Surface anisotropy, hysteretic, and magnetic properties of magnetite nanoparticles: A simulation study

Abstract

In this study we address the role of surface anisotropy on the hysteretic properties of magnetite Fe3O4 nanoparticles and the circumstances yielding both horizontal and vertical shifts in the hysteresis loops. Our analysis involves temperature dependence and particle size effects. Different particle sizes ranging from 2 up to 7 nm were considered. Our theoretical framework is based on a three-dimensional classical Heisenberg model with nearest magnetic neighbor interactions involving tetrahedral (A) and octahedral (B) irons. Cubic magnetocrystalline anisotropy for core spins, single-ion site anisotropy for surface spins, and interaction with a uniform external magnetic field were considered. Our results revealed the onset of low temperature exchange bias field, which can be positive or negative at high enough values of the surface anisotropy constant (KS). Susceptibility data, computed separately for the core and the surface, suggest differences in the hard-soft magnetic character at the core-surface interface. Such differences are KS-driven and depend on the system size. Such a hard-soft interplay, via the surface anisotropy, is the proposed mechanism for explaining the observed exchange bias phenomenology. Our results indicate also that the strongly pinned spins at high enough surface anisotropy values are responsible for both the horizontal and vertical shifts in the hysteresis loops. The dependences of the switching and exchange bias fields with the surface anisotropy and temperature are finally discussed.

Exchange Bias Effects in Iron Oxide-Based Nanoparticle Systems

“…In the case of spherical Fe 3 O 4 MNPs, a Monte Carlo simulation study found an EB effect for particle sizes less than 2.5 nm, where the surface anisotropy ( K S ) resulting from disordered surface spins is assumed to be large compared to the core cubic magnetocrystalline anisotropy ( K C ) [61]. More information on Monte Carlo simulations can be found at the end of the article, in Appendix A.…”

Core-Shell Magnetic Morphology of Structurally Uniform Magnetite Nanoparticles

“…The concept of a chemically uniform, but magnetically distinct, core and canted shell is not without precedent [14,24], though not previously reported experimentally. We speculate that the lack of radial symmetry arises primarily from the competition between interparticle coupling within the nanoparticle array [21] (that sets a net direction) and nanoparticle surface anisotropy [12,13] (that promotes outward spin canting). For example, experiment [3] has shown that intraparticle exchange biasing can be altered by varying nanoparticle packing distance.…”

“…Similarly, we cannot quantify boundary fuzziness or degree of overlap between core and shell, but we can conclude from the M 2 PERP scattering that magnetic shells of nearly uniform magnitude and direction exist. Thus, models involving a disordered outermost shell [6][7][8][9], a canted moment that extends throughout the entire volume of the particle, and ''hedgehoglike'' [12] or ''throttle'' [13] symmetry do not fit M 2 PERP and are excluded. The isolation of M 2 PERP demonstrated here is only possible using diffraction or other spatially sensitive techniques since moments quickly average to zero across the sample, as evidenced by an equivalence of M 2 Y and M 2 Z [22].…”

“…Surfaces can also introduce a cubic anisotropy term when the material otherwise has uniaxial anisotropy [10]. Surface anisotropy has led to predictions of a ''hedgehog'' configuration where the spins spike outward normal to the surface [11][12][13][14], an ''artichoke'' confirmation where they are parallel to the surface and directed from one pole to the other [13], and a ''throttled'' configuration where the spins have been tilted slightly inward at the south pole and outward at the north pole [13]. Experimental verification of these theoretical predictions is extremely challenging because the magnetization from the distorted surface spins typically averages out for macroscopic measurements.…”

Preparation of hydroxyapatite–ferrite composite particles by ultrasonic spray pyrolysis

“…As the particle size is reduced, the density of magnetic bonds decreases as long as the proportion of undercoordinated ions on the surface becomes grater. Therefore, smaller fields enable more easily the reversal of spins and lead to lower switching fields for smaller sizes [42].…”