Magnetic properties of mixed spin (1, 3/2) Ising nanoparticles with core–shell structure Bayram Deviren a,n , Yunus Şener b Q1 a Department of Physics, Nevsehir Hacı Bektaş Veli University, 50300 Nevşehir, Turkey b Institute of Science, Department of Physics, Nevsehir Hacı Bektaş Veli University, 50300 Nevşehir, Turkey article info Article history: Received 7 January 2015 Received in revised form 7 March 2015 Accepted 14 March 2015 Keywords: Nanoparticles Ising model Critical temperature Phase diagram Effective-field theory abstract The magnetic properties of mixed spin-1 and spin-3/2 Ising nanoparticles with core/shell structure are studied by using the effective-field theory with correlations. We investigate the thermal variations of the core, shell and total magnetizations and the Q-, R-, P-, S-, N- and L-types of compensation behavior in Néel classification nomenclature exists in the system. The effects of the crystal-field, core and shell in- teractions and interface coupling, on the phase diagrams are investigated in detail and the obtained phase diagrams are presented in three different planes. The system exhibits both second- and first-order phase transitions besides tricritical point, double critical end point, triple point and critical end point depending on the appropriate values of the interaction parameters. The system strongly affected by the surface situations and some characteristic phenomena are found depending on the ratio of the physical parameters in the surface shell and the core. & 2015 Published by Elsevier B.V. 1. Introduction Nowadays, magnetic nanoparticles are a developing subject of great interest for both theoretical and experimental researchers due to their great potentially technological applications from a wide range of disciplines, including medical applications [1], en- vironmental remediation [2], catalysis [3], sensors [4], bio- technology [5], magnetic particle imaging [6], magnetic recording media [7], data storage [8], nonlinear optics [9], nanofluids [10], bio-separation [11], and propagation losses [12]. The investigation and improvement of the magnetic nanoparticles can lead to the discovery of advanced magnetic materials with great impact on the new challenges and technologies [13,14]. Magnetic nano- particles also display a wide variety of remarkable magnetic properties such as superparamagnetism, high field irreversibility, high saturation field, extra anisotropy contributions or shifted loops after field cooling as compared with those in respective bulk materials. These phenomena arise from the finite size and surface effects that dominate the magnetic behavior of individual nano- particles [15]. Much effort has been devoted to achieve a better understanding of the behavior of magnetic nanoparticles experi- mentally [16], analytically [17], and in computer simulations [18,19]. Over the last few decades, the magnetic properties of mixed spin Ising systems have been investigated both experimentally and theoretically due to their great potential for technological appli- cations [20,21]. Since these systems have less translational sym- metry than their single spin counterparts, they exhibit many new phenomena which cannot be observed in the single-spin Ising systems and the study of these systems can be relevant for un- derstanding of bimetallic molecular systems based magnetic ma- terials that have properties such as low density, electrical insula- tion, and low temperature fabrication [22]. Moreover, these sys- tems are well adapted to study a certain type of ferrimagnetism and nanomagnetic materials which are of great interest because of their interesting and possible useful properties for technological applications as well as academic researches. One of the well- known and most studied mixed spin Ising systems is the mixed spin-1 and spin-3/2 Ising system. From the experimental point of view, Stanica et al. synthesized quasi-one-dimensional heterotri- nuclear complex [NiCr 2 (bipy) 2 (C 2 O 4 ) 4 (H 2 O) 2 ]H 2 O, which shows a rare case [23] of antiferromagnetism between Ni(II) S ¼ 1 and Cr (III) S ¼ 3/2. We should also mention that the mixed spin-1 and spin-3/2 system is stipulated by a possible prototype of the model for the metal-organic compound [Co(hfac) 2 ]. BNOn studied by Numata et al. [24], which embodies Co(II) ions with spin-3/2 and the chiral triplet biradical ligands BNOn with spin-1 [25]. From the theoretical point of view, the mixed spin-1 and spin-3/2 Ising model with core/shell structure have been studied by using a wide variety of methods in equilibrium statistical physics, recently. The phase diagrams of a ferrimagnetic cubic nanoparticle (nanocube) with a spin-3/2 core surrounded by a spin-1 shell have been 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jmmm Journal of Magnetism and Magnetic Materials http://dx.doi.org/10.1016/j.jmmm.2015.03.061 0304-8853/& 2015 Published by Elsevier B.V. n Corresponding author. Fax: þ90 384 2281043. E-mail address: bayram.deviren@nevsehir.edu.tr (B. Deviren). Please cite this article as: B. Deviren, Y. Şener, Journal of Magnetism and Magnetic Materials (2015), http://dx.doi.org/10.1016/j. jmmm.2015.03.061i Journal of Magnetism and Magnetic Materials ∎ (∎∎∎∎) ∎∎∎–∎∎∎