Determining the size distribution of magnetic nanoparticles based on analysis of magnetization curves

Yu, S.C.; Liu, Yi-Hsien; Sun, Andy; Hsu, Jen‐Hwa

doi:10.1063/1.3259424

Cited by 10 publications

(8 citation statements)

References 10 publications

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“…We have also shown an importance of inclusion of the finite size effect when the distributions of magnetic anisotropy are wide. The features found in this study qualitatively agree with experimental data [1,10,11,14,24]. However, more quantitative comparison with experimental data, requires consideration of other factors which are beyond the scope of this work.…”

Section: Discussionsupporting

confidence: 80%

“…Recent experiments showed that magnetic nanoparticles possess either Gaussian distributions f G [3,10,14] or log-normal distributions f LN of sizes [1,11,12]. For small variances, log-normal distributions look similar to Gaussian distributions.…”

Section: B Distributions Of Magnetic Anisotropy Dmentioning

confidence: 99%

“…Ideally, for a given system, magnetic nanoparticles may have uniform particle sizes and shapes, and molecules may have identical ligand orientations. However, scanning electron microscopy (SEM), transmission electron microscopy (TEM) and x-ray diffraction (XRD) data on magnetic nanoparticles/molecules revealed significant distributions of particle sizes and shapes [1][2][3][10][11][12] or distributions of molecular ligand orientations [13]. In addition, various permanent magnets consist of many nanoscale grains with different sizes and shapes [14].…”

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confidence: 99%

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Effect of the size distribution of magnetic nanoparticles on metastability in magnetization relaxation

Yamamoto

Park

2011

Phys. Rev. B

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We theoretically examine metastability occurring in magnetization relaxation for magnetic nanoparticles with size distributions. An array of magnetic nanoparticles is simulated using a spin S=1 ferromagnetic Blume-Capel model on a square lattice. The particle size distributions give rise to distributions of magnetic anisotropy. Including the distributions, we perform kinetic Monte Carlo simulations of magnetization relaxation at low temperatures for the Blume-Capel model. We compute the average lifetime of the metastable state from the simulations and the absorbing Markov chains method in the low temperature limit. We also carry out similar simulations and calculations for a constant value of magnetic anisotropy for comparison. Our results suggest that the lifetime of the metastable state is determined by the smallest particle for a given system, and that the lifetime with size distributions obeys a modified Arrhenius-like law, where the energy barrier depends on even temperature and standard deviation of the distributions as well as magnetic field and magnetic anisotropy.

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Section: Discussionsupporting

confidence: 80%

Section: B Distributions Of Magnetic Anisotropy Dmentioning

confidence: 99%

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confidence: 99%

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Effect of the size distribution of magnetic nanoparticles on metastability in magnetization relaxation

Yamamoto

Park

2011

Phys. Rev. B

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“…Note, that if all f an,i share the property that their slopes at h = 0 are maximal then the same property has their linear combination shown in (17). On the other hand, the approach to saturation of such a combination may exhibit some peculiarities leading to the appearance of more than one knee in compound f an .…”

Section: A Linear Combinationmentioning

confidence: 91%

Anhysteretic Functions for the Jiles–Atherton Model

Kokornaczyk

Gutowski

2015

IEEE Trans. Magn.

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The Jiles-Atherton (JA) model of ferromagnetic hysteresis usually bases on the Langevin function as its anhysteretic part. This leads to a problem, since for some known materials, the anhysteretic curve may not be modeled in view of fact, that the coupling parameter α, as determined from their major hysteresis loop, is too large, i.e., greater than the value permissible for the Langevin function. Therefore, a new function is required in order to omit this mathematical dilemma. Here, we present a set of simple functions, with their knees depending on one parameter only. Also, a more complicated function, with knee location depending on two parameters is analyzed, however, the Brillouin function again does not solve the difficulty with α. Therefore, within the frame of the JA model, a new function is proposed, making possible to have the initial differential susceptibility arbitrarily small. In addition, the strengthening of the effective field is considered and the permissible values of the second coupling parameter β, in respect to the Brillouin and Langevin functions, are presented. Finally, our new function is successfully used to model the measured anhysteretic curve.Index Terms-Anhysteretic functions, effective field, knee, permissible values of coupling parameters.

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“…They also have various applications including information storage devices [1,2], sensors, and contrast agents in magnetic resonance imaging [3][4][5]. Synthesized magnetic nanoparticles have typically large distributions of size and shape which influence their equilibrium and nonequilibrium properties [6][7][8][9][10][11][12][13]. For example, the size and shape distributions induce distributions in the magnetic anisotropy barrier, magnetization switching or relaxation, and blocking temperature.…”

Section: Introductionmentioning

confidence: 99%

Metastability for the Blume-Capel model with distribution of magnetic anisotropy using different dynamics

Yamamoto

Park

2013

Phys. Rev. E

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We investigate the relaxation time of magnetization or the lifetime of the metastable state for a spin S = 1 square-lattice ferromagnetic Blume-Capel model with distribution of magnetic anisotropy (with small variances), using two different dynamics such as Glauber and phonon-assisted dynamics. At each lattice site, the Blume-Capel model allows three spin projections (+1, 0, −1) and a site-dependent magnetic anisotropy parameter. For each dynamic, we examine the low-temperature lifetime in two dynamic regions with different sizes of the critical droplet and at the boundary between the regions, within the single-droplet regime. We compute the average lifetime of the metastable state for a fixed lattice size, using both kinetic Monte Carlo simulations and the absorbing Markov chains method in the zero-temperature limit. We find that for both dynamics the lifetime obeys a modified Arrhenius-like law, where the energy barrier of the metastable state depends on the temperature and standard deviation of the distribution of magnetic anisotropy for a given field and magnetic anisotropy and that an explicit form of this dependence differs in different dynamic regions for different dynamics. Interestingly, the phonon-assisted dynamic prevents transitions between degenerate states, which results in a large increase in the energy barrier at the region boundary compared to that for the Glauber dynamic. However, the introduction of a small distribution of magnetic anisotropy allows the spin system to relax via lower-energy pathways such that the energy barrier greatly decreases. In addition, for the phonon-assisted dynamic, even the prefactor of the lifetime is substantially reduced for a broad distribution of magnetic anisotropy in both regions considered, in contrast to the Glauber dynamic. Our findings show that overall the phonon-assisted dynamic is more significantly affected by the distribution of magnetic anisotropy than the Glauber dynamic.

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Determining the size distribution of magnetic nanoparticles based on analysis of magnetization curves

Cited by 10 publications

References 10 publications

Effect of the size distribution of magnetic nanoparticles on metastability in magnetization relaxation

Effect of the size distribution of magnetic nanoparticles on metastability in magnetization relaxation

Anhysteretic Functions for the Jiles–Atherton Model

Metastability for the Blume-Capel model with distribution of magnetic anisotropy using different dynamics

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