Journal
JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS
Volume 559, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.jmmm.2022.169520
Keywords
Magnetostatics; Bifurcation; Hysteresis; Subcritical bifurcation; Relaxation code; Fold; Cusp catastrophe; Toroidal magnetic moment
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This paper examines the hysteretic transition between two stable arrangements of a cluster of seven dipoles, and clarifies the nature of the two instabilities. The first one is a symmetry-breaking sub-critical bifurcation, and the second one is a fold.
In the paper Smith et al. (2022) a hysteretic transition between two stable arrangements of a cluster of seven dipoles is presented. The relative strength of the center dipole in a hexagonal arrangement serves as the bifurcation parameter. The authors clearly demonstrate the existence of two instabilities accompanied by discontinuous jumps of the dipole arrangement, but leave the question about the nature of these instabilities unanswered. This comment clarifies the nature of the two instabilities: the first one is a symmetry-breaking sub-critical bifurcation with parabolic scaling of the magnetic potential energy difference between the two branches, and the second one is a fold with its characteristic scaling in the form of a semi-cubic parabola.
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