Temperature Dependences of the Electrical Resistivity on the Heusler Alloy System Ni 2 MnGa 1 – x Fe x

Temperature dependences of the electrical resistivity have been measured on the Heusler alloy system Ni2MnGa1–xFex. The phase diagram of Ni2MnGa1–xFex was constructed on the basis of the experimental results. The structural and magnetic transition temperatures are consistent with those previously determined by magnetic measurements. The changes of the electrical resistivity at the martensitic transition temperature, ∆ρ, were studied as a function of Fe concentration x. The ∆ρ abruptly increased in the concentration range between x = 0.15 and 0.20. The magnetostructural transitions were observed at x = 0.275, 0.30, and 0.35.


Introduction
Recently, Ni-Mn based ferromagnetic shape memory alloys (FSMAs) with full Heusler-type structure have attracted much attention because of their potential applications in smart materials. These Heusler alloys exhibit a giant field-induced shape memory effect, large magnetoresistance, and large magnetocaloric effect [1][2][3][4][5][6]. Among FSMAs with a Heusler-type (L21-type) structure, the stoichiometric compound Ni2MnGa has been the most studied. Ni2MnGa orders ferromagnetically with the Curie temperature TC = 365 K [7]. On cooling, the premartensitic phase appears below Tp = 260 K. With further decrease of temperature, Ni2MnGa undergoes a first-order martensitic transition at TM = 200 K [7]. Recently, Singh et al. performed a high-resolution synchrotron X-ray powder diffraction study for Ni2MnGa and discussed the incommensurate nature of the modulate structures of the premartensitic (intermediate) and martensitic phases [8,9]. The ferromagnetic state remains below TM. The spontaneous magnetization of Ni2MnGa just below TM is larger than that just above TM.
The TC, Tp, and TM of Ni2MnGa can be tuned in a wide range by doping with a fourth element. For Ni2Mn1−xCuxGa (0 ≤ x ≤ 0.4) [10], TM increases with increasing the concentration x, while TC decreases with x. With further increase of x, the magnetostructural transitions between the paramagnetic austenite (Para-A) and the ferromagnetic martensite (Ferro-M) phase occur in limited concentration range. The characteristics of the phase diagram of Ni2Mn1−xCuxGa (0 ≤ x ≤ 0.4) are closely similar to those of Ni2+xMn1−xGa (0 ≤ x ≤ 0.36) [11,12]. The effect of the substitution of Fe and Co atoms in Ni-Mn-Ga alloy was studied [13,14]. Recently, Hayasaka et al. determined the phase diagram in the temperature-concentration plane of Ni2MnGa1−xFex (0 ≤ x ≤ 0.40) [15]. The characteristics of the determined phase diagram of Ni2MnGa1−xFex (0 ≤ x ≤ 0.40) are very similar to those of Ni2+xMn1−xGa (0 ≤ x ≤ 0.36) [11,12] and Ni2Mn1−xCuxGa (0 ≤ x ≤ 0.4) [10], where the magnetostructural transition between Para-A and Ferro-M occurs. However the microscopic understanding of the robust phase diagrams observed in Ni2+xMn1−xGa, Ni2Mn1−xCuxGa, and Ni2MnGa1−xFex is not clear in this stage. Furthermore, there is only a small amount of information about the electric properties of the Cu and Fe element doped Ni2MnGa. In this paper, the electric properties are examined experimentally to gain deeper insight into the electronic properties of Ni2MnGa1−xFex alloys.

Experimental Procedures
The experiments were made on the same Ni2MnGa1-xFex (0 ≤ x ≤ 0.40) alloys that were used in our previous studies [15]. Namely, the polycrystalline Ni2MnGa1-xFex (0 ≤ x ≤ 0.40) alloys were prepared by the repeated arc melting of the appropriate quantities of constituent elements, 99.99% Ni, 99.99% Mn, 99.99% Fe, and 99.9999% Ga in an argon atmosphere. The samples with x = 0.30 and 0.35 were prepared by the melting of appropriate quantities of the constituent elements with high purity in an induction furnace (DIAVAC LIMITED, Yachiyo, Japan). The reaction products were sealed in evacuated silica tubes, heated at 850 °C for 3 days and at 600 °C for 1 day, and then quenched into water. The crystal structure was investigated by X-ray diffraction (Rigaku, Tokyo, Japan) measurements at room temperature using Cu-Kα radiation. The lattice parameters for the samples were the same as the previous report [15].
The measurements of the electrical resistivity ρ were carried out by a conventional DC (direct current) four-probe method in the temperature range from 80 K to 450 K. The samples were cut out using a diamond disk saw (BUEHLER, Lake Bluff, IL, USA) into the size of about 1.0 × 1.0 × 10 mm 3 . The thermal process in the measurements started from 80 K, heated up to 450 K, and cooled down again to 80 K.

Results and Discussion
The temperature dependence of the electrical resistivity ρ of the sample with x = 0.05 is given in Figure 1a. The obvious slope change near 377 K is indicative of the ferromagnetic ordering. Below the Curie temperature TC, the ρ shows a steep decrease with decreasing temperature. This can be attributed to the disappearance of electron scattering on magnetic fluctuations. The behavior of ρ around TC is a common feature for the Heusler alloys with ferromagnetic ordering. Assuming that the break point on the ρ vs. T curves corresponds to the Curie temperature of the sample with x = 0.05, the value of TC = 377 K is very close to that determined from the initial permeability μ vs. T curve [15]. A prominent jump-like feature of ρ appears at around 250 K, indicating the occurrence of the martensitic transition. The martensitic transition temperature TM was defined by the equation: TM = (TMs + TAf)/2, where TMs and TAf are the martensitic transition starting temperature and the reverse martensitic transition finishing temperature, respectively. The values of TMs and TAf were defined as the cross points of the linear extrapolation lines of the ρ vs. T curves from both higher and lower temperature ranges. As shown in Figure 1a, a temperature hysteresis is formed around TM between 240 K and 260 K, confirming that the martensitic transition is first-order. On the other hand, such a temperature hysteresis behavior is absent for the ferromagnetic transition around 377 K. With further decrease of temperature from TM, ρ of the sample with x = 0.05 represents a typical metallic behavior.
The inset in Figure 1a shows the temperature dependence of dρ/dT. A noticeable slope change in ρ(T) around 260 K marks the onset of the premartensitic transition. The premartensitic transition temperature Tp is estimated to be 264 K, as shown in the inset in Figure 1a. The values of TM and Tp are in good agreement with those determined from the magnetic measurements earlier [15]. For the sample with x = 0.025, anomalies on dρ/dT vs. T curves are observed around Tp (see the inset in Figure  1b. However, as shown in the insets of Figure 1c-f, no anomalies on dρ/dT vs. T curves are observed in the temperature range between TC and TM, indicating that the premartensitic phase disappears in the concentration range of x ≥ 0.10. As seen in Figure 1a-f, the martensitic transition temperature increases with increase of Fe concentration x. On the other hand, TC increases slightly with x.   Figure 1h, the ρ increases abruptly around 402 K with deceasing temperature, indicating that the magnetic transition between the ferromagnetic phase and the paramagnetic phase was first-order. We did not observe any anomaly below TC on the ρ vs. T curves, so TM is considered to coincide with TC. The TC (=TM) was estimated to be 402 K for the sample with x = 0.30, where TC was defined to be TC = TM = (TMs + TAf)/2. Similar ρ vs. T curves are observed for the samples with x = 0.275 and 0.35 (see Figure 1g,i). As seen in Figure 1a-j, the jump of ρ at TM, ∆ρ, of the samples with x ≥ 0.20 are considerably larger than that of samples with 0.025 ≤ x ≤ 0.15. Figure 2 shows the concentration dependence of ∆ρ for Ni2MnGa1-xFex. As seen in Figure 2, ∆ρ shows a tendency to increase with increasing x, but abruptly increases in the concentration range between x = 0.15 and 0.20.  Figure 3 shows the phase transition temperatures TM, Tp and TC determined from the ρ vs. T curves in this study. The closed triangle in the figure represents the phase transition temperature determined from the magnetic measurement [15]. As shown in Figure 3, the phase transition temperatures determined in this study are in good agreement with those reported earlier [15]. The phase diagram of Figure 3 is very similar to those of Ni2+xMn1−xGa (0 ≤ x ≤ 0.36) [11,12] and Ni2Mn1−xCuxGa (0 ≤ x ≤ 0.4) [10] and Ni2MnGa1−xCux (0 ≤ x ≤ 0.25) [16], as mentioned above. In order to understand the phase diagram of Ni2Mn1−xCuxGa (0 ≤ x ≤ 0.4), the phenomenological Landau-type free energy as a function of the martensitic distortion and magnetization was constructed and analyzed [10]. Satisfactory agreements between the experiments and theory were obtained, except for the appearance of the premartensitic phase. The analysis showed that the biquadratic coupling term of the martensitic distortion and magnetization plays an important role in the interplay between the martensitic phase and ferromagnetic phase. The total electrical resistivity is given for usual ferromagnetic materials as follows, where ρ0 is the residual part, the second term and the third term are the electrical resistivity parts due to electron-phonon scattering and magnetic origin, respectively, with a and b being fitting parameteters. Of course, Equation (1) is a phenomenological fit to the experimental data, and we do not claim that magnetic scattering is purely quadratic in temperature. Many authors fitted Equation (1) to their experimental data for many Heusler alloys. [17][18][19][20][21][22][23]. Table 1 gives the ρ0, a, and b values, the validity range of fit, and TC values of Ni2MnGa1-xFex. The concentration dependence of ρ0 determined by fitting the ρ vs. T data (T < TM) to Equation (1) is shown in Figure 4. As seen in Figure 4, the ρ0 value roughly increases with the concentration x, but abruptly changes in the concentration range between x = 0.15 and 0.20, as well as the behavior of ∆ρ. It can be explained as the impurity effect that the ρ0 increases with increasing x. The values of b for the samples with x ≤ 0.30 are two orders of magnitude smaller than those of typical weak itinerant electron ferromagnets Ni3Al, ZrZn2 and Sc3In [24][25][26][27]. A general theory of electrical resistivity in an itinerant electron system has been proposed by Ueda and Moriya on the basis of spin fluctuations [28]. Their work predicts a strong T 2 dependence of electrical resistivity due to spin fluctuations. Table 1. The ρ0 (μΩ cm), a (μΩ cm K −1 ), b (μΩ cm K −2 ) values according to the fit ρ(T) = ρ0 + aT + bT 2 in the temperature range below TM (i.e., in the Ferro-M (ferromagnetic martensite) phase). The range of validity of the fit, TM and TC are given in Table 1. 1 Quoted from Ref. [15].  Table 1, with dashed lines being guides to the eye. The vertical dotted lines distinguish the electric properties of Ni2MnGa1-xFex to two regions.
In this study, as shown in Figures 2 and 4, we found the borderline which distinguishes the electric properties of Ni2MnGa1-xFex (0 ≤ x ≤ 0.40) alloys. The Fe concentration variation on the temperature dependence of resistivity for Ni2MnGa1-xFex (0 ≤ x ≤ 0.40) alloys may be caused by the change of the charge carrier concentration between the martensite and austenite phases or the change of the mechanism of the martensitic transition. Now, it is not clear for the origin of appearance of the borderline. This may be related to the electron scattering at the twin and domain boundaries which appear in the martensitic phase. An investigation of microstructure observation will also be necessary.

Conclusions
Temperature dependences of the electrical resistivity have been measured on the Heusler alloy system Ni2MnGa1−xFex. The phase diagram of Ni2MnGa1−xFex was constructed on the basis of the experimental results. The magnetostructural transitions were observed at the Fe concentrations x = 0.275, 0.30, and 0.35 in Ni2MnGa1−xFex alloys as well as a previous report [15]. The changes of the electrical resistivity at the martensitic transition temperature were studied as the function of Fe concentration x.