Effective Temperature in an Interacting Vertex System: Theory and Experiment on Artificial Spin Ice

Abstract

Frustrated arrays of interacting single-domain nanomagnets provide important model systems for statistical mechanics, because they map closely onto well-studied vertex models and are amenable to direct imaging and custom engineering. Although these systems are manifestly athermal, we demonstrate that the statistical properties of both hexagonal and square lattices can be described by an effective temperature based on the magnetostatic energy of the arrays. This temperature has predictive power for the moment configurations and is intimately related to how the moments are driven by an oscillating external field.

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

“…For example, artificial spin ice systems were proposed to be constructed as arrays of optical traps [267,268]. A large number of experiments and theories since 2006 have considered artificial spin ice systems, including planes of ferromagnetic islands with square, honeycomb and Kagome lattices [269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295]. In particular, it has been shown using magneto-optical Kerr effect that disorder in the roughness (in shape) of magnetic islands plays essential role in the collective behavior of artificial spin ices [296,297].…”

Realizing three-dimensional artificial spin ice by stacking planar nano-arrays

“…Because of their nano-scale interaction energies (∼ 10 3 − 10 5 K depending on the size of the nanomagnet and mutual spacing) they reveal, at accessible temperatures, emergent features which in natural materials are seen only at very low temperature. Following the pioneering work of Wang et al on the two-dimensional square-ice array [7,8], artificial spin ices have been proposed and studied in diverse types of physical systems [9][10][11][12] and geometries such as honeycomb (kagome ice) [13][14][15][16][17][18][19][20], brickwork [21], triangular [22][23][24], and pentagonal lattices [25]. A systematic approach for designing 2D arrays with emergent ice-type frustration has also been proposed [26,27], and recently realized experimentally [29].…”

Emergent geometric frustration of artificial magnetic skyrmion crystals

“…The most studied artificial spin ice systems are created using arrays of nanomagnets with a bistable single-domain magnetization [43,44,[46][47][48][49][50][51][52][53][54][55][56][57][63][64][65][66][67]. Artificial nanomagnet spin ice systems have been realized experimentally for square [43,50,51,56,66], and honeycomb [49,52,68] lattices, each having different analogous features to the naturally occurring rare-earth pyrochlore lattice [37].…”

“…Although the naturally occurring spin ices exhibit interesting types of topological monopole defects and "ice-rule" states [39,40], the frustrated behaviors occur only at very low temperatures and the individual spin ordering or defects cannot be directly visualized on the atomic scale size. Recent advances in nanofabrication technology have permitted the creation of artificial ice systems [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] that mimic the behavior of geometrically frustrated atomic spin ices at much larger length scales and higher temperatures, where direct visualization of the microscopic effective spin configurations under controlled conditions is possible.…”