Magnetic properties of CoFe$$_{2}$$O$$_{4}$$ nanoparticles: experimental characterization and numerical analysis using the Ising model

Abstract In this work, we synthesized superpara-magnetic cobalt ferrite (CoFe $$_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> O $$_{4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>4</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> ) magnetic nanoparticles using the co-precipitation method and performed a comprehensive structural and magnetic characterization. Structural characterization techniques, including X-ray diffraction, Raman spectroscopy, and HRTEM, confirmed the formation of an inverse spinel structure with a lattice parameter of $$a = 8.41$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>=</mml:mo> <mml:mn>8.41</mml:mn> </mml:mrow> </mml:math> Å and an average crystallite size of $$D= 17.7\pm 6.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>17.7</mml:mn> <mml:mo>±</mml:mo> <mml:mn>6.5</mml:mn> </mml:mrow> </mml:math> nm. Raman peak fitting revealed broadened modes, consistent with phonon confinement effects. SQUID magnetometry confirmed superparamagnetic-like behavior of the nanoparticles at room temperature, characterized by low coercivity and remanence, with a blocking temperature of 210 K and saturation magnetization of $$M_{s}=51$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>51</mml:mn> </mml:mrow> </mml:math> emu/g. Complementing the experimental work, we implemented a two-dimensional Ising model through Monte Carlo simulations to analyze the magnetic response within the nanoparticle system.