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Experimental studies into the forced magnetostriction, magnetization, and temperature dependence of permeability in Ni 2 MnIn and Ni 2 MnSn ferromagnetic Heusler alloys were performed according to the spin fluctuation theory of itinerant ferromagnetism proposed by Takahashi. We investigated the magnetic field ( H ) dependence of magnetization ( M ) at the Curie temperature T C , and at T = 4.2 K, which concerns the ground state of the ferromagnetic state. The M - H result at T C was analyzed by means of the H versus M 5 dependence. At 4.2 K, it was investigated by means of an Arrott plot ( H / M vs. M 2 ) according to Takahashi's theory. As for Ni 2 MnIn and Ni 2 MnSn, the spin fluctuation parameters in k -space (momentum space, T A ) and that in energy space (frequency space, T 0 ) obtained at T C and 4.2 K were almost the same. The average values obtained at T C and 4.2 K were T A = 342 K, T 0 = 276 K for Ni 2 MnIn and T A = 447 K, T 0 = 279 K for Ni 2 MnSn, respectively. The forced magnetostriction at T C was also investigated. The forced linear magnetostriction (Δ L / L ) and the forced volume magnetostriction (Δ V / V ) were proportional to M 4 , which followed Takahashi's theory. We compared the forced volume magnetostriction Δ V / V and mechanical parameter, bulk modulus K . Δ V / V is inversely proportional to K . We also discuss the spin polarization of Ni 2 MnIn and other magnetic Heusler alloys. The p C / p S of Ni 2 MnIn was 0.860. This is comparable with that of Co 2 MnGa, which is a famous half-metallic alloy.

In this article, we review the magnetostriction and magneto-volume effects of Ni 2 MnGa-type ferromagnetic Heusler alloys at the martensitic, premartensitic, and austenitic phases. The correlations of forced magnetostriction (ΔV/V) and magnetization ( M ), using the self-consistent renormalization (SCR) spin fluctuation theory of an itinerant electron ferromagnet proposed by Takahashi, are evaluated for the ferromagnetic Heusler alloys. The magneto-volume effect occurs due to the interaction between the magnetism and volume change of the magnetic crystals. The magnetic field-induced strain (referred to as forced magnetostriction) and the magnetization are measured, and the correlation of magnetostriction and magnetization is evaluated. The forced volume magnetostriction ΔV/V at the Curie temperature, T C is proportional to M 4 , and the plots cross the origin point; that is, ( M 4 , ΔV/V) = (0, 0). This consequence is in good agreement with the spin fluctuation theory of Takahashi. An experimental study is carried out and the results of the measurement agree with the theory. The value of forced magnetostriction is proportional to the valence electron concentration per atom ( e / a ). Therefore, the forced magnetostriction reflects the electronic states of the ferromagnetic alloys. The magnetostriction near the premartensitic transition temperature ( T P ) induces lattice softening; however, lattice softening is negligible at T C . The forced magnetostriction at T C occurs due to spin fluctuations of the itinerant electrons. In the martensitic and premartensitic phases, softening of the lattice occurs due to the shallow hollow (potential barrier) of the total energy difference between the L2 1 cubic and modulated 10M or 14M structures. As a result, magnetostriction is increased by the magnetic field., Competing Interests: The authors declare no conflict of interest.

The magnetization, electric resistivity, and magnetoresistance properties of Pd 2 Mn 1 . 4 Sn 0 . 6 Heusler alloys were investigated. The Curie temperature of the parent phase, martensitic transformation temperatures, and magnetic field dependence of the martensitic transformation temperatures were determined. The magnetoresistance was investigated from 10 to 290 K, revealing both intrinsic and extrinsic magnetoresistance properties for this alloy. A maximum of about - 3 . 5 % of intrinsic magnetoresistance under 90 kOe and of about - 30 % of extrinsic magnetoresistance under 180 kOe were obtained. Moreover, the thermal transformation arrest phenomenon was confirmed in the Pd 2 Mn 1 . 4 Sn 0 . 6 alloy, and an abnormal heating-induced martensitic transformation (HIMT) behavior was observed., Competing Interests: The authors declare no conflict of interest.

Experimental investigations into the field dependence of magnetization and temperature dependences of magnetic susceptibility in Ni 2+ x MnGa 1- x ( x = 0.00, 0.02, 0.04) and Co₂VGa Heusler alloy ferromagnets were performed following the spin fluctuation theory of itinerant ferromagnetism, called as "Takahashi theory". We investigated the magnetic field dependence of magnetization at the Curie temperature T C , which is the critical temperature of the ferromagnetic⁻paramagnetic transition, and also at T = 5 K, which concerns the ground state of the ferromagnetic state. The field dependence of the magnetization was analyzed by means of the H vs. M ⁵ dependence, and the field dependence of the ground state at 5 K was investigated by means of an Arrott plot ( H/M vs. M ²) according to the Takahashi theory. As for Ni 2+ x MnGa 1- x , the spin fluctuation parameter in k -space (momentum space, T A ) and that in energy space ( T ₀) obtained at T C and 5 K were almost the same. On the contrary, as for Co₂VGa, the H vs. M ⁵ dependence was not shown at T C . We obtained T A and T ₀ by means of an Arrott plot at 5 K. We created a generalized Rhodes⁻Wohlfarth plot of p eff / p S versus T C / T ₀ for the other ferromagnets. The plot indicated that the relationship between p eff / p S and T ₀/ T C followed Takahashi's theory. We also discussed the spontaneous magnetic moment at the ground state, p S , which was obtained by an Arrott plot at 5 K and the high temperature magnetic moment, p C , at the paramagnetic phase. As for the localized ferromagnet, the p C / p S was 1. As for weak ferromagnets, the p C / p S was larger than 1. In contrast, the p C / p S was smaller than 1 by many Heusler alloys. This is a unique property of Heusler ferromagnets. Half-metallic ferromagnets of Co₂VGa and Co₂MnGa were in accordance with the generalized Rhodes⁻Wohlfarth plot with a k m around 1.4. The magnetic properties of the itinerant electron of these two alloys appeared in the majority bands and was confirmed by Takahashi's theory.

Experimental investigations into the field dependence of magnetization and the relationship between magnetization and magnetostriction in Ni 2+x MnGa 1-x (x = 0.00, 0.02, 0.04) alloy ferromagnets were performed following the self-consistent renormalization (SCR) spin fluctuation theory of itinerant ferromagnetism. In this study, we investigated the magnetization of and magnetostriction on Ni 2+x MnGa 1-x ( x = 0.02, 0.04) to check whether these relations held when the ratio of Ni to Ga and, the valence electron concentration per atom, e / a were varied. When the ratio of Ni to Ga was varied, e/a increased with increasing x. The magnetization results for x = 0.02 ( e / a = 7.535) and 0.04 ( e / a = 7.570) suggest that the critical index δ of H ∝ M δ is around 5.0 at the Curie temperature T C , which is the critical temperature of the ferromagnetic⁻paramagnetic transition. This result confirms Takahashi's spin fluctuation theory and the experimental results of Ni₂MnGa. The spontaneous magnetization p S slightly decreased with increasing x . For x = 0.00, the spin fluctuation parameter in k -space (momentum space; T A ) and that in energy space ( T ₀) were obtained. The relationship between p eff / p S and T C / T ₀ can also be explained by Takahashi's theory, where p eff indicates the effective magnetic moments. We created a generalized Rhodes-Wohlfarth plot of p eff / p S versus T C / T ₀ for other ferromagnets. The plot indicates that the relationship between p eff / p S and T ₀/ T C follows Takahashi's theory. We also measured the magnetostriction for Ni 2+x MnGa 1-x (x = 0.02, 0.04). As a result, at T C , the plot of the magnetostriction (Δ L / L ) versus M ⁴ shows proportionality and crosses the origin. These magnetization and magnetostriction results were analyzed in terms of Takahashi's SCR spin fluctuation theory. We investigated the magnetostriction at the premartensite phase, which is the precursor state to the martensitic transition. In Ni₂MnGa system alloys, the maximum value of magnetostriction is almost proportional to the e / a ., Competing Interests: The authors declare no conflict of interest.

Thermal strain, permeability, and magnetization measurements of the ferromagnetic shape memory alloys Ni 50+ x Mn 27- x Ga 23 ( x = 2.0, 2.5, 2.7) were performed. For x = 2.7, in which the martensite transition and the ferromagnetic transition occur at the same temperature, the martensite transition starting temperature T Ms shift in magnetic fields around a zero magnetic field was estimated to be d T = 1.1 ± 0.2 K/T, thus indicating that magnetic fields influences martensite transition. We discussed the itinerant electron magnetism of Ms /d B = 1.1 ± 0.2 K/T, thus indicating that magnetic fields influences martensite transition. We discussed the itinerant electron magnetism of x = 2.0 and 2.5. As for x = 2.5, the M ⁴ vs. B/M plot crosses the origin of the coordinate axis at the Curie temperature, and the plot indicates a good linear relation behavior around the Curie temperature. The result is in agreement with the theory by Takahashi, concerning itinerant electron ferromagnets.