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Experimental investigations into the field dependence of magnetization and temperature dependences of magnetic susceptibility in Ni2+xMnGa1−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 TC, 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. M5 dependence, and the field dependence of the ground state at 5 K was investigated by means of an Arrott plot (H/M vs. M2) according to the Takahashi theory. As for Ni2+xMnGa1−x, the spin fluctuation parameter in k-space (momentum space, TA) and that in energy space (T0) obtained at TC and 5 K were almost the same. On the contrary, as for Co2VGa, the H vs. M5 dependence was not shown at TC. We obtained TA and T0 by means of an Arrott plot at 5 K. We created a generalized Rhodes–Wohlfarth plot of peff/pS versus TC/T0 for the other ferromagnets. The plot indicated that the relationship between peff/pS and T0/TC followed Takahashi's theory. We also discussed the spontaneous magnetic moment at the ground state, pS, which was obtained by an Arrott plot at 5 K and the high temperature magnetic moment, pC, at the paramagnetic phase. As for the localized ferromagnet, the pC/pS was 1. As for weak ferromagnets, the pC/pS was larger than 1. In contrast, the pC/pS 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 km 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. [ABSTRACT FROM AUTHOR]

Experimental investigations into the field dependence of magnetization and the relationship between magnetization and magnetostriction in Ni2+xMnGa1−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 Ni2+xMnGa1−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 ∝ Mδ is around 5.0 at the Curie temperature TC, 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 pS slightly decreased with increasing x. For x = 0.00, the spin fluctuation parameter in k-space (momentum space; TA) and that in energy space (T0) were obtained. The relationship between peff/pS and TC/T0 can also be explained by Takahashi's theory, where peff indicates the effective magnetic moments. We created a generalized Rhodes-Wohlfarth plot of peff/pS versus TC/T0 for other ferromagnets. The plot indicates that the relationship between peff/pS and T0/TC follows Takahashi's theory. We also measured the magnetostriction for Ni2+xMnGa1−x (x = 0.02, 0.04). As a result, at TC, the plot of the magnetostriction (ΔL/L) versus M4 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. [ABSTRACT FROM AUTHOR]

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.