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

Kseniia Makarova; Vladislav Strongin; Iuliia Titovets; Aleksandr Syrov; Ivan Zinchenko; Victor Samoylov; Kevin Hofhuis; Michael Saccone; Aleksandr Makarov; Alan Farhan; Konstantin Nefedev

doi:10.1103/PhysRevE.103.042129

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

Phys Rev E. 2021 Apr;103(4-1):042129. doi: 10.1103/PhysRevE.103.042129.

Authors

Kseniia Makarova^{1

2}, Vladislav Strongin^{1

2}, Iuliia Titovets¹, Aleksandr Syrov¹, Ivan Zinchenko^{1

2}, Victor Samoylov^{1

2}, Kevin Hofhuis^{3

4}, Michael Saccone⁵, Aleksandr Makarov^{1

2}, Alan Farhan^{4

6}, Konstantin Nefedev^{1

2}

Affiliations

¹ School of Natural Sciences, Far Eastern Federal University, Vladivostok, Russky Island, 10 Ajax Bay, 690922, Russian Federation.
² Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, Radio 7, 690041, Russian Federation.
³ Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland.
⁴ Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland.
⁵ Physics Department, University of California, 1156 High Street, Santa Cruz, California 95064, USA.
⁶ Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland.

PMID: 34005950
DOI: 10.1103/PhysRevE.103.042129

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.