Thermal Expansion and Magnetization Studies of Novel Ferromagnetic Shape Memory Alloys Ni 52 Mn 12:5 Fe 12:5 Ga 23 and Ni 2 Mn 0:75 Cu 0:25 Ga

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1 Materials Transactions, Vol. 52, No. 6 (211) pp to 1147 #211 The Japan Institute of Metals Thermal Expansion and Magnetization Studies of Novel Ferromagnetic Shape Memory Alloys Ni 52 Mn 12:5 Fe 12:5 Ga 23 and Ni 2 Mn :75 Cu :25 Ga Takuo Sakon 1; *, Hitoshi Nagashio 1, Kenta Sasaki 1, Seiji Susuga 1, Keita Endo 2, Hiroyuki Nojiri 3 and Takeshi Kanomata 2 1 Department of Mechanical Engineering, Graduate School of Engineering and Material Research, Akita University, Akita 1-852, Japan 2 Faculty of Engineering, Tohoku Gakuin University, Tagajo , Japan 3 Institute for Material Research, Tohoku University, Sendai , Japan Thermal expansion, permeability, and magnetization measurements of ferromagnetic shape memory alloys, Ni 52 Mn 12:5 Fe 12:5 Ga 23 and Ni 2 Mn :75 Cu :25 Ga, were performed across the martensitic transformation temperature T M and the reverse martensitic transformation temperature T R. When cooling from austenite phase, a steep decrease in the thermal expansion due to the martensitic transformation was found for both alloys. Considering the permeability and magnetization results of Ni 2 Mn :75 Cu :25 Ga, the region above T M or T R is the paramagneticaustenite (Para-A) phase and the region below T M or T R is the ferromagnetic-martensite (Ferro-M) phase. Magnetic phase diagrams were constructed based on the results of the temperature dependence of thermal expansion. T M and T R increased gradually with increasing magnetic field. For Ni 52 Mn 12:5 Fe 12:5 Ga 23 and Ni 2 Mn :75 Cu :25 Ga, the shifts of T M in magnetic fields (B)wereestimatedasdT M =db :5 K/T and 1.2 T/K, respectively. The shifts of T M indicate that the that magnetization influences martensitic transition and the increase of T M in accordance with the magnetic fields is proportional to the difference between the magnetization of austenite phase with that of martensitic phase. [doi:1.232/matertrans.m21138] (Received January 28, 211; Accepted March 7, 211; Published May 11, 211) Keywords: shape memory alloys, Heusler alloys, phase transition, thermal expansion, magnetization, magnetic phase diagram 1. Introduction Recently, ferromagnetic shape memory alloys (FSMAs) have been studied by many researchers as potential candidates for smart materials. Ni 2 MnGa is the most familiar alloy. 1) It has a cubic L2 1 Heusler structure (space group Fm3m) with lattice parameter a ¼ 5:825 Å at room temperature, and orders ferromagnetically at the Curie temperature T C 365 K. 2,3) Upon cooling from room temperature, martensitic transformation occurs at the martensitic transformation temperature T M 2 K. Below T M, a superstructure forms because of lattice modulation. As for the Heusler Ni-Mn-Ga alloys, T M varies from 2 K to 33 K by nonstoichiometrically changing the concentration of composite elements. Ni-Fe-Ga alloys are the new promising FSMAs for which T M varies from 15 K to room temperature and exhibit excellent ductility. 4 6) The Ni 54 Fe 19 Ga 27 alloy transforms from the high temperature L2 1 phase to the martensite phase having monoclinic structure. 5,6) Kikuchi et al. have reported the magnetic properties of Ni 5þx Mn 12:5 Fe 12:5 Ga 25 x ( x 5:5) ferromagnetic alloys, which were produced by replacing Ga with Ni in Ni 5 Mn 12:5 Fe 12:5 Ga 25 alloy. 7) The measurements of temperature dependence of magnetization for this series were performed. It was observed that T C gradually decreases with the concentration x, while T M and the reverse martensitic transformation temperature T R increase with x and exhibit saturation behavior for x 3:. Kataoka et al. have reported the magnetic properties of Ni 2 Mn 1 x Cu x Ga ( x :4) alloys, which were obtained by replacing Mn with Cu in Ni 2 MnGa alloy. 8) The samples with :23 x :3 show martensite transition at about *Corresponding author, sakon@gipc.akita-u.ac.jp 3 K. The magnetic and crystal states above and below T M are paramagnetic austenite (Para-A) phase and ferromagnetic martensite (Ferro-M) phase, respectively. Such Heusler alloys show the martensitic transformation around room temperature. Therefore, they are candidates for smart materials. The purpose of this study is to investigate the correlation between magnetism and crystallographic structure regarding the martensitic transformation. Two Heusler alloys were selected to achieve this purpose. One is an alloy which occurs martensitic transition in a ferromagnetic phase, and the other is an alloy which occurs martensitic transition at Curie temperature T C, where T C is a Curie temperature of a martensite phase. The former was Ni 52 Mn 12:5 Fe 12:5 Ga 23, which shows the martensitic transformation in the ferromagnetic phase at T M ¼ 284 K, whereas the ferromagnetic transition occurs at T C ¼ 41 K, which is much higher than T M.AtT M, a transition of ferromagnetic austenite (Ferro-A) phase to Ferro-M occurs. 7) The latter alloy was Ni 2 Mn :75 Cu :25 Ga, which shows a transition of Para-A to Ferro-M phase at T M 31 K. 8) Kataoka et al. observed that the ferromagnetic transition and martensite transformation occur around the same temperature. 8) Thermal expansion, permeability and magnetization measurements for both alloys were performed in magnetic fields (B), and magnetic phase diagrams were constructed. The measurement results of both alloys were compared and a thorough investigation of the correlations between magnetic transition and the martensite transformation was performed. 2. Experimental The Ni 52 Mn 12:5 Fe 12:5 Ga 23 and Ni 2 Mn :75 Cu :25 Ga alloys were prepared by the arc melting of 99.9% pure Ni, 99.99%

2 Thermal Expansion and Magnetization Studies of Novel Ferromagnetic Shape Memory Alloys 1143 pure Mn, and Cu, 99.95% pure Fe, and 6N pure Ga in an argon atmosphere. To obtain homogenized samples, the reaction products were sealed in double evacuated silica tubes, which were annealed at 1123 K for 3 days, and quenched into cold water. The samples obtained for both alloys were polycrystalline. Thermal expansion measurements were performed using strain gauges (Kyowa Dengyo Co., Ltd., Chofu, Japan). Electrical resistivity of the strain gauges was measured by the four-probe method. The relationship between strain, ", and deviation of electrical resistivity, R, is given by " ¼ 1 K S R R ¼ 1 K S ðr R Þ R ; ð1þ where K S is the gauge factor (K S ¼ 1:98) and R is the electrical resistivity above T R. The thermal expansion measurements were performed using a 1 T helium-free cryocooled superconducting magnet at the High Field Laboratory for Superconducting Materials, Institute for Material Research, Tohoku University. The magnetic permeability measurements were performed in AC fields with f ¼ 73 Hz and B max ¼ :5 T. The magnetization measurements were performed using a Bittertype water-cooled pulsed magnet at Akita University after zero-field cooling from about 32 K (austenite phase). The M-B curves in Figs. 6(a) 7(c) are shown in increasing field processes of pulse fields. 3. Results and Discussion Figure 1 shows the temperature dependence of the linear thermal expansion of Ni 52 Mn 12:5 Fe 12:5 Ga 23 in static magnetic fields. When cooling from 31 K (Ferro-A phase), the alloy shrinks gradually in zero magnetic fields. Small elongation was observed at 288 K. Then, sudden shrinking occurs below 286 K, which indicates transformation from austenite phase to martensite phase. We define the martensitic transformation temperature T M as the midpoint of the steep decrease in the cooling measurement. The T M of this alloy is 284 K. The reason of small elongation at 288 K is considered that L2 1 and 14M structures coexist each other. Therefore apertures between L2 1 and 14M structures were originated and small expansion occured. As for Ni 2þx Mn 1 x Ga alloys, small elongation was observed just above T M. 9) As shown in Ref. 7), the phase below T M is Ferro-M. When heating from 27 K, expansion occurs at about T R ¼ 288 K, which indicates reverse martensitic transformation. Small elongations just above the temperatures of T M and T R were also observed in polycrystalline Ni 2þx Mn 1 x Ga (:16 x :2). 9) T M and T R gradually changed with increasing magnetic fields. The strain at T M and T R was about 2:5 1 3 ( :25%) and was almost the same as that in magnetic fields. Kikuchi et al. performed the X-ray diffraction experiments of Ni 5þx Mn 12:5 Fe 12:5 Ga 25 x. 7) The X-ray patterns at room temperature (T ¼ 3 K, austenite phase) for the samples of x 2: were indexed with the L2 1 Heusler structure. In the X-ray diffraction pattern at room temperature of the sample with x ¼ 2:, a very weak reflection from a phase was observed, where the phase linear expansion x has a disordered fcc structure. The lattice parameter a of x ¼ 2: was found to be Å. 1) On the other hand, for x 3:, the martensite phase appeared at room temperature. The martensitic structure of x ¼ 3: was indexed as a monoclinic structure with 14M (7R) structure. The lattice parameters of the sample were determined as a ¼ 4:2495 Å, b ¼ 2:7211 Å, c ¼ 29:34 Å, and ¼ 93:36 at room temperature. We also estimated the strain of Ni 52 Mn 12:5 Fe 12:5 Ga 23 (x ¼ 2:) att M using the lattice parameter of x ¼ 2: in the austenite phase and that of x ¼ 3: in the martensite phase. In the austenite phase, for the L2 1 cubic structure, the lattice parameter a was p Å. 1) The distance between Mn-Mn atoms was a= ffiffiffi p2 ¼ 4:961 Å, and the volume of the unit cell was V A ¼ða= ffiffi 2 Þ 3 ¼ð4:961Þ 3 ¼ 68:72 Å 3. Furthermore, the volume V M in the martensite phase was estimated and compared with V A in the same area. In the 14M (7R) martensite phase, a ¼ 4:2495 Å in the basal plane, is parallel to one of the a axis in the L2 1 structure, and is of the same unit. The other axis in the martensite phase corresponds to one of the a axis inpthe ffiffi L2 1 structure of the Mn-Mn ridge in the basal plane ( 2 b). The c axis is almost normal ( ¼ 93:36 ) to the basal plane and the seven Mn-Mn cycles at c ¼ 29:34 Å. Therefore, the volume, pffiffiffi V M ¼ a ðc=7þð 2 bþsin ¼ 4:2495 4:1914 ð1:4142 2:7211Þ sin 93:36 ¼ 68:55 :9983 ¼ 68:43 A 3 : ð2þ The linear strain of a polycrystal is one-third of the volume strain. 11) Therefore, we estimate the linear strain " as, " ¼fðV M V A Þ=V A g1=3 ¼fð68:43 68:72Þ=68:72g1=3 ¼ð :29=68:72Þ1=3 ¼ :14%: ð3þ T 5 T 2 T B = T Fig. 1 Temperature dependences of linear thermal expansion of Ni 52 Mn 12:5 Fe 12:5 Ga 23 in static magnetic fields. 31

3 1144 T. Sakon et al..3 (a) Ni 2 Mn.75 Cu.25 Ga B =1 T Permeability (a. u.).2.1 Ni 2 Mn.75 Cu.25 Ga Linear expansion B = 8 T B = 5 T Ni 2 Mn.75 Cu.25 Ga B = 3 T linear expansion (b) x B = T Fig. 3 Temperature dependences of the linear thermal expansion of Ni 2 Mn :75 Cu :25 Ga in static magnetic fields. Fig. 2 (a) Temperature dependence of the magnetic permeability of Ni 2 Mn :75 Cu :25 Ga in zero magnetic fields. The magnetic permeability measurement was perforemed in AC fields with f ¼ 73 Hz and B max ¼ 1: mt. Zero means the permeability ¼. (b) Temperature dependences of linear thermal expansion of Ni 2 Mn :75 Cu :25 Ga. The strain was defined by the difference from the sample length at 34 K. This estimated value is approximately comparable to the strain value " ¼ :25%ofNi 52 Mn 12:5 Fe 12:5 Ga 23 obtained from this experimental study. Figures 2(a) and (b) show the temperature dependence of magnetic permeability and linear thermal expansion of Ni 2 Mn :75 Cu :25 Ga in zero magnetic fields, respectively. When cooling from a high temperature, it shrinks and the permeability increases at about T M ¼ 38 K. The permeability at austenite phase is very low as compared with that at the martensite phase. These results indicate that the region above T M or T R is Para-A and the region below T M or T R is Ferro-M. When heating from a low temperature, the expansion occurs at about T R ¼ 316 K, which indicates reverse martensitic transformation. The strain at T M or T R is about 3: 1 3 (.3%). This value is higher than that of Ni 52 Mn 12:5 Fe 12:5 Ga 23. Kataoka et al. studied the X-ray powder diffraction of Ni 2 Mn 1 x Cu x Ga ( x :4). 8) In the vicinity of martensitic transformation, the strain exhibits complicated behavior; when cooling from 342 K, it shrinks gradually and rapid shrinking occurs at T M ¼ 38 K, subsequently, exhibiting elongation; repetition of small elongation and shrinking was observed between 33 K and 291 K; in addition, it shrinks linearly below 291 K. When heating from 257 K, the repetition of small elongation and shrinking was observed between 37 K and 311 K. Thereafter, it shrinks by 9: 1 4 and exhibits elongation. This sequential phenomenon has been observed in single crystalline Ni 2:19 Mn :81 Ga. 9) In particular, steep shrinking occurs before elongation due to reverse martensitic transformation during heating. As for polycrystalline Ni 2þx Mn 1 x Ga (:16 x :2), the shape of the small elongation or small shrinking due to the large change of the strain associated with martensitic transformation is broader than that of the single crystalline alloy. In our study, Ni 2 Mn :75 Cu :25 Ga showed steep shrinking before elongation during heating from a low temperature, which is similar to that of single crystalline Ni 2:19 Mn :81 Ga. It is possible that the Ni 2 Mn :75 Cu :25 Ga crystal is oriented to some extent. The X-ray diffraction measurement of Ni 2 Mn :75 Cu :25 Ga indicates that cubic L2 1 phase and the 14M phase coexist in the martensite phase. The reason for the repetition of small elongation and shrinking in Fig. 2(b) is supposed to be this complex structure. Figure 3 shows the temperature dependence of the linear thermal expansion of Ni 2 Mn :75 Cu :25 Ga in static magnetic fields. T M and T R gradually changed with increasing magnetic fields. Next, we compared the two samples. The linear thermal coefficients of Ni 52 Mn 12:5 Fe 12:5 Ga 23 and Ni 2 Mn :75 Cu :25 - Ga in zero magnetic fields obtained in this study are shown in Table 1. In the austenite phase, of Ni 52 Mn 12:5 Fe 12:5 Ga 23 is much lower than that of Ni 2 Mn :75 Cu :25 Ga, which means that Ni 52 Mn 12:5 Fe 12:5 Ga 23 is harder than Ni 2 Mn :75 Cu :25 Ga. is higher in the martensite phase than in the austenite phase of Ni 52 Mn 12:5 Fe 12:5 Ga 23. This is probably due to the 14M martensitic structure. The magnetic phase diagrams constructed from the thermal expansion measurements of this study are shown in Figs. 4 and 5.

4 Thermal Expansion and Magnetization Studies of Novel Ferromagnetic Shape Memory Alloys 1145 Table 1 Linear thermal expansion coefficients of Ni 52 Mn 12:5 Fe 12:5 Ga 23 and Ni 2 Mn :75 Cu :25 Ga in zero magnetic fields. These values were obtained by gradients of the strains in Fig. 1 and Fig. 2(b). sample martensite phase austenite phase Ni 52 Mn 12:5 Fe 12:5 Ga 23 18:2 1 6 /K 1:5 1 6 /K Ni 2 Mn :75 Cu :25 Ga 25:1 1 6 /K 23:1 1 6 /K T M T R Fig. 4 Magnetic phase diagram of Ni 52 Mn 12:5 Fe 12:5 Ga Magnetization, M/Jµ Magnetization, M/Jµ (a) (b) K 15 K 25 K 3 K K 3 K 2. 1 Ni 2 Mn.75 Cu.25 Ga Fig. 5 T M T R Magnetic phase diagram of Ni 2 Mn :75 Cu :25 Ga. Square of Magnetization, M 2 /J 2 µ 2 kg (c) 9 K 15 K 25 K 3 K x1-3 Magnetic Field vs Magnetization, BM 1 /Jµ 1kg 1 T 2 Figure 4 shows the magnetic phase diagram of the thermal expansion of Ni 52 Mn 12:5 Fe 12:5 Ga 23 in static magnetic fields. T M and T R gradually changed with increasing magnetic fields like Ni 2þx Mn 1 x Ga alloys. The shifts of T M and T R in magnetic fields were estimated as dt M =db :5 K/T and dt R =db :5 K/T, respectively. The shifts of T M and T R can be explained by the difference of the magnetization between austenite phase and martensitic phase. Afterwards we discuss about the correlation between magnetization and the shift of T M. Figure 5 shows the magnetic phase diagram of the thermal expansion of Ni 2 Mn :75 Cu :25 Ga in static magnetic fields. T M and T R gradually changed with increasing magnetic fields such as in the Ni 2þx Mn 1 x Ga or Ni 52 Mn 12:5 Fe 12:5 Ga 23 alloys. The shifts of T M and T R in magnetic fields were estimated as dt M =db 1:2 K/T and dt R =db 1:1 K/T, respectively. These ratios are within measurement errors. Figure 6(a) shows the magnetization of Ni 52 Mn 12:5 Fe 12:5 - Ga 23 in a pulsed magnetic field. Below 25 K in the Ferro-M Fig. 6 (a) Magnetization of Ni 52 Mn 12:5 Fe 12:5 Ga 23 in a pulsed magnetic field up to 2 T. (b) High field magnetization of Ni 52 Mn 12:5 Fe 12:5 Ga 23 using a pulsed magnet. (c) Arrott plot of the magnetization of Ni 52 Mn 12:5 - Fe 12:5 Ga 23. Fine straight lines are extrapolated lines. state, the M-B curves resemble each other, and this is consistent with the results in Ref. 7). In the Ferro-A state, the magnetization at 3 K is lower than that in the Ferro-M state. Figure 6(b) shows the high-field magnetization in a pulsed magnetic field. At 9 K, steep increase in magnetization occurs when magnetic field is applied. Above 2 T, the magnetization increases gradually. The magnetization at 3 K, which is above T M and T R, is also ferromagnetic. The magnetization above 5 T is almost flat. This property is quite different from that at T ¼ 9 K. The magnetism of the austenite phase appears to be similar to a localized ferromagnetic state, because the magnetization value is constant in high magnetic fields.

5 1146 T. Sakon et al. Table 2 The spontaneous magnetizations and dt M =db of Ni 2þx Mn 1 x Ga, Ni 52 Mn 12:5 Fe 12:5 Ga 23, and Ni 2 Mn :75 Cu :25 Ga. M M and M A indicate the spontaneous magnetization in martensite phase and austenite phase, respectively. sample M M M A ðm M M A Þ=M M dt M =db (K/T) remarks ref. 2) Ni 2 MnGa 9 J/ kgt at 18 K 1 8 J/ kgt at 22 K 1.11 :4 : ref. 14) 3 ref. 17) ref. 15) Ni 2:19 Mn :81 Ga 5.3 (a.u.) 4 (a.u.) ref. 16) :8 :25 3 Ni 52 Mn 12:5 Fe 12:5 Ga J/ kgt at 25 K 52.7 J/ kgt at 3 K.16.5 this study Ni 2 Mn :75 Cu :25 Ga 42.4 J/ kgt at 3 K J/ kgt at 37 K this study Figure 6(c) shows an Arrott plot, i.e., M 2 vs B=M, of the magnetization of Ni 52 Mn 12:5 Fe 12:5 Ga 23. The spontaneous magnetizations at 9 K and 25 K in a Ferro-M state are 7.1 J/ kgt and 63.1 J/ kgt, respectively. The spontaneous magnetization at 3 K in a Ferro-A state is 52.7 J/ kgt. Figures 7(a) and (b) show the magnetization of Ni 2 Mn :75 - Cu :25 Ga in a pulsed magnetic field. These measurements were performed after zero-field cooling processes at 323 K in the austenite phase. Below T M, the magnetization shows ferromagnetic properties, whereas above T M it exhibits paramagnetic properties. This is consistent with the permeability result shown in Fig. 2. Below T M, for instance, at 3 K, a steep increase occurred around zero fields and a spin-flop like behavior was shown below.6 T. Usually, magnetic alloys such as FeCl 3 show spin-flop behavior, and a linear extrapolation line at the canted magnetic moments phase crosses the origin point of the coordinate axis in the M-B graph. However, in Fig. 7(a), the M-B graph shows that the linear extrapolation line at the canted magnetic moments phase did not cross the origin point at 3 K. It is possible that steep increase just above the zero fields was due to the localized magnetic moments on the Mn atoms, for example, B /Mn atom which was obtained by the neutron scattering experiments of Ni 2þx Mn 1 x Ga alloys. 12,13) The magnetic moments on Ni atoms are considerably low, such as.2 B /Ni atom for Ni 2þx Mn 1 x Ga alloys, 12,13) and therefore, it is possible that the Ni moments that were arranged in a canted-like formation get ordered by the mutual correlations between external magnetic fields and internal magnetic fields due to the Mn moments. Figure 7(c) shows the Arrott plot of Ni 2 Mn :75 Cu :25 Ga. The spontaneous magnetization at 3 K in a Ferro-M state is 42.4 J/ kgt. The obtained T C of the martensite phase is 37 K, which is almost the same as T M ¼ 38 K and this is consistent with the x-t phase diagram of Ni 2 Mn 1 x Cu x Ga, which is obtained experimental and theoretical calculations. 8) Now we will discuss the relationship between magnetism and T M in magnetic fields. Table 2 shows the spontaneous magnetizations and dt M =db of Ni 2þx Mn 1 x Ga, Ni 52 Mn 12:5 - Fe 12:5 Ga 23, and Ni 2 Mn :75 Cu :25 Ga. As for Ni 2þx Mn 1 x Ga alloys, the shifts of T M in magnetic fields have been observed by the magnetization measurements ) T M and T C of Ni 2 MnGa (x ¼ ) are 2 K and 36 K, respectively. The region above T M is Ferro-A. x ¼ composition shows phase Magnetization, M/Jµ Magnetization, M/Jµ Square of Magnetization, M 2 /J 2 µ 2 kg 2 T (a) (b) 2 (c) K Magnetic Field vs Magnetization, BM 1 /Jµ 1kg 1 T K 289 K 3 K 32 K 33 K 34 K 35 K 36 K 37 K 38 K 39 K 311 K 313 K 318 K 323 K 3. 3 K 32 K 33 K 35 K 37 K 39 K 313 K Fig. 7 (a) Magnetization of Ni 2 Mn :75 Cu :25 Ga in a pulsed magnetic field up to 3 T. (b) High field magnetization of Ni 2 Mn :75 Cu :25 Ga using a pulsed magnet. (c) Arrott plot of the magnetization of Ni 2 Mn :75 Cu :25 Ga. Dotted lines at 35 K and 36 K are extrapolated linear lines. 33 K 34 K 35 K 36 K 37 K 38 K 318 K.6

6 Thermal Expansion and Magnetization Studies of Novel Ferromagnetic Shape Memory Alloys 1147 transition from Ferro-A to Ferro-M state at T M. x ¼ :19 composition shows ferromagnetic transition and martensitic transformation at T M. For x ¼, the shift of T M was estimated as dt M =db :2 K/T, 14) and for x ¼ :19, dt M =db :81:5 K/T ) The shift of T M for x ¼ :19 is higher than that of x ¼. These results indicate that the shift of T M for the alloy, which shows Para-A to Ferro-M transition, is larger than that for the alloy that shows Ferro-A to Ferro-M transition. The values of dt M =db are roughly proportional to the change of the spontaneous magnetization, ðm M M A Þ=M M, as shown in Table 2. This indicates that magnetization influences martensitic transition and the increase of T M in accordance with the magnetic fields is proportional to the difference between the magnetization of austenite phase with that of martensitic phase. Khovailo et al. discussed the correlation between the shifts of T M for Ni 2þx Mn 1 x Ga ( x :19) using theoretical calculations. 15,17) The experimental values of this shift of Ni 2þx Mn 1 x Ga ( x :19) are in good correspondence with the theoretical calculation results. In general, in a magnetic field, the Gibbs free energy is lowered by the Zeeman energy MB that enhances the motive force of the martensitic transformation. Thus, T M of the ferromagnetic Heusler alloys Ni 52 Mn 12:5 Fe 12:5 Ga 23 and Ni 2 Mn :75 Cu :25 Ga is considered to have shifted in accordance with the magnetic fields because high magnetic fields are favorable for ferromagnetic martensitic phases. 4. Summary Thermal expansion, magnetization, and permeability measurements were performed on the ferromagnetic Heusler alloys Ni 52 Mn 12:5 Fe 12:5 Ga 23 and Ni 2 Mn :75 Cu :25 Ga. (1) Thermal expansion When cooling from austenite phase, steep decrease due to the martensitic transformation was obtained for both alloys. T M and T R increase gradually with increasing magnetic fields. The shifts of T M for Ni 52 Mn 12:5 Fe 12:5 Ga 23 and Ni 2 Mn :75 Cu :25 Ga in magnetic fields were estimated as dt M =db :5 K/T and 1.2 T/K, respectively. (2) Magnetization and permeability Ni 52 Mn 12:5 Fe 12:5 Ga 23 The M-B curves indicate that the property of the Ferro-M phase is different from the Ferro-A phase. The Ferro-A phase is considered to be a more localized ferromagnetic phase as compared with Ferro-M phase. Ni 2 Mn :75 Cu :25 Ga The permeability abruptly changes around T M. The permeability below T M is about one-tenth times higher than that above T M. The Arrott plot of magnetization indicates that T C of the martensite phase is 37 K, which is almost the same as T M ¼ 38 K. (3) The values of dt M =db are roughly proportional to the change of the spontaneous magnetization ðm M M A Þ=M M. 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