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The multipole moments of in-plane magnetized disks have been calculated based on the fundamental theory of magnetostatics. Analytical solutions for disks with uniform magnetization or an onion state are given explicitly. It is demonstrated that depending on the polarization configuration, higher-order multipole moments beyond the dipole moment appear. The strength of the multipole moments can be of the same order of magnitude as the dipolar moment. The higher-order moments give rise to an additional energy contribution in arrays of close-packed polarized disks.
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Mikuszeit et al. (2005) studied this question.
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