Experimental and theoretical evidences for the ice regime in planar artificial spin ices

Abstract

In this work, we explore a kind of geometrical effect in the thermodynamics of artificial spin ices (ASI). In general, such artificial materials are athermal. Here, We demonstrate that geometrically driven dynamics in ASI can open up the panorama of exploring distinct ground states and thermally magnetic monopole excitations. It is shown that a particular ASI lattice will provide a richer thermodynamics with nanomagnet spins experiencing less restriction to flip precisely in a kind of rhombic lattice. This can be observed by analysis of only three types of rectangular artificial spin ices (RASI). Denoting the horizontal and vertical lattice spacings by a and b, respectively, then, a RASI material can be described by its aspect ratio γ ≡ a/b. The rhombic lattice emerges when γ = √ 3. So, by comparing the impact of thermal effects on the spin flips in these three appropriate different RASI arrays, it is possible to find a system very close to the ice regime.

Advances in artificial spin ice

“…One possible solution is to raise one sublattice with respect to the other [40][41][42][43][44] , so that, at a critical vertical separation, the so-called Coulomb phase is achieved 45 , with emergent magnetic monopoles freely moving in a highly degenerate, divergence-free background. Another possibility to reduce the string tension is to use two different sublattice parameters 46,47 . In lattices of connected nanomagnets, modifying the shape and size of the vertex, for example, by fabricating a hole at the vertex centre or making the nanomagnets narrower, can also make the type I and type II vertices similar in energy 48,49 .…”

“…3a), are easier in terms of the fabrication. For example, stretching the lattice to a rectangular shape increases the degeneracy of vertex states 46,47 . In another example, introducing magnetic nanodiscs into the gaps at the vertices 21 , as so-called 'slave' macrospins, equalizes the energy between type I and type II vertices.…”

“…In further 2D systems, the nanomagnets can be placed on the shuriken 198 , modified shakti 137 , Santa Fe 8 , Ising stripe 199 and rectangular 47 lattices.…”

Colloquium : Ice rule and emergent frustration in particle ice and beyond

“…Because the two components are uncoupled at the lowest order in the effective free energy, dipolar correlations and pinch points survive at non-zero temperature. Artificial realization of topological phases was achieved in the Shakti geometry (Lao et al, 2018) as well as in magnetic square ice (Möller and Moessner, 2006;Perrin et al, 2016) and rectangular (Loreto et al, 2019;Ribeiro et al, 2017) ice. No equivalent phase has yet been realized with colloids, though those magnetic realization provide directions.…”

Dipolar Cairo lattice: Geometrical frustration and short-range correlations

“…Artificial spin ice systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], initially introduced as two-dimensional analogues to pyrochlore spin ice [17], enabled the direct visualization of the consequences of geometrical frustration using appropriate magnetic imaging techniques. In particular, the introduction of artificial spin ices that exhibit thermally induced moment fluctuations paved the way to explore the statistical physics of geometrical frustration [3][4][5][6], emergent magnetic monopoles and macroscopic spin ice degeneracy [18,19], in addition to first attempts in achieving artificial spin glasses [20].…”