Origin of the martensitic and austenitic phase transition in core-surface smart nanoparticles with size effects and hysteretic splitting

Abstract

Blume-Emery-Griffiths model is used to study the effects of the bilinear and biquadratic exchange interactions as well as crystal field interaction on the magnetic properties of core-surface smart nanoparticles. From the minimization of the free energy in pair approximation in Kikuchi version, a set of equations for the bond variables and magnetization are derived. Based on the numerical solutions of these equations, magnetization and hysteresis curves are obtained. Besides the first- and second-order phase transitions, martensitic and austenitic phase regions are observed in the phase diagrams of homogeneous and composite nanoparticles and the origin of martensitic transitions (MT)-austenitic transitions (AT) is investigated. It is found that MT-AT occurred for a nonzero biquadratic exchange parameter. On the other hand, nonzero single-ion anisotropy caused the hysteretic splitting in core-surface type nanoparticles. Martensitic and austenitic results of nanoparticles agree with the experimental results in literature.

Thermal Hysteresis Due to the Structural Phase Transitions in Magnetization for Core-Surface Nanoparticles

“…2) is enlarged to simple cubic lattice (sc) in 3D for a cubic nanoparticle. For the number of shells in both structures, each lattice is related to the radius (R) of the nanoparticle [27][28][29]. Therefore, the value of R contains a number of shells and the size of a nanoparticle increases as the number of shells increases.…”

“…By means of mean-field theory (MFT) and Monte Carlo (MC) simulations, magnetostructural phase transitions in some alloys were described via degenerate BEG models in terms of magnetoelastic interactions [31]. In the light of above applications, we have recently used the ordinary BEG model for the investigation of MT/AT transitions in NP systems and observed the behaviours of the MTH loops [28,29]. In the following, we mention briefly the definition of the BEG Hamiltonian and show clearly how it is modified for the C/S NPs with hexagonal and square lattice structures.…”

“…(12). For some selected exchange energies, the MTH behaviours and the temperature-induced M-A phase transitions within the C/S smart NPs are reproduced from our recent publications [28,29] as in Figs. 3-6.…”

Origins of the Exchange-Bias Phenomenology, Coercivity Enhancement, and Asymmetric Hysteretic Shearing in Core-Surface Smart Nanoparticles

“…For these particles the correlations between nearest-neighbors are significant to establish boundaries between core ( ) and surface ( ) parts with different magnetic properties. A similar approach has recently been used by us to investigate the hysteretic splitting of / NPs [31,32]. In the presence of an external magnetic field, we have taken into account only even interactions (or dipolar, quadrupolar, and single-ion anisotropy) between Ising spins in , interface ( ), and parts within the nanoparticle.…”

“…For a complete description of phase transitions arising in bulk systems, the full BEG Hamiltonian with both even and odd interaction terms was studied using various techniques [34][35][36][37][38][39]. But the odd term has not been considered for the analysis of structural transitions in NPs presented in [31,32]. By incorporating odd interaction the PA formalism may provide a theoretical framework for the EB effect and the asymmetry of the hysteresis loops observed in experiments made on a single (or independent) composite nanoparticle.…”