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Materials 2020, 13, 2017; doi:10.3390/ma13092017 www.mdpi.com/journal/materials Article The Forced Magnetostrictions and Magnetic Properties of Ni 2 MnX (X = In, Sn) Ferromagnetic Heusler Alloys Takuo Sakon 1, *, Junya Yamazaki 1 , Takumi Komori 1 , Takeshi Kanomata 2 , Yasuo Narumi 3 , Masayuki Hagiwara 3 , Hiroyuki Nojiri 4 and Yoshiya Adachi 5 1 Department of Mechanical and Systems Engineering, Faculty of Science and Technology, Ryukoku University, Otsu, Shiga 520-2194, Japan; t170350@mail.ryukoku.ac.jp (J.Y.); t130251@mail.ryukoku.ac.jp (T.K.) 2 Research Institute for Engineering and Technology, Tohoku Gakuin University, Tagajo, Miyagi 985-8537, Japan; c1924007@mail.tohoku-gakuin.ac.jp 3 Center for Advanced High Magnetic Field Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan; narumi@ahmf.sci.osaka-u.ac.jp (Y.N.); hagiwara@ahmf.sci.osaka-u.ac.jp (M.H.) 4 Institute for Materials Research, Tohoku University, Sendai, Miyagi 980-8577, Japan; nojiri@imr.tohoku.ac.jp 5 Graduate School of Science and Engineering, Yamagata University, Yonezawa, Yamagata 992-8510, Japan; adachy@yz.yamagata-u.ac.jp * Correspondence: sakon@rins.ryukoku.ac.jp Received: 27 March 2020; Accepted: 23 April 2020; Published: 25 April 2020 Abstract: 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 (ΔL/L) and the forced volume magnetostriction (ΔV/V) were proportional to M 4 , which followed Takahashi’s theory. We compared the forced volume magnetostriction ΔV/V and mechanical parameter, bulk modulus K. ΔV/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. Keywords: ferromagnetic Heusler alloy; magnetostriction; magnetization; itinerant ferromagnetism; spin polarization 1. Introduction Spin fluctuation theories have been proposed to explain the physical properties and the principles of itinerant electron systems [1–7]. Recently, the spin fluctuation theory of itinerant magnetism, known as Takahashi’s theory, was proposed by Takahashi [1–4]. The self-consistent