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Diffusion-limited deposition of dipolar particles

Deposits of dipolar particles are investigated by means of extensive Monte Carlo simulations. We found that the effect of the interactions is described by an initial, non-universal, scaling regime characterized by orientationally ordered deposits. In the d

a r X i v :c o n d -m a t /0406610v 1 [c o n d -m a t .s t a t -m e c h ] 24 J u n 2004

Di?usion-limited deposition of dipolar particles

F.de los Santos,1J.M.Tavares,2,3M.Tasinkevych,4and M.M.Telo da Gama 2,5

1

Departamento de Electromagnetismo y F´?sica de la Materia,Universidad de Granada,Fuentenueva,18071Granada,Spain 2

Centro de F´?sica Te´o rica e Computacional da Universidade de Lisboa Avenida Professor Gama Pinto 2,P-1649-003Lisbon,Portugal

3

Instituto Superior de Engenharia de Lisboa

Rua Conselheiro Em´?dio Navarro,1,P-1949-014Lisbon,Portugal

4

Max Planck Institute for Metal Research,Heisenbergstrasse 3,70569Stuttgart,Germany

5

Departamento de F´?sica,Faculdade de Ci?e ncias da Universidade de Lisboa,

R.Ernesto Vasconcelos,Lisbon,Portugal

(Dated:today)Deposits of dipolar particles are investigated by means of extensive Monte Carlo simulations.We found that the e?ect of the interactions is described by an initial,non-universal,scaling regime characterized by orientationally ordered deposits.In the dipolar regime,the order and geometry of the clusters depend on the strength of the interactions and the magnetic properties are tunable by controlling the growth conditions.At later stages,the growth is dominated by thermal e?ects and the di?usion-limited universal regime obtains,at ?nite temperatures.At low temperatures the crossover size increases exponentially as T decreases and at T =0only the dipolar regime is observed.

PACS numbers:61.43.Hv,http://doc.xuehai.net,75.30.-m

The growth of deposits by irreversible aggregation of particles is of great technological importance as well as of theoretical interest.A variety of mechanisms are involved in the growth processes but at late times scaling laws de-pending only on a few parameters have been observed.A general assumption,that describes the patterns found in many experiments,is that the deposition process is dominated by thermal di?usion.A simple model for this type of growth is di?usion-limited deposition (DLD)[1],characterized by the formation of branched,fractal struc-tures similar to those found in electrodeposition,dielec-tric breakdown,etc (see [2]and references therein).Un-der certain circumstances,however,interparticle inter-actions,favoring ordered structures that compete with the randomness of the di?usion process,are required to describe the observed growth patterns.A case in point is the di?usion-limited deposition of magnetic particles subject to dipolar interactions.

Dipolar interactions are essential in determining the rich variety of structures exhibited by magnetic materi-als [3],and their interplay with thermal di?usion may lead to novel magnetic properties.On the theoretical side,dipolar interactions provide a simple model to study the e?ects of anisotropic,long-ranged interactions on far from equilibrium aggregation processes.The cen-tral question concerns the change in the fractal dimen-sion of the aggregates,D ,as the dipolar interactions are switched on.Meakin et al.[4]considered the e?ect of isotropic long-ranged,1/r ?,interactions in reaction-limited cluster-cluster aggregation (CCA)models.They found that D is unchanged for short-ranged interactions,i.e.for ?≥2D o where D o is the fractal dimension of the non-interacting aggregates,while for longer-ranged in-

teractions D may change substantially.Accordingly,nu-merical results for di?usion-limitted aggregation (DLA),performed for particles with Ising spins (short-range in-teractions),revealed no changes in the fractal dimension of the aggregates with increasing exchange interactions [5].Finally,results for DLA [6]of dipolar particles in-dicate that D decreases as the strength of the dipolar interactions increases,in line with the results for CCA of dipolar particles [7]and with experimental results for the aggregation of magnetic microspheres [8],but in dis-agreement with preliminary results of ours [9].

In this article we report results of extensive Monte Carlo simulations that provide a general framework where the apparently contradictory results described above may be understood.We show that the initial stage of two dimensional dipolar DLD growth is indeed described by a new nonuniversal scaling regime,charac-terized by clusters (trees)whose shape and fractal di-mension are temperature-dependent.For large enough systems,however,the dipolar regime crosses-over to the di?usion driven universal regime,where the e?ect of the dipolar interactions is dominated by thermal e?ects.It is also shown that the dipolar regime corresponds to ori-entationally ordered deposits and that the onset of the universal regime coincides with the disappearance of the orientational order.At T =0only the dipolar regime is observed.

In the new dipolar regime,the orientational order as well as the shape and fractal dimension of the clusters depend on the strength of the interactions.Thus,the magnetic properties of dipolar deposits may be tuned by controlling the growth conditions,such as temperature.Finally,we found that the fractal dimension of the entire

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