The concentrations of elements by means of EDS spectrometry (at. %).
Ni41Co9Mn31.5Ga18.5 is a re-entrant and metamagnetic Heusler alloy. In order to investigate the magnetic functionality of polycrystalline Ni41Co9Mn31.5Ga18.5, magnetic field-induced strain (MFIS) measurements were performed. A 0.12% MFIS was observed at 340 K and 10 T. Strict MFISs between 330 and 370 K were observed. These magneto-structural variances acted in concert with the metamagnetic property observed by the magnetization measurements and magneto-caloric property observed by the caloric measurements in applied magnetic fields. The MFISs were proportional to the fourth power of the magnetization, and this result is in agreement with Takahashi’s spin fluctuation theory of itinerant electron magnetism. The investigation of time response of the MFIS was performed by means of water-cooled electric magnet, zero magnetic field to 1.66 T in 8.0 s at 354 K. A 2.2×10−4 MFIS was observed, which was 80% of the MFIS in a 60-s mode. This indicates that a high-speed transition has occurred on applying magnetic fields.
- Heusler alloys
- shape memory alloys
- metamagnetic transition
- itinerant magnetism
In recent years, the ferromagnetic shape memory alloy (FSMA) was investigated as a candidate of the functional materials widely. Among FSMA, Ni2MnGa is the most famous alloy . The alloy has a cubic L21 Heusler structure (space group of ), and ferromagnetic transition realized [2, 3]. Cooling from room temperature, a martensite transition occurred at the martensitic transition temperature, TM. Below TM, a superstructure state occurred as a result of lattice deformation [4-6].
New alloys in the FMSAs of NiMnIn-, NiMnSn-, and NiMnSb-type Heusler alloys have been studied [7, 8]. In these alloys, a metamagnetic transition from paramagnetic martensite phase to ferromagnetic austenite phase occurred, and reverse martensitic transition, which was induced by magnetic fields, occurred under high magnetic fields [9, 10]. These alloys are hopeful as a metamagnetic shape memory alloys with a magnetic field-induced shape memory effect (MSIF) and as magnetocaloric materials which can be cooled down or heated up on applying external magnetic fields. It is noticeable that 3% MFIS has been observed for Ni45Co5Mn36.7In13.3 single crystal in compressive stress–strain measurements .
The Co-doped NiCoMnGa-type alloys turned the magnetic order of the parent phase from antiferromagnetic or paramagnetic phase, due to a large magnetization change across the transformation. As a result, it strengthens magnetic field driving force dramatically [12-24]. As for Ni50-xCoxMn31.5Ga18.5, the determined phases are a paramagnetic austenite (Para-A) phase, ferromagnetic austenite phase (Ferro-A), paramagnetic martensite phase (Para-M), and ferromagnetic martensite (Ferro-M) phase, with cooling from a higher temperature than TC, which indicates re-entrant ferromagnetism .
Albertini et al. performed the experimental studies regarding the composition dependence of the structural and magnetic properties of the Ni-Mn-Ga ferromagnetic shape memory alloys substituting Co for Ni atoms around the composition of Ni50Mn30Ga20 [12, 20]. The magnetic and structural properties indicated remarkable discontinuities around the martensitic transition. A metamagnetic transition appeared in the magnetic field around 400 K. The field dependence of the reverse martensitic transition temperature dTR/μ0dH was −2.8 K/T and that of the thermal strain was reported. The most characteristic alloy is Ni41Co9Mn32Ga18. The magnetic susceptibility indicates a re-entrant magnetism property. We studied the magnetic properties of polycrystalline Ni41Co9Mn31.5Ga18.5. Magnetization results indicated the metamagnetic transition between 330 and 370 K for 0–10 T. Moreover, a 0.1% magnetic field-induced strain (MFIS) was observed at the temperature of 340 K .
In our former article , we determined the magnetic field dependence of the magnetization of Ni41Co9Mn31.5Ga18.5 around the Curie temperature in the martensite phase in order to investigate the properties of the itinerant electron magnetism according to Takahashi’s spin fluctuation theory of itinerant electron magnetism [26, 27]. The M4 versus H/M plot was crossed across the coordinate axis at the Curie temperature in the martensite phase, TCM = 263 K, and indicates a good linear relation behavior around TCM. The results were in agreement with the Takahashi’s theory concerning itinerant electron magnetism [26, 27]. Moreover, the spin fluctuation temperature TA can be obtained from the M4 versus H/M plot. The obtained TA was 703 K. This value was much smaller than Ni (1.76 × 104 K). The value was comparable to that of UGe2 (493 K), which is famous for the strongly correlated heavy fermion ferromagnet [27, 28].
Takahashi suggested that the anomalous behavior for the magnetostriction can be observed under the influence of the itinerant spin fluctuations around the critical temperature . It is mentioned that the reason is that the magnetostriction is given by the volume derivative of the free energy. By Eq. (6.101) of , the magnetostriction is proportional to the fourth power of the magnetization, M4. The experimental magnetostriction study of weak itinerant ferromagnet MnSi was performed by Matsunaga et al. . They plotted the magnetostriction against M2. Around the Curie temperature, TC = 30 K, the plot considerably deviated from the linearity. Takahashi mentioned that the linearity was confirmed by plotting the magnetostriction data against M4 at T = 29 K around TC.
In this chapter, we preformed MFIS measurements by means of a 10-T helium-free superconducting magnet and a 1.7-T water-cooled electric magnet. We compared the results of the strain and calorimetric differential scanning colorimetry (DSC) measurements and discussed the irreversibility of the MFIS and the reverse martensitic and metamagnetic transition. We investigated the correlations between magneto-structural variance and the magneto-caloric property observed by the caloric measurements in applied magnetic fields. It is interesting with the investigation of time response of the MFIS for the purpose of industrial use . The time response of the MFIS performed by means of a 1.6-T water-cooled electric magnet and under atmospheric pressure, P = 0.1 MPa, was investigated. We also investigated the relation between the magnetostriction and the magnetization according to Takahashi’s spin fluctuation theory of the itinerant ferromagnet for Ni2MnGa and Ni41Co9Mn31.5Ga18.5.
2. Sample properties and experimental details
The crystal structure of Ni41Co9Mn31.5Ga18.5 is tetragonal DO22 structure, and the sample preparation of polycrystalline alloy was shown in our former article . The nominal concentrations of the elements were Ni 41.0, Co 9.0, Mn 31.5, and Ga 18.5 at.%. The concentrations of the elements after thermal treatment are shown in Table 1. The ratio was almost the same as that of the nominal state. When cooling from 500 K, a ferromagnetic transition in the austenite phase was realized at TCA = 465 K. At the martensitic transition temperature, TM = 315 K, the magnetization decreased drastically. The reverse martensitic transition temperature TR was 380 K. The re-entrant magnetism, ferromagnetic-paramagnetic state, should be interacted with the crystal structures. The hysteresis of temperature, TR - TM was 65 K, which is much larger than that of other Ni2MnGa-type alloys. This is due to the large motive force in order for a martensitic transition to occur .
MFIS measurements were performed with bulk samples with the size of 0.8 × 3.0 × 4.0 mm3. Strain gauges were used (KFH-02-120-C1–16, size: sensor grid 0.2 mm length × 1.0 mm width, film base 2.5 mm length × 2.2 mm width, Kyowa Dengyo Co., Ltd., Yamagata, Japan). Strain gauge was fixed parallel to the long distance direction (4.0 mm) of the sample.
External magnetic field was applied parallel to the long distance direction of the sample, and elongation of the sample was measured in applied magnetic fields and in atmospheric pressure. Measurements were performed by means of a 10-T helium-free magnet (10 T-CSM) at High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University. We also performed MFIS measurements by means of a 1.7-T water-cooled electric magnet at Ryukoku University in order to investigate time response of MFIS. The magnetization measurements were performed by using a pulsed-field magnet with the time constant of 6.3 ms. The absolute value was calibrated against a sample of pure Ni.
3. Results and discussion
3.1. Relation between the magnetic field-induced strain and the magnetic entropy of Ni41Co9Mn31.5Ga18.5
In this section, we compared the results of the strain and calorimetric DSC measurements of Ni41Co9Mn31.5Ga18.5. We considered the correlation between the magnetic field-induced strain and the magnetic entropy.
Figure 1 shows the MFIS under steady field by means of the helium-free superconducting magnet. The MFIS measurements in this study were performed under atmospheric pressure and without the compression to make a pre-strain. The point zero of MFIS at each temperature is moved by 1 × 10−4 below 315 K and by 5 × 10−4 above 330 K. The thermal condition was the same as that for the magnetization measurement . When increasing the magnetic field, distinct MFIS was observed. The maximum MFIS was 0.12%, which was approximately the same value as that of the thermal strain for the reverse martensitic transition. The shape of MFIS is similar to that of polycrystalline Ni41Co9Mn32Ga16In2, where the alloy is also a re-entrant metamagnetic Heusler alloy, and 0.30% MFIS was observed . The field dependence of the reverse martensitic transition temperature, dTR/μ0dH, are −7.9, −6.8, and − 4.8 K/T for Ni41Co9Mn31.5Ga18.5 , Ni41Co9Mn32Ga16In2 , and Ni45Co5Mn36.7In13.3, respectively . The field dependence of the reverse martensitic transition temperature of the ferromagnetic and non-metamagnetic Ni2MnGa type alloys is between 0.2 and 1.0 K/T [2, 31, 32]. As for metamagnetic Heusler alloys, dTR/μ0dH is much larger than that of non-metamagnetic Heusler alloys. Therefore, the MFIS occurs at a wide temperature range. The strain curves shown in Figure 1 and the thermal strain in Ref.  suggest that the magneto-structural transition of Ni41Co9Mn31.5Ga18.5 alloy is very sensitive to magnetic fields. Below 330 K, the MFIS value returned to zero when a magnetic field became zero. By contrast, the MFIS value remained at the limit value without returning zero.
The MFIS of 2, 4, 6, and 8 T is shown in Figure 2. Between 340 and 370 K, large MFIS was observed. Metamagnetic S-shape like M-H curve was observed for the magnetization around 360 K . The decreasing field process shows ferromagnetic behavior. Magnetization process indicates that the paramagnetic to ferromagnetic transition occurred. Considering the magnetization, MFIS indicates that the structural transformation from the paramagnetic martensite phase to the austenite ferromagnetic phase occurred. The MFIS and metamagnetism indicate that the magneto-structural coupling is large. The 0.12% (1200 ppm) MFIS is larger than the magnetostriction of TbDyFe single crystal under atmospheric pressure . In this study, Ni41Co9Mn38.5Ga18.5 is a polycrystalline sample; then, it is easier to process and handle the sample than single crystals. Table 2 indicates the thermal linear striction ΔL/L(t), saturated magnetostriction ΔL/L(m), and relative volume discontinuity at the martensitic transition, ΔV/V.
|Ni41Co9Mn31.5Ga18.5||1.1 10−3||1.2 10−3||0.33||This work|
|Ni41Co9Mn32Ga16In2||3.5 10−3||3.0 10−3||0.9|||
In the former article, we studied the magneto-caloric properties of Ni41Co9Mn31.5Ga18.5 polycrystalline sample by means of the differential scanning calorimetry (DSC) measurements . Magneto-calorimetric measurements and magnetization measurements of Ni41Co9Mn31.5Ga18.5 polycrystalline ferromagnetic shape memory alloy (FSMA) were performed across the TR, at atmospheric pressure. When the sample was warmed from the martensite phase, a gradual increase in the thermal expansion due to the reverse martensitic transition at TR was observed by the thermal expansion experimental study. These transition temperatures decreased steeply with an increasing magnetic field. The field dependence of the reverse martensitic transition temperature, dTR/μ0dH, is −7.9 K/T near zero fields. From the DSC measurements, the value of the latent heat was obtained as 2.6 kJ/kg in zero fields. The maximum value of the entropy change ΔS was 7.0 J/kgK in zero fields, and with increasing magnetic fields, ΔS was gradually increased. The relative cooling power (RCP) is obtained by integration ΔS with the temperature. The RCP was 104 J/kg at 2.0 T, which was almost as same as the value with In-doped Ni41Co9Mn32Ga16In2 alloy .
Now, we compare the results of the strain and calorimetric DSC measurements. Figure 3 shows the temperature dependence of the MFIS and entropy change. The entropy change ΔS = S(6 T) - S(0 T) was obtained from magnetization results and DSC results between zero field and 6 T, from the DSC results ΔS in steady fields .
ΔS shows a finite value above 330 K. On the contrary, the MFIS shows almost zero below 330 K. The reversible MFIS (magnetostriction) was observed below 330 K. Above 330 K, irreversible MFIS and S-shape like M-H curve were observed. Considering these results, in the irreversible region T≥ 330 K, metamagnetic and reverse martensitic transition occurred between the paramagnetic martensite and ferromagnetic parent austenite phases. Around TR, large latent heat was observed by DSC measurement. The irreversible MFIS, S-shape like M-H curve, and the observation of latent heat indicates that this transition is first-order transition. Therefore, in the finite ΔS value region (330 K≤T≤ 390 K), irreversible and large MFIS can be observed. This result indicates the strong influence of magnetic fields for magneto-structural transformation.
3.2. Forced magnetostriction around the critical temperatures
In this section, we offer a topic of forced magnetostriction around the Curie temperature or magneto-structural transition temperature. The spin fluctuation theory of itinerant electron magnetism suggests that the critical index δ is defined by the critical magnetic isotherm function, H ∝ Mδ, where δ is around 5 . Some scientists studied this relation concerning itinerant ferromagnetism. Nishihara et al. studied the magnetic field dependences of Ni and Ni2MnGa . As for Ni, the M4 versus H/M plot shows the reasonable linear relation at the Curie temperature. The critical temperature of the spin fluctuation temperature, TA, was obtained as 1.76 × 104 K. This value is comparable with the value of 1.26 × 104 K, which was obtained by neutron diffraction experiments . As for Ni2MnGa, the critical index δ of the magnetic field dependence of the magnetization, H ∝ Mδ, at the Curie temperature was 4.70 ± 0.5 . We measured the magnetization of Ni2MnGa at the Curie temperature, TC = 375 K. Figure 4 presents the Mδ−1 versus H/M plot. This figure indicates good linearity. These results indicate that the critical index δ of the magnetic field dependence of the magnetization is 4.70 and confirms the result of the former magnetization experiment.
In this study, we measured the magnetostriction of Ni2MnGa at the Curie temperature in order to investigate the magnetization dependence of the forced magnetostriction. Figure 5 presents the magnetostriction ΔL/L versus M4 plot. The dotted line indicates a linear plot in order to guide the eyes. The result shows good linearity. It is considered that this result orders the Takahashi’s spin fluctuation theory. The magnetization analysis of Ni41Co9Mn31.5Ga18.5 around the Curie temperature in the martensite phase according to the Takahashi’s spin fluctuation theory was performed in the former article, as mentioned in Section 1 .
We studied the magnetostriction at the Curie temperature in the martensite phase, TCM = 263 K. At this temperature, no structural phase transition occurred. Therefore, the striction under magnetic fields was decided as the magnetostriction. Figure 6 shows the plot of the magnetostriction against M2 at 263 K for Ni41Co9Mn31.5Ga18.5. The magnetostriction was not proportional to M2. The plot was rounded. The plot of the numerically estimated magnetostriction at TC was also rounded against M2 . Figure 7 shows the plot of the magnetostriction against M4 at 263 K. The dotted lines are linearly fitted lines. The fitted line passed the origin and shows good linearity, as that of Ni2MnGa. It is conceivable that these results indicate that the magnetostriction is proportional to the fourth power of the magnetization, M4.
Further, we investigated the MFIS around the reverse martensitic transition temperature. Figures 8 and 9 show the magnetic field dependences of the magnetization and the MFIS at 330 and 340 K, respectively. These temperatures are around the reverse martensitic transition start temperature. The gradient of the magnetization and magnetostriction has tendencies toward increasing with the magnetic field increases for each temperature. However, the degree of the rate of increase of the magnetostriction is larger than that of the magnetization. From these figures, a correlation between the magnetostriction and magnetization could not be identified. As mentioned in Section 1, Ni41Co9Mn31.5Ga18.5 is an itinerant ferromagnet. The magnetostriction is proportional to M4 at the Curie temperature in the martensite phase. Therefore, it is presumed that the MFIS is also conformed to the power law suggested by Takahashi’s theory.
Figure 10 shows the plot of MFIS against M2 at 330 and 340 K. The dotted lines are linearly fitted lines. These fitted lines did not pass the origin, and the plot was rounded. Figure 11 shows the plot of MFIS against M4 at 330 and 340 K. The dotted lines are linearly fitted lines. These fitted lines passed the origin. It is conceivable that these results indicate that the MFIS is proportional to the fourth power of the magnetization, M4, which was suggested by Takahashi’s theory . It is interesting that the M4 behavior matures until 7 T at 330 K. At this temperature, magneto-structural transition (reverse martensitic and metamagnetic transition) occurred.
3.3. The time response of the magnetic field-induced strain of Ni41Co9Mn31.5Ga18.5
In order to investigate time response of the MFIS, fast speed sweeping of the magnetic fields was performed at 354 K, as shown in Figure 12. The applied magnetic field increased from the zero magnetic field to 1.66 T in 8.0 s and under atmospheric pressure. Figure 13 shows the MFIS, in which the applied magnetic field increased from the zero magnetic field to 1.66 T in 60 s. As for an 8.0-s mode, 2.2 × 10−4 MFIS was observed, which was 80% of the MFIS in a 60-s mode. This indicates that a high-speed transition has occurred on applying magnetic fields.
The MFIS effect occurs at the temperature between room temperature and 370 K; therefore, it is useful for magnetic sensors, or actuators in the high temperature region, ex. the engine room in the motor vehicles.
In order to investigate the magnetic functionality of polycrystalline metamagnetic Heus-ler alloy Ni41Co9Mn31.5Ga18.5, magnetic field-induced strain (MFIS) measurements were performed. Strain gauge was fixed parallel to the long distance direction (4.0 mm) of the sample. The external magnetic field was applied parallel to the long distance direction of the sample, and the elongation of the sample was measured. A 0.12% MFIS was observed at 340 K and 10 T. Strict MFISs between 300 and 370 K were observed. These magneto-structural variances acted in concert with the metamagnetic property observed by the magnetization measurements and magneto-caloric property observed by the caloric measurements in the applied magnetic fields. The MFISs were proportional to the fourth power of the magnetization, and this result is in agreement with Takahashi’s spin fluctuation theory of itinerant electron magnetism. The investigation of time response of the MFIS was performed by means of a sweep water-cooled electric magnet, and zero magnetic field to 1.66 T in 8.0 s at 354 K. 2.2 10−4 MFIS was observed, which was 80% of the MFIS in a 60-s mode. This indicates that a high-speed transition has occurred on applying magnetic fields.
The authors thank Mr. M. Okamoto for helping prepare equipment for MFIS measuring system. This experimental study was partly performed at High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University.
Conflicts of interest
The authors declare no conflict of interest.