Diluted spin ice in an external magnetic field |

A.A. Kuzin, A.A. Peretyatko, K.S. Soldatov, K.V. Nefedev |

2017, issue 1, Ñ. 59-81 |

Abstract |

The paper presents the research results of the effects arising under the effects of an external magnetic field in dilute plane and bulk spin-ice systems in the Ising spin model with the interaction of the nearest neighbors. We investigated systems of spins on the 2D triangular and kagome lattices, as well as the 3D pyrochlore lattice using the replica-exchange Monte Carlo method. In the absence of dilution, only two plateaus are observed, depending on the magnetization from the external field for all three types of lattices considered. The existence of five plateaus on the magnetization curves of the diluted antiferromagnetic Ising model in an external field [111] on a triangular lattice and a pyrochlore lattice is established. For the spin ice, seven plateaus were observed on the kagome lattice. It is shown that the reason for the occurrence of a plateau is related to the presence of critical fields for the realization of the most energetically favorable local spin configurations in dilute models. |

Ising model, Metropolis method, replica exchange Monte Carlo, pyrochlore lattice, triangular lattice, kagome latticeKeywords: |

Download the article (PDF-file) |

## References |

[1] M.J. Harris, S.T. Bramwell, D.F. McMorrow, T. Zeiske, and K.W. Godfrey, “Geometrical Frustration in the Ferromagnetic Pyrochlore Ho2 Ti2 O7 ”, Phys. Rev. Lett., 79:13, (1997), 2554–2557. [2] A.P. Ramirez, A. Hayashi, R.J. Cava, R. Siddharthan, and B.S. Shastry, “Zero-point entropy in ‘spin ice’”, Nature (London), 399, (1999), 333–335. [3] S.T. Bramwell and M.J.P. Gingras, “Spin Ice State in Frustrated Magnetic Pyrochlore Materials”, Science, 294, (2001), 1495–1501. [4] M.J. Harris, S.T. Bramwell, P.C.W. Holdsworth, and J.D.M. Champion, “Liquid-Gas Critical Behavior in a Frustrated Pyrochlore Ferromagnet”, Phys. Rev. Lett., 81:20, (1998), 4496–4499. [5] R. Moessner and S.L. Sondhi, “Theory of the [111] magnetization plateau in spin ice”, Phys. Rev. B, 68:6, (2003), 064411. [6] S.V. Isakov, K.S. Raman, R. Moessner, and S.L. Sondhi, “Magnetization curve of spin ice in a [111] magnetic field”, Phys. Rev. B, 70:10, (2004), 104418. [7] K. Matsuhira, Z. Hiroi, T. Tayama, S. Takagi, and T. Sakakibara, “A New Macroscopically Degenerate Ground State in the Spin Ice Compound Dy2 Ti2 O7 under a Magnetic Field”, J. Phys.: Condens. Matter, 14, (2002), L559. [8] Z. Hiroi, K. Matsuhira, S. Takagi, T. Tayama, T. Sakakibara, “Specific Heat of Kagome Ice in the Pyrochlore Oxide Dy2 Ti2 O7”, J. Phys. Soc. Jpn., 72:2, (2003), 411–418. [9] R. Higashinaka, H. Fukazawa, and Y. Maeno, “Anisotropic release of the residual zero-point entropy in the spin ice compound Dy2 Ti2 O7: Kagome ice behavior”, Phys. Rev. B, 68:1, (2003), 014415. [10] H. Fukazawa, R.G. Melko, R. Higashinaka, Y. Maeno, and M.J.P. Gingras, “Magnetic anisotropy of the spin-ice compound Dy2 Ti2 O7”, Phys. Rev. B, 65:1, (2002), 054410. [11] L. Pauling, “The structure and entropy of ice and of other crystals with some randomness of atomic arrangement”, J. Am. Chem. Soc., 57:12, (1935), 2680–2684. [12] X. Ke, R.S. Freitas, B.G. Ueland, G.C. Lau, M.L. Dahlberg, R.J. Cava, R. Moessner, and P. Schiffer, “Nonmonotonic zero-point entropy in diluted spin ice”, Phys. Rev. Lett., 99:13, (2007), 137203. [13] T. Lin, X. Ke, M. Thesberg, P. Schiffer, R.G. Melko, and M.J.P. Gingras, “Nonmonotonic residual entropy in diluted spin ice: A comparison between Monte Carlo simulations of diluted dipolar spin ice models and experimental results”, Phys. Rev. B, 90, (2014), 214433. [14] S. Scharffe, O. Breunig, V. Cho, P. Laschitzky, M. Valldor, J.F. Welter, and T. Lorenz, “Suppression of Pauling’s residual entropy in the dilute spin ice (Dy1?x Yx )2 Ti2 O7”, Phys. Rev. B, 92:18, (2015), 180405(R). [15] Yu.A. Shevchenko, K.V. Nefedev, Y. Okabe, Phys. Rev. E, unpublished. [16] K. Hukushima and K. Nemoto, “Exchange Monte Carlo Method and Application to Spin Glass Simulations”, J. Phys. Soc. Jpn., 65, (1996), 1604–1608. [17] E. Marinari, “Optimized Monte Carlo methods”, Advances in Computer Simulation, ed. J. Kertesz and I. Kondor, Springer-Verlag, 1998, 50–81. [18] L.W. Lee and A.P. Young, “Single spin- and chiral-glass transition in vector spin glasses in three-dimensions”, Phys. Rev. Lett., 90, (2003), 227203. [19] Y. Sugita and Y. Okamoto, “Replica-exchange molecular dynamics method for protein folding”, Chem. Phys. Lett., 314, (1999), 141–151. [20] X. Yao, “Dilute modulation of spin frustration in triangular Ising antiferromagnetic model: Wang–Landau simulation”, Solid State Commun, 150:3–4, (2010), 160–163. [21] M Zukovic, M. Borovsky, and A. Bobak, “Phase diagram of a diluted triangular lattice Ising antiferromagnet in a field”, Phys. Lett. A, 374:41, (2010), 4260–4264. [22] A. Peretyatko, K. Nefedev, and Yu. Okabe, “Interplay of dilution and magnetic field in the nearest-neighbor spin-ice model on the pyrochlore lattice”, Phys. Rev. B, 95:14, (2017), 144410. [23] Y. Qi, T. Brintlinger, and J. Cumings, “Direct observation of the ice rule in demagnetized artificial kagome spin ice”, Phys. Rev. B, 77:9, (2008), 094418. [24] P.W. Kasteleyn, “Dimer Statistics and Phase Transitions”, J. Math. Phys., 4:2, (1963), 287–293. |