How to Store Energy in Dirac Strings

Dynamics of Bound Monopoles in Artificial Spin Ice: How to Store Energy in Dirac Strings.

E. Y. Vedmedenko

Phys. Rev. Lett. 116, 077202 (2016)

(a, b) Examples of microscopic configurations used for static calculations. Color scheme gives the energy per dipole. (c) Total energy cost due to formation of DSs of length r in a sample 200a×200a. Numerical data (dots) are fitted by Eq. (1) with T0≈7.3w/a and γ≈0.5wa. The inset gives the difference between the total potential and the linear term T0r. (d) Spatial energy profile along the DSs of panel (a) and schematic drawing of T1 and T2 vertices. (e) Interaction potential between two BMs of opposite sign in different backgrounds calculated analytically (dots). Lines are fits by function γ/r with γ≈1/2. The γ/r term is repulsive.

 

Frustration in artificial spin ice

The unhappy wanderer.
R. L. Stamps
Nature Physics 10, 623 (2014)

Emergent ice rule and magnetic charge screening from vertex frustration in artificial spin ice.

Ian Gilbert, Gia-Wei Chern, Sheng Zhang, Liam O’Brien, Bryce Fore,, Cristiano Nisoli and Peter Schi effer

Nature Physics 10, 670 (2014)

An initial spin (green) is placed arbitrarily on an empty lattice. A second spin is placed on a neighbouring lattice segment in a direction parallel to the first, unless the spins share a vertex, in which case the direction of the spin reverses (if the vertex is traversed in a straight line) or rotates (if a turn is taken). Subsequent spins placed in the same way eventually reach the starting position and close the loop (red). A lattice is considered 'happy' (a) when these rules can be obeyed at every segment along the loop, and 'unhappy' or vertex-frustrated (b) when they fail.

Monopoles in FMs

Monopoles in ferromagnetic metals.
Gen Tatara, Akihito Takeuchi, Noriyuki Nakabayashi, and Katsuhisa Taguchi
ArXiv 1203.2709 (2012)

Monopole defects in spin-ice

Direct observation and control of magnetic monopole defects in an artificial spin-ice material.
S Ladak, D E Read, W R Branford1 and L F Cohen
New Journal of Physics 13, 063032 (2011)

The movement of magnetic monopole defects through the honeycomb lattice.

Dipolar spin-ice on the kagomé

Two-Stage Ordering of Spins in Dipolar Spin Ice on the Kagome Lattice.
Gia-Wei Chern, Paula Mellado, and O. Tchernyshyov
Phys. Rev. Lett.106,.207202 (2011)

 Magnetic configurations of the dipolar kagome ice and their alternative representations. (a) A spin-ice microstate lacking spin order but possessing charge order. The latter is manifested in the dumbbell representation (b). (c) One of the ground states exhibiting the magnetic order and its depiction in terms of dimers (d) . Monte Carlo results of specific heat and entropy signalign the PM/spin-ice, charge-order and spin-order transitions as T decreases.

Nanostructure of magnetic monopole defects

Nanoscale structure of the magnetic induction at monopole defects in artificial spin-ice lattices.
C. Phatak, A. K. Petford-Long, O. Heinonen, M. Tanase, and M. De Graef
Phys. Rev. B 83, 174431 (2011)

Magnetic induction color maps reconstructed after (a) the first demagnetization cycle, showing the formation
of defect strings and two magnetic monopole defects, and (b) after the second demagnetizing loop.

Magnetic monopoles in spin ice

Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice.
Elena Mengotti, Laura J. Heyderman , Arantxa Fraile Rodríguez , Frithjof Nolting , Remo V. Hügli , Hans-Benjamin Braun
Nature Physics 7, 68 (2011)

a, Schematic view of the nanolithographic array of permalloy islands with anisotropy axes along honeycomb links and the orientation of the magnetization indicated by arrows. . b, Corresponding charge distribution with magnetic moments replaced by dumbbells carrying charge q and −q (in red and blue).