Dipolar interaction energy for a system of magnetic nanoparticles

Lamba, Subhalakshmi

doi:10.1002/pssb.200402067

Cited by 12 publications

(10 citation statements)

References 16 publications

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“…Others have reported that the method fails for slab nanosheet (2D + h) geometries and simple nanostructures. 5 When there is an interest in exploring the rate of convergence to a bulk value, an alternative approach that is often used is called "the method of expanding cubes" (EC) which takes various forms. [6][7][8] Most recently, papers by Gaio and Silvestrelli (GS) 8 and by Harrison 4 have focused on improving EC convergence rates obtained by adopting spherical or cubic expansions around a central core, and applying a suitable Q/R charge correction.…”

Section: Introductionmentioning

confidence: 99%

Madelung Constants of Nanoparticles and Nanosurfaces

Baker

2009

J. Phys. Chem. C

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Specific ion Madelung Constants (MCs) were calculated for ionic nanostructures and nanosurfaces using Coulomb sums. The magnitude of these values was tracked through a succession of progressively larger structures having the same symmetry. A significantly faster convergence to limiting bulk values than obtained previously was achieved when the structures used in the convergence were constrained to be electrically neutral. Evaluation of specific ion MCs for all surface ions allows the construction of surface Madelung maps. Calculated MCs for MgO nanotubes correlate well with the minimum total energies from DFT methods.

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Section: Introductionmentioning

confidence: 99%

Madelung Constants of Nanoparticles and Nanosurfaces

Baker

2009

J. Phys. Chem. C

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“…In a recent paper of this journal, S. Lamba derived a Lekner type summation of the dipolar interaction energy for magnetic nanoparticles systems [1]. He also presented that the results can be used in Monte Carlo simulation.…”

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confidence: 97%

“…It must be noted that the dipolar system Lekner considered is only 2-dimensional periodic and in 3-dimensional periodic system, Lekner calculated the force directly rather than energy. Equations (12) and (13) of S. Lamba [1], namely the double sum Ref. [3].…”

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confidence: 99%

Comment on “Dipolar interaction energy for a system of magnetic nanoparticles” [phys. stat. sol. (b) 241, No. 13, 3022–3028 (2004)]

Tang

Zhang

Zhong

2005

Physica Status Solidi (b)

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It is pointed out that there exist singularities in the equations describing the dipolar interaction energy derived by S. Lamba. In a recent paper of this journal, S. Lamba derived a Lekner type summation of the dipolar interaction energy for magnetic nanoparticles systems [1]. He also presented that the results can be used in Monte Carlo simulation. This topic is very interesting due to its importance for understanding the dipolar interaction effects on the nano-magnetism and the perpendicular recording systems. However, this paper neglected some essential problems on using the Lekner type summation techniques. Here, we bring forward these problems in order to discuss them with whoever is interested in this topic.Basically, S. Lamba extended the Lekner summation to 3-dimensional periodic magnetic dipolar systems with a cubic simulation box following the same procedure as described by Lekner [2]. It must be noted that the dipolar system Lekner considered is only 2-dimensional periodic and in 3-dimensional periodic system, Lekner calculated the force directly rather than energy. Equations (12) and (13) 4 β = p/ and the constants η, φ have no effects on the convergence property. Obviously, this extension is not successful. Moreover, the Eqs. (18), (23) and (26) of S. Lamba are not non-singular. For 0 η φ = = , the modified Bessel function of the second kind and the fractions have poles at 0 m n = = . In computer simulation, this case,which should be treated separately, will be encountered when two magnetic moments lie on the x-axis defined by S. Lamba.

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“…The dipolar interaction energy between a pair of finite sized magnetic particles, as expressed in Eqs. (1) and (2) of the original article [1] obviously assumes a finite separation between the particles, i.e. the distance between the i-th and j-th particle 0 ij r > and the term i j = is excluded from the summation.…”

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confidence: 99%

“…In the article "Dipolar interaction energy for a system of magnetic nanoparticles" [1] the dipolar energy for a system of single domain magnetic particles was calculated, based on the summation techniques used by Lekner for two dimensional and quasi two dimensional systems.…”

mentioning

confidence: 99%

Reply to “Comment on ‘Dipolar interaction energy for a system of magnetic nanoparticles’” [phys. stat. sol. (b), DOI 10.1002/pssb.200540104]

Lamba

2005

Physica Status Solidi (b)

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In this reply we clarify some points regarding the applicability of the expressions for the dipolar interaction energy between magnetic nanoparticles as calculated by an extension of the Lekner summation methods. The calculation is shown to be valid for any finite separation between the particles.In the article "Dipolar interaction energy for a system of magnetic nanoparticles" [1] the dipolar energy for a system of single domain magnetic particles was calculated, based on the summation techniques used by Lekner for two dimensional and quasi two dimensional systems.The questions raised by Tang et al. [2] are not at all pertinent to the systems studied by these methods. The dipolar interaction energy between a pair of finite sized magnetic particles, as expressed in Eqs. (1) and (2) of the original article [1] obviously assumes a finite separation between the particles, i.e. the distance between the i-th and j-th particle 0 ij r > and the term i j = is excluded from the summation. This is the standard assumption in most calculations of the dipolar interaction energy (Refs. [5], [10], [14][15][16] of the original article). With this condition we show below that there are no anomalies in the summation results. Also since i j π is explicit, there is no question of the calculation of the magnetic self energy. Details of the simulation system have been published earlier (Ref.[21] of the original article). The relevant features are emphasized here. A single domain magnetic particle has a finite volume and the magnetic moment of the particle is represented by a uniform magnetization vector proportional to its volume centered on the particle. The distance between any two particles in the array is greater than L α (where 0 α > and L is the side of the simulation cube). α can be set to a relevant cutoff depending on the average size of the particles in the system. This implies that in the expression for the dipolar interaction energy (Eq. (5) of the original article), at least one of the coordinates ξ , η or φ must be non-zero.It can be seen easily that with this condition, none of the equations derived for the expression of the dipolar interaction energy are singular. To elucidate we study a special case where 0 ξ φ = = whereas η is finite. It is then obvious that Eq. (13) never reduces to the form is convergent. Likewise there is no singularity at 0 m n = = in Eqs. (18) or (26), which represent the terms A and G respectively, since the argument of the Bessel's functions ( 0 K and 1 K ) which is

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Dipolar interaction energy for a system of magnetic nanoparticles

Cited by 12 publications

References 16 publications

Madelung Constants of Nanoparticles and Nanosurfaces

Madelung Constants of Nanoparticles and Nanosurfaces

Comment on “Dipolar interaction energy for a system of magnetic nanoparticles” [phys. stat. sol. (b) 241, No. 13, 3022–3028 (2004)]

Reply to “Comment on ‘Dipolar interaction energy for a system of magnetic nanoparticles’” [phys. stat. sol. (b), DOI 10.1002/pssb.200540104]

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