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Possible martensitic transformation and ferrimagnetic properties in Heusler alloy Mn2NiSn
Journal of Magnetism and Magnetic Materials 386 (2015) 102–106
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Possible martensitic transformation and ferrimagnetic properties in Heusler alloy Mn2NiSn Ying-Ni Duan a,n, Xiao-Xi Fan a, Abdugheni Kutluk a, Xiu-Juan Du b, Zheng-Wei Zhang c, Yu-Ling Song d a
Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, Xinjiang, PR China School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, Shanxi, PR China c Chemistry and Chemical Engineering Laboratory, The Xinjiang Technical Institute of Physics & Chemistry, Chinese Academy of Sciences, Urumqi 830011, Xinjiang, PR China d College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, Henan, PR China b
art ic l e i nf o
a b s t r a c t
Article history: Received 21 December 2014 Received in revised form 7 March 2015 Accepted 13 March 2015 Available online 14 March 2015
The electronic structure and magnetic properties of Hg2CuTi-type Mn2NiSn have been studied by performing the first-principle calculations. It is found that the phase transformation from the cubic to the tetragonal structure reduces the total energy, indicating that the martensitic phase is more stable and the phase transition from austenite to martensite may happen at low temperature for Hg2CuTi-type Mn2NiSn. Concerning the magnetism of Hg2CuTi-type Mn2NiSn, both austenitic and martensitic phases are suggested to be ferrimagnets. Furthermore, martensitic transformation decreases the magnetic moment per formula unit compared with austenitic phase. The results are helpful to accelerate the use of Mn2NiSn alloys in the series for magnetic shape memory applications. & 2015 Elsevier B.V. All rights reserved.
Keywords: Ferrimagnetism Martensitic transformation Heusler alloy First-principle
1. Introduction Recently, researches on ferromagnetic shape memory alloys (FSMAs) have attracted considerable attention for their potential applications in many technical fields like magnetic actuator or magnetocaloric materials. The first FSMA is Ni2MnGa, which is a Heusler alloy and large magnetic field-induced strain (MFIS) has been observed in it [1–4]. However, the problems in using Ni2MnGa as a commercial magnetic field induced actuator are its brittleness and that the MFIS is highly dependent on the crystal quality. To overcome these problems, current research efforts are directed toward search for new FSMAs [5]. Ni–Fe–Ga could have been an alternative but it exhibits only 0.02% reversible MFIS at 100 K. However, addition of Co in Ni–Fe–Ga increases the MFIS to 0.7% at 300 K [6]. From density functional theory and experimental studies, the results showed Ga2MnNi to be a FSMA at room temperature (TC ¼330 K) with high martensitic start temperature (TM ¼780 K) [7]. In nonstoichiometric Ni–Mn–Ga compositions, evidence of reversible martensites that are also ferromagnetic has been reported [8,9]. The martensitic transformation can be n
Corresponding author. E-mail address: [email protected] (Y.-N. Duan).
http://dx.doi.org/10.1016/j.jmmm.2015.03.047 0304-8853/& 2015 Elsevier B.V. All rights reserved.
induced by external magnetic filed [10–12]. Accompanied with this, many interesting physical properties have been observed. So, exploring new FSMAs and investigating their properties can be a quite meaningful work. Till now, research on the fully stoichiometric Mn2NiX is rather limited and experimental information on phase stability and magnetic property of Mn2NiAl and Mn2NiIn are not yet available. The results from first-principles calculations in these systems have started to come up only recently [13–21]. So it is necessary to make a systematic analysis on the trends in the structural and magnetic properties in these systems based upon their electronic structures for two reasons: (1) to ascertain the usefulness of the alloys in the series for magnetic shape memory applications that is whether martensitic transformation can be realized around room temperature and the other key parameter like the magnetization is substantial; (2) to ascertain the role of the electronic structure in interpreting the similarities and the differences among the members in the series with regard to their properties related to magnetic shape memory effects. In this work, the magnetic and electronic properties of Mn2NiSn alloys with cubic and tetragonal phases are investigated by using the first-principle. Also, the possibility of martensite transformation behavior in the alloy is predicted. These results can
Y.-N. Duan et al. / Journal of Magnetism and Magnetic Materials 386 (2015) 102–106
help to discover and prepare new FSMAs. The rest of the paper is organized as follows: The computational methods and model are summarized in Section 2, and the calculated results as well as the corresponding discussions are presented in Section 3. Finally, in Section 4, we propose some conclusive remarks.
In this paper, the calculations are performed using the Vienna ab-initio simulation package (VASP) based on the density function theory (DFT) [22–24]. The electron-ionic core interaction is represented by the projector augmented wave (PAW) potentials [25] which are more accurate than the ultra-soft pseudopotentials. To treat electron exchange and correlation, we choose the Perdew– Burke–Ernzerhof (PBE) [26] formulation of the generalized gradient approximation (GGA). A conjugate-gradient algorithm is used to relax the ions into their ground states, and the energies and the forces on each ion are converged within 1.0 10 4 eV/atom and 0.02 eV/Å, respectively. The cutoff energy for the plane-waves is chosen to be 450 eV. A 9 9 9 MonkhorstPack grid for k-point sampling is adopted for Brillouin zone integration, together with a Gaussian smearing broadening of 0.2 eV. The Heusler alloys represent a class of ternary intermetallic compounds with the general formula X2YZ where X and Y are transition metal elements and Z is a main group element [27]. Usually, the Heusler structure can be looked as four interpenetrating face-centered-cubic (fcc) lattices and has four unique crystal sites namely A (0,0,0), B (1/4,1/4,1/4), C (1/2,1/2,1/2), D (3/ 4,3/4,3/4) in Wyckoff coordinates, as shown in Fig. 1. It is found that the site preference of the X and Y atoms is strongly influenced by the number of their valence electrons [28]. The Y atom will occupy B site (Cu2MnAl-type structure) or C site (Hg2CuTi-type structure), which rests with its less or more valence electrons compared with X atom. For alloy Mn2NiSn the two Mn atoms occupy the A (0,0,0) and B (1/4,1/4,1/4) sites, and residual Ni and
3
2
Energy (eV)
2. Computational methods and model
103
Mn 2 NiSn Austenite
1 a=6.142 Å
0 6.0
6.2
6.4
6.6
Lattice constant ( Å) Fig. 2. Calculated total energy as a function of the lattice constant for Mn2NiSn with the Hg2CuTi-type structure in ferrimagnetic state. The minimum total energy at equilibrium lattice constant is chosen as zero. Table 1 The calculated lattice constants a, b, c and atomic magnetic moments for austenitic and martensitic Mn2NiSn. Compounds
a (Å)
b (Å)
c (Å)
c/a
MMn(A) (μΒ) MMn(B) (μΒ)
MNi (μΒ)
Mn2NiSn austenite Mn2NiSn martensite
6.142
6.142
6.142
1.000
2.981
3.400
0.111
5.813 5.813 6.859 1.180
3.045
3.335
0.033
0.08
ΔE (eV)
0.04
0.00
-0.04
-2% -1% 0% +1% +2%
Mn 2NiSn martensitic 0.9
1.0
1.1 1.2 c/a ratio
1.3
1.4
Fig. 3. Total energy as a function of the c/a ratio for the Hg2CuTi-type Mn2NiSn with martensitic phase. The total energy of the cubic austenitic phase (c/a ¼1) is chosen as zero.
Sn atoms enter the C (1/2,1/2,1/2) and D (3/4,3/4,3/4) sites respectively, which is known as the Hg2CuTi-type of the structure [29–32]. This structure is different from the Cu2MnAl-type structure in which the two Mn atoms occupy the A (0,0,0) and C (1/2,1/ 2,1/2) sites equally and leave the B (1/4,1/4,1/4) site to Ni. Fig. 1. Crystal structure of Heusler alloy. The unit cell has four crystal sites as the basis: A (0,0,0), B (1/4,1/4,1/4), C (1/2,1/2,1/2) and D (3/4,3/4,3/4) in Wyckoff coordinates.
3. Results and discussion To determine the lattice constant the austenitic Mn2NiSn alloy,
104
Y.-N. Duan et al. / Journal of Magnetism and Magnetic Materials 386 (2015) 102–106
EF
EF
20 Austenite 0
Martensite
up-spin down-spin
-20
total
total
Mn(A)
Mn(A)
Mn(B)
Mn(B)
3
DOS (electrons/eV)
0 -3 3 0 -3 3 0 -3 0.5 0.0 -0.5 -6
-4
-2
0
2
Ni
Ni
Sn
Sn
4
6
-6
-4
-2
0
2
4
6
Energy (eV) Fig. 4. Calculated total densities of states (DOS), partial DOS projected on Mn, Ni and Sn atoms for the Hg2CuTi-type Mn2NiSn with (a) austenitic and (b) martensitic phases. The black dashed and red solid lines represent the up-spin and down-spin channels, respectively. The Fermi level EF is set to zero energy and indicated with vertical solid lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
0.6
Mn2NiSn
0.4
total moment
0.2
Magnetic moment (μΒ)
-3.0 -3.1
Mn(A) moment
3.4 3.3
Mn(B) moment
0.1 0.0
Ni moment
0.01 0.00 -0.01
Sn moment 0.9
1.0
1.1
1.2
1.3
c/a ratio Fig. 5. Total and atomic spin moments as a functions of the c/a ratio for Hg2CuTi-type Mn2NiSn in martensitic phase. The vertical gray dashed and solid lines correspond to the austenitic and martensitic phases, respectively.
the calculated total energies for cubic alloy as a function of the lattice constant is shown in Fig. 2. The minimum total energy at equilibrium lattice constant is chosen as zero. The equilibrium lattice constant of the austenitic Mn2NiSn alloy is listed in Table 1. The equilibrium lattice constant corresponding to the minimum energy is found to be 6.142 Å for Mn2NiSn with the Hg2CuTi-type in austenitic phase, which is close to the value of 6.099 Å in the previous theoretical calculation [28]. At the equilibrium state, the austenitic Mn2NiSn is ferrimagnetic and in which we determine an antiparallel alignment of magnetic moment between Mn (A) and
Mn (B) atoms. These agree well with preceding studies on other Ni-Mn-based Heusler alloys [13,14,28,33]. Fig. 3 shows the structural optimization results of the martensitic Mn2NiSn alloy. The total energy of the cubic austenitic phase (c/a¼ 1) is chosen as zero without cell change for reference. The minimum total energy, Etot, is obtained by varying c/a ratio as a function of a non-modulated tetragonal lattice constant. Usually, one assumes that there is no cell volume change between the austenitic and martensitic phases. That is just the case in many FSMAs such as Mn2NiIn [28], Mn2NiGa [34] or Ni2MnGa [35]. However, it is also found that in some specific materials like Mn2CoGe, the volume change between the austenite and martensite is as much as 3% [36]. Recently, Lou et al. predicted the volume change between the austenite and martensite in Mn2NiGe is as much as 0.5% [34]. In view of the results mentioned above, we consider a 72% cell change of the martensitic phase with respect to the equilibrium volume of austenitic Mn2NiSn in this paper and investigate the influence of which in detail. For the Etot–c/a curve of Mn2NiSn, the c/ao 1.05 side is rather flat and, only one minima is observed at c/a ¼1.180 except for -2% and -1% decrease of the martensitic cell volume. The Etot–c/a curve without volume change has the lowest total energy, which is more clearly shown in the inset of Fig. 3 (the enlargement of the region of 1.140rc/a r1.210), and the corresponding lattice constants are a¼ b¼5.813 Å and c ¼6.859 Å, as listed in Table 1, which are well agreement with the previous value [16]. A small contraction or expansion will increase the energy obviously, and the structure with c-axis lattice expansion and a, b-axis lattice contraction may be more stable during the possible martensitic transformation in Mn2NiSn. It can be seen that the energy of the expansion (contraction) increases with increasing (decreasing) the cell. From Fig. 3 we can also see that the energy of the contraction is higher than that of the expansion corresponding to the same scale of the cell change. Experimentally, such structural transformation has
Y.-N. Duan et al. / Journal of Magnetism and Magnetic Materials 386 (2015) 102–106
been confirmed in Mn2NiGa [34]. For example, the total energy difference between the martensitic and austenitic phase is -37meV/f.u. similar results have also been observed in Mn2NiAl, Mn2NiIn and Mn2NiGe [13,16,33]. As it was reported by Chernenko [19] et al., two types of fairly independent lattice instabilities of parent phase exist in the shape memory alloys, namely: (1) towards the martensitic transformation, and (2) towards phonon freezing. The phonon with the low energy at the low temperature will not be important on changing the lattice constant of the alloys. So at the low temperature, the vibrational effect can be negligible. It is indicated that the phase transformation from austenitic to martensitic structure could effectively lower the total energy, indicating the possibility of a martensitic phase transition at low temperature. It is known that the energy difference between the tetragonal martensitic and the cubic austenitic phases can be used to predict the possible martensitic transformation and to estimate the phase transformation temperature qualitatively [14]. Therefore, the martensitic phase is more likely to be observed in Mn2NiSn alloy according to the results indicated in Fig. 3. This can be explained from their electronic density of states (DOS), as illustrated in Fig. 4. The relative stability of the austenitic and martensitic phases is strongly related to their electronic structures near the Fermi level (EF ). In Mn2NiSn alloy, the character of its total DOS is mainly determined by the d states of Mn and Ni atoms. For the down-spin total DOS of austenitic Mn2NiSn, there is a valley in the down-spin channel around 1 eV, which is related to the accumulation of delectrons of Ni atom. As can be seen in Fig. 4, the shape of this valley is mainly determined by the partial DOS of Ni atom. With the tetragonal distortion, the cubic symmetry in austenitic Mn2NiSn is destroyed and, below and near EF , the electronic accumulated states in down-spin (up-spin) channel are partly pushed to the region of low energy for Mn(A) (Mn(B)) atom. Such electronic redistribution for Mn atoms may contribute to an increase in the stability of the martensitic phase in the Hg2CuTi-type Mn2NiSn. The atomic magnetic moments are also inspected for the Hg2CuTi-type Mn2NiSn with martensitic phase and, the corresponding results are listed in Table 1. Remarkably, the Mn2NiSn with martensitic phase is also a ferrimagnet, similar to the case of austenitic phase. However, the overall magnetization per formula unit (f.u) for martensitic phase ( 0.324 mB/f.u) slightly decreases compared with austenitic phase ( 0.543 mB/f.u), which is related to the atomic magnetic moments. Fig. 5 shows the total and atomic magnetic moment of Hg2CuTi-type Mn2NiSn as a function of c/a ratio. The variation of the total moment with c/a ratio is close to the partial moments except for some detailed difference. With the transformation from austenitic phase (corresponding to the case of c/a ¼1) to martensitic phase (corresponding to the case of c/a ¼1.18), a decrease in atomic magnetic moment occur for all the atoms. Consequently, magnetization decreases in martensitic phase, compared with austenitic phase (the largest magnetization in Hg2CuTi-type Mn2NiSn). Mn (A) has four Mn (B) and four Sn while Mn (B) has four Mn (A) and four Sn as nearest neighbors in martensitic Mn2NiSn. Its influence on the chemical surroundings and hybridization effect of Mn (A) and Mn (B) can be different, which will make the difference in atomic magnetic moment between Mn (A) and Mn (B). The atomic magnetic moment of Ni contributions the magnetic moment modulate the overall trend dictated by Mn(A) and Mn(B) atoms (due to the value or absolute values of their being lager), While the atomic magnetic moment of Sn is negligible. 4. Conclusions The electronic structure and magnetic properties of the
105
Hg2CuTi-type Mn2NiSn have been studied by using the firstprinciple PAW potential within GGA. The possible non-modulated martensitic transformation in this alloy has been considered. It is found that the phase transformation from austenitic to martensitic structure effectively reduces the total energy, indicating the possibility of a martensitic phase transition at low temperature. Concerning the magnetism of Hg2CuTi-type Mn2NiSn, both austenitic and martensitic phases are suggested to be ferrimagnetic, and martensitic transformation decreases the overall magnetization per f.u compared with austenitic phase. The results may be helpful for using the Hg2CuTi-type Mn2NiSn as magnetic shape memory alloys.
Acknowledgments This work was supported by National Natural Science Foundation of China (Grant no. 61201125), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (Grant no. [2013]-277), Innovation Founds of Xinjiang Medical University for science research (Grant No. XJC2013237) and Nanyang Normal University Science Foundation (Grant no. ZX2013018).
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Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Possible martensitic transformation and ferrimagnetic properties in Heusler alloy Mn2NiSn Ying-Ni Duan a,n, Xiao-Xi Fan a, Abdugheni Kutluk a, Xiu-Juan Du b, Zheng-Wei Zhang c, Yu-Ling Song d a
Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, Xinjiang, PR China School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, Shanxi, PR China c Chemistry and Chemical Engineering Laboratory, The Xinjiang Technical Institute of Physics & Chemistry, Chinese Academy of Sciences, Urumqi 830011, Xinjiang, PR China d College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, Henan, PR China b
art ic l e i nf o
a b s t r a c t
Article history: Received 21 December 2014 Received in revised form 7 March 2015 Accepted 13 March 2015 Available online 14 March 2015
The electronic structure and magnetic properties of Hg2CuTi-type Mn2NiSn have been studied by performing the first-principle calculations. It is found that the phase transformation from the cubic to the tetragonal structure reduces the total energy, indicating that the martensitic phase is more stable and the phase transition from austenite to martensite may happen at low temperature for Hg2CuTi-type Mn2NiSn. Concerning the magnetism of Hg2CuTi-type Mn2NiSn, both austenitic and martensitic phases are suggested to be ferrimagnets. Furthermore, martensitic transformation decreases the magnetic moment per formula unit compared with austenitic phase. The results are helpful to accelerate the use of Mn2NiSn alloys in the series for magnetic shape memory applications. & 2015 Elsevier B.V. All rights reserved.
Keywords: Ferrimagnetism Martensitic transformation Heusler alloy First-principle
1. Introduction Recently, researches on ferromagnetic shape memory alloys (FSMAs) have attracted considerable attention for their potential applications in many technical fields like magnetic actuator or magnetocaloric materials. The first FSMA is Ni2MnGa, which is a Heusler alloy and large magnetic field-induced strain (MFIS) has been observed in it [1–4]. However, the problems in using Ni2MnGa as a commercial magnetic field induced actuator are its brittleness and that the MFIS is highly dependent on the crystal quality. To overcome these problems, current research efforts are directed toward search for new FSMAs [5]. Ni–Fe–Ga could have been an alternative but it exhibits only 0.02% reversible MFIS at 100 K. However, addition of Co in Ni–Fe–Ga increases the MFIS to 0.7% at 300 K [6]. From density functional theory and experimental studies, the results showed Ga2MnNi to be a FSMA at room temperature (TC ¼330 K) with high martensitic start temperature (TM ¼780 K) [7]. In nonstoichiometric Ni–Mn–Ga compositions, evidence of reversible martensites that are also ferromagnetic has been reported [8,9]. The martensitic transformation can be n
Corresponding author. E-mail address: [email protected] (Y.-N. Duan).
http://dx.doi.org/10.1016/j.jmmm.2015.03.047 0304-8853/& 2015 Elsevier B.V. All rights reserved.
induced by external magnetic filed [10–12]. Accompanied with this, many interesting physical properties have been observed. So, exploring new FSMAs and investigating their properties can be a quite meaningful work. Till now, research on the fully stoichiometric Mn2NiX is rather limited and experimental information on phase stability and magnetic property of Mn2NiAl and Mn2NiIn are not yet available. The results from first-principles calculations in these systems have started to come up only recently [13–21]. So it is necessary to make a systematic analysis on the trends in the structural and magnetic properties in these systems based upon their electronic structures for two reasons: (1) to ascertain the usefulness of the alloys in the series for magnetic shape memory applications that is whether martensitic transformation can be realized around room temperature and the other key parameter like the magnetization is substantial; (2) to ascertain the role of the electronic structure in interpreting the similarities and the differences among the members in the series with regard to their properties related to magnetic shape memory effects. In this work, the magnetic and electronic properties of Mn2NiSn alloys with cubic and tetragonal phases are investigated by using the first-principle. Also, the possibility of martensite transformation behavior in the alloy is predicted. These results can
Y.-N. Duan et al. / Journal of Magnetism and Magnetic Materials 386 (2015) 102–106
help to discover and prepare new FSMAs. The rest of the paper is organized as follows: The computational methods and model are summarized in Section 2, and the calculated results as well as the corresponding discussions are presented in Section 3. Finally, in Section 4, we propose some conclusive remarks.
In this paper, the calculations are performed using the Vienna ab-initio simulation package (VASP) based on the density function theory (DFT) [22–24]. The electron-ionic core interaction is represented by the projector augmented wave (PAW) potentials [25] which are more accurate than the ultra-soft pseudopotentials. To treat electron exchange and correlation, we choose the Perdew– Burke–Ernzerhof (PBE) [26] formulation of the generalized gradient approximation (GGA). A conjugate-gradient algorithm is used to relax the ions into their ground states, and the energies and the forces on each ion are converged within 1.0 10 4 eV/atom and 0.02 eV/Å, respectively. The cutoff energy for the plane-waves is chosen to be 450 eV. A 9 9 9 MonkhorstPack grid for k-point sampling is adopted for Brillouin zone integration, together with a Gaussian smearing broadening of 0.2 eV. The Heusler alloys represent a class of ternary intermetallic compounds with the general formula X2YZ where X and Y are transition metal elements and Z is a main group element [27]. Usually, the Heusler structure can be looked as four interpenetrating face-centered-cubic (fcc) lattices and has four unique crystal sites namely A (0,0,0), B (1/4,1/4,1/4), C (1/2,1/2,1/2), D (3/ 4,3/4,3/4) in Wyckoff coordinates, as shown in Fig. 1. It is found that the site preference of the X and Y atoms is strongly influenced by the number of their valence electrons [28]. The Y atom will occupy B site (Cu2MnAl-type structure) or C site (Hg2CuTi-type structure), which rests with its less or more valence electrons compared with X atom. For alloy Mn2NiSn the two Mn atoms occupy the A (0,0,0) and B (1/4,1/4,1/4) sites, and residual Ni and
3
2
Energy (eV)
2. Computational methods and model
103
Mn 2 NiSn Austenite
1 a=6.142 Å
0 6.0
6.2
6.4
6.6
Lattice constant ( Å) Fig. 2. Calculated total energy as a function of the lattice constant for Mn2NiSn with the Hg2CuTi-type structure in ferrimagnetic state. The minimum total energy at equilibrium lattice constant is chosen as zero. Table 1 The calculated lattice constants a, b, c and atomic magnetic moments for austenitic and martensitic Mn2NiSn. Compounds
a (Å)
b (Å)
c (Å)
c/a
MMn(A) (μΒ) MMn(B) (μΒ)
MNi (μΒ)
Mn2NiSn austenite Mn2NiSn martensite
6.142
6.142
6.142
1.000
2.981
3.400
0.111
5.813 5.813 6.859 1.180
3.045
3.335
0.033
0.08
ΔE (eV)
0.04
0.00
-0.04
-2% -1% 0% +1% +2%
Mn 2NiSn martensitic 0.9
1.0
1.1 1.2 c/a ratio
1.3
1.4
Fig. 3. Total energy as a function of the c/a ratio for the Hg2CuTi-type Mn2NiSn with martensitic phase. The total energy of the cubic austenitic phase (c/a ¼1) is chosen as zero.
Sn atoms enter the C (1/2,1/2,1/2) and D (3/4,3/4,3/4) sites respectively, which is known as the Hg2CuTi-type of the structure [29–32]. This structure is different from the Cu2MnAl-type structure in which the two Mn atoms occupy the A (0,0,0) and C (1/2,1/ 2,1/2) sites equally and leave the B (1/4,1/4,1/4) site to Ni. Fig. 1. Crystal structure of Heusler alloy. The unit cell has four crystal sites as the basis: A (0,0,0), B (1/4,1/4,1/4), C (1/2,1/2,1/2) and D (3/4,3/4,3/4) in Wyckoff coordinates.
3. Results and discussion To determine the lattice constant the austenitic Mn2NiSn alloy,
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EF
EF
20 Austenite 0
Martensite
up-spin down-spin
-20
total
total
Mn(A)
Mn(A)
Mn(B)
Mn(B)
3
DOS (electrons/eV)
0 -3 3 0 -3 3 0 -3 0.5 0.0 -0.5 -6
-4
-2
0
2
Ni
Ni
Sn
Sn
4
6
-6
-4
-2
0
2
4
6
Energy (eV) Fig. 4. Calculated total densities of states (DOS), partial DOS projected on Mn, Ni and Sn atoms for the Hg2CuTi-type Mn2NiSn with (a) austenitic and (b) martensitic phases. The black dashed and red solid lines represent the up-spin and down-spin channels, respectively. The Fermi level EF is set to zero energy and indicated with vertical solid lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
0.6
Mn2NiSn
0.4
total moment
0.2
Magnetic moment (μΒ)
-3.0 -3.1
Mn(A) moment
3.4 3.3
Mn(B) moment
0.1 0.0
Ni moment
0.01 0.00 -0.01
Sn moment 0.9
1.0
1.1
1.2
1.3
c/a ratio Fig. 5. Total and atomic spin moments as a functions of the c/a ratio for Hg2CuTi-type Mn2NiSn in martensitic phase. The vertical gray dashed and solid lines correspond to the austenitic and martensitic phases, respectively.
the calculated total energies for cubic alloy as a function of the lattice constant is shown in Fig. 2. The minimum total energy at equilibrium lattice constant is chosen as zero. The equilibrium lattice constant of the austenitic Mn2NiSn alloy is listed in Table 1. The equilibrium lattice constant corresponding to the minimum energy is found to be 6.142 Å for Mn2NiSn with the Hg2CuTi-type in austenitic phase, which is close to the value of 6.099 Å in the previous theoretical calculation [28]. At the equilibrium state, the austenitic Mn2NiSn is ferrimagnetic and in which we determine an antiparallel alignment of magnetic moment between Mn (A) and
Mn (B) atoms. These agree well with preceding studies on other Ni-Mn-based Heusler alloys [13,14,28,33]. Fig. 3 shows the structural optimization results of the martensitic Mn2NiSn alloy. The total energy of the cubic austenitic phase (c/a¼ 1) is chosen as zero without cell change for reference. The minimum total energy, Etot, is obtained by varying c/a ratio as a function of a non-modulated tetragonal lattice constant. Usually, one assumes that there is no cell volume change between the austenitic and martensitic phases. That is just the case in many FSMAs such as Mn2NiIn [28], Mn2NiGa [34] or Ni2MnGa [35]. However, it is also found that in some specific materials like Mn2CoGe, the volume change between the austenite and martensite is as much as 3% [36]. Recently, Lou et al. predicted the volume change between the austenite and martensite in Mn2NiGe is as much as 0.5% [34]. In view of the results mentioned above, we consider a 72% cell change of the martensitic phase with respect to the equilibrium volume of austenitic Mn2NiSn in this paper and investigate the influence of which in detail. For the Etot–c/a curve of Mn2NiSn, the c/ao 1.05 side is rather flat and, only one minima is observed at c/a ¼1.180 except for -2% and -1% decrease of the martensitic cell volume. The Etot–c/a curve without volume change has the lowest total energy, which is more clearly shown in the inset of Fig. 3 (the enlargement of the region of 1.140rc/a r1.210), and the corresponding lattice constants are a¼ b¼5.813 Å and c ¼6.859 Å, as listed in Table 1, which are well agreement with the previous value [16]. A small contraction or expansion will increase the energy obviously, and the structure with c-axis lattice expansion and a, b-axis lattice contraction may be more stable during the possible martensitic transformation in Mn2NiSn. It can be seen that the energy of the expansion (contraction) increases with increasing (decreasing) the cell. From Fig. 3 we can also see that the energy of the contraction is higher than that of the expansion corresponding to the same scale of the cell change. Experimentally, such structural transformation has
Y.-N. Duan et al. / Journal of Magnetism and Magnetic Materials 386 (2015) 102–106
been confirmed in Mn2NiGa [34]. For example, the total energy difference between the martensitic and austenitic phase is -37meV/f.u. similar results have also been observed in Mn2NiAl, Mn2NiIn and Mn2NiGe [13,16,33]. As it was reported by Chernenko [19] et al., two types of fairly independent lattice instabilities of parent phase exist in the shape memory alloys, namely: (1) towards the martensitic transformation, and (2) towards phonon freezing. The phonon with the low energy at the low temperature will not be important on changing the lattice constant of the alloys. So at the low temperature, the vibrational effect can be negligible. It is indicated that the phase transformation from austenitic to martensitic structure could effectively lower the total energy, indicating the possibility of a martensitic phase transition at low temperature. It is known that the energy difference between the tetragonal martensitic and the cubic austenitic phases can be used to predict the possible martensitic transformation and to estimate the phase transformation temperature qualitatively [14]. Therefore, the martensitic phase is more likely to be observed in Mn2NiSn alloy according to the results indicated in Fig. 3. This can be explained from their electronic density of states (DOS), as illustrated in Fig. 4. The relative stability of the austenitic and martensitic phases is strongly related to their electronic structures near the Fermi level (EF ). In Mn2NiSn alloy, the character of its total DOS is mainly determined by the d states of Mn and Ni atoms. For the down-spin total DOS of austenitic Mn2NiSn, there is a valley in the down-spin channel around 1 eV, which is related to the accumulation of delectrons of Ni atom. As can be seen in Fig. 4, the shape of this valley is mainly determined by the partial DOS of Ni atom. With the tetragonal distortion, the cubic symmetry in austenitic Mn2NiSn is destroyed and, below and near EF , the electronic accumulated states in down-spin (up-spin) channel are partly pushed to the region of low energy for Mn(A) (Mn(B)) atom. Such electronic redistribution for Mn atoms may contribute to an increase in the stability of the martensitic phase in the Hg2CuTi-type Mn2NiSn. The atomic magnetic moments are also inspected for the Hg2CuTi-type Mn2NiSn with martensitic phase and, the corresponding results are listed in Table 1. Remarkably, the Mn2NiSn with martensitic phase is also a ferrimagnet, similar to the case of austenitic phase. However, the overall magnetization per formula unit (f.u) for martensitic phase ( 0.324 mB/f.u) slightly decreases compared with austenitic phase ( 0.543 mB/f.u), which is related to the atomic magnetic moments. Fig. 5 shows the total and atomic magnetic moment of Hg2CuTi-type Mn2NiSn as a function of c/a ratio. The variation of the total moment with c/a ratio is close to the partial moments except for some detailed difference. With the transformation from austenitic phase (corresponding to the case of c/a ¼1) to martensitic phase (corresponding to the case of c/a ¼1.18), a decrease in atomic magnetic moment occur for all the atoms. Consequently, magnetization decreases in martensitic phase, compared with austenitic phase (the largest magnetization in Hg2CuTi-type Mn2NiSn). Mn (A) has four Mn (B) and four Sn while Mn (B) has four Mn (A) and four Sn as nearest neighbors in martensitic Mn2NiSn. Its influence on the chemical surroundings and hybridization effect of Mn (A) and Mn (B) can be different, which will make the difference in atomic magnetic moment between Mn (A) and Mn (B). The atomic magnetic moment of Ni contributions the magnetic moment modulate the overall trend dictated by Mn(A) and Mn(B) atoms (due to the value or absolute values of their being lager), While the atomic magnetic moment of Sn is negligible. 4. Conclusions The electronic structure and magnetic properties of the
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Hg2CuTi-type Mn2NiSn have been studied by using the firstprinciple PAW potential within GGA. The possible non-modulated martensitic transformation in this alloy has been considered. It is found that the phase transformation from austenitic to martensitic structure effectively reduces the total energy, indicating the possibility of a martensitic phase transition at low temperature. Concerning the magnetism of Hg2CuTi-type Mn2NiSn, both austenitic and martensitic phases are suggested to be ferrimagnetic, and martensitic transformation decreases the overall magnetization per f.u compared with austenitic phase. The results may be helpful for using the Hg2CuTi-type Mn2NiSn as magnetic shape memory alloys.
Acknowledgments This work was supported by National Natural Science Foundation of China (Grant no. 61201125), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (Grant no. [2013]-277), Innovation Founds of Xinjiang Medical University for science research (Grant No. XJC2013237) and Nanyang Normal University Science Foundation (Grant no. ZX2013018).
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