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Di Pietro Martínez M, Buceta RC. Energetic analysis of disorder effects in an artificial spin ice with dipolar interactions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:285801. [PMID: 32155604 DOI: 10.1088/1361-648x/ab7e58] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study the effect of quenched disorder in square artificial spin ice by means of numerical simulations. We introduce disorder in the length of magnetic islands using two kinds of distributions: Gaussian and uniform. As the system behavior depends on its geometrical parameters, we focus on studying it in the proximity of the ice regime which is quite difficult to thermalize both in experiments and simulations. We show how length disorder affect the antiferromagnetic and (locally) ferromagnetic ordering, by inducing the system, in the case of weak disorder, to intermediate or mix states. Moreover, in the case of strong disorder, ferromagnetic plaquettes prevail regardless of whether the mean length of the islands corresponds to an antiferromagnetic ordering.
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Andriushchenko P, Soldatov K, Peretyatko A, Shevchenko Y, Nefedev K, Otsuka H, Okabe Y. Large peaks in the entropy of the diluted nearest-neighbor spin-ice model on the pyrochlore lattice in a [111] magnetic field. Phys Rev E 2019; 99:022138. [PMID: 30934316 DOI: 10.1103/physreve.99.022138] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2017] [Indexed: 06/09/2023]
Abstract
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.
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Affiliation(s)
- Petr Andriushchenko
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, 8 Sukhanova, 690091, Russian Federation
- Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, 7 Radio, 690041, Russian Federation
| | - Konstantin Soldatov
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, 8 Sukhanova, 690091, Russian Federation
- Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, 7 Radio, 690041, Russian Federation
| | - Alexey Peretyatko
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, 8 Sukhanova, 690091, Russian Federation
| | - Yuriy Shevchenko
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, 8 Sukhanova, 690091, Russian Federation
- Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, 7 Radio, 690041, Russian Federation
| | - Konstantin Nefedev
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, 8 Sukhanova, 690091, Russian Federation
- Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, 7 Radio, 690041, Russian Federation
| | - Hiromi Otsuka
- Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
| | - Yutaka Okabe
- Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
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Otsuka H, Okabe Y, Nefedev K. Husimi-cactus approximation study on the diluted spin ice. Phys Rev E 2018; 97:042132. [PMID: 29758667 DOI: 10.1103/physreve.97.042132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Indexed: 06/08/2023]
Abstract
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.
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Affiliation(s)
- Hiromi Otsuka
- Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | - Yutaka Okabe
- Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | - Konstantin Nefedev
- School of Natural Sciences, Far Eastern Federal University, Vladivostok 690091, Russian Federation
- Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok 690041, Russian Federation
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Jurčišinová E, Jurčišin M. Adiabatic cooling processes in frustrated magnetic systems with pyrochlore structure. Phys Rev E 2017; 96:052128. [PMID: 29347644 DOI: 10.1103/physreve.96.052128] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2017] [Indexed: 06/07/2023]
Abstract
We investigate in detail the process of adiabatic cooling in the framework of the exactly solvable antiferromagnetic spin-1/2 Ising model in the presence of the external magnetic field on an approximate lattice with pyrochlore structure. The behavior of the entropy of the model is studied and exact values of the residual entropies of all ground states are found. The temperature variation of the system under adiabatic (de)magnetization is investigated and the central role of the macroscopically degenerated ground states in cooling processes is explicitly demonstrated. It is shown that the model parameter space of the studied geometrically frustrated system is divided into five disjunct regions with qualitatively different processes of the adiabatic cooling. The effectiveness of the adiabatic (de)magnetization cooling in the studied model is compared to the corresponding processes in paramagnetic salts. It is shown that the processes of the adiabatic cooling in the antiferromagnetic frustrated systems are much more effective especially in nonzero external magnetic fields. It means that the frustrated magnetic materials with pyrochlore structure can be considered as very promising refrigerants mainly in the situations with nonzero final values of the magnetic field.
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Affiliation(s)
- E Jurčišinová
- Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
| | - M Jurčišin
- Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
- Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovakia
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Shevchenko Y, Nefedev K, Okabe Y. Entropy of diluted antiferromagnetic Ising models on frustrated lattices using the Wang-Landau method. Phys Rev E 2017; 95:052132. [PMID: 28618636 DOI: 10.1103/physreve.95.052132] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2016] [Indexed: 06/07/2023]
Abstract
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.
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Affiliation(s)
- Yuriy Shevchenko
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, Sukhanova 8, 690091, Russian Federation
- Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, Radio 7, 690041, Russian Federation
| | - Konstantin Nefedev
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, Sukhanova 8, 690091, Russian Federation
- Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, Radio 7, 690041, Russian Federation
| | - Yutaka Okabe
- Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
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Fortin JY. Random site dilution properties of frustrated magnets on a hierarchical lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:296004. [PMID: 23807800 DOI: 10.1088/0953-8984/25/29/296004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We present a method to analyze the magnetic properties of frustrated Ising spin models on specific hierarchical lattices with random dilution. Disorder is induced by dilution and geometrical frustration rather than randomness in the internal couplings of the original Hamiltonian. The two-dimensional model presented here possesses a macroscopic entropy at zero temperature in the large size limit, very close to the Pauling estimate for spin-ice on the pyrochlore lattice, and a crossover towards a paramagnetic phase. The disorder due to dilution is taken into account by considering a replicated version of the recursion equations between partition functions at different lattice sizes. An analysis to first order in replica number allows a systematic reorganization of the disorder configurations, leading to a recurrence scheme. This method is numerically implemented to evaluate thermodynamical quantities such as specific heat and susceptibility in an external field.
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Affiliation(s)
- Jean-Yves Fortin
- CNRS, Institut Jean Lamour, Département de Physique de la Matière et des Matériaux, UMR 7198, Vandoeuvre-les-Nancy, F-54506, France.
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Sen A, Moessner R, Sondhi SL. Coulomb phase diagnostics as a function of temperature, interaction range, and disorder. PHYSICAL REVIEW LETTERS 2013; 110:107202. [PMID: 23521289 DOI: 10.1103/physrevlett.110.107202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2012] [Indexed: 06/01/2023]
Abstract
The emergent gauge field characteristic of the Coulomb phase of spin ice betrays its existence via pinch points in the spin structure factor S in reciprocal space which takes the form of a transverse projector P at low temperature: S(q) ~ P ~ q perpendicular(2)/q(2). We develop a theory which establishes the fate of the pinch points at low and high temperature, for hard and soft spins, for short- and long-ranged (dipolar) interactions, as well as in the presence of disorder. We find that their detailed shape can be used to read off the relative sizes of entropic and magnetic Coulomb interactions of monopoles in spin ice, and we resolve the question of why pinch points have been experimentally observed for Ho(1.7)Y(0.3)Ti(2)O(7) even at high temperature in the presence of strong disorder.
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Affiliation(s)
- Arnab Sen
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
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Orendáč M, Vrábel P, Orendáčová A, Prokleška J, Sechovský V, Singh S, Suryanarayanan R, Revcolevschi A. Magnetic order in hybrid frustrated magnets Gd(2-x)Tb(x)Ti2O7 (x = 0.2 and 0.5). JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:186003. [PMID: 22499160 DOI: 10.1088/0953-8984/24/18/186003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We report on the specific heat, magnetization and ac susceptibility measurements of single crystals of hybrid frustrated magnets Gd(1.8)Tb(0.2)Ti(2)O(7) and Gd(1.5)Tb(0.5)Ti(2)O(7). The analysis of experimental data revealed that, although partial replacing of the Gd(3+) ions by the Tb(3+) ions in the Gd(2)Ti(2)O(7) host lattice slightly enhances antiferromagnetic coupling, as inferred from the evolution of the paramagnetic Curie-Weiss temperature, the ordering temperature gradually decreases. Paramagnetic correlations introduced by the Tb(3+) ions cause this perturbation, altering the effective further neighbor interactions and destabilizing the ground state in Gd(2)Ti(2)O(7). In addition, the low-energy states of Gd(2-x)Tb(x)Ti(2)O(7) are suggested to possess a nature different from those in parent members Tb(2)Ti(2)O(7) and Gd(2)Ti(2)O(7). Finally, the frequency-dependent magnetic susceptibility behavior in Gd(1.5)Tb(0.5)Ti(2)O(7) is consistent with the formation of a spin-glass-like state indicating a pronounced slowing down of the dynamical response of the studied hybrid magnets.
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Affiliation(s)
- M Orendáč
- Faculty of Science, Center of Low Temperature Physics, P J Šafárik University and Institute of Physics SAS, Park Angelinum 9, SK-041 54 Košice, Slovakia
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Gingras MJP, Henelius P. Collective Phenomena in the LiHoxY1−xF4Quantum Ising Magnet: Recent Progress and Open Questions. ACTA ACUST UNITED AC 2011. [DOI: 10.1088/1742-6596/320/1/012001] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Prando G, Carretta P, Giblin SR, Lago J, Pin S, Ghigna P. Dilution effects in Ho2-xYxSn2O7: From the spin ice to the single-ion magnet. ACTA ACUST UNITED AC 2009. [DOI: 10.1088/1742-6596/145/1/012033] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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