0.5. Also, the equilibrium lattice constant may be different from the experimental sample in some degree, which can also have influence on the magnetic properties of samples with specific composition. But the calculation results from Ni2Mn1.5In0.5 may still be used to described the magnetic structure of NieMneIn with higher In contents, only a slightly increase of In content is necessary. In Ref. [29], as it increases slightly from 0.5 to 0.6, the martensitic phase has a Ms larger than 1.5μB at 5 K (2.5 T field) and jumps to 6μB in a field of 15 T. This just corresponds to the AFM and FM states in NieMneIn. In Ni2Mn1.5Sb0.5 the AFM curve is always lower in energy and more stable than the FM curve, indicating in this alloy, antiferromagnetic coupling between Mn (B) and Mn (D) is preferable. This is due to the relatively small atomic radius of Sb, which results in an equilibrium lattice constant of 5.97 Å and is smaller than the 6.00 Å in Ni2Mn1.5In0.5. The doping of Fe has different influence on the magnetic structure of Ni2Mn1.5In0.5 and Ni2Mn1.5Sb0.5. In Ni1.75Fe0.25Mn1.5In0.5, the FM curve moves completely below the AFM curve, indicating the ferromagnetism state is enhanced. This is similar to the results in Ni50−xFexMn39Sn11 [17]. But in Ni1.75Fe0.25Mn1.5Sb0.5, the AFM curve is still lower in energy, suggesting Fe-doping does not change the antiferromagnetic coupling between Mn (B) and Mn (D). From the equilibrium lattice constants listed in Table 1, we can also found that, the substitution of Fe leads to a slightly contraction of the lattice.
transition in these alloys deeply and improve their properties effectively. 2. Computational methods In this paper, CASTEP code was employed to calculate the electronic structure and magnetic properties in martensitic and austenitic Ni2Mn0.5Z1.5 and Ni1.75Fe0.25Mn0.5Z1.5 (Z = In, Sb) [22,23]. The interactions between the atomic core and the valence electrons were described by the ultrasoft pseudopotential [24]. The electronic exchange–correlation energy was treated under the generalized-gradientapproximation (GGA) [25]. Supercell approach is used for the calculations of Fe-doped NieMneZ alloys in a 16-atom supercell, in which one Ni atom is replaced by Fe. In order to ensure good convergences for total energy, the plane-wave basis set cut-off was used as 500eV and meshes of 16 × 16 × 16 and 14 × 14 × 16 k-points were employed for Brillouin zone integrations in cubic austenitic and non-modulated tetragonal martensitic structures, respectively. The convergence tolerance for the calculations was selected as a difference on total energy within 1 × 10−6 eV/atom. 3. Results and discussion As we know, in Mn-rich NieMneZ alloys, the extra Mn content will enter the main group element site D (0.75, 0.75, 0.75) and become next nearest neighbor to Mn at B (0.25, 0.25, 0.25) site [26]. In Ni1.75Fe0.25Mn0.5Z1.5, Fe atoms substitute for Ni at A (0, 0, 0) and C (0.5, 0.5, 0.5) sites will enter Ni site, for in Heusler alloys, transitional metal atoms with more valence electrons usually prefer entering A, C sites [17]. Here both Ni and Fe have more electrons than Mn does. The distance between Mn is mainly influenced by the atomic radii of different main group elements Z. The coupling between Mn (B) and Mn (D) spin moments is sensitive to this distance and may be FM or AFM in austenitic NieMneZ alloys. During the martensitic transformation, the distance of Mn (B)eMn (D) will be changed and the magnetic structure can be affected accordingly. Fig. 1 presented the calculated total energies of FM and AFM type Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) as functions of the lattice constants (E-a curve). It is clear that, before Fe-doping, the
Fig. 1. Calculated total energies as functions of lattice and constant for Heusler alloys Ni2Mn0.5Z1.5 Ni1.75Fe0.25Mn0.5Z1.5 (Z = In, Sb) in FM and AFM states.
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Table 1 The equilibrium lattice constants a, stable magnetic structure, total and partial spin moments for Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) in cubic austenitic state. Alloys
Magnetic structure
a (Å)
Mt (μB)
MNi (μB)
MFe (μB)
MMn(B) (μB)
MMn(D) (μB)
MIn/Sb (μB)
Ni2Mn1.5In0.5 Ni1.75Fe0.25Mn1.5In0.5 Ni2Mn1.5Sb0.5 Ni1.75Fe0.25Mn1.5Sb0.5
FM FM AFM AFM
6.00 5.98 5.97 5.96
6.64 6.74 1.80 1.75
0.25 0.24 −0.04 0.00
– 1.65 – −0.78
4.07 3.92 4.13 4.12
4.15 3.99 −4.42 −4.31
−0.04 −0.07 −0.07 −0.06
spin channel, which makes the Fe moment in Ni1.75Fe0.25Mn1.5Sb0.5 relatively small and antiparallel to that of Mn (B). In the next step, we compared the stability of FM and AFM states in Ni2Mn1.5Z0.5 martensitic phase before and after Fe-doping. The ground state of the martensite was obtained by relaxing the c/a ratio of a nonmodulated tetragonal lattice and reaching the minimum of the total energy. During the calculation, we assume that there is no volume change between the austenitic and martensitic lattices. This is a common method in Heusler alloys and the detail can be found in Ref. [33]. Structural optimization results have been presented in Fig. 3, here the zero point was set as the total energy of the cubic austenitic phase (c/a = 1). For FM Ni2Mn1.5In0.5 only one minimum is observed in the E-c/a curve at c/a = 1.10 and the energy difference between c/a = 1.00 is quite small. In FM Ni1.75Fe0.25Mn1.5In0.5, the E-c/a curve increases directly when c/a deviates from 1.00. This means the FM martensitic phase is not energetically preferred in the martensite. The AFM E-c/a curve is lower in energy compared with the FM curve and is more stable in martensitic state. The lowest total energy is obtained at c/a = 1.30 for Ni2Mn1.5In0.5 and 1.33 for Ni1.75Fe0.25Mn1.5In0.5, respectively. Then the FM-AFM transition will occur together with the structural transformation, which can lead to a large ΔM of 4.53μB (undoped) and 5.20μB (doped) in the two alloys. This agrees with the results in Ni50Mn33.7In16.3, in which the ΔM is about 3.5μB [30]. That is why MFIMT can be realized in NieMneIn without doping of Co. In Fig. 3, for martensitic type Ni2Mn1.5Sb0.5 and Ni1.75Fe0.25Mn1.5Sb0.5, the low energy ground state is still AFM, similar to the austenitic phase. Then the total moments of them are not so large and close to each other, there is no obvious ΔM observed in them. Total magnetic moments of Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) are mainly determined by Mn (B) and Mn (D) moment as can be found in Table 2. But if we compare the magnetic data in Tables 1 and 2, we can find that the sign of Fe moment is opposite in austenite and martensite. For example, it is 1.79μB in austenitic Ni1.75Fe0.25Mn1.5In0.5 but becomes −2.40μB in martensite. Then if more Fe can be introduced to NiMn-based MSMAs, it may be possible to adjust the magnetic properties by Fe moment reversal. The calculated total DOS for martensitic type Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 have been presented in Fig. 4. Compared with the austenitic DOS in Fig. 2, one can find that more peaks appear in the martensitic DOS due to change of symmetry. It may be noticed that more states appear in majority spin channel above EF, corresponding to the AFM ground state in these martensites. In Ni50Mn33.7In16.3, the martensite is a poor-metallic ferrimagnet and austenite is a metallic ferromagnet [30]. In Fig. 4 we can find that the states at EF is lower in martensitic DOS compared with the austenite. Then the conduction electrons concentration becomes fewer after the phase transition, which agrees with the experimental observation qualitatively. Compared with undoped Ni2Mn1.5Z0.5, the doping of Fe introduced pronounced DOS peak at EF, which is not preferable for the stability of the martensite and may lower the phase transition temperature. By comparing the ground state energy difference ΔEM between the cubic austenite and tetragonal martensite, one can tell if a martensitic transformation can occur or not in an alloy with certain composition [34–37]. In alloys with similar compositions, a large ΔEM means a large
The calculated total and partial spin moments for Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) under their ground state have been listed in Table 1. The total moment of FM Ni2Mn1.5In0.5 is as high as 6.64 μB, this is a rather large value in Heusler alloys and agrees well with the results in Ref. [30]. In that literature, the austenitic phase in Ni50Mn33.7In16.3 single crystal was retained till 5 K in a magnetic field of 3 T. The saturation magnetization Ms of it is about 6.5μB. Now we can say that this large moment comes from parallel coupled partial moments of Mn (B) and Mn (D). The substitution of Fe leads to a small increase of the total moment, which mainly comes from the larger partial moment of Fe compared with Ni, which couples parallel to the Mn moment and enhance the ferromagnetism. The total moments for Ni2Mn1.5Sb0.5 and Ni1.75Fe0.25Mn1.5Sb0.5 are 1.80μB and 1.75μB, respectively, and much smaller than that of Ni2Mn1.5In0.5. In Ref. [31], Siewert et al. also investigated the magnetic ordering and phase transition in NieMneZ (Z = Ga, In, Sn,Sb) theoretically, in their work, the equilibrium lattice constant for Ni2Mn1.5Sb0.5 was 5.95 Å and total moment was 1.76μB. Our results agree well with them and indicate the theoretical method in present work is reliable. This coincides with the AFM ground state and is determined by the antiparallel coupled Mn (B) and Mn (D) moments. The Fe moment in Ni1.75Fe0.25Mn1.5Sb0.5 is −0.78μB, antiparallel to that of Mn (B). As has been discussed above, the FM and AFM coupling between Mn (B) and Mn (D) is sensitive to their distance. The different effect of Fe-doping may be related to the decreasing lattice constant from Ni2Mn1.5In0.5 to Ni2Mn1.5Sb0.5. In Fig. 2 we presented the total and partial density of states (DOS) for ground state Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb). In the total DOS of FM Ni2Mn1.5In0.5 and AFM Ni2Mn1.5Sb0.5, the most obvious difference is the antibonding parts locating high above the Fermi level EF. In FM DOS, the antibonding peaks locate mainly in minority spin channel and the majority states at 0–2eV are rather low, while in the AFM DOS, the states are high in both spin directions between +1 and +2eV. This difference can be traced back to the PDOS of Mn (B) and Mn (D), as we can see, in Ni2Mn1.5In0.5, the configuration of Mn (B) and Mn (D) DOS is similar. The minority antibonding peak locates high above EF and majority DOS peaks locate far below it. That is the origin of the FM coupling between Mn spin moments at B and D sites. But in Ni2Mn1.5Sb0.5, the PDOS of Mn (B) and Mn (D) are just opposite to each other, then an antiparallel coupling between Mn moments is observed. After Fe doping, in the DOS of Ni1.75Fe0.25Mn1.5In0.5 the d states of Fe show strong exchange splitting and hybridize with the d states of Mn, which also have a high antibonding peak at +2eV in minority spin. In majority spin channel, the DOS peaks locate below EF, this configuration makes Fe have a large moment and parallel to that of Mn, agreeing with preceding discussions on magnetic properties. In minority spin, Fe contributes a sharp DOS peak just below EF. As we know, the states at EF (N(EF)) are important for the phase stability of alloys and compounds, a lower N(EF) corresponds a more stable structure, while a higher N(EF) will make the structure lose stability [32]. Then the doping of Fe changes the electronic structure near EF and can influence the possible martensitic transformation. In the DOS of Ni1.75Fe0.25Mn1.5Sb0.5, more Fe states appear above the Fermi level in the majority spin channel and below EF in minority
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Fig. 2. Spin projected total and partial DOS for and austenitic type Ni2Mn1.5Z0.5 Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) under their stable magnetic structure.
martensitic transformation was investigated theoretically in Ni2Mn1.5Z0.5 (Z = In, Sb) MSMAs. Fe-doping does not change the general magnetic structure of Ni2Mn1.5Z0.5. In Ni2Mn1.5In0.5 and Ni1.75Fe0.25Mn1.5In0.5 the austenitic phase is FM and martensitic phase is AFM, which leads to the large ΔM observed experimentally. But in Ni2Mn1.5Sb0.5 and Ni1.75Fe0.25Mn1.5Sb0.5, the AFM state is stable in both austenite and martensite. This difference mainly related to the different atomic radii of In and Sb, which change the distance between Mn (B) and Mn (D). It is mainly the parallel or antiparallel coupled Mn moments determine the magnetic properties of these alloys. But the partial moment of Fe is interesting for its direction reverses after martensitic
phase transition driving force and corresponds to a high transition temperature. In Table 2, the ΔEM decreases in both Ni2Mn1.5In0.5 and Ni2Mn1.5Sb0.5 after Fe-doping. Then it can be inferred that the substitution of Fe for Ni in these alloys will lower their martensitic transition temperatures. In Ni50−xFexMn39Sn11, this decreasing tendency has been observed experimentally [17], which supports present theoretical results. 4. Conclusions Influence of Fe substitution for Ni on the magnetic structure and 4
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Fig. 3. Total energies as functions of the c/a ratio for martensitic type Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb). The stability of FM and AFM states were compared in the figure.
Table 2 The equilibrium lattice constants a, c/a ratio, stable magnetic structure, total and partial spin moments for Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) in martensitic state. Alloys
Magnetic structure
c/a ratio
Mt (μB)
MNi (μB)
MFe (μB)
MMn(B) (μB)
MMn(D) (μB)
MIn/Sb (μB)
Ni2Mn1.5In0.5 Ni1.75Fe0.25Mn1.5In0.5 Ni2Mn1.5Sb0.5 Ni1.75Fe0.25Mn1.5Sb0.5
AFM AFM AFM AFM
1.30 1.32 1.32 1.31
2.07 1.54 2.09 2.44
0.11 0.13 0.15 0.16
– −2.40 – 2.14
4.07 4.04 3.98 3.85
−4.30 −4.14 −4.28 −4.28
−0.15 −0.12 −0.12 −0.11
Acknowledgments This work is supported by the National Natural Science Foundation of China in Grant No. 11474343 and 51371075, the Foundation of Hebei Provincial Education Department in Grant No. BJ2014012. References [1] P.J. Webster, K.R.A. Ziebeck, S.L. Town, M.S. Peak, Philos. Mag. B 49 (1984) 295. [2] K. Ullakko, J.K. Huang, C. Kanter, V.V. Kokorin, R.C. O'Handley, Appl. Phys. Lett. 69 (1996) 1966. [3] Y. Sutou, Y. Imano, N. Koeda, T. Omori, R. Kainuma, K. Ishid, K. Oikawa, Appl. Phys. Lett. 85 (2004) 4358. [4] R. Kainuma, Y. Imano, W. Ito, Y. Sutou, H. Morito, S. Okamoto, O. Kitakami, K. Oikawa, A. Fujita, T. Kanomata, K. Ishida, Nature 439 (2006) 957. [5] G.D. Liu, J.L. Chen, Z.H. Liu, X.F. Dai, G.H. Wu, B. Zhang, X.X. Zhang, Appl. Phys. Lett. 87 (2005) 262504. [6] Z.H. Liu, M. Zhang, Y.T. Cui, Y.Q. Zhou, W.H. Wang, G.H. Wu, X.X. Zhang, Appl. Phys. Lett. 82 (2003) 424. [7] M. Wuttig, J. Li, C. Craciunescu, Scr. Mater. 44 (2001) 2393. [8] H.E. Karaca, I. Karaman, D.C. Lagoudas, H.J. Maier, Y.I. Chumlyakov, Scr. Mater. 49 (2003) 831. [9] T. Omori, K. Watanabe, R. Umetsu, R. Kainuma, K. Ishida, Appl. Phys. Lett. 95 (2009) 082508. [10] H. Yang, Y. Chen, H. Bei, C.R. dela Cruz, Y.D. Wang, K. An, Mater. Des. 104 (2016) 327. [11] T. Krenke, E. Duman, M. Acet, E.F. Wassermann, X. Moya, L. Mañosa, A. Planes, E. Suard, B. Ouladdiaf, Phys. Rev. B 75 (2007) 104414. [12] M. Khan, I. Dubenko, S. Stadler, N. Ali, Appl. Phys. Lett. 91 (2007) 072510. [13] V.K. Sharma, M.K. Chattopadhyay, K.H.B. Shaeb, A. Chouhan, S.B. Roy, Appl. Phys. Lett. 89 (2006) 222509. [14] H.C. Xuan, Y.Q. Zhang, H. Li, P.D. Han, D.H. Wang, Y.W. Du, Appl. Phys. A 119 (2015) 597. [15] T. Gottschall, K.P. Skokov, B. Frincu, O. Gutfleisch, Appl. Phys. Lett. 106 (2015) 021901.
Fig. 4. Calculated total DOS for martensitic type Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb).
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Intermetallics journal homepage: www.elsevier.com/locate/intermet
Influence of Fe-doping on magnetic structure and martensitic transformation in NieMneIn and NieMneSb alloys Yuexing Ma, Hongyue Hao, Xiaotong Liu, Hongzhi Luo∗, Fanbin Meng, Heyan Liu School of Materials Science and Engineering, Hebei University of Technology, Tianjin, 300130, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: A. Magnetic alloys B. Magnetic properties Electronic structure Martensitic transformation E. Ab-initio calculations
Influence of Fe substitution for Ni on the magnetic properties and martensitic transformation was investigated theoretically in Heusler alloys Ni2Mn1.5Z0.5 (Z = In, Sb). Fe-doping does not change the general magnetic structure of Ni2Mn1.5Z0.5. In both Ni2Mn15In0.5 and Ni1.75Fe0.25Mn1.5In0.5 the austenitic phase is ferromagnetic and martensitic phase is antiferromagnetic, which leads to the large ΔM observed experimentally. But in Ni2Mn1.5Sb0.5 and Ni1.75Fe0.25Mn1.5Sb0.5, the antiferromagnetic state is stable in both austenite and martensite. This difference is mainly related to the different atomic radii of In and Sb, which change the distance between Mn (B) and Mn (D). Parallel or antiparallel coupled Mn moments determine the magnetic properties of these alloys. But the partial moment of Fe is large and its direction reverses after martensitic transformation, which makes it a possible way to adjust the magnetic properties of MSMAs. Calculation also suggests that the substitution of Fe for Ni can lower the martensitic transition driving force and lead to the decrease of phase transition temperature. These results agree well with preceding experimental results and make reasonable explanation for them.
1. Introduction Magnetic shape memory alloys (MSMAs) have received more and more attention for their various applications in magnetic refrigeration and actuator. Since the first MSMA Ni2MnGa was reported [1,2], different series of alloys like NieMneZ (In, Sn, Sb), MneNieGa, Ni2FeGa, CoeNieGa(Al) and FeeMneGa were also synthesized [3–10]. Among them, NieMneZ (In, Sn, Sb) alloys are particularly interesting for the valuable properties like magnetic field induced martensitic transformation (MFIMT), large magnetocaloric effect and exchange-bias effect in them [4,11–13]. These properties are associated with the structural and magnetic transition between austenite and martensite. Therefore, NieMneZ alloys are regarded as promising candidates for multifunctional applications. A large ΔM is quite preferable for MFIMT, which means a ferromagnetic-antiferromagnetic (FM-AFM) or ferromangetic-paramagnetic (FM-PM) transition during the structural transformation (here AFM refers to the antiparallel coupling between Mn moments) [4,14]. To realize this, doping other main group or transition metal elements to Heusler alloys is a common method. According to literature, Co is the first choice as the doping elements in NieMneZ alloys. The substitution of Co for Mn or Ni can help to stabilize the FM state in austenitic NieMneZ while retain AFM state in martensite [15,16]. Till now, there
∗
are few reports on the similar effect of other transition metal elements. Quite recently, Ref. [17] reported that Fe substitution for Ni in Ni50Mn39Sn11 can enhance ferromagnetism in austenitic state. If so, the effect of Fe doping can be of great value in MSMAs and worth further investigation. Meanwhile, the mechanical property is significantly improved with Fe doping. This is meaningful for industrial applications, for the brittleness is a big problem in Heusler type MSMAs. The substitution of Fe for Mn or main group elements has also been performed in other NieMneZ alloys and its influence on the magnetic properties and phase transition temperature has been discussed experimentally [18–20]. Recently, Lobo et al. synthesized Ni2MnIn1-xFex alloys and investigated the influence of Fe substitution for In on their structure, phase transition and magnetic properties [21]. But till now, the detailed mechanism of Fe-doping on the phase transformation, magnetic structure of NieMneZ alloys has not been thoroughly studied. As we know, these properties are related to the electronic structures of the alloys, then first-principles calculation can be a useful way to discuss the physical nature in these MSMAs. In this paper, the electronic structure, magnetic properties of Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) have been calculated. The influence of Fe doping on phase transformation temperature and magnetic structure was explained and compared with experimental results in literature. This work can help to understand the phase
Corresponding author. E-mail address: [email protected] (H. Luo).
http://dx.doi.org/10.1016/j.intermet.2017.10.003 Received 8 September 2017; Received in revised form 5 October 2017; Accepted 6 October 2017 0966-9795/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Ma, Y., Intermetallics (2017), http://dx.doi.org/10.1016/j.intermet.2017.10.003
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magnetic structures of Ni2Mn1.5In0.5 and Ni2Mn1.5Sb0.5 are different. In Ni2Mn1.5In0.5, a crossover between the FM and AFM curves is observed, when the lattice constant is smaller than 5.96 Å, AFM state is lower in energy, but above 5.96 Å, FM state energy decreases rapidly and reaches ground state at 6.00 Å. Then in Ni2Mn1.5In0.5 the FM state is more stable. However, it should be noticed that no obvious ferromagnetic character was observed in the experimental curves of Ni2Mn1.5In0.5 [21,27]. We think one possible reason for this difference may be related to the atomic ordering. The calculation is based on a simple ordered structure with supercell approach. But in experimental sample, the case is rather complicated. In NieMneIn, with decreasing In content, the sample may become partly disordered [28], then the next nearest neighbor Mn in calculation may become nearest neighbor, this can change the distance between Mn and have influence on the magnetic properties of Ni2Mn1.5In0.5. Also, the equilibrium lattice constant may be different from the experimental sample in some degree, which can also have influence on the magnetic properties of samples with specific composition. But the calculation results from Ni2Mn1.5In0.5 may still be used to described the magnetic structure of NieMneIn with higher In contents, only a slightly increase of In content is necessary. In Ref. [29], as it increases slightly from 0.5 to 0.6, the martensitic phase has a Ms larger than 1.5μB at 5 K (2.5 T field) and jumps to 6μB in a field of 15 T. This just corresponds to the AFM and FM states in NieMneIn. In Ni2Mn1.5Sb0.5 the AFM curve is always lower in energy and more stable than the FM curve, indicating in this alloy, antiferromagnetic coupling between Mn (B) and Mn (D) is preferable. This is due to the relatively small atomic radius of Sb, which results in an equilibrium lattice constant of 5.97 Å and is smaller than the 6.00 Å in Ni2Mn1.5In0.5. The doping of Fe has different influence on the magnetic structure of Ni2Mn1.5In0.5 and Ni2Mn1.5Sb0.5. In Ni1.75Fe0.25Mn1.5In0.5, the FM curve moves completely below the AFM curve, indicating the ferromagnetism state is enhanced. This is similar to the results in Ni50−xFexMn39Sn11 [17]. But in Ni1.75Fe0.25Mn1.5Sb0.5, the AFM curve is still lower in energy, suggesting Fe-doping does not change the antiferromagnetic coupling between Mn (B) and Mn (D). From the equilibrium lattice constants listed in Table 1, we can also found that, the substitution of Fe leads to a slightly contraction of the lattice.
transition in these alloys deeply and improve their properties effectively. 2. Computational methods In this paper, CASTEP code was employed to calculate the electronic structure and magnetic properties in martensitic and austenitic Ni2Mn0.5Z1.5 and Ni1.75Fe0.25Mn0.5Z1.5 (Z = In, Sb) [22,23]. The interactions between the atomic core and the valence electrons were described by the ultrasoft pseudopotential [24]. The electronic exchange–correlation energy was treated under the generalized-gradientapproximation (GGA) [25]. Supercell approach is used for the calculations of Fe-doped NieMneZ alloys in a 16-atom supercell, in which one Ni atom is replaced by Fe. In order to ensure good convergences for total energy, the plane-wave basis set cut-off was used as 500eV and meshes of 16 × 16 × 16 and 14 × 14 × 16 k-points were employed for Brillouin zone integrations in cubic austenitic and non-modulated tetragonal martensitic structures, respectively. The convergence tolerance for the calculations was selected as a difference on total energy within 1 × 10−6 eV/atom. 3. Results and discussion As we know, in Mn-rich NieMneZ alloys, the extra Mn content will enter the main group element site D (0.75, 0.75, 0.75) and become next nearest neighbor to Mn at B (0.25, 0.25, 0.25) site [26]. In Ni1.75Fe0.25Mn0.5Z1.5, Fe atoms substitute for Ni at A (0, 0, 0) and C (0.5, 0.5, 0.5) sites will enter Ni site, for in Heusler alloys, transitional metal atoms with more valence electrons usually prefer entering A, C sites [17]. Here both Ni and Fe have more electrons than Mn does. The distance between Mn is mainly influenced by the atomic radii of different main group elements Z. The coupling between Mn (B) and Mn (D) spin moments is sensitive to this distance and may be FM or AFM in austenitic NieMneZ alloys. During the martensitic transformation, the distance of Mn (B)eMn (D) will be changed and the magnetic structure can be affected accordingly. Fig. 1 presented the calculated total energies of FM and AFM type Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) as functions of the lattice constants (E-a curve). It is clear that, before Fe-doping, the
Fig. 1. Calculated total energies as functions of lattice and constant for Heusler alloys Ni2Mn0.5Z1.5 Ni1.75Fe0.25Mn0.5Z1.5 (Z = In, Sb) in FM and AFM states.
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Table 1 The equilibrium lattice constants a, stable magnetic structure, total and partial spin moments for Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) in cubic austenitic state. Alloys
Magnetic structure
a (Å)
Mt (μB)
MNi (μB)
MFe (μB)
MMn(B) (μB)
MMn(D) (μB)
MIn/Sb (μB)
Ni2Mn1.5In0.5 Ni1.75Fe0.25Mn1.5In0.5 Ni2Mn1.5Sb0.5 Ni1.75Fe0.25Mn1.5Sb0.5
FM FM AFM AFM
6.00 5.98 5.97 5.96
6.64 6.74 1.80 1.75
0.25 0.24 −0.04 0.00
– 1.65 – −0.78
4.07 3.92 4.13 4.12
4.15 3.99 −4.42 −4.31
−0.04 −0.07 −0.07 −0.06
spin channel, which makes the Fe moment in Ni1.75Fe0.25Mn1.5Sb0.5 relatively small and antiparallel to that of Mn (B). In the next step, we compared the stability of FM and AFM states in Ni2Mn1.5Z0.5 martensitic phase before and after Fe-doping. The ground state of the martensite was obtained by relaxing the c/a ratio of a nonmodulated tetragonal lattice and reaching the minimum of the total energy. During the calculation, we assume that there is no volume change between the austenitic and martensitic lattices. This is a common method in Heusler alloys and the detail can be found in Ref. [33]. Structural optimization results have been presented in Fig. 3, here the zero point was set as the total energy of the cubic austenitic phase (c/a = 1). For FM Ni2Mn1.5In0.5 only one minimum is observed in the E-c/a curve at c/a = 1.10 and the energy difference between c/a = 1.00 is quite small. In FM Ni1.75Fe0.25Mn1.5In0.5, the E-c/a curve increases directly when c/a deviates from 1.00. This means the FM martensitic phase is not energetically preferred in the martensite. The AFM E-c/a curve is lower in energy compared with the FM curve and is more stable in martensitic state. The lowest total energy is obtained at c/a = 1.30 for Ni2Mn1.5In0.5 and 1.33 for Ni1.75Fe0.25Mn1.5In0.5, respectively. Then the FM-AFM transition will occur together with the structural transformation, which can lead to a large ΔM of 4.53μB (undoped) and 5.20μB (doped) in the two alloys. This agrees with the results in Ni50Mn33.7In16.3, in which the ΔM is about 3.5μB [30]. That is why MFIMT can be realized in NieMneIn without doping of Co. In Fig. 3, for martensitic type Ni2Mn1.5Sb0.5 and Ni1.75Fe0.25Mn1.5Sb0.5, the low energy ground state is still AFM, similar to the austenitic phase. Then the total moments of them are not so large and close to each other, there is no obvious ΔM observed in them. Total magnetic moments of Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) are mainly determined by Mn (B) and Mn (D) moment as can be found in Table 2. But if we compare the magnetic data in Tables 1 and 2, we can find that the sign of Fe moment is opposite in austenite and martensite. For example, it is 1.79μB in austenitic Ni1.75Fe0.25Mn1.5In0.5 but becomes −2.40μB in martensite. Then if more Fe can be introduced to NiMn-based MSMAs, it may be possible to adjust the magnetic properties by Fe moment reversal. The calculated total DOS for martensitic type Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 have been presented in Fig. 4. Compared with the austenitic DOS in Fig. 2, one can find that more peaks appear in the martensitic DOS due to change of symmetry. It may be noticed that more states appear in majority spin channel above EF, corresponding to the AFM ground state in these martensites. In Ni50Mn33.7In16.3, the martensite is a poor-metallic ferrimagnet and austenite is a metallic ferromagnet [30]. In Fig. 4 we can find that the states at EF is lower in martensitic DOS compared with the austenite. Then the conduction electrons concentration becomes fewer after the phase transition, which agrees with the experimental observation qualitatively. Compared with undoped Ni2Mn1.5Z0.5, the doping of Fe introduced pronounced DOS peak at EF, which is not preferable for the stability of the martensite and may lower the phase transition temperature. By comparing the ground state energy difference ΔEM between the cubic austenite and tetragonal martensite, one can tell if a martensitic transformation can occur or not in an alloy with certain composition [34–37]. In alloys with similar compositions, a large ΔEM means a large
The calculated total and partial spin moments for Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) under their ground state have been listed in Table 1. The total moment of FM Ni2Mn1.5In0.5 is as high as 6.64 μB, this is a rather large value in Heusler alloys and agrees well with the results in Ref. [30]. In that literature, the austenitic phase in Ni50Mn33.7In16.3 single crystal was retained till 5 K in a magnetic field of 3 T. The saturation magnetization Ms of it is about 6.5μB. Now we can say that this large moment comes from parallel coupled partial moments of Mn (B) and Mn (D). The substitution of Fe leads to a small increase of the total moment, which mainly comes from the larger partial moment of Fe compared with Ni, which couples parallel to the Mn moment and enhance the ferromagnetism. The total moments for Ni2Mn1.5Sb0.5 and Ni1.75Fe0.25Mn1.5Sb0.5 are 1.80μB and 1.75μB, respectively, and much smaller than that of Ni2Mn1.5In0.5. In Ref. [31], Siewert et al. also investigated the magnetic ordering and phase transition in NieMneZ (Z = Ga, In, Sn,Sb) theoretically, in their work, the equilibrium lattice constant for Ni2Mn1.5Sb0.5 was 5.95 Å and total moment was 1.76μB. Our results agree well with them and indicate the theoretical method in present work is reliable. This coincides with the AFM ground state and is determined by the antiparallel coupled Mn (B) and Mn (D) moments. The Fe moment in Ni1.75Fe0.25Mn1.5Sb0.5 is −0.78μB, antiparallel to that of Mn (B). As has been discussed above, the FM and AFM coupling between Mn (B) and Mn (D) is sensitive to their distance. The different effect of Fe-doping may be related to the decreasing lattice constant from Ni2Mn1.5In0.5 to Ni2Mn1.5Sb0.5. In Fig. 2 we presented the total and partial density of states (DOS) for ground state Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb). In the total DOS of FM Ni2Mn1.5In0.5 and AFM Ni2Mn1.5Sb0.5, the most obvious difference is the antibonding parts locating high above the Fermi level EF. In FM DOS, the antibonding peaks locate mainly in minority spin channel and the majority states at 0–2eV are rather low, while in the AFM DOS, the states are high in both spin directions between +1 and +2eV. This difference can be traced back to the PDOS of Mn (B) and Mn (D), as we can see, in Ni2Mn1.5In0.5, the configuration of Mn (B) and Mn (D) DOS is similar. The minority antibonding peak locates high above EF and majority DOS peaks locate far below it. That is the origin of the FM coupling between Mn spin moments at B and D sites. But in Ni2Mn1.5Sb0.5, the PDOS of Mn (B) and Mn (D) are just opposite to each other, then an antiparallel coupling between Mn moments is observed. After Fe doping, in the DOS of Ni1.75Fe0.25Mn1.5In0.5 the d states of Fe show strong exchange splitting and hybridize with the d states of Mn, which also have a high antibonding peak at +2eV in minority spin. In majority spin channel, the DOS peaks locate below EF, this configuration makes Fe have a large moment and parallel to that of Mn, agreeing with preceding discussions on magnetic properties. In minority spin, Fe contributes a sharp DOS peak just below EF. As we know, the states at EF (N(EF)) are important for the phase stability of alloys and compounds, a lower N(EF) corresponds a more stable structure, while a higher N(EF) will make the structure lose stability [32]. Then the doping of Fe changes the electronic structure near EF and can influence the possible martensitic transformation. In the DOS of Ni1.75Fe0.25Mn1.5Sb0.5, more Fe states appear above the Fermi level in the majority spin channel and below EF in minority
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Fig. 2. Spin projected total and partial DOS for and austenitic type Ni2Mn1.5Z0.5 Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) under their stable magnetic structure.
martensitic transformation was investigated theoretically in Ni2Mn1.5Z0.5 (Z = In, Sb) MSMAs. Fe-doping does not change the general magnetic structure of Ni2Mn1.5Z0.5. In Ni2Mn1.5In0.5 and Ni1.75Fe0.25Mn1.5In0.5 the austenitic phase is FM and martensitic phase is AFM, which leads to the large ΔM observed experimentally. But in Ni2Mn1.5Sb0.5 and Ni1.75Fe0.25Mn1.5Sb0.5, the AFM state is stable in both austenite and martensite. This difference mainly related to the different atomic radii of In and Sb, which change the distance between Mn (B) and Mn (D). It is mainly the parallel or antiparallel coupled Mn moments determine the magnetic properties of these alloys. But the partial moment of Fe is interesting for its direction reverses after martensitic
phase transition driving force and corresponds to a high transition temperature. In Table 2, the ΔEM decreases in both Ni2Mn1.5In0.5 and Ni2Mn1.5Sb0.5 after Fe-doping. Then it can be inferred that the substitution of Fe for Ni in these alloys will lower their martensitic transition temperatures. In Ni50−xFexMn39Sn11, this decreasing tendency has been observed experimentally [17], which supports present theoretical results. 4. Conclusions Influence of Fe substitution for Ni on the magnetic structure and 4
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Fig. 3. Total energies as functions of the c/a ratio for martensitic type Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb). The stability of FM and AFM states were compared in the figure.
Table 2 The equilibrium lattice constants a, c/a ratio, stable magnetic structure, total and partial spin moments for Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb) in martensitic state. Alloys
Magnetic structure
c/a ratio
Mt (μB)
MNi (μB)
MFe (μB)
MMn(B) (μB)
MMn(D) (μB)
MIn/Sb (μB)
Ni2Mn1.5In0.5 Ni1.75Fe0.25Mn1.5In0.5 Ni2Mn1.5Sb0.5 Ni1.75Fe0.25Mn1.5Sb0.5
AFM AFM AFM AFM
1.30 1.32 1.32 1.31
2.07 1.54 2.09 2.44
0.11 0.13 0.15 0.16
– −2.40 – 2.14
4.07 4.04 3.98 3.85
−4.30 −4.14 −4.28 −4.28
−0.15 −0.12 −0.12 −0.11
Acknowledgments This work is supported by the National Natural Science Foundation of China in Grant No. 11474343 and 51371075, the Foundation of Hebei Provincial Education Department in Grant No. BJ2014012. References [1] P.J. Webster, K.R.A. Ziebeck, S.L. Town, M.S. Peak, Philos. Mag. B 49 (1984) 295. [2] K. Ullakko, J.K. Huang, C. Kanter, V.V. Kokorin, R.C. O'Handley, Appl. Phys. Lett. 69 (1996) 1966. [3] Y. Sutou, Y. Imano, N. Koeda, T. Omori, R. Kainuma, K. Ishid, K. Oikawa, Appl. Phys. Lett. 85 (2004) 4358. [4] R. Kainuma, Y. Imano, W. Ito, Y. Sutou, H. Morito, S. Okamoto, O. Kitakami, K. Oikawa, A. Fujita, T. Kanomata, K. Ishida, Nature 439 (2006) 957. [5] G.D. Liu, J.L. Chen, Z.H. Liu, X.F. Dai, G.H. Wu, B. Zhang, X.X. Zhang, Appl. Phys. Lett. 87 (2005) 262504. [6] Z.H. Liu, M. Zhang, Y.T. Cui, Y.Q. Zhou, W.H. Wang, G.H. Wu, X.X. Zhang, Appl. Phys. Lett. 82 (2003) 424. [7] M. Wuttig, J. Li, C. Craciunescu, Scr. Mater. 44 (2001) 2393. [8] H.E. Karaca, I. Karaman, D.C. Lagoudas, H.J. Maier, Y.I. Chumlyakov, Scr. Mater. 49 (2003) 831. [9] T. Omori, K. Watanabe, R. Umetsu, R. Kainuma, K. Ishida, Appl. Phys. Lett. 95 (2009) 082508. [10] H. Yang, Y. Chen, H. Bei, C.R. dela Cruz, Y.D. Wang, K. An, Mater. Des. 104 (2016) 327. [11] T. Krenke, E. Duman, M. Acet, E.F. Wassermann, X. Moya, L. Mañosa, A. Planes, E. Suard, B. Ouladdiaf, Phys. Rev. B 75 (2007) 104414. [12] M. Khan, I. Dubenko, S. Stadler, N. Ali, Appl. Phys. Lett. 91 (2007) 072510. [13] V.K. Sharma, M.K. Chattopadhyay, K.H.B. Shaeb, A. Chouhan, S.B. Roy, Appl. Phys. Lett. 89 (2006) 222509. [14] H.C. Xuan, Y.Q. Zhang, H. Li, P.D. Han, D.H. Wang, Y.W. Du, Appl. Phys. A 119 (2015) 597. [15] T. Gottschall, K.P. Skokov, B. Frincu, O. Gutfleisch, Appl. Phys. Lett. 106 (2015) 021901.
Fig. 4. Calculated total DOS for martensitic type Ni2Mn1.5Z0.5 and Ni1.75Fe0.25Mn1.5Z0.5 (Z = In, Sb).
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