Studies on Approximation Methods in Calculating the Magnetic Dipolar Interaction Energy, and Its Impact on the Relaxation Time of Magnetic Nanoparticle Systems

Cacciola, Matteo; Berdie, Adela Diana

doi:10.12693/aphyspola.129.88

Cited by 5 publications

(4 citation statements)

References 45 publications

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“…As we hypothesized, the interaction of magnetic particles caused by the applied magnetic field creates this increase in UCS y and E y . When two Fe 3 O 4 particles have magnetic moments

\overset{m_{1}}{true}

and

\overset{m_{2}}{true}

, the magnetic dipole interaction energy (

E_{normalm}

) is given by:

E_{m} = - true(\frac{μ}{4 π} true) true[\frac{3 true(\overset{true\to}{m_{1}} \cdot \vec{r} true) true(\overset{}{{\overset{true\to}{m}}_{2}} \cdot \overset{true\to}{r} true)}{r^{5}} - \frac{\overset{true\to}{m_{1}} \cdot \overset{true\to}{m_{2}}}{r^{3}} true]

where

μ

is the medium permeability,

r

is the distance between the center of the two particles, and

true \vec{r}

is the vector of the line between the two magnetic dipoles . As the applied magnetic field increases, so do the magnetic moments, resulting in a higher dipole interaction energy between particles.…”

Section: Resultsmentioning

confidence: 99%

Freeze‐Casting of Surface‐Magnetized Iron(II,III) Oxide Particles in a Uniform Static Magnetic Field Generated by a Helmholtz Coil

Nelson¹,

Ogden²,

Khateeb

et al. 2019

Adv Eng Mater

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Research is conducted into freeze-casting of surface-magnetized Fe 3 O 4 particles under uniform, low-strength magnetic fields (5.2 mT) to mimic the mechanical characteristics of natural human bone. Freeze-casting is a technique that fabricates porous materials by directionally freezing and sublimating an aqueous slurry. A novel, Helmholtz coil-based freeze-caster is developed and it is shown that, during freeze-casting, the use of this Helmholtz coil generates a more uniform magnetic field than permanent magnets. This uniform magnetic field, applied in the direction of ice growth, keeps particles from agglomerating and results in an increase of 55% in both the ultimate compressive strength and the elastic modulus of porous surfacemagnetized Fe 3 O 4 scaffolds. These increases can be linked to a reduction in the porosity that occurs due to magnetic interactions between particles in the presence of the field. These results offer a novel method for the fabrication of bone-inspired biomaterials and structural materials.

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“…As we hypothesized, the interaction of magnetic particles caused by the applied magnetic field creates this increase in UCS y and E y . When two Fe 3 O 4 particles have magnetic moments

\overset{m_{1}}{true}

and

\overset{m_{2}}{true}

, the magnetic dipole interaction energy (

E_{normalm}

) is given by:

E_{m} = - true(\frac{μ}{4 π} true) true[\frac{3 true(\overset{true\to}{m_{1}} \cdot \vec{r} true) true(\overset{}{{\overset{true\to}{m}}_{2}} \cdot \overset{true\to}{r} true)}{r^{5}} - \frac{\overset{true\to}{m_{1}} \cdot \overset{true\to}{m_{2}}}{r^{3}} true]

where

μ

is the medium permeability,

r

is the distance between the center of the two particles, and

true \vec{r}

Section: Resultsmentioning

confidence: 99%

Freeze‐Casting of Surface‐Magnetized Iron(II,III) Oxide Particles in a Uniform Static Magnetic Field Generated by a Helmholtz Coil

Nelson¹,

Ogden²,

Khateeb

et al. 2019

Adv Eng Mater

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“…In the first instance, we consider the dipolar interactions between pairs of NPs and then consider how to sum up the contributions of pairs over the entire population of NPs. We start by considering the energy expression for the dipolar interaction between two magnetic NPs, as characterized by their magnetic moments m i and mj, which we can write as [35]:…”

Section: Contributions To the Free Energy In Magnetic Nanoparticle Sy...mentioning

confidence: 99%

Ferromagnetic Resonance in Magnetic Oxide Nanoparticules: A Short Review of Theory and Experiment

Mokhtari

Schmool

2023

Magnetochemistry

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This review article aims to provide a comprehensive overview of recent FMR studies on magnetic oxide nanoparticles and their potential applications. The use of the FMR technique is a powerful tool to study the magnetic properties of magnetic nanoparticles and can provide valuable information on their behavior. For this, we will start by discussing the purpose of these magnetic nanoparticles and their application in various fields, including biomedical applications, energy storage, and environmental remediation. We will then discuss the methods used to prepare magnetic nanoparticles and the theory behind FMR including the superparamagnetic effect. Additionally, we will present the most recent studies on FMR for magnetic oxide nanoparticles by highlighting the effect of temperature and doping on the magnetic properties of these nanoparticles.

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“…The most expensive part of the atomistic simulations of the magnetic properties of periodic magnetic systems of certain thickness, such as nanowires and films of ferromagnetic atoms, is the calculation of the magnetostatic dipolar energy, MDE [9,[23][24][25][26][27][28]. To simulate these materials with realistic models, it is necessary to consider a large number of atoms and the details of the geometric structure.…”

Section: Introductionmentioning

confidence: 99%

Magnetostatic dipolar energy of large periodic Ni fcc nanowires, slabs and spheres

Cabria

2019

Applied Surface Science

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The computational effort to calculate the magnetostatic dipolar energy, MDE, of a periodic cell of N magnetic moments is an O(N 2) task. Compared with the calculation of the Exchange and Zeeman energy terms, this is the most computationally expensive part of the atomistic simulations of the magnetic properties of large periodic magnetic systems. Two strategies to reduce the computational effort have been studied: An analysis of the traditional Ewald method to calculate the MDE of periodic systems and parallel calculations. The detailed analysis reveals that, for certain types of periodic systems, there are many matrix elements of the Ewald method identical to another elements, due to some symmetry properties of the periodic systems. Computation timing experiments of the MDE of large periodic Ni fcc nanowires, slabs and spheres, up to 32000 magnetic moments in the periodic cell, have been carried out and they show that the number of matrix elements that should be calculated is approximately equal to N, instead of N 2 /2, if these symmetries are used, and that the computation time decreases in an important amount. The time complexity of the analysis of the symmetries is O(N 3), increasing the time complexity of the traditional Ewald method. MDE is a very small energy and therefore, the usual required precision of the calculation of the MDE is so high, about 10 −6 eV/cell, that the calculations of large periodic magnetic systems are very expensive and the use of the symmetries reduces, in practical terms, the computation time of the MDE in a significant amount, in spite of the increase of the time complexity. The second strategy consists on parallel calculations of the MDE without using the symmetries of the periodic systems. The parallel calculations have been compared with serial calculations that use the symmetries.

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Studies on Approximation Methods in Calculating the Magnetic Dipolar Interaction Energy, and Its Impact on the Relaxation Time of Magnetic Nanoparticle Systems

Cited by 5 publications

References 45 publications

Freeze‐Casting of Surface‐Magnetized Iron(II,III) Oxide Particles in a Uniform Static Magnetic Field Generated by a Helmholtz Coil

Freeze‐Casting of Surface‐Magnetized Iron(II,III) Oxide Particles in a Uniform Static Magnetic Field Generated by a Helmholtz Coil

Ferromagnetic Resonance in Magnetic Oxide Nanoparticules: A Short Review of Theory and Experiment

Magnetostatic dipolar energy of large periodic Ni fcc nanowires, slabs and spheres

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