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

Abstract

Geometric frustration and the ice rule are two concepts that are intimately connected and widespread across condensed matter. The first refers to the inability of a system to satisfy competing interactions in the presence of spatial constraints. The second, in its more general sense, represents a prescription for the minimization of the topological charges in a constrained system. Both can lead to manifolds of high susceptibility and non-trivial, constrained disorder where exotic behaviors can appear and even be designed deliberately. In this Colloquium, we describe the emergence of geometric frustration and the ice rule in soft condensed matter. This Review excludes the extensive developments of mathematical physics within the field of geometric frustration, but rather focuses on systems of confined micro-or mesoscopic particles that emerge as a novel paradigm exhibiting spin degrees of freedom. In such systems, geometric frustration can be engineered artificially by controlling the spatial topology and geometry of the lattice, the position of the individual particle units, or their relative filling fraction. These capabilities enable the creation of novel and exotic phases of matter, and also potentially lead towards technological applications related to memory and logic devices that are based on the motion of topological defects. We review the rapid progress in theory and experiments and discuss the intimate physical connections with other frustrated systems at different length scales.

Advances in artificial spin ice

“…Note added in proof At the time of publication, two important reviews on the dynamics in artificial spin ice 203 and on particle ice 204 have been published.…”

Low-energy states, ground states, and variable frustrations of the finite-size dipolar Cairo lattices

“…Frustrations are often, but not always, observed in systems with slow relaxation, degeneracy, and, accordingly, a nonzero value of the residual entropy. Usually, in an ensemble with limited disorder, violations of local ordering rules manifest themselves in the form of localized excitations of low-energy states of the system [19][20][21][22][23][24]. Since frustrations give rise to various forms of the so-called forced disorder, it is quite natural that the disorder obeys some nontrivial rules, either locally or globally.…”

“…Since frustrations give rise to various forms of the so-called forced disorder, it is quite natural that the disorder obeys some nontrivial rules, either locally or globally. The ice rule [24][25][26][27] and the quasi-ice rule [28] are well-known and important examples of local rules.…”

Modelos do gelo e transições de fase

“…Atualmente, modelos similares aos modelos do gelo (ou oriundos deles) ainda são estudados. Conforme o artigo de revisão [12], podemos citar os modelos do gelo artificiais e os modelos do tipo 'spin ice' magnético. Tal artigo aborda a conexão entre a regra do gelo e a frustração geométrica (a qual se refereà incapacidade de um sistema de satisfazer interações concorrentes na presença de restrições espaciais), além de apresentar a origem de tais técnicas na matéria condensada 'soft' e exemplificar sua atuação possibilitando a criação de novas e exóticas fases da matéria, potencialmente direcionando-as para aplicações tecnológicas relacionadas a memória e dispositivos lógicos que se baseiam no movimento de defeitos topológicos.…”