Micromagnetic Modeling of Reversal Nucleation in Core/Shell Exchange-Spring Structures

Nanocomposite exchange-spring permanent magnet materials promise superior performance and are a potential solution to the supply criticality in rare earth elements [1]. The nucleation of magnetization reversal in cylindrical and spherical soft core/hard shell exchange-spring structures has been investigated by solving the linearized Brown's equation perturbatively, and has been verified with numerical simulations [2]. Accounting for the magnetostatic self-interaction field leads to a modification to the proposed quasi-coherent ``bulging'' mode[3] of nucleation for small core sizes. The modified curling mode, where the magnetization configuration is vortex-like and flux-closed, becomes favored at large core sizes. The mode crossover occurs at a core diameter of approximately twice the exchange length for the cylindrical geometry. Since flux-closure allows magnetic elements to be densely packed without affecting the nucleation field, a potential direction for improving permanent magnet materials is to induce the modified curling mode by creating a soft-cylinder-in-hard-matrix exchange-spring microstructure.\\[4pt] [1] J. M. D. Coey, \textit{IEEE Trans. Magn.} \textbf{47}, 4671 (2011).\\[0pt] [2] J. S. Jiang, S. D. Bader, \textit{J. Phys.: Condens. Matter}, \textbf{26}, 064214 (2014).\\[0pt] [3] R. Skomski, J. P. Liu, D. J. Sellmyer, \textit{Phys. Rev.} \textbf{B60}, 7359 (1999).