ACTA PHYSICA POLONICA A No. 1 Vol. 139 (2021) Transverse Field Effects of Al Concentration on Magnetic Properties of B2-FeAl Nanoparticle H. Yaşar Ocak a , G. Dikici Yıldız b , Y. Göktürk Yıldız c,* , B. Saatçi d , R. Başar a , G. Sarıoğlu e a Department of Physics, Dumlupınar University, 43100, Kütahya, Turkey b Department of Physics, Kırıkkale University, 71450, Kırıkkale, Turkey c Department of Electronics and Automation, Kırıkkale University, 71450, Kırıkkale, Turkey d Department of Physics, Erciyes University, 38280, Kayseri, Turkey e Vocational School of Gediz, Dumlupınar University, 43100, Kütahya, Turkey Received: 19.05.2020 & Accepted: 28.09.2020 Doi: 10.12693/APhysPolA.139.20 ∗ e-mail: gokturk@kku.edu.tr Transverse field dependence of magnetic properties of the B2-FeAl nanoparticle (B2-FeAl-np) is inves- tigated by using the effective field theory (or the Kaneyoshi theory) at H =0 and H =0.25. It is found that the magnetization and the Curie temperature of B2-FeAl-np decrease as the transverse field increases. A similar decrease in the magnetization and the Curie temperature of B2-FeAl is experi- mentally observed by Plazaola et al. with the increase (27.5%, 30%, 32.5% and 35%) of the Al content in B2-FeAl. These theoretical and experimental results revealed that the increase of the Al content in B2-FeAl-np causes an increase in the transverse field of B2-FeAl-np. Thus, the magnetization and the Curie temperature of B2-FeAl-np decrease. However, the ferromagnetic and antiferromagnetic spin splitting of paramagnetic Fe and Al atoms is obtained by a non-zero external magnetic field (H =0.25) at T>TC. topics: B2-FeAl nanoparticle, magnetism, transverse Ising model, effective field theory 1. Introduction FeAl alloys have been extensively studied because of their particular mechanical, electrical, and mag- netic properties. These alloys are potential candi- dates to replace stainless steels due to their high strength, excellent corrosion resistance and low den- sity. Since the FeAl alloys show different mag- netic and physical properties with their composition change and heat treatment, FeAl-based magnetic systems have been extensively investigated [1–3]. The studied issues included the magnetic proper- ties of the binary Fe 90 Al 10 , Fe 80 Al 20 and Fe 50 Al 50 alloys [4], magnetic properties of the FeAl alloys [5], magnetic hysteresis properties of the Fe, FeAl alloys and Fe/Al core/shell cluster composite [6], tempera- ture dependence of magnetization and susceptibility and magnetic hysteresis loops of the B2-type FeAl alloys [7], magnetic hysteresis properties of the D03 and B2-types FeAl alloys [8], temperature and ap- plied magnetic field dependence of magnetization of the FeAl alloys [9, 10], magnetic hysteresis proper- ties (saturation magnetization and coercivity) of the FeAl multilayer samples [11] and magnetic proper- ties of A2, B2, B32, D03 of FeAl alloys [12–22]. In this paper, we consider the unit cell of B2-FeAl reported by Plazaola et al. [23] and Yan et al. [24] for the modeling of the B2-FeAl-np. We focus, how- ever, on the experimental M –T results of B2-FeAl obtained with a different Al content (27.5%, 30%, 32.5% and 35%) by Plazaola et al. [23]. They re- ported that the magnetization and the Curie tem- perature of B2-FeAl decrease with the increase of the Al content. On the other hand, in the transverse Ising model (TIM), a transverse field (Ω ) causes a similar decrease in the magnetization and the Curie temperature of the magnetic systems. There- fore, for the modeling and investigation of the ef- fects of the Al content on magnetic properties of B2-FeAl, we use the TIM within the effective field theory developed by Kaneyoshi [25–27]. 2. Theoretical method We use the TIM within the effective field the- ory developed by Kaneyoshi [25] and focus on the unit cell of B2-FeAl reported by Plazaola et al. [23] and Yan et al. [24] for the modeling of the B2-FeAl nanoparticle (B2-FeAl-np), as shown in Fig. 1. We assume that the iron and aluminum atoms of B2-FeAl-np are the spin-1/2 Ising particles. Ac- cording to the nearest neighbors, B2-FeAl-np has five different magnetic atoms and they are m Fe(1) , m Fe(2) , m Fe(3) , m Fe(4) and m Al . Note that the iron atoms have four different magnetizations ac- cording to their locations on the B2 unit cell of B2-FeAl-np in Fig. 1. 20