Forced Magnetostrictions and Magnetizations of Ni2+xMnGa1−x at Its Curie Temperature

Abstract

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.

Investigation of the Itinerant Electron Ferromagnetism of Ni2+xMnGa1−x and Co2VGa Heusler Alloys

“…The theory proposed by Takahashi indicates that the magnetic field dependence, H , is proportional to the magnetization, M 5 , at the Curie temperature, T C . This property was obtained by the differential calculus of the magnetization of the spin fluctuation free energy [7,8,9].…”

“…In this theory, the relation between the magnetic fields H and magnetization M is obtained theoretically by the equation of, H=cfalse(TCfalse)M5 where c ( T C ) is the constant value at T C (refer to the references for the derivation process of Equation (1) [7,9]). MnSi [10], Fe x Co 1− x Si [11], CoS 2 [12], and Ni [13] followed the relationship provided in Equation (1).…”

Dynamic magnetic characterization and magnetic particle imaging enhancement of magnetic-gold core–shell nanoparticles

“…It is known that saturation magnetization of magnetic materials is dependent on the crystal lattice. 26,27 Since lattice mismatch at the interface between MNPs and Au can cause structural strain, it is likely that the spin disorder or canting induced by the interfacial strain contributed to the reduction of the saturation magnetization after gold shell coating. 28…”

Magnetic Domain Walls and Macroscopic Magnetization-Related Elastic and Anelastic Effects during Premartensitic Transition in Ni2MnGa

“…λs, μr, and EU are the parameters controlling relaxations and suffering strong variations during the PMT. The absolute value of magnetostriction increases more than three times [6,43], whereas the permeability drops two times, Figure 1b. We could not determine EU directly, since the applied field was well below saturation in our experiments.…”

“…Variations of these two parameters during PMT are opposite: μr drops sharply by ca. 50%, as shown in Figure 1b, whereas the absolute value of λs increases nearly three times [6,43]. Figure 3 visualizes the overall effect of these two competing parameters: it shows the temperature spectra of μr and magnetostriction in [100] direction λ100 (λ100 values are taken from [6]) and of their product, which is proportional to Δμ.…”