Order and disorder, crossovers, and phase transitions in dipolar artificial spin ice on the Cairo lattice.

We study the thermodynamic properties of the magnetic dipolar spin ice on a 2D pentagonal Cairo lattice by using the numerical Metropolis and the complete enumeration methods. We use the model of point Ising-like dipoles considering long-range interactions with up to 100 nearest neighbors and with periodic boundary conditions. There are two explicit peaks both in the temperature behavior of the heat capacity and in the magnetic susceptibility. The low-temperature peak is caused only by long-range interactions and is not present in the model where each dipole interacts only with four nearest neighbors. The height of the peak depends logarithmically on the quantity of dipoles, which indicates a phase transition. The nature of the low-temperature phase transition is related to the transformation from order to disorder in orthogonal sublattices while maintaining the spin ice state and the spin ice rule in the sublattice of crosses. The high-temperature heat capacity peak is associated with the melting of spin ice, i.e., with the crossover from spin ice to paramagnetic chaos. Its height is constant and does not depend on the quantity of dipoles. It is shown that the choice of the radius of the dipole-dipole interaction has a significant effect on the statistical properties of the model. The model may even show the appearance of the long-range order and the phase transition in the case of long-range interaction or its absence in the case of short-range interaction.

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

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.

Large peaks in the entropy of the diluted nearest-neighbor spin-ice model on the pyrochlore lattice in a [111] magnetic field.

We study the residual entropy of the nearest-neighbor spin-ice model in a magnetic field along the [111] direction using the Wang-Landau Monte Carlo method, with a special attention to dilution effects. For a diluted model, we observe a stepwise decrease of the residual entropy as a function of the magnetic field, which is consistent with the finding of the five magnetization plateaus in a previous replica-exchange Monte Carlo study by Peretyatko et al. [Phys. Rev. B 95, 144410 (2017)2469-995010.1103/PhysRevB.95.144410]. We find large peaks of the residual entropy due to the degeneracy at the crossover magnetic fields, h_{c}/J=0, 3, 6, 9, and 12, where h and J are the magnetic field and the exchange coupling, respectively. In addition, we also study the residual entropy of the diluted antiferromagnetic Ising models in a magnetic field on the kagome and triangular lattices. We again observe large peaks of the residual entropy, which are associated with multiple magnetization plateaus for the diluted model. Finally, we discuss the interplay of dilution and magnetic fields in terms of the residual entropy.

Husimi-cactus approximation study on the diluted spin ice.

We investigate dilution effects on the classical spin-ice materials such as Ho_{2}Ti_{2}O_{7} and Dy_{2}Ti_{2}O_{7}. In particular, we derive a formula of the thermodynamic quantities as functions of the temperature and a nonmagnetic ion concentration based on a Husimi-cactus approximation. We find that the formula predicts a dilution-induced crossover from the cooperative to the conventional paramagnets in a ground state, and that it also reproduces the "generalized Pauling's entropy" given by Ke et al. To verify the formula from a numerical viewpoint, we compare these results with Monte Carlo simulation calculation data, and then find good agreement for all parameter values.

Entropy of diluted antiferromagnetic Ising models on frustrated lattices using the Wang-Landau method.

We use a Monte Carlo simulation to study the diluted antiferromagnetic Ising model on frustrated lattices including the pyrochlore lattice to show the dilution effects. Using the Wang-Landau algorithm, which directly calculates the energy density of states, we accurately calculate the entropy of the system. We discuss the nonmonotonic dilution concentration dependence of residual entropy for the antiferromagnetic Ising model on the pyrochlore lattice, and compare it to the generalized Pauling approximation proposed by Ke et al. [Phys. Rev. Lett. 99, 137203 (2007)PRLTAO0031-900710.1103/PhysRevLett.99.137203]. We also investigate other frustrated systems, the antiferromagnetic Ising model on the triangular lattice and the kagome lattice, demonstrating the difference in the dilution effects between the system on the pyrochlore lattice and that on other frustrated lattices.