Designing a New Ni-Mn-Sn Ferromagnetic Shape Memory ... - MDPI

metals Article

Designing a New Ni-Mn-Sn Ferromagnetic Shape Memory Alloy with Excellent Performance by Cu Addition Kun Zhang 1 , Xiaohua Tian 2, *, Changlong Tan 1,2 , Erjun Guo 1 , Wenbin Zhao 2 and Wei Cai 3 1

2 3

*

School of Materials Science and Engineering, Harbin University of Science and Technology, Harbin 150080, China; [email protected] (K.Z.); [email protected] (C.T.); [email protected] (E.G.) School of Science, Harbin University of Science and Technology, Harbin 150080, China; [email protected] School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China; [email protected] Correspondence: [email protected]; Tel.: +86-451-8639-0788

Received: 3 February 2018; Accepted: 24 February 2018; Published: 28 February 2018

Abstract: Both magnetic-field-induced reverse martensitic transformation (MFIRMT) and a high working temperature are crucial for the application of Ni-Mn-Sn magnetic shape memory alloys. Here, by first-principles calculations, we demonstrate that the substitution of Cu for Sn is effective not only in enhancing the MFIRMT but also in increasing martensitic transformation, which is advantageous for its application. Large magnetization difference (∆M) in Ni-Mn-Sn alloy is achieved by Cu doping, which arises from the enhancement of magnetization of austenite due to the change of Mn-Mn interaction from anti-ferromagnetism to ferromagnetism. This directly leads to the enhancement of MFIRMT. Meanwhile, the martensitic transformation shifts to higher temperature, owing to the energy difference between the austenite L21 structure and the tetragonal martensite L10 structure increases by Cu doping. The results provide the theoretical data and the direction for developing a high temperature magnetic-field-induced shape memory alloy with large ∆M in the Ni-Mn-Sn Heusler alloy system. Keywords: Ni-Mn-Sn; ferromagnetic shape memory alloys; martensitic transformation; magnetic properties; first-principle calculation; Cu addition

1. Introduction Owing to the coupling of structure and magnetism, the ferromagnetic shape memory alloys (FSMAs) have attracted considerable attention [1–6]. The magnetic shape memory arises from a magnetic-field-induced rearrangement of martensite variants in Ni-Mn-Ga [7]. Based on this mechanism, because the driving force is limited by the anisotropy energy, the output stress induced by the external magnetic field is restricted [3]. Different from Ni-Mn-Ga FSMAs, Ni-Mn-X (X = In, Sn, and Sb) FSMAs can obtain larger output stress resulting from the magnetic-field-induced transformation [8]. The shift of the reverse martensitic transformation temperature induced by magnetic field, ∆T, is given by the Clausius–Clapeyron equation: dB ∆S = and ∆T ≈ dT ∆M



 ∆M ∆B ∆S

(1)

where B is the applied magnetic field, and ∆M and ∆S are the differences in magnetization and entropy between parent and martensite phase, respectively. Recently, the Mn-rich Ni-Mn-Sn FSMAs have

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stood out due to their remarkable properties such as giant caloric effects [9] and complex magnetic behavior with easily-tunable transformation characteristics by a variation of the composition and doping [7–14]. Most of these fascinating properties are related to the magnetic-field-induced reverse transformation (MFIRT). Unfortunately, practical applications of these alloys are restricted because of the drawback which is the requirement for a high magnetic field. As Equation (1) shows, to use MFIRT, a larger ∆M is urgently required for the martensitic transformation. Up to now, some efforts have been devoted to enlarge ∆M in Ni-Mn-based FSMAs, such as tuning the stoichiometric, substituting foreign atoms, and applying external pressure [15–19]. Among these, substituting a small amount of Co/Fe for Ni is an efficient method to enhance the ∆M. This is mainly due to the local ferromagnetic structure achieved in the antiferromagnetic matrix and the magnetization of the high temperature phase which was effectively enhanced [20]. The disadvantage of Co doping is that it makes martensitic transformation (MT) temperature too low, even below room temperature. However, the working temperature of Ni-Mn-Sn FSMAs is usually at room temperature or at higher temperatures. Thus, developing the Ni-Mn-Sn FSMAs with a large ∆M and high MT temperature is essential. In Ni-Mn-Sn FSMAs, a fourth element addition normally seeks to enhance the magnetic properties, although it can also modify the structure. Cu, for instance, has been shown to have an important effect on the properties of Ni-Mn-Sn compounds. Castillo-Villa et al. have reported improved refrigeration capacity in Ni-Mn-Sn-Cu polycrystalline through the magnetocaloric and elastocaloric combination [21]. Lately, Li et al. shows that Ni44 Mn41 Sn11 Cu4 exhibits a giant adiabatic cooling of −8 K at small transformation strains of 1.3%. Ni-Mn-Sn-Cu alloys are proposed as a candidate for the elastocaloric materials [22]. As for the martensitic transformation, Wang et al. reported that Mn substitution by Cu increased the martensitic transformation (MT) temperature as well as the magnetocaloric effect [23], while other researchers found that the replacement of Ni by Cu atoms can generate an obvious martensitic transformation temperature change to a lower temperature [24]. So far, numerous works have focused on adjusting the transformation temperatures or improving the magnetic properties. However, research has rarely been carried out to improve the ∆M and MT temperature at the same time. Thus, we expect that doping proper Cu in the Ni-Mn-Sn FSMAs can simultaneously enhance the ∆M and improve MT temperature. However, due to the restrictions of a long experimental period, limited scope, and high costs, experimental studies have limitations when designing a new material. Before the experiment, calculation by the first principle plays an important role in predicting new ferromagnetic shape memory alloys. The theoretical calculation can simulate substitution or addition elements with any desired composition and accordingly select the most promising one, which can provide useful guidance for experiments. Up to this day, first-principle calculations have been successfully used to calculate the electronic structure, formation energy and magnetic structure of the off-stoichiometric Ni–Mn based FSMAs. Meanwhile, the calculated results are consistent with the experimental results. Thus, by first-principle calculation, we expect to design a new FSMAs material with excellent performance through Cu doping. In the present paper, the electronic structure and magnetic properties of Ni16 Mn12 Sn4−x Cux alloys (x = 0, 1, 2, 3, and 4) have been calculated by the first principle. The influence of Cu doping on phase transformation temperature, Curie temperature and magnetic structure was clarified. This work can help to understand the phase transformation deeply and design new Ni-Mn-Sn alloys with excellent properties by doping another element. Calculated results showed that the substitution of Cu for Sn is effective not only in enhancing the MFIRMT, but also in increasing martensitic transformation. The results provide the theoretical data and the direction for developing high temperature magnetic-field-induced shape memory alloy in the Ni-Mn-Sn Heusler alloy system. 2. Materials and Methods The Heusler alloys (X2 YZ) studies here possess a L21 structure that consists of four interpenetrating face-centered-cubic (fcc) sublattices with origin at fractional positions, (0.25, 0.25,

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0.25), (0.75, 0.75, 0.75), (0.5, 0.5, 0.5), and (0, 0, 0). For the conventional Heusler alloy structure, the first twofirst sub-lattices are occupied by X by atom and and the third by by Y and fourth there are two sub-lattices are occupied X atom the third Y and fourthbybyZZatom. atom. In In total, total, there are 16in atoms in the model, as in shown in 1a. Figure The stoichiometrical 8Mn 4Sn4 alloy not 16 atoms the model, as shown Figure The1a. stoichiometrical Ni8 MnNi does does not undergo 4 Sn 4 alloy undergo aphase martensitic phasefrom transition from the cubic L21tostructure to the non-modulated a martensitic transition the cubic Heusler L21Heusler structure the non-modulated structure [25]. The previous research the Ni8Mn4+xSn4−x alloys have shown that the martensitic Thestructure previous[25]. research about the Ni8 Mnabout 4+x Sn4−x alloys have shown that the martensitic transformation transformation can be observed only under the Mn-rich with ≥ 2. Here, we have focused on the offcan be observed only under the Mn-rich with x ≥ 2. Here, wex have focused on the off-stoichiometrical stoichiometrical Ni8Mn6Sn2 alloy substitution of Sn by Cu. Moreover, in order to calculate the Ni8 Mn6 Sn2 alloy substitution of Sn by Cu. Moreover, in order to calculate the influence of different influence of different Cu content more accurately, the 2 × 1 × 1 supercell approach is used for the Cu content more accurately, the 2 × 1 × 1 supercell approach is used for the calculations, as shown calculations, as shown in Figure 1b. In the model, MnMn represents the Mn atoms in the Mn sites, and in Figure 1b. In the model, MnMn represents the Mn atoms in the Mn sites, and MnSn for represents MnSn represents Mn atoms in the Sn sites. In the case of the model of the cubic structure the Mnaustenitic atoms inphase the Sn sites. In the case of the model of the cubic structure for the austenitic phase of of Ni16Mn12Sn4−xCux alloys (x = 1, 2, 3, and 4), the same size of the model is used except Ni16for Mnsome = 1,being 2, 3, replaced and 4), the same sizeCu of atoms. the model is used except 12 Sn4appropriate −x Cux alloys Sn (x atoms by the doped It is worth noting thatfor thesome appropriate Sn atoms being replaced by the doped Cu atoms. It is worth noting that the simulated simulated structure here is an ordered one, whereas in a real material the Cu and Mn ions on the Sn structure here isbean ordereddistributed. one, whereas inmay a real material theon Cuthe and Mn ionsofonthe thematerial. Sn sitesAll would sites would randomly This have an effect properties calculationsdistributed. have been performed density functional theory, CASTEP All (Cambridge be randomly This maybased haveon anthe effect on the properties of using the material. calculations Sequential Total Energy Package) [26].functional The plane–wave is 400 eV which isSequential found have been performed based on the code density theory,cutoff usingenergy CASTEP (Cambridge to converge the total energy efficiently of the physical models. A (8, 8, 8) Monkhorst–Pack grid is Total Energy Package) code [26]. The plane–wave cutoff energy is 400 eV which is found to converge employed to sample the Brillouin zone. The interaction between ions and electrons is described by the total energy efficiently of the physical models. A (8, 8, 8) Monkhorst–Pack grid is employed ultra-soft pseudopotentials [27]. The spin-polarized generalized gradient approximation is used to to sample the Brillouin zone. The interaction between ions and electrons is described by ultra-soft describe the exchange correlation energy. The tetragonal martensite has been obtained by calculation pseudopotentials [27]. The spin-polarized generalized gradient approximation is used to describe the of the stability of L21 austenite with respect to volume-conserving tetragonal distortions. Then, the exchange correlation energy. The tetragonal martensite has been obtained by calculation of the stability total energy of both austenite and martensite, electronic structure and magnetic moment have been of L2 1 austenite with respect to volume-conserving tetragonal distortions. Then, the total energy of calculated. both austenite and martensite, electronic structure and magnetic moment have been calculated.

(a)

(b)

Figure 1. The unit cell of the cubic structure for the parent of the Ni-Mn-Sn alloy (a) Ni Mn Sn4 alloy; Figure 1. The unit cell of the cubic structure for the parent of the Ni-Mn-Sn alloy (a) Ni8Mn8 4Sn44alloy; (b) Ni Mn 16 12 Sn 4 4alloy. 16Mn 12Sn alloy. (b) Ni

3. Results and Discussion 3. Results and Discussion 12SnSn 4−xCux Cu alloys To determine magnetic groundand andtheoretical theoreticallattice lattice parameter parameter of To determine thethe magnetic ground of Ni Ni1616Mn Mn x alloys 12 4−x (x = 0, 1, 2, 3, and 4) in the austenitic phase, we performed total energy calculations with spin spin (x = 0, 1, 2, 3, and 4) in the austenitic phase, we performed total energy calculations with polarization. considered situations where magnetic moments excess Mn polarization. WeWe considered twotwo situations where thethe magnetic moments ofof thethe excess to to thethe Mn atoms atoms in the Sn sites (denoted as MnSn) are parallel or anti-parallel to the Mn atoms in the Mn subin the Sn sites (denoted as MnSn ) are parallel or anti-parallel to the Mn atoms in the Mn sub-lattice site lattice site (denoted as MnMn). The parallel and antiparallel MnSn-MnMn magnetic interactions are (denoted as MnMn ). The parallel and antiparallel MnSn -MnMn magnetic interactions are denoted as P denoted as P and AP states, respectively. Results for the lattice constants of the Ni16Mn12Sn4−xCux (x = and0,AP states, respectively. Results for the lattice constants of the Ni Mn12 Sn42. Cuxcalculated (x = 0, 1, 2, 3, −xThe 1, 2, 3, and 4) cubic phases for both the AP and P states are plotted16in Figure andenergies 4) cubicof phases for both the AP and P states are plotted in Figure 2. The calculated energies of the the equilibrium lattice constants are −29,898.73 eV and −29,898.80 eV for the AP and P equilibrium lattice constants are − 29,898.73 eV and − 29,898.80 eV for the AP and P states for states for x = 0, respectively. For x = 1, these total energies are −31,280.29 eV and −31,280.41 eV for thex = 0, respectively. x =respectively. 1, these totalInenergies are −31,280.29 eV and 31,280.41 eVenergy for thescale AP and states, AP and P For states, both structures, the AP states are−lower on the and P are respectively. In bothmore structures, the AP lowerthe onequilibrium the energy lattice scale and are thus thus significantly stable than the states P statesare around parameter forsignificantly the case of xstable = 0 and 1. This the magnetic moment of the Mn Sn in Ni16Mn 4−xCu x alloys (x 0= 0, more than the indicates P states that around the equilibrium lattice parameter for12Sn the case of x = and 1.

This indicates that the magnetic moment of the MnSn in Ni16 Mn12 Sn4−x Cux alloys (x = 0, and 1) cubic

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phase is anti-ferromagnetically coupled to the magnetic moment of Mn moment . On theofcontrary, as for the and 1) cubic phase is anti-ferromagnetically coupled to the magneticMn MnMn. On the case contrary, of x = 2, the P states are slightly lower on the energy scale than the AP states with nearly the same as for the case of x = 2, the P states are slightly lower on the energy scale than the AP states energy corresponding to energy the ground state lattice constant ofstate ~6.0 lattice Å. With the further of Cu with nearly the same corresponding to the ground constant of ~6.0increasing Å. With the content, it is worth noting that, in itcontrast the alloys doping, P state of alloys is further increasing of Cu content, is worthto noting that, inwithout contrastCu to the alloys the without Cu doping, evidently moreofstable the AP state equilibrium constant. This result obviously the P state alloysthan is evidently moreatstable than thelattice AP state at equilibrium lattice constant.indicates This obviously indicates proper Cu for Sn converts antiferromagnetic that result substitution of proper Cuthat forsubstitution Sn convertsofantiferromagnetic austenite to ferromagneticaustenite state in the ferromagnetic the increases cubic austenite phase, and hence increasesMeanwhile, the magnetization cubictoaustenite phase,state and in hence the magnetization of austenite. it can beofseen austenite. Meanwhile, it can be seen that the equilibrium lattice constants of Ni 16Mn12Sn4−xCux alloys that the equilibrium lattice constants of Ni16 Mn12 Sn4−x Cux alloys (x = 0, 1, 2, 3, and 4) decrease with (x = 0, 1,Cu 2, 3, and 4) decrease increasing Cu content. the than radius of Cu (1.57 Å) Å), increasing content. Probablywith because the radius of CuProbably (1.57 Å)because is smaller that of Sn (1.72 is smaller than that of Sn (1.72 Å), the addition of Cu causes the unit-cell volume to shrink. the addition of Cu causes the unit-cell volume to shrink. -29896

(a) x=0

a=6.0Å

-29898

(b) x=1 -31278

a=5.95Å Anti-Parallel Parallel

E (eV/ f.u)

-31280

a=5.95Å (c) x=2

-32660

a=5.9Å

(d) x=3

-34042

a=5.85Å

(e) x=4

-35422

5.7

5.8

5.9

6.0

Lattice constant (Å)

6.1

6.2

Figure 2. Equation statesofofNi Ni1616Mn Mn12 12Sn Cux cubic phase (x = 0, 1, 2, 3, and 4) for both parallel and Figure 2. Equation of of states Sn4−x 4−x Cux cubic phase (x = 0, 1, 2, 3, and 4) for both parallel antiparallel magnetic interaction. and antiparallel magnetic interaction.

In order theeffect effect of of Cu transformation in a Cu-doped Ni-Mn-Sn alloy, the In order to to seesee the Cu on onmartensitic martensitic transformation in a Cu-doped Ni-Mn-Sn alloy, total energy as a function of the tetragonal ratio c/a is calculated for both parallel and antiparallel the total energy as a function of the tetragonal ratio c/a is calculated for both parallel and antiparallel magnetic interactions Ni16Mn Mn12Sn 4−xCux alloys (x = 0, 1, 2, 3 and 4). Figure 3 shows the total energies magnetic interactions ofofNi 16 12 Sn4−x Cux alloys (x = 0, 1, 2, 3 and 4). Figure 3 shows the total of Ni 16Mn12Sn4−xCux alloys (x = 0, 2, and 4) with a variation of the tetragonal ratio c/a, because the energies of Ni16 Mn12 Sn4−x Cux alloys (x = 0, 2, and 4) with a variation of the tetragonal ratio c/a, curves of the other specimens are similar. For the alloy without Cu doping as shown in Figure 3a, for because the curves of the other specimens are similar. For the alloy without Cu doping as shown in structures under the P state, Ni16Mn12Sn4 has only one minimum in the E-c/a curve at c/a = 0.98 and Figure 3a, for structures under the P state, Ni16 Mn12 Sn4 has only one minimum in the E-c/a curve the energy difference between c/a = 1.00 is rather small. However, as to the E-c/a curve of structure at c/a = 0.98 and the energy difference between c/a = 1.00 is rather small. However, as to the E-c/a under AP state, the energy is lower compared with the E-c/a curve of structure under P state. This curve of structure APisstate, theenergetically energy is lower with the E-c/a structure indicates that theunder AP state favored for all compared c/a ranges, which means thatcurve the Mnof Sn-MnMn under P state. This indicates that the AP state is favored energetically for all c/a ranges, which means magnetic interactions in both austenite and martensite are antiparallel. Also, it is found that, when that the thestructure MnSn -Mn magnetic interactions both austenite and martensite Also, it is isMn under AP state, the energyin minimum can be observed at c/a = are 1.3, antiparallel. which corresponds found that, the structure under state, the that energy minimum can be observed c/a = 1.3, to the L1when 0 structure of Ni16Mnis 12Sn 4. ThisAP result shows the AP austenite phase is unstableatagainst thecorresponds tetragonal distortion in Ni16Mnof 12Sn undergoes the martensitic transformation fromphase AP is which to the L10 structure Ni4.16ItMn result shows that the AP austenite 12 Sn4 . This austenite phase to AP tetragonal martensite. Due to both austenite and martensite being in the AP unstable against the tetragonal distortion in Ni16 Mn12 Sn4 . It undergoes the martensitic transformation the ΔM between structural phases is small.Due Thisto directly leads to the weak MFIRMT being in fromstate, AP austenite phasethe to two AP tetragonal martensite. both austenite and martensite Ni 16Mn12Sn4 alloy without Cu addition. in the AP state, the ∆M between the two structural phases is small. This directly leads to the weak The addition of Cu, from the change of the E-c/a curves, shows that the energy behaviors along MFIRMT in Ni16 Mn12 Sn4 alloy without Cu addition. the variation of the c/a do not change. However, Cu introduction changes the relative stability of the The addition of Cu, from the change of the E-c/a curves, shows that the energy behaviors along structure. As shown in Figure 3b,c, for the case of x = 2 and 4, we find that the P state is more stable the variation of the c/a do not change. However, Cu introduction changes the relative stability of the than the AP state only around the equilibrium lattice constant for the austenitic phase, as indicated structure. shown in Figure forstate the case of x = 2 and 4, wefavorable find thatwhen the P the state is more stable by theAs blue rectangle. Here,3b,c, the AP becomes energetically martensitic phasethan

the AP state only around the equilibrium lattice constant for the austenitic phase, as indicated by the blue rectangle. Here, the AP state becomes energetically favorable when the martensitic phase transition

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transition appears, which indicates that a magneto-structural martensitic transition occurs. Thus, a

transition appears, which that a magneto-structural occurs. Thus, a appears, which indicates thatindicates a magneto-structural martensiticmartensitic transition transition occurs. Thus, a competition competition between the P and AP states is evidently observed from the E-c/a curve of competition between the isP evidently and AP observed states is evidently observed from E-c/a curve of between the P and AP states from the E-c/a curve of Nithe 16 Mn12 Sn0 Cu4 . In the Ni 16Mn12Sn0Cu4. In the vicinity of c/a = 1, the structure under P state is more stable than that of AP Ni16Mn 12Sn0Cu4. In the vicinity of c/a = 1, the structure under P state is more stable than that of AP vicinity ofThe c/a = 1, theminimum structurecan under P state is than that The energy minimum state. energy be reached reached atmore c/a == 11stable with respect respect to of theAP L21state. 1 structure under P state. state. The energy minimum can be at c/a with to the L2 structure under P state. can be reached at c/a = 1 with respect to the L2 structure under P state. With the deviating from 1, With the the c/a c/a deviating deviating from from 1, 1, the the total total energy energy1 of of structure structure under under PP state state increases. increases.c/a However, for the the With However, for the total energy of structure under P state increases. However, for the structure under AP state, the structure under under AP AP state, state, the the total total energy energy decreases decreases to to the the value value lower lower than than that that of of PP state state and and reaches reachestotal structure energy decreases to the value than that of P state and reaches thephase energy at c/a = 1.4, the energy energy minimum minimum at c/a c/a ==lower 1.4, which which corresponds to the the martensitic martensitic L100 minimum structure under under the the at 1.4, corresponds to phase L1 structure the AP state. Thus, we find that the martensite L1 00structure for each system keeps the AP state, whereas which corresponds to the martensitic phase L1 structure under the AP state. Thus, we find that AP state. Thus, we find that the martensite L10 structure for each system keeps the AP state, whereas the the antiferromagnetic antiferromagnetic austenite has been been tuned to AP ferromagnetic statethe by substitution substitution of proper proper Cu martensite L10 structure austenite for each system keeps the state, whereas antiferromagnetic austenite the has tuned to ferromagnetic state by of Cu for Sn. has for been Sn.tuned to ferromagnetic state by substitution of proper Cu for Sn. -29898 -29898

(a) x=0 (a) x=0

Anti-Parallel Anti-Parallel Parallel Parallel

EE(eV/ (eV/f.u.) f.u.)

-29899 -29899

(b) x=2 (b) x=2 -32661 -32661 -32662 -32662 -35422 -35422 -35423 -35423 -35424 -35424

(c) x=4 (c) x=4 ΔEAM ΔEAM

0.8 0.8

0.9 0.9

1.0 1.0

1.1 1.1

c/a c/a

1.2 1.2

1.3 1.3

1.4 1.4

Figure 3. The total energy difference as a function of the tetragonality, c/a, in the tetragonal structure

Figure 3. The total energy differenceasasaafunction function of the in in thethe tetragonal structure Figure 3. The total energy difference the tetragonality, tetragonality,c/a, c/a, tetragonal structure Mn1212Sn Sn4−x 4−xCux with x = 0, 2, calculated for for both both parallel parallel and and antiparallel antiparallel magnetic magnetic interaction interaction for for Ni Ni1616Mn Cu x with x = calculated calculated for both parallel and antiparallel magnetic interaction x 2, = 0, 2, 16 Mn12 Sn4−x Cux with0, and 4, 4, respectively. respectively. The The vertical vertical line line located located at at c/a c/a == 11denotes denotes the the position position of of the the cubic cubic austenite austenite phase. phase. and and 4, respectively. The vertical line located at c/a = 1 denotes the position of the cubic austenite phase.

A good good deal deal of of previous previous research research has has shown shown the the ferromagnetic ferromagnetic activation activation effect effect of of Co. Co. or or Fe Fe A A good deal the of previous research has shown thefunction ferromagnetic activation effect of Co or elements. From above analysis, we found the same of Cu addition in Ni-Mn-Sn alloy. elements. From the above analysis, we found the same function of Cu addition in Ni-Mn-Sn alloy. Fe elements. Fromthe theconcentration above analysis, we foundofthemagnetic same function of Cu Ni-Mn-Sn Furthermore, dependence moment per addition formula in unit for Furthermore, the concentration dependence of magnetic moment per formula unit for alloy.Ni16Furthermore, the (x concentration dependence of inmagnetic moment per formula unit for Mn 12Sn4−xCux alloys = 0, 1, 2, 3, and 4) is depicted Figure 4. In the case of x = 0 and 1, the Ni16Mn12Sn4−xCux alloys (x = 0, 1, 2, 3, and 4) is depicted in Figure 4. In the case of x = 0 and 1, the Ni16magnetization Mn12 Sn4−x Cudifference alloys (x = 0, 1, 2, 3, and 4) is depicted in Figure 4. In the case of x = 0 and 1, magnetization difference between the austenite and the martensite is very small. With the increasing x between the austenite and the martensite is very small. With the increasing of Cu content, in the case of x = 2, 3, and 4, the magnetic moment of austenite was significantly the magnetization austenite the martensite small.was With the increasing of Cu content, difference in the casebetween of x = 2,the 3, and 4, theand magnetic moment is ofvery austenite significantly enhanced, while the magnetic moment of martensite changed little. Thus, the magnetization of Cu content, in the case of x = 2, 3, and 4, the magnetic moment of austenite was significantly enhanced, while the magnetic moment of martensite changed little. Thus, the magnetization difference between the austenite and the martensite is enlarged evidently. This result is consistent enhanced, while the magnetic moment of martensite changed little. Thus, the magnetization difference difference between the austenite and the martensite is enlarged evidently. This result is consistent with the conclusion of the E-c/a curves. This should be attributed to a change of magnetic structure between theconclusion austenite of and martensite is should enlarged evidently.toThis result consistent with the with the thethe E-c/a curves. This be attributed a change of is magnetic structure of austenite austenite caused caused by by the the substitution substitution of of proper proper Cu for Ni, Ni, which which turns the Mn-Mn Mn-Mn interaction interaction from from of for the conclusion of the E-c/a curves. This should beCuattributed to aturns change of magnetic structure of anti-ferromagnetism to ferromagnetism. Such a high magnetization difference provides a strong anti-ferromagnetism ferromagnetism. Such Cu a high magnetization difference provides a strongfrom austenite caused by thetosubstitution of proper for Ni, which turns the Mn-Mn interaction driving force force for for magnetic-field-induced magnetic-field-induced transformation. transformation. Thus, Thus, aa large large ΔM ΔM can be be obtained obtained by by Cu Cu driving anti-ferromagnetism to ferromagnetism. Such a high magnetization differencecan provides a strong driving addition in the Ni-Mn-Sn alloy system. We finished the first step in designing the new material with in the Ni-Mn-Sn alloy transformation. system. We finished the afirst step in designing the newby material with in forceaddition for magnetic-field-induced Thus, large ∆M can be obtained Cu addition large ΔM. aa large ΔM.

the Ni-Mn-Sn alloy system. We finished the first step in designing the new material with a large ∆M. Magnetic Magneticmoment moment(μB/f.u.) (μB/f.u.)

7.0 7.0

Martensite Martensite Austensite Austensite

6.8 6.8 6.6 6.6 6.4 6.4 2.4 2.4 2.2 2.2 2.0 2.0 1.8 1.8 1.6 1.6 0 0

1

2

3

1 3 Cu doping2 content (x) Cu doping content (x)

4 4

Figure 4. Concentration dependence of magnetic moment per formula unit for Ni16 Mn12 Sn4−x Cux alloys (x = 0, 1, 2, 3, and 4).

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Figure 4. Concentration dependence of magnetic moment per formula unit for Ni16Mn12Sn4−xCux alloys (x = 0, 1, 2, 3, and 4).

As ever, researchers have pointed out that the total energy difference between the austenite L21 structureAs and theresearchers tetragonalhave martensite L10 that structure (∆E EAP(Cub.) − EAP(Tetra.) can be used AM =difference ever, pointed out the total energy between the )austenite L21 to predict the possible transformation and to estimate MT temperature, structure and themartensitic tetragonal martensite L10 structure (ΔEAM = Ethe AP(Cub.) −E AP(Tetra.)) can beapproximately used to predict[28]. the possible martensitic and to estimate the MT temperature, approximately [28]. Generally, the larger energytransformation difference implies a higher MT temperature. In order to clarify the effect Generally, energytransformation, difference impliesthe a higher order to clarify of Cu element the on larger martensitic ∆EAMMT (astemperature. indicated byInthe black arrowthe in effect Figure 4) of Cu element on martensitic transformation, the ΔEAM (asfor indicated the black arrow in Figure 4) is calculated. Figure 5 shows the ∆EAM per formula unit Ni16 Mnby 12 Sn4−x Cux alloys (x = 0, 1, 2, 3, is calculated. Figure 5 shows the ΔE AM per formula unit for Ni16Mn12Sn4−xCux alloys (x = 0, 1, 2, 3, and and 4). Firstly, we can see that ∆EAM increases markedly with a little amount of Cu doping. In the case we can see that ΔEAM increases markedly with a little amount of Cu doping. In the case of of x 4). = 2,Firstly, the ∆E AM increases to the maximum. As x further increases to 3 and 4, the ∆EAM gradually x = 2, the ΔEAM increases to the maximum. As x further increases to 3 and 4, the ΔEAM gradually decreases, which is also higher than that of alloy without Cu addition. Thus, due to a larger ∆EAM decreases, which is also higher than that of alloy without Cu addition. Thus, due to a larger ΔEAM corresponds to a higher TM temperature, the results show that the TM temperature first increases and corresponds to a higher TM temperature, the results show that the TM temperature first increases thenand decreases with thewith increasing of Cu content. ProperProper substitution of Cuoffor the MT then decreases the increasing of Cu content. substitution CuSn forcan Sn increase can increase temperature. Now, we finished the second step to design a new material with high MT temperature. the MT temperature. Now, we finished the second step to design a new material with high MT These results provide forprovide the design of high-temperature shape memory temperature. Theseorigin results origin for the design of magnetic high-temperature magneticalloys shapewith low memory magneticalloys field.with low magnetic field. 1.6

ΔEAM （eV/f.u.）

1.4

1.2

1.0

0.8

0.6

0.4 0

1

2

3

4

Cu doping content (x)

Figure 5. The energy difference between austenite L21 structure and the tetragonal martensite L10 Figure 5. The energy difference between austenite L21 structure and the tetragonal martensite L10 structure (ΔEAM) per formula unit for Ni16Mn12Sn4−xCux alloys (x = 0, 1, 2, 3, and 4). structure (∆EAM ) per formula unit for Ni16 Mn12 Sn4−x Cux alloys (x = 0, 1, 2, 3, and 4).

In practice, elevating the Curie temperature (Tc) while keeping the martensitic transformation In practice, elevating the Curie Since temperature (Tc ) while keeping thethe martensitic transformation temperature high is essential. Ni-Mn-Sn-Cu alloys satisfy Stone condition of temperature high is essential. Ni-Mn-Sn-Cu alloys satisfytothe condition of ferromagnetism ferromagnetism [29], the TSince c can be taken to be proportional theStone total energy difference between the[29], and ferromagnetictostate (ΔEtotenergy ) [30]. According the Heisenberg model andand the the the Tparamagnetic to the be proportional the total differencetobetween the paramagnetic c can be taken molecular field linkAccording between ΔEto tot and c is given bymodel and the molecular field theory, ferromagnetic statetheory, (∆Etot )the [30]. the T Heisenberg

the link between ∆Etot and Tc is given by

∆

=−

,

(2)

where represents the ratio M/M0 of the magnetic M at T ≠ 0 K and the equilibrium (2) ∆Etot = −kb Tmoment c ξ, magnetic moment M0 at T = 0 K. A number of researchers predict the Tc by using the Equation (2). Though the predicted values have of some experimental values, only where ξ represents the ratio M/M thedeviations magneticcompared moment with M atthe T 6= 0 K and the equilibrium 0 from the total energy difference results, we can still draw the conclusion that the Tc can be taken to magnetic moment M0 at T = 0 K. A number of researchers predict the Tc by using the Equation (2). be proportional to the ΔEtot. In order to investigate the effect of Cu introduction on the Tc, the total Though the predicted values have some deviations compared with the experimental values, only from energies of both ferromagnetic and paramagnetic cubic phase of Ni16Mn12Sn4−xCux alloys (x = 0, 1, 2, the total we can results still draw conclusion that the Tc can be taken to be 3, andenergy 4) weredifference calculated.results, The calculated showthe that the total energy of paramagnetic cubic proportional to thehigher ∆Etotthan . In order the one effect of Cu introduction studied, on the Twhich c , theistotal phase is much that ofto theinvestigate ferromagnetic at all the compositions energies of both ferromagnetic and paramagnetic cubic phase of Ni Mn Sn Cu alloys (x = 0, 1, x 16 12 phase. 4−x Figure consistent with the fact that the paramagnetic cubic is the high-temperature 6 shows 2, 3, the andtotal 4) were calculated. calculated results showaustenite that the total energy of paramagnetic cubic energy differenceThe between the paramagnetic and ferromagnetic austenite per phase is much that ofx the ferromagnetic one 4). at Obviously, all the compositions studied, formula unithigher for Ni16than Mn12Sn 4−xCu alloys (x = 0, 1, 2, 3, and it can be seen that thewhich ΔEtot is linearlywith decreases with of Cu content. indicates thatphase. Tc of Ni 16Mn126 Snshows 4−xCux the consistent the fact thatthe theincrease paramagnetic cubic isThis the result high-temperature Figure alloys decreases with the Cu addition. Though we find that Cu doping shift the MT temperature to total energy difference between the paramagnetic austenite and ferromagnetic austenite per formula

unit for Ni16 Mn12 Sn4−x Cux alloys (x = 0, 1, 2, 3, and 4). Obviously, it can be seen that the ∆Etot linearly decreases with the increase of Cu content. This result indicates that Tc of Ni16 Mn12 Sn4−x Cux alloys decreases with the Cu addition. Though we find that Cu doping shift the MT temperature to

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higher temperature, thethe Tc Tchanges ininthe Magnetic-field-induced martensitic higher temperature, c changes theopposite opposite directions. directions. Magnetic-field-induced martensitic transformation indicates a transformation sequence of ferromagnetic martensite, ferromagnetic transformation indicates a transformation sequence ferromagnetic martensite, ferromagnetic austenite and paramagnetic austenite upon upon heating. The TcThe of austenite is higheristhan MT than temperature austenite and paramagnetic austenite heating. Tc of austenite higher MT temperature is essential to using Magnetic-field-induced martensitic transformation. it is to is essential to using Magnetic-field-induced martensitic transformation. Therefore,Therefore, it is necessary necessary to study how to synchronously Tc and MT temperature in the further studies. study how to synchronously increase the Tcincrease and MTthe temperature in the further studies.

ΔEtot（eV/f.u.）

1.9

1.8

1.7

1.6 0

1

2

3

4

Cu doping content (x)

Figure 6. The energy difference betweenthe theparamagnetic paramagnetic austensite austenite per per Figure 6. The energy difference between austensiteand andferromagnetic ferromagnetic austenite formula unit for Ni16Mn12Sn4−xCux alloys (x = 0, 1, 2, 3, and 4). formula unit for Ni16 Mn12 Sn4−x Cux alloys (x = 0, 1, 2, 3, and 4).

In order to have a further insightinto intothe theelectronic electronic structure, properties, andand the the In order to have a further insight structure,the themagnetic magnetic properties, martensitic transformation of Ni16Mn12Sn4−xCux alloys (x = 0, 1, and 2), we investigated the total martensitic transformation of Ni16 Mn12 Sn4−x Cux alloys (x = 0, 1, and 2), we investigated the total density of states (DOS) for both the austenite (as indicated by the black line in Figure 7) and density of states (DOS) for both the austenite (as indicated by the black line in Figure 7) and martensite martensite phases (as indicated by the red line in Figure 7). It can be seen from Figure 7 that, in the phases (as indicated by the red line in Figure 7). It can be seen from Figure 7 that, in the down-spin DOS down-spin DOS of the austenite phase, there exists a sharp DOS peak at the Fermi level, indicating of thethe austenite therebetween exists a the sharp DOSinpeak at the Fermi level, indicating the bonding character bondingphase, character atoms Ni16Mn 12Sn4−xCux around the Fermi level, and this is between the atoms in Ni16for Mnthe the Fermi level, and apparently responsible 12 Sn 4−x Cux around apparently responsible martensitic transformation. However, the this DOSispeak at the Fermi level for the martensitic transformation. However, the DOS peak at the Fermi level (E ) almost disappears (Ef) almost disappears when the transition of the tetragonal martensite phase fto/from the cubic whenaustenite the transition of theplace, tetragonal martensite phase(expanded to/from the austenite takes place, phase takes as seen from the inset the cubic regions near Ef).phase This behavior suggests DOS in the vicinity of the Enear f is anEimportant factor that triggers that the occurrence of the as seen fromthat the the inset (expanded the regions suggests the DOS in f ). This behavior martensitic [31]. vicinity of the Etransformation is an important factor that triggers the occurrence of martensitic transformation [31]. f 60

Austenite Martensite

40

0

20 0 -20 -40

(a) x=0

DOS (States/eV)

60 -60 40 0

20 0 -20

(b) x=1

-40 60 40

0

20 0 -20 -40

(c) x=2

-60 -8

-6

-4

-2

0

2

Energy (eV)

Figure 7. The total dos plots for the Ni16Mn12Sn4−xCux (x = 0, 1, 2) for both cubic austenite and tetragonal

Figure 7. The total dos plots for the Ni16 Mn12 Sn4−x Cux (x = 0, 1, 2) for both cubic austenite martensite phase. Each phase is consisting of the up-spin and sown-spin channels. The vertical dashed and tetragonal martensite phase. Each phase is consisting of the up-spin and sown-spin channels. The vertical dashed line is chosen as Fermi level Ef . The regions near the Fermi level are shown in an expanded scale in the inset.

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the inset.

TheThe aforementioned thatMn-Mn Mn-Mn magnetic interaction the phase cubic of phase aforementionedresults results suggest suggest that magnetic interaction in theincubic Ni- of Ni-Mn-Sn alloy has been turned from anti-ferromagnetism to ferromagnetism by the substitution Mn-Sn alloy has been turned from anti-ferromagnetism to ferromagnetism by the substitution of Cu of and magnetostructural transformation Cu for Sn. To To gain gain insight insightinto intothe theorigin originofofmagnetic magneticproperties properties and magnetostructural transformation in Ni-Mn-Sn-Cu, have investigatedthe theelectronic electronic structure. the trend of each change in Ni-Mn-Sn-Cu, wewe have investigated structure.Also, Also,because because the trend of each change in other specimens similartotothe thecase case of of xx = = 2, case of of x =x0=and 2 for in other specimens is is similar 2, here here we weonly onlychoose choosethe the case 0 and 2 for comparison. Figure 8 illustrates the DOS for the cubic and martensitic phase of Ni 16Mn12Sn4−xCux comparison. Figure 8 illustrates the DOS for the cubic and martensitic phase of Ni16 Mn12 Sn4−x Cux alloys 0, and 2).the In case the case x =Mn 0, 3d Mnstate 3d state of majority minority are split alloys (x =(x0,=and 2). In of x of = 0, of majority and and minority spinspin are split withwith respect respect to the Fermi level. This distribution makes Mn mostly responsible for the magnetization. to the Fermi level. This distribution makes Mn mostly responsible for the magnetization. Moreover, Moreover, it can be noted that the magnetic moment of MnSn is anti-parallel to that of MnMn (as it can be noted that the magnetic moment of MnSn is anti-parallel to that of MnMn (as indicated by the indicated by the arrow). Ni 3d states have similar distribution in the majority and minority spin, arrow). Ni 3d states have similar distribution in the majority and minority spin, resulting in a rather resulting in a rather small magnetization. With Cu addition, the MnMn 3d state is similar to that of small magnetization. With Cu addition, the MnMnstate 3d state is similar to that of before. However, before. However, MnSn 3d state is altered. MnSn 3d of majority spin is mostly below the Fermi MnSn 3d state is altered. Mn 3d state of majority spin is mostly below Fermi moment level, while that of level, while that of minoritySnspin is mostly above the Fermi level. Thus, thethe magnetic of Mn Sn minority spin is mostly above the Fermi level. Thus, the magnetic moment of Mn is parallel to that Sn is parallel to that of MnMn, giving rise to the enhancement of the total magnetic moment. This is in of Mn risethe to the enhancement of the This total result magnetic moment. This in agreement with the Mn , giving agreement with aforementioned results. further clarifies theischange of magnetic aforementioned results. This result further clarifies the change of magnetic moment of Ni-Mn-Sn-Cu. moment of Ni-Mn-Sn-Cu. 60 30 0 -30 -60 2

DO S (States/eV)

(a) x=0

Austenite Martensite

Total Up

0 MnMn 3d

-2 0 -2

Down

MnSn 3d

2 0 -2

Ni 3d

-8

-6

-4

-2

0

2

Energy (eV) 60 30 0 -30

Austenite Martensite

Total

2

DOS (States/eV)

(b) x=2

Up

0 MnMn 3d

2 -2

Up

0 Down

MnSn 3d

-2 2 0 -2

Ni 3d

-8

-6

-4

-2

0

2

Energy (eV)

Figure 8. The partial density of states (DOS) plots for Ni16Mn12Sn4−xCux alloys in both cubic austenite

Figure 8. The partial density of states (DOS) plots for Ni16 Mn12 Sn4−x Cux alloys in both cubic austenite and tetragonal martensite phase, (a) x = 0; and (b) x = 2. The vertical dashed line is chosen as the Fermi and tetragonal martensite phase, (a) x = 0; and (b) x = 2. The vertical dashed line is chosen as the Fermi level Ef. level Ef .

4. Conclusions In summary, in order to design the new magnetic shape memory alloy material which can show a large ∆M and a higher MT temperature, first principle electronic structure calculations were

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employed. We have studied the total energy, the magnetic properties, and the magnetic-field-induced martensitic transformation for Ni16 Mn12 Sn4−x Cux alloys (x = 0, 1, 2, 3, and 4). The equilibrium equation of state results shows that antiferromagnetic cubic austenite becomes ferromagnetic cubic austenite in Ni-Mn-Sn alloys by Cu addition. Especially in the case of x = 2, drastic changes in the magnetic properties are expected to occur between the ferromagnetic austensite (6.74 µB/f.u.) and the antiferromagnetic martensite phase (1.98 µB/f.u.). This directly leads to the large ∆M and enhances the MFIRMT. Meanwhile, the martensitic transformation shifts to the higher temperature, owing to the energy difference between the austenite L21 structure, and the tetragonal martensite L10 structure increases by Cu doping. The calculations mentioned above may help in gaining an insight into the doping of Cu behavior in Ni-Mn-Sn and provide guidance to the new material design. Furthermore, the total energy difference between paramagnetic and ferromagnetic austenite indicates the decrease in Tc with Cu addition. We expect that the restriction would be resolved in the further studies. Acknowledgments: The authors acknowledge the supports of National Natural Science Foundation of China (Grant Nos. 51471064, 51301054 and 50901026); and Program for Youth Academic Backbone in Heilongjiang Provincial University (Grant No. 1251G022); and Scientific Research Fund of Heilongjiang Provincial Education Department (No. 12541138). Author Contributions: Kun Zhang conceived and designed the experiments; Xiaohua Tian, Kun Zhang and Wenbin Zhao performed the experiments; Changlong Tan, Erjun Guo, and Xiaohua Tian analyzed the data; Kun Zhang, Changlong Tan, Xiaohua Tian, and Wei Cai wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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