We study the ground state and magnetic hysteresis properties of 2$d$ arrays ($L^{}_x\times L^{}_y$) of dipolar interacting magnetic nanoparticles (MNPs) by performing micromagnetic simulations. Our primary interest is to understand the effect of sample shape, $Θ$- the ratio of the dipolar strength to the anisotropy strength, and the direction of the applied field $\vec{H} = H_{o}\hat{e}^{}_H$ on the ground state and the magnetic hysteresis in an array of MNPs. To study the effect of shape of the sample, we have varied the aspect ratio $A^{}_r=L^{}_y/L^{}_x$ which in turn, is found to induce shape anisotropy in the system. Our main observations are: (a) When the dipolar interaction is strong $(Θ>1)$, the ground state morphology has in-plane ordering of magnetic moments. (b) The ground state morphology has randomly oriented magnetic moments which is robust with respect to system sizes and $A^{}_r$ for weakly interacting MNPs ($Θ<1$). (c) Micromagnetic simulations suggests that the dipolar interaction decreases the coercive field $H^{}_c$. (d) The remanence magnetization $M^{}_r$ is found to be strongly dependent not only on the strength of dipolar interaction but also on the shape of the sample. (e) Due to anisotropic nature of dipolar interaction, a strong effect of shape anisotropy is observed when the field is applied along longer axis of the sample. The dipolar interaction in such a case induces an effective ferromagnetic coupling when the aspect ratio is very large. These results are of vital importance in high-density recording systems, magneto-impedance sensors, etc.
Influence of a transverse static magnetic field on the magnetic hyperthermia properties and high-frequency hysteresis loops of ferromagnetic FeCo nanoparticles
We present a general study of frequency and magnetic field dependence of the specific heat power produced during field-driven hysteresis cycles in magnetic nanoparticles with relevance to hyperthermia applications in biomedicine. Employing a kinetic Monte-Carlo method with natural time scales allows us to go beyond the assumptions of small driving field amplitudes and negligible inter-particle interactions, which are fundamental to applicability of the standard approach based on linear response theory. The method captures the superparamagnetic and fully hysteretic regimes and the transition be…
We perform computer simulations to probe the magnetic hysteresis in a two-dimensional ($L^{}_x\times L^{}_y$) assembly of magnetic nanoparticles as a function of dipolar interaction strength $h^{}_d$, temperature $T$, aspect ratio $A^{}_r=L^{}_y/L^{}_x$, and the applied alternating magnetic field's direction. In the absence of magnetic interaction ($h^{}_d\approx0$) and thermal fluctuations ($T=0$ K), the hysteresis follows the Stoner and Wohlfarth model, as expected. For weak dipolar interaction and substantial temperature, the hysteresis has the dominance of superparamagnetic behaviour, irre…
A general method for the quantification of dipolar interactions in assemblies of nanoparticles has been developed from a model sample constituted by magnetite nanoparticles of 5 nm in diameter, in powder form with oleic acid as a surfactant so that the particles were solely separated from each other through an organic layer of about 1 nm in thickness. This quantification is based on the comparison of the distribution of energy barriers for magnetization reversal obtained from time-dependent relaxation measurements starting from either (i) an almost random orientation of the particles magnetiza…
Using first-principle calculations and kinetic Monte Carlo simulation, we study the local and averaged hysteresis in tiny clusters of k magnetic nanoparticles (MNPs) or k-mers. We also analyze the variation of local dipolar field acting on the constituent nanoparticles as a function of the external magnetic field. The dipolar interaction is found to promote chain-like arrangement in such a cluster. Irrespective of cluster size, the local hysteresis response depends strongly on the corresponding dipolar field acted on a nanoparticle. In a small k-mer, there is a wide variation in local hysteres…
The main aim of the present work is to analyse the effect of dipolar interaction strength $λ$, particle size $D$ and temperature $T$ on the hysteresis mechanism in ordered arrays of magnetic nanoparticles (MNPs) using computer simulations. The anisotropy axes of the MNPs are assumed to have random orientation to mimic the real system. In the absence of thermal fluctuations and dipolar interaction, the hysteresis follows the Stoner and Wohlfarth model irrespective of $D$, as expected. The hysteresis loop area is minimal for particle sizes $D \approx8-16$ nm at $T=300$ K and $λ=0.0$, indicating …
The dipolar interaction is known to substantially affect the properties of magnetic nanoparticles. This is particularly important when the particles are kept in a fluid suspension or packed inside nano-carriers. In addition to its usual long-range nature, in these cases the dipolar interaction may also induce the formation of clusters of particles, thereby strongly modifying their magnetic anisotropies. In this paper we show how AC susceptibility may be used to obtain important information regarding the influence of the dipolar interaction in a sample. We develop a model which includes both as…
Increase of magnetic hyperthermia efficiency due to dipolar interactions in low anisotropy magnetic nanoparticles : theoretical and experimental results
Materials that have a hysteretic response to an external field are essential in modern information storage and processing technologies. The magnetization curves of several natural and artificial materials have previously been measured and explained in terms of the Neel model, Preisach phenomenological model, the creation, propagation, and annihilation of topological defects, or by resonant quantum tunnelling of the magnetization in single molecule magnets. However, a simple way to design the magnetic response of a material is missing. Here, we propose and experimentally realize an elementary m…
Bubbles have a rich history as transducers in particle-physics experiments. In a solid-state analogue, we use bubble domains in nanomagnetic films to measure magnetic nanoparticles. This technique can determine the magnetic orientation of a single nanoparticle in a fraction of a second, and generate a full hysteresis loop in a few seconds, which is much faster than any other reported technique. We achieve this unprecedented speed by tuning the nanomagnetic properties of the films, including the Dzyaloshinskii-Moriya interaction, in the first application of topological protection from the skyrm…
Micromagnetic simulation results on dynamic hysteresis loops of clusters of iron oxide nanoparticles (NPs) with internal structure composed of nanorods are compared with the widely used macrospin approximation. Such calculations allowing for nanorod-composed NPs is facilitated by a previously developed coarse-graining method based on the renormalization group approach. With a focus on applications to magnetic hyperthermia, we show that magnetostatic interactions improve the heating performance of NPs in chains and triangles, and reduce heating performance in fcc arrangements. Hysteresis loops …
Understanding the influence of dipolar interactions in magnetic hyperthermia (MH) experiments is of crucial importance for a fine optimization of nanoparticle (NP) heating power. In this study, we use a kinetic Monte-Carlo algorithm to calculate hysteresis loops, so both time and temperature are correctly taken into account. It is demonstrated that this algorithm correctly reproduces the high-frequency hysteresis loop of both superparamagnetic NPs and ferromagnetic ones without any ad-hoc parameters. The algorithm is easily parallelizable so calculation on several processors decreases consider…
We implement extensive computer simulations to investigate the hysteresis characteristics in the ordered arrays ($l^{}_x\times l^{}_y$) of magnetic nanoparticles as a function of aspect ratio $A^{}_r=l^{}_y/l^{}_x$, dipolar interaction strength $h^{}_d$, and external magnetic field directions. We have considered the aligned anisotropy case, $α$ is the orientational angle. It provides an elegant en route to unearth the explicit role of anisotropy and dipolar interaction on the hysteresis response in such a versatile system. The superparamagnetic character is dominant with weak dipolar interacti…
We address the issue of inter-particle dipolar interactions in the context of magnetic hyperthermia. More precisely, the main question dealt with here is concerned with the conditions under which the specific absorption rate is enhanced or reduced by dipolar interactions. For this purpose, we propose a theory for the calculation of the AC susceptibility, and thereby the specific absorption rate, for a monodisperse two-dimensional assembly of nanoparticles with oriented anisotropy, in the presence of a DC magnetic field, in addition to the AC magnetic field. We also study the competition betwee…
Using the two-level approximation of the energy barrier, we perform extensive kinetic Monte Carlo simulations to probe the relaxation characteristics in a two-dimensional ($L^{}_x\times L^{}_y$) array of magnetic nanoparticle as a function of dipolar interaction strength $h^{}_d$, aspect ratio $A^{}_r=L^{}_y/L^{}_x$, and temperature $T$. In the case of weak dipolar interaction ($h^{}_d\approx0$) and substantial temperature, the magnetic relaxation follows the Néel Brown model as expected. Interestingly, the dipolar interaction of enough strength is found to induce antiferromagnetic coupling in…
Applications based on aggregates of magnetic nanoparticles are becoming increasingly widespread, ranging from hyperthermia to magnetic recording. However, although some uses require a collective behavior, other need a more individual-like response, the conditions leading to either of these behaviors are still poorly understood. Here we use nanoscale-uniform binary random dense mixtures with different proportions of oxide magnetic nanoparticles with low$/$high anisotropy as a valuable tool to explore the crossover from individual to collective behavior. Two different anisotropy scenarios have b…
We investigate the dependence of magnetic properties on the out-of-plane disorder strength $Δ$, dipolar interaction strength $h^{}_d$ in two-dimensional ($l^{}_x\times l^{}_y$) ensembles of nanoparticles using numerical simulations. Such positional defects are redundantly observed in experiments. The superparamagnetic character is dominant with negligible and weak interaction strength $h^{}_d$, irrespective of $Δ$ and aspect ratio of the system $A^{}_r=l^{}_y/l^{}_x$. The double-loop hysteresis curve, characteristics of antiferromagnetic coupling dominance, emerges with large $h^{}_d$ and $Δ(\…
There is so far no clear-cut experimental analysis that can determine whether dipole-dipole interactions enhance or reduce the blocking temperature $T_{B}$ of nanoparticle assemblies. It seems that the samples play a central role in the problem and therefore, their geometry should most likely be the key factor in this issue. Yet, in a previous work, Jönsson and Garcia-Palacios did investigate theoretically this problem in a weak-interaction limit and without the presence of an external DC field. Based on symmetry arguments they reached the conclusion that the variation of the relaxation rate i…
Magnetic properties of dense nanoparticle arrays with core/shell morphology
我们计算了有序阵列的复合磁性纳米粒子的铁磁（FM）的核心和反铁磁（AFM）壳，位于三角形晶格和耦合通过静磁力的磁滞。每个纳米颗粒由一对交换耦合（J）的各向异性自旋（Meiklejohn-Bean模型）描述。使用Metropolis Monte Carlo算法获得磁化磁滞回线。对于硬磁纳米颗粒，我们发现随着偶极耦合强度的增加，矫顽磁力减小，而交换偏置场则表现出非单调行为，这是由于随机各向异性和颗粒间偶极相互作用之间的竞争造成的。讨论了通过增加堆积密度来提高交换偏置场的可能性。
