Nambu monopoles interacting with lattice defects in a two-dimensional artificial square spin ice

Abstract

The interactions between an excitation (similar to a pair of Nambu monopoles connected by their associated string) and a lattice defect are studied in an artificial two-dimensional square spin ice. This is done by considering a square array of islands containing only one island different from all others. This difference is incorporated in the magnetic moment (spin) of the "imperfect" island and several cases are studied, including the special situation in which this distinct spin is zero (vacancy). We show that the two extreme points of a defective island behave like two opposite magnetic charges. Then, the effective interaction between a pair of Nambu monopoles with the defective island is a problem involving four magnetic charges (two pairs of opposite poles) and a string. We also sketch the configuration of the field lines of these four charges to confirm this picture. The influence of the string on this interaction decays rapidly with the string distance from the defect.

New physics in frustrated magnets: Spin ices, monopoles, etc. (Review Article)

“…As a result of the magnetic frustration, these systems can exhibit magnetic monopole type states, which are an example of an exotic emergent quasiparticle [280,299,300,301,302,303,304,305,306,307,308,309,310,311]. For example, magnetic monopoles and associated Dirac-like strings have been directly observed in the artificial honeycomb (on Co films of 20 nm thickness) and Kagome spin ice (permalloy films) systems [312,313,314] using magnetic force microscopy and X-ray photoemission microscopy.…”

Defect Dynamics in Artificial Colloidal Ice: Real-Time Observation, Manipulation, and Logic Gate

“…Artificial spin ice systems (ASI) are lattices of interacting nanoscale ferromagnetic islands, recently introduced as a versatile model to investigate geometrically frustrated states [9,10], including the role of disorder [11,12], thermalization [13][14][15], and the excitation dynamics [16][17][18][19][20]. In opposition to bulk spin ice such as pyrochlore compounds, ASI allow us to directly visualize the spin textures and to tailor the spatial arrangement of the system elements.An intriguing aspect in ASI, which is attracting much theoretical interest, is the dynamics of defects [21][22][23][24][25][26][27][28]. The interactions between pairs of defects is one of the distinctive features between three dimensional (3D) and two dimensional (2D) spin ice.…”

“…An intriguing aspect in ASI, which is attracting much theoretical interest, is the dynamics of defects [21][22][23][24][25][26][27][28]. The interactions between pairs of defects is one of the distinctive features between three dimensional (3D) and two dimensional (2D) spin ice.…”

“…[34], both defects approach via a stepwise flipping of the colloids position and the system recovers the GS. Theoretical work [22] based on the dumbbell model [31] predicts the interaction potential between the two defects in the 2D ASI as VðlÞ ¼ −Q=l þ κl þ c. Here, Q is the topological Coulombic charge, κ the line tension, and c a constant associated with the creation of the defect pairs [25]. We confirm the validity of this assumption in our system, by explicitly calculating the energy cost VðlÞ ¼ E exc ðlÞ − E GS of a defect line of length l in the GS, which can be obtained by subtracting the GS energy from the energy of the excited configuration.…”

Pinning of thermal excitations at defects in artificial dipolar arrays: A theoretical investigation

“…Investigations of defects in 2D artificial spin ice have been performed e.g. by Silva et al [30] who addressed the interaction between magnetic string excitations caused by defects and string excitations. Other studies consider disorder as random displacements, as random island orientation, as random switching field or as random exchange strengths in square [31] or honeycomb [32,33] dipolar arrays.…”