We study the magnetic field effects on the diluted spin-ice materials using the replica-exchange Monte Carlo simulation. We observe five plateaus in the magnetization curve of the diluted nearestneighbor spin-ice model on the pyrochlore lattice when a magnetic field is applied in the [111] direction. This is in contrast to the case of the pure model with two plateaus. The origin of five plateaus is investigated from the spin configuration of two corner-sharing tetrahedra in the case of the diluted model. [7][8][9][10][11].In spin-ice materials, magnetic ions (Dy 3+ or Ho 3+ ) occupy the pyrochlore lattice of corner-sharing tetrahedra, and the local crystal field environment causes magnetic moments to point along the lines connecting the centers of the two tetrahedra at low temperatures. In the low-temperature spin-ice state, magnetic moments are highly constrained locally and obey the so-called "ice rules": two spins point in and two spins point out of each tetrahedron of the pyrochlore lattice. This 2-in 2-out spin configuration is equivalent to the situation for hydrogen atoms in water ice [12].The dilution effect on frustration was studied by Ke et al.[13] for spin-ice materials. Magnetic ions Dy or Ho are replaced by nonmagnetic Y ions. Nonmonotonic zeropoint entropy as a function of the dilute concentration was observed experimentally, and further studies on the dilution effects have been reported [14][15][16].In this communication, we study the diluted nearestneighbor (NN) antiferromagnetic (AFM) Ising model on the pyrochlore lattice under a magnetic field in the [111] direction. We treat the NN interaction as a theoretical model; a more complicated model, such as the dipolar model, may be required to make connections to actual materials. For the simulation method, we use the replicaexchange Monte Carlo method [17] to avoid the trap at * Electronic address: peretiatko.aa@dvfu.ru † Electronic address: nefedev.kv@dvfu.ru ‡ Electronic address: okabe@phys.se.tmu.ac.jp local-minimum configurations.We are concerned with the Hamiltonian, which is given in Eq. (2.2) of Ref. [6]; For convenience, the illustration of the pyrochlore lattice, which is a three-dimensional network of cornersharing tetrahedra, is given in Fig. 1, where the apical spins, d κ(i) = d 0 , are shown in red, whereas other spins are in blue.In the case of the site dilution of spins, the Hamiltonian becomes

We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antiferromagnetic Ising model on the three-dimensional pyrochlore lattice in a magnetic field pointing in the [111] direction, sometimes referred to as the "kagome-ice" problem. We discuss the similarity and dissimilarity of the magnetization curves of the "kagome-ice" state and the twodimensional kagome lattice.

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The research method for the investigation of magnetic states of single nanoparticles, 1D arrays, 2D, and quasi-2D arrays is used. The possibility of the nanodots magnetic states reconstruction by the space distribution of gradient dipole-dipole interaction force is theoretically justified. The comparison is made between the results of nanoarchitecture numerical simulation in an external magnetic field and experimental data.

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)]. We find large peaks of the residual entropy due to the degeneracy at the crossover magnetic fields, hc/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.