All Physics Faculty Publications
Document Type
Article
Journal/Book Title/Conference
Journal of Magnetism and Magnetic Materials
Author ORCID Identifier
Peter T. Haugen https://orcid.org/0000-0003-3779-1806
Andrew D. P. Smith https://orcid.org/0000-0002-3142-2105
Boyd F. Edwards https://orcid.org/0000-0002-2309-1350
Volume
549
Publisher
Elsevier
Publication Date
1-15-2022
Award Number
NSF, Division of Chemistry (CHE) 1808225
Funder
NSF, Division of Chemistry (CHE)
First Page
1
Last Page
18
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Abstract
By minimizing the magnetostatic potential energy and by finding zeros in the sum of the squares of the torques, we find the equilibrium states of six dipoles of identical strength at the vertices of a regular hexagon and a variable-strength dipole at the center. The seven dipoles spin freely about fixed axes that are perpendicular to the plane of the hexagon, with their dipole moments directed parallel to the plane. When the central dipole is weak compared with the perimeter dipoles, a ‘‘circular’’ state applies in which the perimeter dipole moments circle around the central dipole, which points toward a perimeter dipole. When the central dipole is strong, a more symmetric ‘‘dipolar’’ state applies in which the perimeter dipole moments align approximately with the field of the central dipole. Over an intermediate range of dipole strengths bounded by two critical values, both states are locally stable and the state of the system depends upon its history. Iron filings are used to observe both states in experiments on small spherical neodymium magnets. A ‘‘misaligned’’ state that is barely unstable theoretically is also observed experimentally; this state resembles the circular state except that the central dipole moment points toward a point of contact between two perimeter magnets.
Recommended Citation
Smith, A. D., Haugen, P. T., & Edwards, B. F. (2022). Hysteretic transition between states of a filled hexagonal magnetic dipole cluster. Journal of Magnetism and Magnetic Materials, 549, 168991.
