Shapes and textures of ferromagnetic liquid droplets

Banerjee, Shubho; Widom, Michael

doi:10.1590/s0103-97332001000300005

Cited by 6 publications

(6 citation statements)

References 29 publications

(32 reference statements)

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“…The lowest energy magnetization texture depends on the shape of the domain formed [19]. At relatively lower temperatures, the spin ordering attains equilibrium quickly within 10 K MC cycles and large changes in entropy are not observed with run cycles because of the reduced mobility for the spins, which is temperature-dependent.…”

Section: Resultsmentioning

confidence: 99%

First observations of entropy vs free energy for lattice based Ising model for spin coarsening in conserved and non-conserved binary mixtures: a phenomenological study of phase transitions in 2D thin films

Pal¹

2015

Nanosist.: fiz. him. mat.

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This paper presents the results of Monte Carlo (MC) simulation for paramagnetic, ferromagnetic and anti-ferromagnetic transitions in 2D thin films. The spin coarsening which lowers energy brings order at the cost of lowering entropy in the presence of an external magnetic field, which in turn, may increase the free energy at relatively higher temperatures because of spin mixing. There is a competition between energy of the system and entropy in conserved and non-conserved binary mixtures in the presence of an external magnetic field. The simulation is done on a lattice of size 100 × 100 using Metropolis algorithm with periodic boundary conditions. All data are sampled for 20 K MC cycles after a regular interval of 100 MC cycles. The paramagnetic case with spin coupling coefficient and the ferromagnetic and anti-ferromagnetic cases with |ε(AB)| = 0.0J 0 , 0.25J 0 , 0.50J 0 , 0.75J 0 & 1.0J 0 (keeping |ε(AA)| = |ε(BB)| = 1.0J 0 ) (Here J 0 = 1.0 unit of energy) are studied at temperatures kT = 0.25J 0 , 0.50J 0 , 0.75J 0 , 1.0J 0 , 1.25J 0 , 1.5J 0 , 1.75J 0 , & 2.0J 0 in presence of varying external magnetic field strengths in order to observe the organizational behavior of spins and the interplay between the free energy and entropy. The induced magnetization and the magnetic susceptibilities are found to be in qualitative agreement with the theory. The paramagnetic to ferromagnetic transition has been observed and explored at high T values. The spin correlation function plotted helps to reveal the spin transport properties of the systems. The spontaneous ferromagnetic transition temperatures for ε(AB) = 1.0J 0 , 0.75J 0 & 0.50J 0 are observed as k B T = 0.44J 0 , 0.39J 0 & 0.33J 0 (i.e. nearly 96 % magnetizations are observed at these temperatures) respectively at B = 0.0J 0 /µ (i.e. absence of any external magnetic field). This is in quantitative agreement with theory. The spin correlation function diverges at these transition temperatures, which can be understood as the theoretical evidence supporting the observation of spontaneous magnetization. The ferromagnetic to paramagnetic transitions are not very sharp but the range of the spin-spin interaction can be said to decay gradually. Even at higher temperature as kT = 2.0J 0 , the opposite spin pair correlation function supports formation of tiny domains with spin transport from one domain to another, whereas for lower temperatures below kT = 1.0J 0 , the presence of majority +1/2 spins diminish the effect. Tiny domain walls have lower energy surrounded by opposite spins and seem to be energetically preferred. This quasi nature of spin-spin interaction with temperature is also supported by the corresponding ensemble entropy averages.

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Section: Resultsmentioning

confidence: 99%

First observations of entropy vs free energy for lattice based Ising model for spin coarsening in conserved and non-conserved binary mixtures: a phenomenological study of phase transitions in 2D thin films

Pal¹

2015

Nanosist.: fiz. him. mat.

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“…4). Other examples of optimal shapes for ferromagnetic liquid droplets that are not ellipsoidal are given in [7]. The energy considered there includes an exchange and core energy in addition to surface and demagnetization energy in our paper.…”

Section: Setting and Statement Of Resultsmentioning

confidence: 99%

“…In this paper, we investigate the shape and energetics of isolated magnetic domains from the view point of calculus of variations without relying on any specific ansatz function. We note that the shape and properties of magnetic domains in solids and fluids have been studied in the physical literature both experimentally and numerically [7][8][9]; for applications see e.g. [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic shape of isolated magnetic domains

Knüpfer

Stantejsky

2022

Proc. R. Soc. A.

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We investigate the energy of an isolated magnetized domain Ω ⊂ R n for n = 2 , 3 . In non-dimensionalized variables, the energy given by E ( Ω ) = ∫ R n | ∇ χ Ω | d x + ∫ R n | ∇ h Ω | 2 d x penalizes the interfacial area of the domain as well as the energy of the corresponding magnetostatic field. Here, the magnetostatic potential h Ω is determined by Δ h Ω = ∂ 1 χ Ω , corresponding to uniform magnetization within the domain. We consider the macroscopic regime | Ω | → ∞ , in which we derive compactness and Γ -limit which is formulated in terms of the cross-sectional area of the anisotropically rescaled configuration. We then give the solutions for the limit problems.

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“…Other examples of optimal shapes for ferromagnetic liquid droplets that are not ellipsoidal are given in [6]. The energy considered there includes an exchange and core energy in addition to surface and demagnetization energy in our paper.…”

Section: Remark 11 (Micromagnetic Model)mentioning

confidence: 99%

“…In this paper, we investigate the shape and energetics of an isolated magnetic domain from the view point of calculus of variations without the use of any ansatz function, thus considering the problem among all possible shapes of the domain, without geometrical or topological restrictions. We note that the shape and properties of magnetic domains in solids and fluids have been studied in the physical literature both experimentally as well as numerically [6,17,58], for applications see e.g. [12,32,43,49,51,64,66].…”

Section: Introductionmentioning

confidence: 99%

Optimal Shape of Isolated Ferromagnetic Domains

Knüpfer¹,

Nolte²

2018

SIAM J. Math. Anal.

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We investigate the energy of an isolated magnetized domain Ω ⊂ R n for n = 2, 3. In non-dimensionalized variables, the energy given bypenalizes the interfacial area of the domain as well as the energy of the corresponding magnetostatic field. Here, the magnetostatic potential Φ is determined by ∆Φ = ∂ 1 χ Ω , corresponding to uniform magnetization within the domain. We consider the macroscopic regime |Ω| → ∞, in which we derive compactness and Γlimit for the cross-section of the anisotropically rescaled configuration. The limit energy is local and the limiting shape of minimizers can be calculated.

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Shapes and textures of ferromagnetic liquid droplets

Cited by 6 publications

References 29 publications

First observations of entropy vs free energy for lattice based Ising model for spin coarsening in conserved and non-conserved binary mixtures: a phenomenological study of phase transitions in 2D thin films

First observations of entropy vs free energy for lattice based Ising model for spin coarsening in conserved and non-conserved binary mixtures: a phenomenological study of phase transitions in 2D thin films

Asymptotic shape of isolated magnetic domains

Optimal Shape of Isolated Ferromagnetic Domains

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