TOPICAL REVIEW: Supermagnetism

The magnetic properties of nanoparticles of antiferromagnetic materials are reviewed. The magnetic structure is often similar to the bulk structure, but there are several examples of size-dependent magnetic structures. Owing to the small magnetic moments of antiferromagnetic nanoparticles, the commonly used analysis of magnetization curves above the superparamagnetic blocking temperature may give erroneous results, because the distribution in magnetic moments and the magnetic anisotropy are not taken into account. We discuss how the magnetic dynamics can be studied by use of magnetization measurements, Mossbauer spectroscopy and neutron scattering. Below the blocking temperature, the magnetic dynamics in nanoparticles is dominated by thermal excitations of the uniform mode. In antiferromagnetic nanoparticles, the frequency of this mode is much higher than in ferromagnetic and ferrimagnetic nanoparticles, but it depends crucially on the size of the uncompensated moment. Excitation of the uniform mode results in a so-called thermoinduced moment, because the two sublattices are not strictly antiparallel when this mode is excited. The magnetic dipole interaction between antiferromagnetic nanoparticles is usually negligible, and therefore such particles present a unique possibility to study exchange interactions between magnetic particles. The interactions can have a significant influence on both the magnetic dynamics and the magnetic structure. Nanoparticles can be attached with a common crystallographic orientation such that both the crystallographic and the magnetic order continue across the interfaces.

https://iopscience.iop.org/article/10.1088/0953-8984/19/21/213202/pdf

Experimental and theoretical studies of nanoparticles of antiferromagnetic materials

The original magnetic properties of nanometre-sized particles are due to the distinct contributions of volume, surface and step atoms. To disentangle these contributions is an ongoing challenge of materials science. Here we introduce a method enabling the identification of the remarkably different contributions of surface and perimeter atoms to the magnetic anisotropy energy of two-dimensional nanostructures. Our method uses the generally nonlinear relationship between perimeter length and surface area. Atomic-scale characterization of the morphology of ensembles of polydisperse nanostructures, combined with in situ measurements of their temperature-dependent magnetic susceptibility, gives access to the role played by the differently coordinated atoms. We show for Co nanostructures on a Pt(111) surface that their uniaxial out-of-plane magnetization is entirely caused by edge atoms having 20 times more anisotropy energy than their bulk and surface counterparts. Identification of the role of perimeter and surface atoms opens up unprecedented opportunities for materials engineering. As an example, we separately tune magnetic hardness and moment in bimetallic core-shell nanostructures.

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The remarkable difference between surface and step atoms in the magnetic anisotropy of two-dimensional nanostructures

The effects of magnetostatic interactions between monodisperse single-domain nanoparticles are described in terms of the particle concentration and structural ordering within the assembly. The resulting energy level distribution, time-dependent behaviour and spatial correlations are discussed in the context of the properties of bulk dipolar ferromagnets, bulk spin glasses and non-interacting monodomain particles. Both standard measurements and novel characterization techniques are described. The results from research groups studying monodisperse magnetic nanoparticles are compared to illustrate the distinguishing characteristics of interacting assemblies and to highlight important questions that remain.

https://iopscience.iop.org/article/10.1088/0022-3727/39/21/R02/pdf

Magnetostatic interactions in magnetic nanoparticle assemblies: energy, time and length scales

Temperature variations of the magnetization $M$ and the electron magnetic resonance (EMR) parameters of maghemite $(\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3})$ nanocrystals are reported for the $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ range. Transmission electron microscopy of the nanocrystals shows them to be nearly spherical samples (aspect ratio $a∕b=1.15$) with diameter $D=7(1)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, and analysis of x-ray diffraction lines yields $D=6.4\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ with negligible strain. $M$ versus $T$ data show blocking temperatures ${T}_{B}\ensuremath{\simeq}101\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, $89\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and $68\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in measuring fields $H=50$, 100, and $200\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$ respectively. $M$ versus $H$ data for $Tg{T}_{B}$ fits the modified Langevin function $M={M}_{s}\mathcal{L}({\ensuremath{\mu}}_{p}H∕{k}_{B}T)+{\ensuremath{\chi}}_{a}H$ with ${\ensuremath{\mu}}_{p}=8000(500){\ensuremath{\mu}}_{B}∕\text{particle}$ and ${M}_{s}=80\phantom{\rule{0.3em}{0ex}}\mathrm{emu}∕\mathrm{g}$, identical to ${M}_{s}$ for bulk $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$. It is argued that this large value of ${M}_{s}$, the small value of coercivity ${H}_{c}\ensuremath{\simeq}20\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$ at $5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the lack of exchange bias in a field-cooled sample, and negligible strain point to nearly defect-free nanocrystals. In the EMR studies, two resonance lines are observed, one with the resonance field ${H}_{r}$ greater than that for the free-electron value and the other smaller. From the temperature variations of ${H}_{r}$ and the linewidths of the two lines, it is argued that the two lines are, respectively, due to nanocrystals with easy-axis aligned perpendicular and parallel to the applied field. The relatively narrow intrinsic linewidths $(\ensuremath{\simeq}400\phantom{\rule{0.3em}{0ex}}\mathrm{Oe})$ of the two lines in nearly defect-free nanocrystals facilitated their observation.

Magnetic properties of nearly defect-free maghemite nanocrystals

A model of the magnetic properties of a dispersion of interacting superparamagnetic particles in a solid matrix is presented. The model uses Monte Carlo techniques and is capable of predicting the time and temperature dependence of the magnetic properties. The model is applied to the study of the magnetic behavior of a cobalt granular system, particularly the low-field susceptibility. It is shown that strongly interacting systems at high density exhibit non-Langevin behavior and give a strongly nonlinear variation of susceptibility with packing density. The temperature dependence of the initial susceptibility shows the characteristic peak observed experimentally, with the peak temperature increasing with packing density. The field cooled (FC) and zero field cooled (ZFC) magnetization are also studied. The field dependence of the FC magnetization is shown to depend on the interparticle interactions and also on the orientational easy axis distribution. The FC magnetization is found to exhibit a peak resulting from the interactions. This behavior is finally related to the energy barrier distribution of the system (and its dependence on the interactions) using the temperature decay of remanence. It is also shown that the remanence calculated from the complete hysteresis loop at each temperature differs from the values obtained by increasing the temperature of a system initially at saturation remanence. The evolution of magnetic properties as a function of the magnetic state and history points to the importance of collective phenomena. Calculations of a spin-spin correlation function show the existence of a state with short-ranged order at low temperatures.

Calculations of the susceptibility of interacting superparamagnetic particles

The magnetic properties of densely packed composite granular materials are strongly affected by interactions between the grains. This paper addresses the influence of the interactions, as a function of the packing density, on the initial susceptibility. Our calculations are based on systems with realistic physical microstructures which are free from an artificially imposed lattice. The introduction of particle elongation via demagnetizing factors due to prolate spheroids is shown to enhance the susceptibility and give results which are in good agreement with experimental observations of composite soft materials prepared by dispersing large Fe particles in a non-magnetic matrix.

N S Walmsley

Papers

Calculations of the susceptibility of interacting superparamagnetic particles

Experimental and computational investigation of the magnetic susceptibility of composite soft materials