Magnetocaloric and Magnetic Properties of Meta‐Magnetic Heusler Alloy Ni41Co9Mn31.5Ga18.5

Ni41Co9Mn31.5Ga18.5 is a magnetic Heusler alloy, which indicates metamagnetic transition at the reverse martensite transition. In this paper, caloric measurements were performed and discussed about magnetocaloric effect. We also performed magnetization measurements around Curie temperature TC in the martensite phase and analyzed by means of the spin fluctuation theory of itinerant electron magnetism. From the differential scanning calorimetry (DSC) measurements in zero fields, the value of the latent heat λ was obtained as 2.63 kJ/kg, and in magnetic fields the value was not changed. The entropy change ΔS was − 7.0 J/(kgK) in zero fields and gradually increases with increasing magnetic fields. The relative cooling power (RCP) was 104 J/kg at 2.0 T, which was comparable with In doped Ni41Co9Mn32Ga16In2 alloy. The results of magnetization measurement were in agreement with the theory of Takahashi, concerning itinerant electron magnetism. From the M4 vs H/M plot, the spin fluctuation temperature TA can be obtained. The obtained TA was 703 K and which was 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.


Introduction
Recently, ferromagnetic shape memory alloys (FSMA) have been studied extensively as candidates for highly functional materials.Between FSMA, Ni 2 MnGa is the most renowned alloy [1].The alloy has a cubic L2 1 Heusler structure, with a space group of Fm3m, and ferromagnetic transition occurs at the Curie temperature, T C , 365 K [2,3].Cooling from ordinary temperature, a martensite transition occurs at the martensite transition temperature, T M , 200 K. Below T M , a superstructure state is realized as a result of lattice modulation [4,5].For Ni 2 MnGa type alloys, T M 's are varied from 200 to 330 K by non-stoichiometrically varying the concentration of constituent elements of the alloys.Sakon et al. studied about the magnetic properties of Ni 50+x Mn 27-x Ga 23 [6].The martensite transition and the ferromagnetic transition occurred at the same temperature at the martensite transition temperature T M for x = 2.5, 2.7.The T M shift in magnetic fields around a zero magnetic field was estimated to be dT M /dB = 1.1 ± 0.2 K/T, thus indicating that magnetization influences martensite transition.
New alloys in the Ni-Mn-In, Ni-Mn-Sn, and Ni-Mn-Sb Heusler alloy systems that are expected to be ferromagnetic shape memory alloys have been studied [7,8].A metamagnetic transition from paramagnetic martensite phase to ferromagnetic austenite phase was observed, and reverse martensite transition induced by magnetic fields was occurred under high magnetic fields [9,10].These alloys are promising as a metamagnetic shape memory alloys with a magnetic field-induced shape memory effect (MSIF) and as magnetocaloric materials.Ni-Co-Mn-In alloys, in which Co is substituted for Ni in Ni-Mn-In alloys to increase the Curie temperature, indicate shape memory behaviors in compressive stress-strain measurements.It is noticeable that 3% MFIS has been observed for Ni 45 Co 5 Mn 36.7 In 13.3 [11].
The substitution of Co for Ni or Ga atoms in Ni 2 MnGa type alloys has turned the magnetic ordering of the parent phase from partially antiferromagnetic or paramagnetic to ferromagnetic, resulting in a large magnetization change across the transformation, which dramatically enhances the magnetic field driving force .The phase diagram in the temperatureconcentration plane is determined on the basis of the experimental results.The determined phase diagram is spanned by a paramagnetic austenite (Para-A) phase, paramagnetic martensite phase, ferromagnetic austenite phase, ferromagnetic martensite (Ferro-M) phase of Ni 50-x Co x Mn 31.5 Ga 18.5 [41].The measurements indicated that a magnetostructural transition between the Para-A and Ferro-M phases.As for Ni 2 MnGa 1-x Co x (0 ≤ x ≤ 0.20), which was substituted of Co for Ga, the measurements showed that a magnetostructural transition between the Para-A and Ferro-M phases does not appear in this alloy system [21].Therefore, the experimental studies of the Ni 2 MnGa type Heusler compounds, which were substituted of Co for Ni atoms, are important to clarify the nature of the magnetostructural interactions, which is one of the important problems in the physics of Heusler compounds.The transformation temperature can be downshifted by magnetic field at a rate dT R /μ 0 dH or dT M /μ 0 dH up to 14 K/T in Ni 37 Co 13 Mn 32 Ga 18 [39].The aging effect is also important.Segui et al. measured the thermo-magnetization, M-T, of Ni 43 Co 7 Mn 32 Ga 18 at the constant magnetic fields of 5 mT [13,15,42].As longer aging time, the larger value of the magnetization was obtained at ferromagnetic austenite phase around 420 K.This indicates that the improvement of atomic order enhances the ferromagnetic character.Castillo-Villa et al. reported about the elastocaloric effect in a Ni 50 Mn 25-x Ga 25 Co x [25].They also studied the influence of applied magnetic fields on this effect experimentally, and a comparative investigation with the magnetocaloric effect, which was exhibited by the alloy, was performed.Both of the elastocaloric and magnetocaloric effects are a result of the martensite transition incurred by the alloy.The influence of a compressive stress and of a magnetic field is to gain the stability of the martensite phase.It leads to an increase of the transition temperature with applied stress and magnetic field.The magnetic properties of Ni 33.0 Co 13.4 Mn 39.7 Ga 13.9 were investigated by Xu et al. [28].It is noticeable that the kinetic arrest phenomenon was observed at about 120 K by thermomagnetization measurements.Magnetic field-induced transformation was also detected at the temperatures between 4.2 and 300 K.In this phenomenon, martensite transition is interrupted at certain temperatures (kinetic arrest temperature, T KA ) during field cooling and does not proceed with further cooling.It was confirmed that the transformation entropy change below 120 K becomes almost zero, which results in the kinetic arrest phenomenon by evaluation of the equilibrium magnetic fields and temperatures based on the transformation fields and temperatures.
Albertini et al. has been performed experimental studies about the composition dependence of the structural and magnetic properties of the Ni-Mn-Ga ferromagnetic shape memory alloy substituted of Co for Ni atoms around the composition of Ni 50 Mn 30 Ga 20 [12,31].The magnetic and structural properties displayed remarkable discontinuities across the martensite transition.There was a clear jump (ΔM) in the saturation magnetization at the transformation, which indicates that a metamagnetic transition appeared in the magnetic field.The field dependence of the martensite transition temperature, dT M /μ 0 dH, and that of the crystalline volume change, ΔV/V, was reported.The most notable alloy is Ni 41 Co 9 Mn 32 Ga 18 .When cooling from 500 K, a ferromagnetic transition in the austenite phase at T C A = 456 K.At the martensite transition temperature, T M = 420 K, the AC susceptibility decreased drastically.Below 300 K, the AC susceptibility gradually increased and a distinct peak was found at the Curie temperature T C M = 257 K in the martensite phase.Heating from 200 K, the Curie temperatures T C M and T C A were just the same with the temperatures in the cooling procedure.The reverse martensite temperature T R was 436 K. Therefore, the AC susceptibility indicates re-entrant magnetism, ferromagnetic-paramagnetic state, which should be released to the crystal structures.The dT M /μ 0 dH and ΔV/V were found to be considerably enhanced by the additional in-doping of the Ni-Co-Mn-Ga alloy [12].The entropy change is larger than that of Ni-Co-Mn-Ga, which suggests large relative cooling power (RCP).
We studied about the physical properties and magnetism of Ni 50-x Co x Mn 31.5 Ga 18.5 [41].Crystallographic, thermal strain, and magnetic properties of Ni 50-x Co x Mn 38.5 Ga 18.5 (0 ≤ x ≤ 9) were investigated across the martensite transition temperature T M and the reverse martensite transition temperature T R at atmospheric pressure above T C M = 263 K.These transition temperatures increased gradually with increasing Co component x.Moreover, temperature hysteresis in the thermal cycles of the magnetization across the T R and T M , became larger with increasing x.As for x = 9, Ni 41 Co 9 Mn 31.5 Ga 18.5 , extensive temperature hysteresis of T M - T R = 65 K was found in the thermal strain measurement.The metamagnetic transition was observed from the paramagnetic martensite phase to the ferromagnetic austenite phase between 330 and 390 K.Under atmospheric pressure, the observed magnetostriction value of this alloy at 350 K was 0.11%.This value is larger than that of Tb-Dy-Fe single crystal [43].In this study, Ni 50-x Co x Mn 38.5 Ga 18.5 was polycrystal, and it is easy for processing and handling.Moreover, the magnetostriction effect occurred at a temperature between room temperature and 400 K, which was suggested that it is useful in the high temperature region, for example, apparatus in the engine room of the motorcar.
The effects of Co addition on the properties of Ni 8-x Mn 4 Ga 4 Co x (x = 0, 1, 2) ferromagnetic shape memory alloys are systematically investigated by first-principles calculations by Bai et al. [26].The results of formation energy indicate that the added Co preferentially occupies the Ni sites in Ni 2 MnGa alloy.The total energy difference between the paramagnetic and the ferromagnetic austenite plays an important role on the Curie transformation.Increasing Co content, electron density of states, DOS, of down spins around the Fermi level gradually decreases.On the contrary, those of the up spin almost remain without changing.This causes enhancement of the magnetic moments in these alloys.This result indicates that the investigation of the itinerant electron magnetism is important to understand the physics and magnetism of these alloys more deeply.
In this paper, caloric measurements were performed.On the basis of the experimental results, magnetocaloric effect was discussed.We also studied about the itinerant electron magnetic properties of Ni 41 Co 9 Mn 31.5 Ga 18.5 .We performed the magnetization measurements by means of the pulsed magnetic fields.The M 4 vs H/M plot crossed the coordinate axis at the Curie temperature in the martensite phase, T C M , and the plot indicates a good linear relation behavior around the T C M .The magnetization results were analyzed by means of the theory of Takahashi, concerning itinerant electron magnetism [44,45] and the spin fluctuation temperature T A can be obtained.We discussed about the itinerant magnetism of Ni 41 Co 9 Mn 31.5 Ga 18.5 by means of the magnetization measurements.

Experimental procedures
The sample used in this study was synthesized at Yamagata University.The Ni 41 Co 9 Mn 31.5 Ga 18.5 alloy was prepared by arc melting 4N Ni, 4N Co, 4N Mn, and 6N Ga in an argon atmosphere.The sample annealed at 1123 K for three days to homogenize the sample in a double evacuated silica tube, and then quenched in cold water.The obtained sample was polycrystalline.DSC measurements were performed by means of Helium-free magnet at High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University.The bore of this magnet is 100 mm in the air and which installed the factory-made DSC equipment.
Magnetization measurements were performed by means of the pulsed field magnet at Ryukoku University.The absolute value was adjusted by Ni.The diamagnetism of the sample was also concerned to analyze the field dependence of the magnetization.The calorimetric measurements, which allowed for the estimation of the latent heat and magnetocaloric analysis, were performed with factory-made differential scanning calorimeter able to work up to 6 T.This setup exploits Peltier cells in order to measure heat flow of the sample.Calorimetric measurements of Ni 41 Co 9 Mn 31.5 Ga 18.5 polycrystalline ferromagnetic shape memory alloy (FSMA) were performed across the T R .As for the reference value of the latent heat λ at zero magnetic fields, calorimetric measurements were performed by the commercial DSC system, DSC3300 (Materials Analysis and Characterization Co., Ltd.).The measured value of the λ at zero fields was 2.63 kJ/kg around T R = 380 K.The thermodynamic properties of the presented sample in magnetic fields were studied experimentally by measuring the heat flow by means of the DSC equipment.The four panels of Figure 4 show the heat flow of Ni 41 Co 9 Mn 31.5 Ga 18.5 in zero and magnetic fields.The endothermic reaction was occurred around the reverse martensite temperature T R .These calorimetry experiments confirm the values of the ratio of field change of the transition temperature dT R /μ 0 dH deduced from thermal expansion measurements [46].The latent heat λ of the fully transformed reverse martensite transition, as shown in the four panels of      Figure 7 shows the entropy change ΔS = S(μ 0 H) - S(0) of Ni 41 Co 9 Mn 31.5 Ga 18.5 .The relative cooling power (RCP) was calculated by integrating the ΔS in the temperature, as shown in Figure 8.The calculated RCP was 104 J/kg at 2.0 T, which was comparable with Ni 50 Mn 35 In 14 Si 1 and Ni 41 Co 9 Mn 32 Ga 16 In 2 alloy [47].

Magnetocaloric effect of
We also performed the DSC measurement of Ni 52.5 Mn 24.5 Ga 23 in zero and magnetic fields by means of the water-cooled electromagnet in Ryukoku University.Figure 9a shows the heat flow of Ni 52.5 Mn 24.5 Ga 23 in a heating process.The endothermic reaction was occurred around T R = 348 K.In the external magnetic field of 1.5 T, the reaction was also occurred.The dT R /μ 0 dH obtained from DSC measurements in Figure 9a were 1.1 K/T, which is comparable to the results of the thermal strain measurements [6]. Figure 9b shows the latent heat λ of Ni 52.5 Mn 24.5 Ga 23 .The λ is larger than that of Ni 41 Co 9 Mn 31.5 Ga 18.5 .Figure 9c shows the entropy change ΔS of Ni 52.5 Mn 24.5 Ga 23 .The value was 4.6 J/kg K, which is comparable to the value of Ni 52.6 Mn 23.1 Ga 24.3 [48].Figure 9d shows the RCP of Ni 52.5 Mn 24.5 Ga 23 .The value was 36 J/kg.
Table 1 shows the T M , ΔS, δT, and RCP at 2 T. δT indicates the half width of the ΔS.The ΔS, δT, and RCP of Ni 52.5 Mn 24.5 Ga 23 were estimated from the DSC result at zero field and 1.5 T in this study.The three alloys of the beginning cause martensite phase transition at temperature of the T M in paramagnetic austenite from ferromagnetic martensite.Four last alloys cause reentrant magnetism at the temperature of T M .The dT M /μ 0 dH of the four last alloys is larger than that of the three alloys of the beginning.Therefore, the RCP is relatively larger than former alloys.The magnetostructural transformation in this system can be described, in the frame of a simple geometrical model, by a relation linking the field-induced adiabatic temperature change ΔT ad with dT M /μ 0 dH, with the martensite specific heat value C p Mart = 490 J/kg K, which was obtained by means of DSC in zero fields, the transformation temperature T M and the entropy change ΔS [47], as the formula of,

Sample
Here, ΔT M = (dT M /μ 0 dH) • μ 0 ΔH is the effective transformation shift in temperature induced by a magnetic field variation μ 0 ΔH.Fabbrici et al. commented about the relation between ΔT ad and dT M /μ 0 dH.Eq. ( 1) provides important information about the relation between ΔT ad , dT M / μ 0 dH and ΔS.ΔT ad is not instantaneously proportional either to dT M /μ 0 dH or ΔS.This is a immediate consequence of the fact that the minute relation ΔT ad = (T M /C p Mart ) ΔS cannot be directly extrapolated to finite differences.This is because that the specific heat, C p (H, T) depends on magnetic field and the temperature.
In order to obtain an adiabatic temperature change ΔT ad from the results of the thermal measurements, the model proposed by Procari et al. is used [19,53].In Figure 11, the gradient of the entropy curve between AC in zero fields is equal to C p /T = 1.5 ± 0.1 J/kg K 2 is considered, where C p is the specific heat.According to Porcali's model, the ΔT ad is obtained as −4.5 K, which was shown in an arrow.The error between the calculated value ΔT ad = −3.2K from Eq. ( 1) and experimentally obtained value ΔT ad = −4.5 K from Figure 10 is 30%.It is correct qualitatively.Table 2 shows the adiabatic temperature change of the Heusler alloys.The absolute value of ΔT ad of the alloys, which shows re-entrant magnetism and metamagnetism is larger than that of the alloys which shows the magnetostructural transition from martensite ferromagnet to austenite paramagnet.This result is due to the large dT M /μ 0 dH value of Ni 41 Co 9 Mn 32 Ga 16 [41].The T M of Ni 50-x Co x Mn 31.5 Ga 18.5 gradually decreases with increasing content x and temperature above x = 9, T M drastically decreases.The T M of Ni 50-x Co x Mn 39 Sn 11 also shows same x dependence.Around x = 8.5, T M drastically decreases.Entel et al. also suggested that superparamagnetic behavior or superspin glass phase has been appeared in martensite phase.As observed for some nonmagnetic martensitic systems, disorder and local structural distortions can lead to strain glass in austenite.Wang et al. reported that both a strain glass transition and a ferromagnetic transition take place in a Ni 55-x Co x Mn 20 Ga 25 Heusler alloys [22], which results in a ferromagnetic strain glass with coexisting short-range strain ordering and long-range magnetic moment ordering for 10 ≤ x ≤ 18.As for Ni 50-x Co x Mn 31.5 Ga 18.5 , microscopic (X-ray diffraction, neutron diffraction, μSR, etc.), measurements should be needed to clarify these problems.The complex magnetic and structural properties of Co-doped Ni-Mn-Ga Heusler alloys have been investigated by using a combination of first-principles calculations and classical Monte Carlo simulations by Sokolovskiy et al. [54].The Monte Carlo simulations with ab initio exchange coupling constants as input parameters allow one to discuss the behavior at finite temperatures and to determine magnetic transition temperatures.The simulated magnetic and magnetocaloric properties of Co-and in-doped Ni-Mn-Ga alloys were in good qualitative agreement with the available experimental data.A similar calculation is expected in Ni 50-x Co x Mn 31.5 Ga 18.5 .

Sample λ (kJ/kg) ΔS (J/kg K) ΔT M (K) T M (K) ΔT ad (μ 0 H[T]) (K) Reference
Ni 50 Mn 30 Ga 20  We performed the magnetization measurements by means of the pulsed magnetic fields in order to investigate the itinerant electron magnetic properties of Ni 41 Co 9 Mn 31.5 Ga 18.5 .Takahashi proposed a spin fluctuation theory of itinerant electron magnetism [44,45].The induced magnetization M is written as the formula of, where, = 0 is a spontaneous magnetization in a ground state.N 0 is a molecular number.= , where g is the Landé g-factor and S is a spin angular momentum.T A is the spin fluctuation parameter in k-space (momentum space).In most cases, the critical temperature dependence was determined using the Arrott plot.The analysis is based on the implicit assumption that the linearity is always satisfied.Takahashi suggested that the Arrott plot is not applicable in much itinerant d-electron ferromagnets and the revision is necessary in the itinerant electron magnetism [45].
Figure 11 shows the magnetization process of Ni 41 Co 9 Mn 31.5 Ga 18.5 around the T C M .The horizontal axis is the external magnetic fields.As for the ferromagnetic materials, the diamagnetic effect should be concerned.The effective field H eff is written as the formula of, where H is the external magnetic fields, M is the measured magnetization value, and N is a diamagnetic factor.As for this sample, N = 0.11.
Eq. ( 2) can be written as the formula of, and δ = 5, and D is the constant value.From Eq. ( 4), δ was demanded using such an expression as below [56].where H eff max is the maximum value of the effective magnetic fields, and M max is the maximum value of the measured magnetization.δ can be demanded when a logarithm of the statement are taken, as the formula of, Eq. ( 5).
Figure 12 shows the logarithm plot of Eq. ( 5).The gradient of the X-Y plots indicate the critical index δ.Table 3 shows the index δ and the standard deviation of δ around T C M = 263 K. Between 262 and 264 K, the error of δ is small.These results indicate that the critical index δ is 5.2(+-, plusminus sign) 0.2.  .The result was in agreement with the theory of Takahashi, concerning itinerant electron magnetism [21,22].From the M 4 vs H/M plot, the spin fluctuation temperature T A can be obtained.The obtained T A was 7.03 × 10 2 K and which was much smaller than Ni (1.76 × 10 4 K).
Table 4 indicates the values of p s , T C , and T A estimated from magnetization measurements by means of Eq. ( 1).MnSi and URhGe are the compounds, which indicate small magnetic moment.The smallness of the moment p s is due to the spin polarization.UGe 2 also indicate small magnetic moment compared to the full moment of U 5f electron, 3.6 μ B /U.This is due to the large magnetic anisotropy, due to the spin polarization band [58][59][60].The magnetic anisotropy energy is estimated as 6.17 meV = 107 T [58].T A is the spin fluctuation temperature, and it reflects width of the quasiparticle at the Fermi surface.Supposing that T A is large, narrow quasi-fermion (electron) band is formed at the Fermi level and the correlations between quasi fermions are strong.The Zommerfeld coefficient γ also indicates the strength of the correlations of the fermions (electrons).The γ of URhGe and UGe 2 are 163 and 110 mJ mol -1 K -2 , respectively.The γ of normal metals, Cu, Ni is around 1 mJ mol -1 K -2 .Therefore, the γ is two orders larger than that of normal metals.Supposing that γ is large, the narrow quasi-fermion (electron) band is formed at the Fermi level.The density of states of the band is large, which indicates the correlations of the electrons are large in U compounds.As for Ni 41 Co 9 Mn 31.5 Ga 18.5 , the T A is 7.03 × 10  to the Jahn-Teller effect as a source of the tetragonal distortion of the crystal structure of these alloys.However, they also suggested that the external magnetic field of 60 T seems to be high enough to suppress the Jahn-Teller distortion of crystal lattice of Ni

Conclusions
We studied about the magnetocaloric properties of Ni 41 Co 9 Mn 31.5 Ga 18.5 by means of differential scanning calorimetry (DSC) measurements.Magnetocalorimetric measurements and magnetization measurements of Ni 41 Co 9 Mn 31.5 Ga 18.5 polycrystalline ferromagnetic shape memory alloy (FSMA) were performed across the T R , at atmospheric pressure.When heating from the martensite phase, a steep increase in the thermal expansion due to the reverse martensite transition at T R was observed by the thermal expansion measurements.These transition temperatures decreased gradually with increasing magnetic field.The field dependence of the reverse martensite transition temperature, dT R /d(μ 0 H), is -7.0 K/T around zero fields.From the DSC measurements in zero fields, the value of the latent heat λ was obtained as 2.6 kJ/kg, and in magnetic fields, the value was not changed.The entropy change ΔS was -7.0 J/(kgK) in zero fields and gradually increases with increasing magnetic fields.The relative cooling power (RCP) was 104 J/kg at 2.0 T, which was comparable with in-doped Ni 41 Co 9 Mn 32 Ga 16 In 2 alloy [47].
In order to investigate the itinerant electron magnetic properties of Ni 41 Co 9 Mn 31.5 Ga 18.5 , we performed the magnetization measurements by means of the pulsed magnetic fields.The M 4 vs H/M plot crossed the coordinate axis at the Curie temperature in the martensite phase, T CM , and the plot indicates a good linear relation behavior around the T CM .The result was in agreement with the theory of Takahashi, concerning itinerant electron magnetism [44,45].
From the M 4 vs H/M plot, the spin fluctuation temperature T A can be obtained.The obtained T A was 7.03 × 10 2 K and which was smaller than Ni (1.76 × 10 4 K).The value was comparable to that of UGe 2 (4.93 × 10 2 K), which is famous for the strongly correlated heavy fermion ferromagnet [58].

3. 1 .
Crystallography of Ni 41 Co 9 Mn 31.5 Ga 18.5 From X-ray powder diffraction shown in Figure 1, the sample was confirmed as a single phase with a tetragonal D0 22 structure at 298 K, as shown in Figure 2. The lattice parameters of the tetragonal structure were a = 3.8794 Å and c = 6.6247Å.The size of the sample was 0.8 mm × 3.0 mm × 4.0 mm.

Figure 2 .
Figure 2. Schematic drawings of crystal structures in austenite phase and martensite phase.

Figure 3 .
Figure 3. Scanning electron microscope i m age of Ni 41 Co 9 Mn 31.5 Ga 18.5 at 298 K by means of FE-SEM.

Figure 5
was calculated by integrating the heat flow profile in Figure4for each magnetic field.The entropy S was calculated as S = λ/T.The entropy of Ni 41 Co 9 Mn 31.5 Ga 18.5 at 0 and 2 T are shown in Figure6.

Figure 4 .
Figure 4. Heat flow of Ni 41 Co 9 Mn 31.5 Ga 18.5 in zero and magnetic fields.
In 2 and Ni 41 Co 9 Mn 31.5 Ga 18.5 .Consequently, large MCE has been appeared in Ni 41 Co 9 Mn 31.5 Ga 18.5 .Entel et al. studied about Ni 50-x Co x Mn 39 Sn 11 for 0 ≤ x ≤ 10 [16].The experimental phase diagram of Ni 50-x Co x Mn 39 Sn 11 resembles that of Ni 50-x Co x Mn 31.5 Ga 18.5

Figure 10 .
Figure 10.Real heating calorimetric S(T, H) curves across the reverse martensite transition of Ni 41 Co 9 Mn 31.5 Ga 18.5 .The geometrical construction has superimposed on them.

Figure 13
Figure 13 shows the M 4 vs H eff /M plot of Ni 41 Co 9 Mn 31.5 Ga 18.5 at T C M = 263 K.The M 4 vs H eff /M plot crossed the coordinate axis at the Curie temperature in the martensite phase, T C M , and the plot indicates a good linear relation behavior around the T C M

Figure 13 .
Figure 13.M 4 vs H eff /M plot of Ni 41 Co 9 Mn 31.5 Ga 18.5 at 263 K. Dotted line is the extrapolated line.The value p s of Ni 41 Co 9 Mn 31.5 Ga 18.5 , suggested in Table4, is smaller than that of Ni 2 MnGa.The small value of p s has been observed at Ni 1.65 Co 0.28 Mn 1.31 Ga 0.62 In 0.67[14].The p s of this alloy was 1.61 μ B /f.u. at 5 T in ferromagnetic martensite phase.M-H curve shows metamagnetic transition at 42 and at 60 T, the magnetic moment reached to 5.0 μ B /f.u.Karamad et al. point

Table 1 .
The martensite transition temperature T M , the maximum value of the entropy change ΔS, the half width of the entropy change δT, and the relative cooling power (RCP) at 2 T.

Table 2 .
The adiabatic temperature change of the Heusler alloys.
Nishihara et al. measured the magnetization of Ni and Ni 2 MnGa precisely [55].Direct proportionality was observed in the M 4 vs H/M plot at the Curie temperature for Ni.The critical index δ (defined as ∝ ) for Ni and Ni 2 MnGa is 4.73 and 4.77, respectively.The critical index δ for Fe, CoS 2 and ferromagnetic Heusler alloys, Co 2 VGa is 4.6, 5.2 and 4.93, respectively ([45] and references there in).

Table 3 .
2 K, 6.45 × 10 2 K for Ni 52.5 Mn 24.5 Ga 23 , and 4.93 × 10 2 K for Ni 2 MnGa.These values are comparable to that of UGe 2 (4.93 × 10 2 K), This result indicates that the correlations of the electrons are strong in Ni 41 Co 9 Mn 31.5 Ga 18.5 , Ni 52.5 Mn 24.5 Ga 23 , and Ni 2 MnGa.The critical index δ and the standard deviation of δ around T C M = 263 K.

Table 4 .
1.65 Co 0.28 Mn 1.31 Ga 0.62 In 0.67 .Further experimental and theoretical investigations are needed to clarify this problem.Experimentally estimated values of p s , T C , and T A from magnetization measurements.