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Monte Carlo study of finite-temperature transition in R2(R = Yb and Er)M2(M = Ti and Sn)O7 anisotropic pyrochlore

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Abstract

The Monte Carlo simulations based on the Metropolis algorithm was used to investigate the magnetic behavior of Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7 systems using classical Heisenberg spin model. The thermodynamic observables are averaged over Monte Carlo simulations. The order parameter was computed as a function of temperature for two different configurations. The results show that the thermal phase transition is probably continuous and at most very weakly first order. The variation of the spin components with temperature for the two configurations exhibits different magnetic phases, and the spin configurations are deduced and presented.

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References

  1. J.S. Gardner, M.J.P. Gingras, J.E. Greedan, Magnetic pyrochlore oxides. Rev. Mod. Phys. 82, 53–107 (2010)

    Article  CAS  Google Scholar 

  2. M.A. Subramanian, G. Aravamudan, G.V. Subba Rao, Oxide pyrochlores—a review. Prog. Solid State Chem. 15, 55–143 (1983)

    Article  CAS  Google Scholar 

  3. A.P. Ramirez, Strongly geometrically frustrated magnets. Annu. Rev. Mater. Sci. 24, 453–480 (1994)

    Article  CAS  Google Scholar 

  4. J.S. Gardner, B.D. Gaulin, D.M. Paul, Single crystal growth by the floating-zone method of a geometrically frustrated pyrochlore antiferromagnet, Tb2Ti2O7. J. Cryst. Growth. 191, 740–745 (1998)

    Article  CAS  Google Scholar 

  5. S.T. Bramwell, M.J.P. Gingras, Spin ice state in frustrated magnetic pyrochlore materials. Science. 294, 1495–1501 (2001)

    Article  CAS  Google Scholar 

  6. Z.F. Ezawa, G. Tsitsishvili, Quantum Hall ferromagnets. Rep. Prog Phys. 72, 086502 (2009)

    Article  Google Scholar 

  7. R. Masrour, A. Jabar, A. Benyoussef et al., Magnetic properties in kagomé lattice with RKKY interaction: a Monte Carlo study. J. Magn. Magn. Mater. 401, 695–699 (2016)

    Article  CAS  Google Scholar 

  8. C.L. Henley, Power-law spin correlations in pyrochlore antiferromagnets. Phys. Rev. B 71, 014424 (2005)

    Article  Google Scholar 

  9. S. Onoda, Y. Tanaka, Quantum fluctuations in the effective pseudospin-1 2 model for magnetic pyrochlore oxides. Phys. Rev. B 83, 094411 (2011)

    Article  Google Scholar 

  10. El A. Maazouzi, R. Masrour, A. Jabar, Magnetocaloric effects and magnetic properties in A-site cation-ordered chromate LiM(Ga and In)Cr4O8 spinels. Phys. B: Condens. Matter. 631, 413712 (2022)

    Article  Google Scholar 

  11. K. Khallouq, R. Masrour, A.E. Maazouzi, Magnetic properties and magnetocaloric effect on ACr2Se4 (A = hg and cd): a Monte Carlo study. Indian J. Phys. 97, 3515–3522 (2023)

    Article  CAS  Google Scholar 

  12. El A. Maazouzi, R. Masrour, A. Jabar, Study of the magnetic properties of LiMn1.5Ni0.5O4 spinel: ab initio calculation and Monte Carlo simulation. J. Cryst. Growth. 584, 126552 (2022)

    Article  Google Scholar 

  13. C. Castelnovo, R. Moessner, S.L. Sondhi, Spin ice, fractionalization, and topological order. Annu. Rev. Condens. Matter Phys. 3, 35–55 (2012)

    Article  CAS  Google Scholar 

  14. M.J.P. Gingras, P.A. McClarty, Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets. Rep. Prog Phys. 77, 056501 (2014)

    Article  CAS  Google Scholar 

  15. Z. Hao, A.G.R. Day, M.J.P. Gingras, Bosonic many-body theory of quantum spin ice. Phys. Rev. B 90, 214430 (2014)

    Article  Google Scholar 

  16. L. Pan, S.K. Kim, A. Ghosh et al., Low-energy electrodynamics of novel spin excitations in the quantum spin ice Yb2Ti2O7. Nat. Commun. 5, 4970 (2014)

    Article  CAS  Google Scholar 

  17. L. Pan, N.J. Laurita, K.A. Ross et al., A measure of monopole inertia in the quantum spin ice Yb2Ti2O7. Nat. Phys. 12, 361–366 (2016)

    Article  CAS  Google Scholar 

  18. Y. Tokiwa, T. Yamashita, M. Udagawa et al., Possible observation of highly itinerant quantum magnetic monopoles in the frustrated pyrochlore Yb2Ti2O7. Nat. Commun. 7, 10807 (2016)

    Article  CAS  Google Scholar 

  19. K.A. Ross, L. Savary, B.D. Gaulin et al., Quantum excitations in Quantum Spin Ice. Phys. Rev. X. 1, 021002 (2011)

    Google Scholar 

  20. L. Savary, K.A. Ross, B.D. Gaulin et al., Order by Quantum Disorder in Er2Ti2O7. Phys. Rev. Lett. 109, 167201 (2012)

    Article  Google Scholar 

  21. S. Guitteny, S. Petit, E. Lhotel et al., Palmer-Chalker correlations in the XY pyrochlore antiferromagnet Er2 sn2O7. Phys. Rev. B 88, 134408 (2013)

    Article  Google Scholar 

  22. J.-S. Wang, R.H. Swendsen, Replica Monte Carlo Simulation (revisited). Prog Theor. Phys. Suppl. 157, 317–323 (2005)

    Article  Google Scholar 

  23. J.G. Charles, “Computing Science and Statistics”. In: Proceedings of the 23rd Symposium on the Interface. (1991), p. 156

  24. M. Creutz, Overrelaxation and Monte Carlo simulation. Phys. Rev. D 36, 515–519 (1987)

    Article  CAS  Google Scholar 

  25. W. Selke, Finite-size effects in the rough phase of the 3d ising model. Phys. A: Stat. Mech. Appl. 565, 125568 (2021)

    Article  Google Scholar 

  26. M.E. Fisher, M.N. Barber, Scaling theory for finite-size effects in the critical region. Phys. Rev. Lett. 28, 1516–1519 (1972)

    Article  Google Scholar 

  27. Ã. Iglesias, A. Labarta, Finite-size and surface effects in maghemite nanoparticles: Monte Carlo simulations. Phys. Rev. B 63, 184416 (2001)

    Article  Google Scholar 

  28. C.R. Menyuk, Statistical errors in biasing Monte Carlo simulations with Applications to Polarization-Mode Dispersion Compensators. J. Lightwave Technol. 24, 4184–4196 (2006)

    Article  Google Scholar 

  29. P. Bonville, J.A. Hodges, E. Bertin et al., Transitions and spin dynamics at very low temperature in the pyrochlores Yb2Ti2O7 and Gd2Sn2O7. Hyperfine Interact 156/157, 103–111 (2004)

    Article  CAS  Google Scholar 

  30. J.S. Gardner, S.R. Dunsiger, B.D. Gaulin et al., Cooperative paramagnetism in the geometrically frustrated pyrochlore antiferromagnet Tb2Ti2O7. Phys. Rev. Lett. 82, 1012–1015 (1999)

    Article  CAS  Google Scholar 

  31. Q. Wang, A. Ghasemi, A. Scheie, et al., “Synthesis, crystal growth and characterization of the pyrochlore Er2Ti2O7” (2018)

  32. D.R. Yahne, D. Pereira, L.D.C. Jaubert et al., Understanding reentrance in frustrated magnets: the case of the Er2Sn2O7 Pyrochlore. Phys. Rev. Lett. 127, 277206 (2021)

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Laboratory of Solid Physics, Faculty of Science Dhar El Mahraz, Sidi Mohammed Ben Abdellah University, Box 1796, Fez, Morocco

    K. Khallouq, R. Masrour & A. El Maazouzi

Authors
  1. K. Khallouq
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  2. R. Masrour
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  3. A. El Maazouzi
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Contributions

KK: conceptualization, methodology, software, investigation, validation, formal,  analysis, Formal analysis, no funding acquisition, writing-original draft preparation, writing- reviewing and editing, supervision, project administration.  RM:  conceptualization, methodology, software, investigation, validation, formal  analysis, formal analysis, no funding acquisition, writing- original draft preparation,  writing- reviewing and editing, supervision, project administration.  AEM:  conceptualization, methodology, software, investigation, validation, formal analysis, formal analysis, no funding acquisition, writing-original draft preparation, writing- reviewing and editing, supervision, project administration.

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Correspondence to R. Masrour.

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Khallouq, K., Masrour, R. & El Maazouzi, A. Monte Carlo study of finite-temperature transition in R2(R = Yb and Er)M2(M = Ti and Sn)O7 anisotropic pyrochlore. J. Korean Ceram. Soc. (2024). https://doi.org/10.1007/s43207-023-00349-7

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