Dipolar and Quadrupolar Hysteresis in Core-Surface Magnetic Nanoparticles

Abstract

Blume-Emery-Griffiths (BEG) model [1] is used to investigate the hysteretic behaviour of dipole (M) and quadrupole ordering (Q) properties peculiar to core/surface (C/S) type hexagonal Ising nanoparticles (HINPs) [2-3]. The bond energy parameters ( ij  ) and bond variables ( Pij ) are computed using the BEG Hamiltonian for HINPs. Dipole and quadrupole order parameters are calculated from numerical solutions of Pij . It has also been shown that the dipole order parameter as a function magnetic field (M-h) and quadrupole order parameter as a function single-ion isotropy parameter (Q-D) has ‘‘hysteresis’’ character which is generally called quadrupole hysteresis (QD). Shifted QD loops with an asymmetry are observed in the increasing of K and magnetic field (h) values one by one. The observed M˗h hysteresis loops depend on T and D values while Q˗D hysteresis loops depend on T and h values. These are also discussed in relation with the experimental and theoretical findings [4, 5].