Multipolar Ordering and Magnetization Reversal in Two-Dimensional Nanomagnet Arrays

The low-temperature stable states and the magnetization reversal of realistic two-dimensional nanoarrays with higher-order magnetostatic interactions are studied theoretically. For a general calculus of the multipole-multipole interaction energy we introduce a Hamiltonian in spherical coordinates into the Monte Carlo scheme. We demonstrate that higher-order interactions considerably change the dipolar ground states of in-plane magnetized arrays favoring collinear configurations. The multipolar interactions lead to enhancement or decrease of the coercivity in arrays with in-plane or out-of-plane magnetization.

Figure 1

Hysteresis loops for a $20\times 20$ square nanoarray with $Q_{30}=0.5Q_{10}$ and a pure dipolar system [inset (d)]. The magnetic field is applied in the $x$ direction. Insets (a)–(c) give a part of the intermediate magnetic configurations; (f) and (e) show stable zero-field configurations for combined multipoles and the pure dipolar case, respectively. Thermal energy is $kT=0.6E_{\parallel }$. The field is expressed in $\frac{{\mu }_0{M}_{\mathrm{S}}{V}_{\mathrm{D}}}{E_{\parallel }}$ with ${\mu }_0$—the permeability of free space and $V_{\mathrm{D}}$—the volume of a dot.

Figure 2

(a) Internal energy of ideal parallel, antiparallel, coexisting, and superdomain configurations for $L=20$ as a function of $Q_{30}/Q_{10}$ on a square lattice; (b) Size dependence of different contributions of the magnetostatic energy for parallel and antiparallel lines (scatter) for $Q_{30}/Q_{10}=0.5$.

Figure 3

MC results for the order parameter (a), specific heat (b), and susceptibility (c) of a system with $Q_{30}/Q_{10}=0.5$ on a square lattice.