Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-11T02:56:06.926Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of Dzyaloshinsky-Moriya Interaction on Planar Rotator Model on Triangular Lattice

Published online by Cambridge University Press:  20 August 2015

Yun-Zhou Sun ,
Lin Yi  and
Jian-Sheng Wang
Yun-Zhou Sun*
Affiliation:
Department of Physics, Wuhan Textile University, Wuhan 430073, China
Lin Yi*
Affiliation:
Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
Jian-Sheng Wang*
Affiliation:
Department of Physics, National University of Singapore, Singapore 117542, Singapore
*
Corresponding author.Email:syz1979@163.com
Email:yilin@mail.hust.edu.cn
Email:phywjs@nus.edu.sg
Get access

Abstract

The thermodynamic properties and some critical properties of the planar rotator model with chiral Dzyaloshinsky-Moriya (DM) interaction on triangular lattice are analyzed using a hybrid Monte Carlo method. It has been shown that there is a XY-like Berezinskii-Kosterlitz-Thouless (BKT) phase transition in this model. The ground state of this spiral system and the effects of size mismatch are also discussed.

Keywords

07.05.Tp21.60.Ka05.10.Ln75.10.HkCritical temperatureDzyaloshinsky-Moriya interactionMonte-Carlo simulationvortex
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 4 , April 2012 , pp. 1169 - 1181
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Dzyaloshinskii, I. E., A thermodynamic theory of “weak” ferromagnetism of antiferromag-netics, J. Phys. Chem. Solids, 4 (1958), 241–255.Google Scholar
[2]Moriya, T., New mechanism of anisotropic superexchange interaction, Phys. Rev. Lett., 4 (1960), 228–230.CrossRefGoogle Scholar
[3]Wills, A. S., Long-range ordering and representational analysis of the jarosites, Phys. Rev. B, 63 (2001), 064430–064443.Google Scholar
[4]Inami, T., Morimoto, T., Nishiyama, M., Maegawa, S., Oka, Y. and Okumura, H., Magnetic ordering in the kagomé lattice antiferromagnet KCr3(OD)6(SO4)2, Phys. Rev. B, 64 (2001), 054421–054427.Google Scholar
[5]Wills, A. S., Harrison, A., Ritter, C. and Smith, R. I., Magnetic properties of pure and diamag-netically doped jarosites: model kagomé antiferromagnets with variable coverage of the magnetic lattice, Phys. Rev. B, 61 (2000), 6156–6169.Google Scholar
[6]Inami, T., Nishiyama, M., Maegawa, S. and Oka, Y., Magnetic structure of the kagomé lattice antiferromagnet potassium jarosite KFe3(OH)6(SO4)2, Phys. Rev. B, 61 (2000), 12181–12186.Google Scholar
[7]Koshibae, W., Ohta, Y. and Maekawa, S., Electronic and magnetic structures of cuprates with spin-orbit interaction, Phys. Rev. B, 47 (1993), 3391–3400.Google Scholar
[8]Elhajal, M., Canals, B. and Lacroix, C., Ordering in pyrochlore compounds due to Dzyaloshinsky-Moriya interactions: the case of Cu4O3, J. Phys. Condens. Matter, 16 (2004), S917–S922.Google Scholar
[9]Yi, L., Buttner, G., Usadel, K. D. and Yao, K. L., Quantum Heisenberg spin glass with Dzyaloshinskii-Moriya interactions, Phys. Rev. B, 47 (1993), 254–261.CrossRefGoogle ScholarPubMed
[10]Coomer, F., Harrison, A., Oakley, G. S., Kulda, J., Stewart, J. R., Stride, J. A., Fak, B., Taylor, J. W. and Visser, D., Inelastic neutron scattering study of magnetic excitations in the kagome antiferromagnet potassium jarosite, J. Phys. Condens. Matter, 18 (2006), 8847–8855.Google Scholar
[11]Bak, P. and Jensen, M. H., Theory of helical magnetic structures and phase transitions in MnSi and FeGe, J. Phys. C, 13 (1980), L881–L887.CrossRefGoogle Scholar
[12]Nakanishi, O., Yanase, A., Hasegawa, A. and Kataoka, M., The origin of the helical spin density wave in MnSi, Solid State Commun., 35 (1980), 995–998.Google Scholar
[13]Uchida, M., Onose, Y., Matsui, Y. and Tokura, Y., Real-space observation of helical spin order, Science, 311 (2006), 359–361.Google Scholar
[14]Vedmedenko, E. Y., Udvardi, L., Weinberger, P. and Wiesendanger, R., Chiral magnetic ordering in two-dimensional ferromagnets with competing Dzyaloshinsky-Moriya interactions, Phys. Rev. B, 75 (2007), 104431–104439.Google Scholar
[15]Elhajal, M., Canals, B. and Lacroix, C., Symmetry breaking due to Dzyaloshinsky-Moriya in-teractions in the kagomé lattice, Phys. Rev. B, 66 (2002), 014422–014428.Google Scholar
[16]Yildirim, T. and Harris, A. B., Magnetic structure and spin waves in the Kagomé jarosite compound KFe3(SO4)2(OH)6, Phys. Rev. B, 73 (2006), 214446–214470.Google Scholar
[17]Matan, K., Grohol, D., Nocera, D. G., Yildirim, T., Harris, A. B., Lee, S. H., Nagler, S. E. and Lee, Y. S., Spin waves in the frustrated Kagomé lattice antiferromagnet KFe3(OH)6(SO4)2, Phys. Rev. Lett., 96 (2006), 247201–247205.CrossRefGoogle Scholar
[18]Benyoussef, A., Boubekri, A. and Ez-Zahraouy, H., Spin-wave analysis of the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction, Phys. B, 266 (1999), 382–390.Google Scholar
[19]Zhao, J. Z., Wang, X. Q., Xiang, T., Su, Z. B. and Yu, L., Effects of the Dzyaloshinskii-Moriya interaction on low-energy magnetic excitations in copper Benzoate, Phys. Rev. Lett., 90 (2003), 207204–207208.Google Scholar
[20]Biegala, L., Drzewiński, A. and Sznajd, J., Low temperature phase of the quantum triangular lattice XY model with Dzyaloshinsky-Moriya interaction, Phys. A, 225 (1996), 254–270.CrossRefGoogle Scholar
[21]Liu, L. L., Physics has changed, Phys. Rev. Lett., 13 (1973), 459–460.Google Scholar
[22]Pires, A. S. T., Kosterlitz-Thouless transition in the Heisenberg model with antisymmetric exchange interaction, Solid State Commun., 112 (1999), 705–706.Google Scholar
[23]Lee, K. W. and Lee, C. E., Monte Carlo study of the Kosterlitz-Thouless transition in the Heisenberg model with antisymmetric exchange interactions, Phys. Rev. B, 72 (2005), 054439–054445.Google Scholar
[24]Sun, Y. Z., Liu, H. P. and Yi, L., Monte Carlo study of planar rotator model with weak Dzyaloshinsky-Moriya interaction, Commun. Theor. Phys., 46 (2006), 663–667.Google Scholar
[25]Liu, H. P., Sun, Y. Z. and Yi, L., New Monte Carlo simulations to a generalized XY model, Chin. Phys. Lett., 23 (2006), 316–319.Google Scholar
[26]Franzese, G., Cataudella, V., Korshunov, S. E. and Fazio, R., Fully frustrated XY model with next-nearest-neighbor interaction, Phys. Rev. B, 62 (2000), R9287–R9290.Google Scholar
[27]Korshunov, S. E., Kink pairs unbinding on domain walls and the sequence of phase transitions in fully frustrated XY models, Phys. Rev. Lett., 88 (2002), 167007–167011.Google Scholar
[28]Wang, J.-S. and Swendsen, R. H., Cluster Monte Carlo algorithms, Phys. A, 167 (1990), 565–579.Google Scholar
[29]Swendsen, R. H. and Wang, J.-S., Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett., 58 (1987), 86–88.Google Scholar
[30]Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E., Equation of state calculation by fast computing machines, J. Chem. Phys., 21 (1953), 1087–1092.CrossRefGoogle Scholar
[31]Rastelli, E., Regina, S. and Tassi, A., Monte Carlo simulation for square planar model with a small fourfold symmetry-breaking field, Phys. Rev. B, 70 (2004), 174447–174452.CrossRefGoogle Scholar
[32]Kawamura, H., Universality of phase transitions of frustrated antiferromagnets, J. Phys. Cond. Matter, 10 (1998), 4707–4754.Google Scholar
[33]Kawamura, H., Critical properties of helical magnets and triangular antiferromagnets, J. Appl. Phys., 63 (1988), 3086–3098.CrossRefGoogle Scholar
[34]Saslow, W. M., Gabay, M. and Zhang, W.-M., “Spiraling” algorithm: collective Monte Carlo trial and self-determined boundary conditions for incommensurate spin systems, Phys. Rev. Lett., 68 (1992), 3627–3630.CrossRefGoogle ScholarPubMed
[35]Diep, H. T., Magnetic transitions in helimagnets, Phys. Rev. B, 39 (1989), 397–404.Google Scholar
[36]Mermin, N. D. and Wagner, H., Absence of Ferromagnetism or Antiferromagnetism in one-or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett., 17 (1966), 1133–1136.Google Scholar
[37]Kosterlitz, J. M. and Thouless, D. J., Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C, 6 (1973), 1181–1191.Google Scholar
[38]Kosterlitz, J. M., The critical properties of the two-dimensional XY model, J. Phys. C, 7 (1974), 1046–1152.Google Scholar
[39]Ramirez-Santiago, G. and Jose, J. V., Critical exponents of the fully frustrated two-dimensional XY model, Phys. Rev. B, 49 (1994), 9567–9582.Google Scholar
[40]Weber, H. and Minnhagen, P., Monte Carlo determination of the critical temperature for the two-dimensional XY model, Phys. Rev. B, 37 (1988), 5986–5989.Google Scholar
[41]Lee, D. H., Joannopoulos, J. D., Negele, J. W. and Landau, D. P., Symmetry analysis and Monte Carlo study of a frustrated antiferromagnetic planar (XY) model in two dimensions, Phys. Rev. B, 33 (1986), 450–475.CrossRefGoogle ScholarPubMed
[42]Butera, P. and Comi, M., High-temperature study of the Kosterlitz-Thouless phase transition in the XY model on the triangular lattice, Phys. Rev. B, 50 (1994), 3052–3057.Google Scholar
[43]Campostrini, M., Pelissetto, A., Rossi, P. and Vicari, E., Strong-coupling analysis of two-dimensional O(N)σ models with N≤2 on square, triangular and honeycomb lattices, Phys. Rev. B, 54 (1996), 7301–7317.Google Scholar
[44]Cuccoli, A., Tognetti, V. and Vaia, R., Two-dimensional XXZ model on a square lattice: a Monte Carlo simulation, Phys. Rev. B, 52 (1995), 10221–10231.Google Scholar
[45]Wysin, G. M. and Bishop, A. R., Dynamic correlations in a classical two-dimensional Heisenberg antiferromagnet, Phys. Rev. B, 42 (1990), 810–819.Google Scholar
[46]Wysin, G. M., Vacancy effectsinan easy-plane Heisenberg model: reduction of Tc and doubly charged vortices, Phys. Rev. B, 71 (2005), 094423–094434.CrossRefGoogle Scholar
[47]Gupta, R. and Baillie, C. F., Critical behavior of the two-dimensional XY model, Phys. Rev. B, 45 (1992), 2883–2898.Google Scholar