Temperature Dependences of the Electrical Resistivity on the Heusler Alloy System Ni₂MnGa_1−xFe_x

Abstract

Temperature dependences of the electrical resistivity have been measured on the Heusler alloy system Ni₂MnGa_1−xFe_x. The phase diagram of Ni₂MnGa_1−xFe_x 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.

1. 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 T_C = 365 K [7]. On cooling, the premartensitic phase appears below T_p = 260 K. With further decrease of temperature, Ni₂MnGa undergoes a first-order martensitic transition at T_M = 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 T_M. The spontaneous magnetization of Ni₂MnGa just below T_M is larger than that just above T_M.

The T_C, T_p, and T_M of Ni₂MnGa can be tuned in a wide range by doping with a fourth element. For Ni₂Mn_1−xCu_xGa (0 ≤ x ≤ 0.4) [10], T_M increases with increasing the concentration x, while T_C 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 Ni₂Mn_1−xCu_xGa (0 ≤ x ≤ 0.4) are closely similar to those of Ni_2+xMn_1−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 Ni₂MnGa_1−xFe_x (0 ≤ x ≤ 0.40) [15]. The characteristics of the determined phase diagram of Ni₂MnGa_1−xFe_x (0 ≤ x ≤ 0.40) are very similar to those of Ni_2+xMn_1−xGa (0 ≤ x ≤ 0.36) [11,12] and Ni₂Mn_1−xCu_xGa (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 Ni_2+xMn_1−xGa, Ni₂Mn_1−xCu_xGa, and Ni₂MnGa_1−xFe_x 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 Ni₂MnGa_1−xFe_x alloys.

2. Experimental Procedures

The experiments were made on the same Ni₂MnGa_1–xFe_x (0 ≤ x ≤ 0.40) alloys that were used in our previous studies [15]. Namely, the polycrystalline Ni₂MnGa_1–xFe_x (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 mm³. The thermal process in the measurements started from 80 K, heated up to 450 K, and cooled down again to 80 K.

3. 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 T_C, 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 T_C 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 T_C = 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 T_M was defined by the equation: T_M = (T_Ms + T_Af)/2, where T_Ms and T_Af are the martensitic transition starting temperature and the reverse martensitic transition finishing temperature, respectively. The values of T_Ms and T_Af 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 T_M 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 T_M, 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 T_p is estimated to be 264 K, as shown in the inset in Figure 1a. The values of T_M and T_p 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 T_p (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 T_C and T_M, 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, T_C increases slightly with x.

Figure 1g–j show the temperature dependence of ρ for the samples with x = 0.275, 0.30, 0.35, and 0.40. According to the phase diagram of Ni₂MnGa_1–xFe_x (0 ≤ x ≤ 0.40) reported by Hayasaka et al. [15], the samples with 0.27 ≤ x ≤ 0.37 underwent the magnetostructural transition from the Ferro-M state to the Para-A state. For the sample with x = 0.40, the Ferro-M to the paramagnetic martensite (Para-M) transition appeared. As shown in 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 T_C on the ρ vs. T curves, so T_M is considered to coincide with T_C. The T_C (=T_M) was estimated to be 402 K for the sample with x = 0.30, where T_C was defined to be T_C = T_M = (T_Ms + T_Af)/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 T_M, ∆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 Ni₂MnGa_1–xFe_x. 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 T_M, T_p and T_C 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 Ni_2+xMn_1−xGa (0 ≤ x ≤ 0.36) [11,12] and Ni₂Mn_1−xCu_xGa (0 ≤ x ≤ 0.4) [10] and Ni₂MnGa_1−xCu_x (0 ≤ x ≤ 0.25) [16], as mentioned above. In order to understand the phase diagram of Ni₂Mn_1−xCu_xGa (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,

ρ(T) = ρ₀ + aT + bT²,

(1)

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. The ρ₀ (μΩ cm), a (μΩ cm K⁻¹), b (μΩ cm K⁻²) values according to the fit ρ(T) = ρ₀ + aT + bT² in the temperature range below T_M (i.e., in the Ferro-M (ferromagnetic martensite) phase). The range of validity of the fit, T_M and T_C are given in Table 1.

Alloys	ρ0	a × 10−2	b × 10−4	Range (K)	TM (K)	TC (K)
Ni2MnGa0.975Fe0.025 (x = 0.025)	22.2	4.73	6.37	100~220	235	383
Ni2MnGa0.95Fe0.05 (x = 0.05)	18.2	3.34	3.54	100~230	257	377
Ni2MnGa0.90Fe0.10 (x = 0.10)	31.1	8.61	1.84	100~260	282	390
Ni2MnGa0.85Fe0.15 (x = 0.15)	60.8	9.18	1.41	100~270	314	393
Ni2MnGa0.80Fe0.20 (x = 0.20)	101.6	6.47	1.67	100~270	347	392
Ni2MnGa0.775Fe0.225 (x = 0.225)	80.8	5.25	0.84	100~320	356	390
Ni2MnGa0.725Fe0.275 (x = 0.275)	75.0	4.91	0.86	100~350	395	395
Ni2MnGa0.70Fe0.30 (x = 0.30)	139	4.42	1.04	100~370	402	402
Ni2MnGa0.65Fe0.35 (x = 0.35)	118	5.06	0.43	100~390	431	431
Ni2MnGa0.60Fe0.40 (x = 0.40)	110	5.27	0.26	100~390	442	414 1

¹ Quoted from Ref. [15].

gives the ρ₀, a, and b values, the validity range of fit, and T_C values of Ni₂MnGa_1–xFe_x. The concentration dependence of ρ₀ determined by fitting the ρ vs. T data (T < T_M) 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 T² dependence of electrical resistivity due to spin fluctuations.

In this study, as shown in Figure 2 and Figure 4, we found the borderline which distinguishes the electric properties of Ni₂MnGa_1–xFe_x (0 ≤ x ≤ 0.40) alloys. The Fe concentration variation on the temperature dependence of resistivity for Ni₂MnGa_1–xFe_x (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.

4. Conclusions

Temperature dependences of the electrical resistivity have been measured on the Heusler alloy system Ni₂MnGa_1−xFe_x. The phase diagram of Ni₂MnGa_1−xFe_x 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 Ni₂MnGa_1−xFe_x 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.