Trans. Nonferrous Met. Soc. China 24(2014) 1053-1057

Effect of Co substitution on magnetic properties of Ni-Mn-Sn magnetic shape memory alloys

Jia-mu CAO¹, Chang-long TAN¹, Xiao-hua TIAN¹, Qin-ci LI¹, Er-jun GUO², Li-ping WANG², Yi-jiang CAO¹

1. School of Applied Science, Harbin University of Science and Technology, Harbin 150080, China;

2. School of Materials Science and Engineering, Harbin University of Science and Technology, Harbin 150080, China

Received 27 March 2013; accepted 15 October 2013

Abstract: The effect of Co substitution on magnetic properties of Ni-Mn-Sn shape memory alloy was revealed by first-principles calculations. Large magnetization difference in Ni-Mn-Sn alloy obtained by addition of Co arises from enhancement of magnetization of austenite due to change of Mn-Mn interaction from anti-ferromagnetism to ferromagnetism. Total energy difference between paramagnetic and ferromagnetic austenite plays an important role in magnetic transition of Ni-Co-Mn-Sn. The altered Mn 3d states due to Co substitution give rise to difference in magnetic properties.

Key words: ferromagnetic shape memory alloys; Ni-Mn-Sn; first-principles calculation; magnetic properties

1 Introduction

Off-stoichiometric Ni-Mn-Sn ferromagnetic shape memory alloys have attracted great interest due to the observations of magnetic field-induced reverse martensitic transformation [1-4]. The magnetization in martensite phase of these alloys is smaller than that in the austenite one. Ni-Mn-Sn alloys undergo martensitic transformation in a magnetically ordered state, and the interplay between the structure and magnetism gives rise to great interesting effects such as inverse magnetocaloric effect [5-8], giant strain due to field-induced reverse martensitic transformation [9,10], and giant magnetoresistivity [11,12]. These make Ni-Mn-Sn alloys good candidates for multifunctional application. A large magnetization difference between the austenite and martensite phases is of great importance to develop higher performance both in magnetoelastic properties and in magnetocaloric effect, due to the improved possibility of driving structural transformation by magnetic fields. The magnetic properties of the austenite and martensite phases in the Ni-Mn-Sn alloys have been intensively studied by many researchers [13-18]. It has been reported that the substitution of Co for Ni in Ni-Mn-Sn alloys is an effective way to increase the difference in magnetization between austenite and martensite phases [15,16]. Recently, the magnetic properties of Ni-Mn-Sn and Ni-Co-Mn-Sn alloys have been studied by neutron powder diffractions and it is found that the ferromagnetic enhancement in Ni-Co-Mn-Sn occurs as result of the change in the magnetic structure due to the substitution of Co [16]. So far, although Co substitution has prominent effects on magnetic properties and magnetic field-induced reverse martensitic transformation, the mechanism for them is still unclear.

In this work, we revealed the effect of Co substitution on magnetic properties of Ni_2-xCo_xMn_1+ySn_1-y from the electronic structure point of view by first-principles calculations. The results provide the theoretical data and directions for developing high- performance metamagnetic shape memory alloy in Ni-Mn-based Heusler alloys system.

2 Calculational methods

First-principles calculations have been performed based on the density functional theory, using CASTEP code [19]. The interaction between ions and electrons is described by ultra-soft pseudo-potentials [20]. The spin-polarized generalized gradient approximation was used to describe the exchange correlation energy. The plane-wave cutoff energy was 400 eV and a (8, 8, 8) Monkhorst-Pack grid was employed to sample the Brillouin zone. For the cubic L2₁ structures of Ni₂Mn_1+ySn_1-y (y=0, 0.25, 0.5), 16-atom unit cell is built with appropriate Sn atoms replaced by Mn atoms. In the case of Co substitution for Ni, the cubic structure of Ni_2-xCo_xMn_1+ySn_1-y (x=0, 0.25, 0.5; y=0, 0.25, 0.5) is built with appropriate Ni atoms replaced by Co atoms on the basis of Ni₂Mn_1+ySn_1-y structure.

3 Results and discussion

For the cubic phase of Ni₂MnSn, the magnetic interaction between Mn atoms is ferromagnetic. However, in the case of Ni₂Mn_1+ySn_1-y and the corresponding alloys with Co substitution for Ni, the origin of magnetic interaction is still open. Thus, we first calculated the equation of states of Ni_2-xCo_xMn_1+ySn_1-y cubic phases, taking into account two situations that magnetic moment of excess Mn at the Sn sites (denoted as Mn_Sn) is parallel or anti-parallel to that of Mn at the Mn sites (denoted as Mn_Mn). For both situations, it is noted that, if starting with parallel or anti-parallel Mn-Mn magnetic coupling, the spin-polarized self-consistent calculations converge to the solutions without changing the initial magnetic orientation. Hereafter, the parallel and anti-parallel Mn-Mn magnetic interactions are denoted as P and AP states, respectively.

Figure 1 shows the curves of total energy E versus lattice constants for Ni_2-xCo_xMn_1+ySn_1-y (x=0, 0.25, 0.5; y=0.25) cubic phases. From Fig. 1(a), it is seen that around equilibrium lattice constant, the AP state of Ni₂Mn_1+ySn_1-y (y=0.25) is more stable than its P state. The latter becomes more stable only if the lattice constant is expanded. This indicates that the magnetic moment of the Mn_Sn in Ni₂Mn_1+ySn_1-y cubic phase is anti-ferromagnetically coupled to the magnetic moment of Mn_Mn. Thus, it is expected that with excess Mn substitution for Sn, the total magnetic moment decreases, which is agreement with the experiments [18]. However, in the similar Ni-Mn-In metamagnetic shape memory alloy, the magnetic moment per formula increases with increasing Mn content. Our previous studies show that this opposite concentration dependence is attributed to the different coupling conditions of magnetic moment [21]. In the case of Ni-Mn-In alloys, the Mn-Mn interaction between the Mn atoms at Mn and In sites is suggested to prefer the ferromagnetic coupling. In contrast to the case of Ni₂Mn_1+ySn_1-y (y=0.25), when substitution of Co for Ni with x=0.25, the P state of Ni_2-xCo_xMn_1+ySn_1-y (x=0.25, y=0.25) is slightly more stable than the AP state at equilibrium lattice constant, whereas the latter is more stable when the system is contracted, as shown in Fig. 1(b). However, the energy difference between two states is much small. Figure 1(c) shows that with the further substitution of Co for Ni (x=0.5), the P state of Ni_2-xCo_xMn_1+ySn_1-y (x=0.5, y=0.25) obviously becomes more stable than the AP state at equilibrium lattice constant. Moreover, for Ni_2-xCo_xMn_1+ySn_1-y with y=0.5, the effect of Co substitution for Ni on magnetic interactions is similar to that with y=0.25. Therefore, it is suggested that for Ni_2-xCo_xMn_1+ySn_1-y with x>0.25, the P state would be more stable than AP state. This suggests that Mn-Mn magnetic interaction in the cubic phases of Ni-Mn-Sn has been turned from anti-ferromagnetism to ferromagnetism by substitution Co for Ni.

Fig. 1 Equation of states of Ni_2-xCo_xMn_1+ySn_1-y (x=0, 0.25, 0.5; y=0.25) cubic phases for both parallel and anti-parallel magnetic interactions

The concentration dependences of the magnetic moment per formula unit for Ni₂Mn_1+ySn_1-y and Ni_2-xCo_xMn_1+ySn_1-y (x=0.25) cubic phases are shown in Fig. 2. It can be seen that the magnetic moment decreases with increasing Mn content (y) in the Ni₂Mn_1+ySn_1-y alloys, while increases in the Ni_2-xCo_xMn_1+ySn_1-y (x=0.25). This suggests that the magnetization of the high temperature cubic phase in Ni₂Mn_1+ySn_1-y is enhanced by the substitution of Co for Ni. Furthermore, we have performed the geometrization for Ni_2-xCo_xMn_1+ySn_1-y, and found that the cubic phase is energetically favorable for Ni₂MnSn. Interestingly, the cubic phase is unstable against the tetragonal distortion for Ni_2-xCo_xMn_1+ySn_1-y (y=0.25, 0.5) and undergoes the martensitic transformation to form tetragonal martensite. It should be noted that both in the martensite of Ni₂Mn_1+ySn_1-y and Ni_2-xCo_xMn_1+ySn_1-y, the magnetic moment of Mn_Sn is always anti-parallel to that of Mn_Mn. The anti-parallel arrangement of the Mn_Sn-Mn_Mn magnetic moment causes the decrease of total magnetization of martensite.

Fig. 2 Concentration dependence of magnetic moment per formula unit for Ni₂Mn_1+ySn_1-y and Ni_2-xCo_xMn_1+ySn_1-y (x=0.25)

It can be seen from Figs. 1 and 2 that the large magnetization difference in Ni-Mn-Sn obtained by addition of Co arises from substantial enhancement of the magnetization of the high-temperature cubic phase. This can be attributed to a change of magnetic structure caused by the substitution of Co for Ni, which turns the Mn-Mn interaction from anti-ferromagnetism to ferromagnetism. Therefore, the Co atoms work as a ferromagnetic activator. Such a high magnetization difference provides a strong driving force for magnetic field-induced transformation, making this material a promising candidate for magnetic actuation applications. Actually, the ferromagnetic activation effect of Co has also been verified by our theoretical calculation in other Heusler alloys system such as Ni-Mn-Sb and Mn-rich Ni-Mn-Ga. Thus, the substitution of Co for Ni is a general way to enhance the magnetic field-induced transformation in Ni-Mn-X (X=Ga, Sn and Sb) alloys, which is very useful for the application and material design of metamagnetic shape memory alloy.

From the application point of view, the Curie temperature (T_c) is very important since it limits the operational temperature range of Ni-Mn-Sn-based alloys. In order to investigate the effect of Co substitution for Ni on T_c, the total energies of both ferromagnetic and paramagnetic cubic phases of Ni₂Mn_1+ySn_1-y and Ni_2-xCo_xMn_1+ySn_1-y (x=0.25) alloys were calculated. It is found that the total energy of paramagnetic cubic phase is much higher than that of the ferromagnetic one at all the compositions studied, which is consistent with the fact that the paramagnetic cubic phase is the high-temperature phase. According to the Stoner theory, the total energy difference between the paramagnetic and the ferromagnetic state, △E, can give an estimation of T_c. The link between △E and T_c is given by △E =-k_bT_cξ, where ξ represents the ratio of M to M₀ of the magnetic moment M at T≠0 K and the equilibrium magnetic moment M₀ at 0 K [22]. Our studies show that the total energy difference increases by about 140 meV when Ni is substituted by 6.25% Co (mole fraction; x=0.25) for Ni_2-xCo_xMn_1+ySn_1-y compared with Ni₂Mn_1+ySn_1-y. Even the Stoner theory cannot be applied to describing high-temperature magnetic properties, T_c of Ni_2-xCo_xMn_1+ySn_1-y alloys increases with the Co content, which is in fair agreement with the experimental observations [15]. The reason for increase of T_c should be attributed to the enhanced ferromagnetic exchange due to Co substitution for Ni.

To gain further insight into the origin of effect of Co substitution on magnetic properties in the Ni-Mn-Sn, the electronic structure of Ni₂Mn_1+ySn_1-y (y=0.25) and Ni_2-xCo_xMn_1+ySn_1-y (x=0.25, y=0.25) was studied as an example. Figure 3(a) illustrates the density of states (DOS) for the cubic phase of Ni₂Mn_1+ySn_1-y (y=0.25). Mn 3d states of majority and minority spin are split with respect to the Fermi level. This distribution makes Mn mostly responsible for the magnetization. Moreover, it can be noted that the magnetic moment of Mn_Sn is anti-parallel to that of Mn_Mn. Ni 3d states have similar distribution in the majority and minority spin, resulting in a rather small magnetization. Figure 3(b) shows the DOS for cubic phase of Ni_2-xCo_xMn_1+ySn_1-y (x=0.25, y=0.25). The Mn_Mn 3d state is similar to that of Ni₂Mn_1+ySn_1-y. But, when the cubic Ni₂Mn_1+ySn_1-y is doped by Co, Mn_Sn 3d state is altered. Mn_Sn 3d state of majority spin is mostly below the Fermi level, while that of minority spin is mostly above the Fermi level. Thus, the magnetic moment of Mn_Sn is parallel to that of Mn_Mn, giving rise to the enhancement of the total magnetic moment. This is attributed to that exchange interaction of Co-Mn is several times larger that of Ni-Mn [15].

Fig. 3 DOS in cubic phases of Ni₂Mn_1+ySn_1-y (y=0.25) (a) and Ni_2-xCo_xMn_1+ySn_1-y (x=0.25, y=0.25) (b) (The Fermi level is indicated by vertical line at 0)

4 Conclusions

1) The effect of Co substitution on magnetic properties of Ni_2-xCo_xMn_1+ySn_1-y shape memory alloy is revealed by first-principles calculations. The large magnetization difference in Ni-Mn-Sn obtained by addition of Co arises from substantial enhancement of the magnetization of the high-temperature cubic phase. This can be attributed to a change of magnetic structure caused by the substitution of Co for Ni, which turns the Mn-Mn interaction from anti-ferromagnetism to ferromagnetism.

2) The total energy difference between paramagnetic and ferromagnetic austenite indicates the increase in T_c with Co content.

3) The altered 3d state of Mn at the Sn site due to Co substitution plays an important role in establishing the magnetic properties.

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Co掺杂对Ni-Mn-Sn铁磁形状记忆合金磁性质的影响

曹伽牧¹，谭昌龙¹，田晓华¹，李钦赐¹，郭二军²，王丽萍²，曹一江¹

1. 哈尔滨理工大学 应用科学学院，哈尔滨 150080；

2. 哈尔滨理工大学 材料科学与工程学院，哈尔滨 150080

摘  要：采用第一性原理计算揭示了Co掺杂对Ni-Mn-Sn形状记忆合金磁性质的影响。结果表明，掺杂Co使Ni-Mn-Sn合金中两相饱和磁化强度差增大的原因在于其奥氏体的Mn-Mn磁交换作用由反铁磁性转变为铁磁性。奥氏体的顺磁态与铁磁态的能量差对Ni-Co-Mn-Sn的磁转变有重要影响。此外，Co掺杂对磁性的影响与Mn 3d态的改变有关。

关键词：磁性形状记忆合金；Ni-Mn-Sn；第一性原理计算；磁性质

(Edited by Xiang-qun LI)

Foundation item: Project (1253-NCET-009) supported by Program for New Century Excellent Talents in Heilongjiang Provincial University, China; Project (1251G022) supported by Program for Youth Academic Backbone in Heilongjiang Provincial University, China; Projects (50901026, 51301054) supported by the National Natural Science Foundation of China

Corresponding author: Chang-long TAN; Tel: +86-451-86390728; E-mail: changlongtan@hrbust.edu.cn

DOI: 10.1016/S1003-6326(14)63161-7