Magnetization Changes with Decoration in an Ising Nanoparticle with High Critical Temperature
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ORIGINAL PAPER
Magnetization Changes with Decoration in an Ising Nanoparticle with High Critical Temperature T. Kaneyoshi 1 Received: 10 July 2020 / Accepted: 25 August 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The phase diagram and the thermal variations of total magnetization in Ising nanoparticles with high critical temperature are investigated by decorating the magnetic atoms to the basic nanoparticle, in order to clarify how they may change with the increase of decoration. The thermal variations of magnetizations in nanoparticles under an applied magnetic field are also studied. These are examined by using the effective field theory with correlations. A lot of characteristic phenomena are reported. Keywords Phase diagram . Magnetization . Compensation point . Nanoparticles . Decoration . Effective field theory
1 Introduction Now, two-dimensional (2D) nanoscale materials have been successfully fabricated by using several techniques, such as the adsorption of small gas molecules on the graphene sheet [1]. Experimentally and theoretically, the shell-core concept has been applied for the description of nanoscale materials. The study of 2D magnetic nanoparticles becomes one of the important topics in material science. This is due to their promising biomedical and clinical applications [2]. However, the transition temperatures of magnetic nanoparticles are normally far below from those of bulk magnetic materials. For the actual application of such nanoparticles, it seems to be necessary that the transition temperature TC (N) of a magnetic nanoparticle at least is higher than that (TC (B)) of a corresponding bulk magnetic material. In recent years, the possibility of such nanoscale magnetic materials with TC (N) > TC (B) has been investigated experimentally and theoretically [3–7]. From the theoretical point of view, in order to realize such a nanoparticle with TC (N) > TC (B), one is necessary to that the exchange interaction JS at the surface shell is larger than a critical value, such as the value of exchange interaction at the special point in
* T. Kaneyoshi [email protected] 1
Nagoya University, 1-510, Kurosawadai, Midoriku, Nagoya 458-0003, Japan
the surface magnetism [8]. As discussed in [5–7], the other is the decorations of nanoparticles. The aim of this work is to clarify how the total magnetization mT in a basic magnetic nanoparticle with a high critical temperature (Fig. 1 (a)) may change with the variations (Fig. 1 (b) and (c)) of decoration. The other aim is to clarify how the thermal variation of mT of these nanoparticles is changed, when the value of an applied magnetic field H is changed. In Fig. 1, the part of white circles connected by thin solid bonds is the core and the part connected by bold solid bonds is the surface shell. The bold and thin bonds respectively represent the surface exchange interaction JS and the core (or a corresponding bulk (or square lattice)) exchange interaction J (J > 0.0). Particularly, when the value of JS takes a n
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