Effect of dipolar interactions on the magnetization of a cubic array of nanomagnets

Abstract

We investigated the effect of intermolecular dipolar interactions on an ensemble of 100 three-dimensional systems of $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}4$ nanomagnets, each with spin $S=5$, arranged in a cubic lattice. We employed the Landau-Lifshitz-Gilbert equation to solve for the magnetization curves for several values of the damping constant, the induction sweep rate, the lattice constant, the temperature, and the magnetic anisotropy. We find that the smaller the damping constant, the stronger the maximum induction required to produce hysteresis. The shape of the hysteresis loops also depends on the damping constant. We find further that the system magnetizes and demagnetizes at decreasing magnetic field strengths with decreasing sweep rates, resulting in smaller hysteresis loops. Variations of the lattice constant within realistic values (1.5--2.5 nm) show that the dipolar interaction plays an important role in the magnetic hysteresis by controlling the relaxation process. The temperature dependencies of the damping constant and of the magnetization are presented and discussed with regard to recent experimental data on nanomagnets. Magnetic anisotropy enhances the size of the hysteresis loops for external fields parallel to the anisotropy axis, but decreases it for perpendicular external fields. Finally, we reproduce and test a previously reported magnetization curve for a two-dimensional system [M. Kayali and W. Saslow, Phys. Rev. B 70, 174404 (2004)]. We show that its hysteretic behavior is only weakly dependent on the shape anisotropy field and the sweep rate, but depends sensitively upon the dipolar interactions. Although in three-dimensional systems, dipole-dipole interactions generally diminish the hysteresis, in two-dimensional systems, they strongly enhance it. For both square two-dimensional and rectangular three-dimensional lattices with $\mathbf{B}\ensuremath{\Vert}(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{x}}+\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{y}})$, dipole-dipole interactions can cause large jumps in the magnetization.