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

Abstract

We investigated the effect of intermolecular dipolar interactions on a cubic 3D ensemble of 5X5X4=100 nanomagnets, each with spin $S=5$. We employed the Landau-Lifshitz-Gilbert equation to solve for the magnetization $M(B)$ curves for several values of the damping constant $\alpha$, the induction sweep rate, the lattice constant $a$, the temperature $T$, and the magnetic anisotropy field $H_A$. We find that the smaller the $\alpha$, 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 $a$ within realistic values (1.5 nm - 2.5 nm) show that the dipolar interaction plays an important role in the magnetic hysteresis by controlling the relaxation process. The $T$ dependencies of $\alpha$ and of $M$ are presented and discussed with regard to recent experimental data on nanomagnets. $H_A$ 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 an $M(B)$ curve for a 2D-system [M. Kayali and W. Saslow, Phys. Rev. B {\bf 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 3D systems, dipole-dipole interactions generally diminish the hysteresis, in 2D systems, they strongly enhance it. For both square 2D and rectangular 3D lattices with $\mathbf{B}||(\hat{\mathbf{x}}+\hat{\mathbf{y}})$, dipole-dipole interactions can cause large jumps in the magnetization.

15 pages 14 figures, submitted to Phys. Rev. B

References in corpus (14)

• Quantum Computing in Molecular Magnets
• Low-Temperature Quantum Relaxation in a System of Magnetic Nanomolecules
• Spin-spin cross-relaxation in single-molecule magnets
• Crossover between Thermally Assisted and Pure Quantum Tunneling in Molecular Magnet Mn12-Acetate
• Spin quantum tunneling via entangled states in a dimer of exchange coupled single-molecule magnets
• Magnetization relaxation in (Ga,Mn)As ferromagnetic semiconductors
• Ordering of dipolar Ising crystals
• NMR as a probe of the relaxation of the magnetization in magnetic molecules
• Magnetic long-range order induced by quantum relaxation in single-molecule magnets
• Long-range ferromagnetic dipolar ordering of high-spin molecular clusters
• Magnetization Process of Single Molecule Magnets at Low Temperatures
• Heisenberg Dimer Single Molecule Magnets in a Strong Magnetic Field
• Hysteresis multicycles in nanomagnet arrays
• Two-body tunnel transitions in a Mn4 Single-Molecule Magnet

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