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

Abstract

To investigate the influence of geometric frustration on the properties of low-energy configurations of systems of ferromagnetic nanoislands located on the edges of the Cairo lattice, the model of interacting Ising-like magnetic dipoles is used. By the method of complete enumeration, the densities of states of the Cairo pentagonal lattices of a finite number of Ising-like point dipoles are calculated. The calculated ground and low-energy states for systems with a small number of dipoles can be used to solve the problem of searching for the ground states in a system with a relatively large number of dipoles. It is shown that the ground-state energy of the Cairo pentagonal lattices exhibits nonmonotonic behavior on one of the lattice parameters. The lattice parameters can be used to control the degree of geometric frustration. For the studied lattices of a finite number of Ising dipoles on the Cairo lattice in the ground-state configurations, a number of closed pentagons is observed, which are different from the obtained maximum closed pentagons. The magnetic order in the ground-state configurations obeys the ice rule and the quasi-ice rules.

Geometrical frustration and competing orders in the dipolar trimerized triangular lattice

“…It exhibits various competing interactions, which can be directly controlled by the lattice parameter b. Tuning of the strengths of the interactions allows it to transition from a long-range ordered ground state dominated by clockwiseand anticlockwise vortices, through a highly disordered state, when competing interactions are equalized, to a phase manifested by an increasing ice-rule obedience and a preference for ferromagnetic-type moment alignments. The variety of ordering preferences as interactions J 1 and J 2 are varied and equalized pose interesting questions, regarding its ground state and potential phase transitions at lower or higher temperatures, which can be either addressed via simulations [41,53,54] or experimentally, if structures with lowered block-ing temperatures can be generated [55]. Newly emerging coherent x-ray scattering techniques [56] appear to be the best method for shedding light on these open questions.…”

Ice rule breakdown and frustrated antiferrotoroidicity in an artificial colloidal Cairo ice

“…ASIs are lattice of ferromagnetic elements that interact via in-plane dipoles and are arranged to produce geometric frustration effects [13][14][15][16][17][18][19][20]. In the Cairo geometry, recent experimental works have found a rich behavior due to frustration [21,22], while Monte Carlo simulations reported the presence of long-range order [23]. Even mechanical analogues of Cairo artificial spin ice were realized via 3D-printing [24].…”