Infinite geometric frustration in a cubic dipole cluster

Titelangaben

Schönke, Johannes ; Schneider, Tobias M. ; Rehberg, Ingo:
Infinite geometric frustration in a cubic dipole cluster.
In: Physical Review B. Bd. 91 (Januar 2015) Heft 2 . - No. 020410(R).
ISSN 0163-1829
DOI der Verlagsversion: https://doi.org/10.1103/PhysRevB.91.020410

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Abstract

The geometric arrangement of interacting (magnetic) dipoles is a question of fundamental importance in physics, chemistry, and engineering. Motivated by recent progress concerning the self-assembly of magnetic structures, the equilibrium orientation of eight interacting dipoles in a cubic cluster is investigated in detail. Instead of discrete equilibria we find a type of ground state consisting of infinitely many orientations. This continuum of energetically degenerate states represents a yet unknown form of magnetic frustration. The corresponding dipole rotations in the flat potential valley of this Goldstone mode enable the construction of frictionless magnetic couplings. Using computer-assisted algebraic geometry methods, we moreover completely enumerate all equilibrium configurations. The seemingly simple cubic system allows for exactly 9536 unstable discrete equilibria falling into 183 distinct energy families.