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, nonuniversal, 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 effects and the diffusion-limited universal regime obtains, at finite temperatures. At low temperatures the crossover size increases exponentially as $T$ decreases and at $T=0$ only the dipolar regime is observed.

Figure 1

(Color online) Average height $\overline{H}\left(s\right)$ and width $\overline{W}\left(s\right)$ as a function of the size of the tree, $s$, at $T^{*}={10}^{-1}$ and various system sizes. The lines are power laws (2) with the exponents listed in Table . Dashed line: universal regime.

Figure 2

(Color online) Average height $\overline{H}\left(s\right)$ and width $\overline{W}\left(s\right)$ as a function of the size of the tree, $s$, at $T^{*}={10}^{-3}$ and various system sizes. The lines are power laws (2) with the exponents listed in Table . Solid line: dipolar regime. Dashed line: universal regime.

Figure 3

(Color online) Average number of trees of size $s$ divided by $L\left({\overline{n}}_s∕L\right)$ as a function of $s$, at various temperatures and system sizes. Lines as in Fig. 2.

Figure 4

(Color online) Average particle density and mean-square magnetization densities at height $h$. Inset: diagonal elements, $Q_{xx}$ and $Q_{yy}$, of the ordering matrix $\mathbf{Q}$.