Chirality in artificial spin ice

Emerging Chirality in Artificial Spin Ice.
W. R. Branford, S. Ladak, D. E. Read, K. Zeissler, L. F. Cohen
Science 335, 1597 (2012)

Magnetic vertex configurations and equilibrium phase diagram for artificial spin ice honeycombs. The background (A to D) is a SEM of a small section of the array. (A) The magnetic charge ±q = ±m/l dumbbell representation of a magnetic moment m of length l on a honeycomb of lattice parameter a. Deviations from ideal Ising behavior are characterized by ε = 1 – l/a. (B) Charges on neighboring dumbbells reside on the circumference of a circle of diameter εa. This is equivalent to (C) a point charge Q = Σq and a vertex dipole moment (VDM) of magnitude εaΔq/2 colocated at the vertex center. (Δq = q_max – q_min at the vertex.) In connected arrays, the local magnetic structure at the vertex minimizes the VDM (21). (D) The eight possible configurations of magnetic moments (black arrows) at a kagome spin ice vertex. Vertices a to f obey the ice rule and have Q = ±q; VDM = εaq (purple arrows) and spin chirality Ω = –1/3; vertices g and h are ice rule defects with Q = ±3q; VDM = 0 and Ω = +1 (21). (E) The predicted phase diagram for artificial spin ice honeycombs (6, 8) (only the Ice I phase is observed in zero-field). There are four distinct phases: the gas-like Ising paramagnet; the liquid-like short-range spin ice (Ice I) phase; the long-range spin ice (Ice II) phase where the near order extends to second nearest neighbor macrospins, giving favored vertex pairs [ab], [cd], and [ef]; and the long-range ordered macrospin solid state.