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Toward Discord: Code for Simulating Continuous Spin Systems

  • Magnetic Structure Characterization over Multiple Length Scales
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Abstract

A new computational tool to simulate classical spin systems with frustrated crystal structures is presented. Complementary single- and cluster-spin flip algorithms are implemented to calculate the diffuse scattering patterns, spin-pair correlations, and thermodynamic quantities. Test cases of geometrically frustrated kagome, pyrochlore, and cubic systems are detailed. Two recent scientific cases are also shown. This new method, together with recent developments of the rmc-discord package (https://github.com/zjmorgan/rmc-discord), represent integrated and strategic step in a complete forward and reverse Monte Carlo framework discord.

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References

  1. J. Rodríguez-Carvajal, and J. Villain, C R Phys. 20(7), 770–802 (2019).

    Article  Google Scholar 

  2. D.A. Keen, and A.L. Goodwin, Nature 521(7552), 303–309 (2015).

    Article  Google Scholar 

  3. D.J.P. Morris, K. Siemensmeyer, J.-U. Hoffmann, B. Klemke, I. Glavatskyi, K. Seiffert, D.A. Tennant, S.V. Isakov, S.L. Sondhi, and R. Moessner,Phys. Rev. B 99(17), 174111 (2019).

    Article  Google Scholar 

  4. T. Fennell, P.P. Deen, A.R. Wildes, K. Schmalzl, D. Prabhakaran, A.T. Boothroyd, R.J. Aldus, D.F. McMorrow, and S.T. Bramwell, Science 326(5951), 415–417 (2009).

    Article  Google Scholar 

  5. R. Moessner, and A.P. Ramirez, Physics Today 59(2), 24–29 (2006).

  6. A.P. Ramirez, Annu. Rev. Mater. Sci. 24, 453–480 (1994).

    Article  Google Scholar 

  7. Z.J. Morgan, H.D. Zhou, B.C. Chakoumakos, and F. Ye, J. Appl. Crystallogr. 54(6), 1867–1885 (2021).

    Article  Google Scholar 

  8. U. Nowak, Classical spin models. In: Kronmüller, H. (ed.) Micromagnetism. Handbook of magnetism and advanced magnetic materials, 858–876. Wiley, Chichester (2007).

  9. E. Prince, Mathematical crystallography: An introduction to the mathematical foundations of crystallography. Reviews in mineralogy, Washington, DC (1993).

  10. H. Stokes, D. Hatch, and B. Campbell, ISOTROPY Software Suite. http://stokes.byu.edu/iso/isotropy.php

  11. B.J. Campbell, H.T. Stokes, D.E. Tanner, and D.M. Hatch,J. Appl. Crystallogr. 39(4), 607–614 (2006).

    Article  Google Scholar 

  12. N.W. Ashcroft, and N.D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).

  13. I. Dzyaloshinsky, J. Phys. Chem. Solids 4(4), 241–255 (1958).

    Article  Google Scholar 

  14. T. Moriya, Phys. Rev. 120(1), 91–98 (1960).

    Article  Google Scholar 

  15. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, J. Chem. Phys. 21(6), 1087–1092 (1953).

    Article  Google Scholar 

  16. I.O. Bohachevsky, M.E. Johnson, and M.L. Stein, Technometrics 28(3), 209–217 (1986).

  17. R.H. Swendsen, and J.S. Wang, RPhys. Rev. Lett. 57(21), 2607–2609 (1986).

    Article  MathSciNet  Google Scholar 

  18. D.P. Landau, and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, 4th edn. (Cambridge University Press, Cambridge, 2014).

    Book  Google Scholar 

  19. R.H. Swendsen, and J.-S. Wang, Phys. Rev. Lett. 58(2), 86–88 (1987).

    Article  Google Scholar 

  20. H. Gould, and J. Tobochnik, Comput. Phys. 3(4), 82–86 (1989).

    Article  Google Scholar 

  21. J.-S. Wang, and R.H. Swendsen, Physica A 167(3), 565–579 (1990).

    Article  MathSciNet  Google Scholar 

  22. F. Liang, C. Liu, and R.J. Carroll, Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples, 1, publ. (Wiley series in computational statistics. Wiley, Chichester, 2010).

  23. U. Wolff, Phys. Rev. Lett. 62(4), 361–364 (1989).

    Article  Google Scholar 

  24. M. D’Onorio De Meo, and S.K. Oh, Physical Review B 46(1), 257–260 (1992).

  25. G.L. Squires, Introduction to the Theory of Thermal Neutron Scattering by G. L. Squires (2012).

  26. J.A.M. Paddison, Acta Crystallogr. Sect. A: Found. Adv. 75(1), 14–24 (2019).

    Article  MathSciNet  Google Scholar 

  27. J.A.M. Paddison, J.R. Stewart, and A.L. Goodwin, J. Phys.: Condens. Matter 25(45), 454220 (2013).

    Google Scholar 

  28. E.J. Lisher, and J.B. Forsyth, Acta Crystallogr. A 27(6), 545–549 (1971).

    Article  Google Scholar 

  29. K.N. Trueblood, H.B. Bürgi, H. Burzlaff, J.D. Dunitz, C.M. Gramaccioli, H.H. Schulz, U. Shmueli, and S.C. Abrahams, Acta Crystallogr. Sect. A Found. Crystallogr. 52(5), 770–781 (1996).

    Article  Google Scholar 

  30. N.W. Thomas, Acta Crystallogr. Sect. A: Found. Crystallogr. 66(1), 64–77 (2010).

    Article  Google Scholar 

  31. J.S. Gardner, M.J.P. Gingras, and J.E. Greedan,Rev. Modern Phys. 82(1), 53–107 (2010).

    Article  Google Scholar 

  32. N. Roth, A.F. May, F. Ye, B.C. Chakoumakos, and B.B. Iversen, IUCrJ 5(4), 410–416 (2018).

    Article  Google Scholar 

  33. N. Roth, F. Ye, A.F. May, B.C. Chakoumakos, and B.B. Iversen, =Phys. Rev. B 100(14), 144404 (2019).

    Article  Google Scholar 

  34. L. Pauling, and M. Shappell, = Zeitschrift für Kristallographie-Crystalline Materials 75(1), 128–142 (1930).

  35. H.T. Diep, A. Ghazali, and P. Lallemand, J. Phys. C: Solid State Phys. 18(31), 5881–5895 (1985).

    Article  Google Scholar 

  36. M.A. Khan, Q. Zhang, J.-K. Bao, R.S. Fishman, A.S. Botana, Y. Choi, G. Fabbris, D. Haskel, J. Singleton, and J.F. Mitchell, Phys. Rev. Mater. 3(11), 114411 (2019).

    Article  Google Scholar 

  37. F. Ye, Z. Morgan, W. Tian, S. Chi, X. Wang, M.E. Manley, D. Parker, M.A. Khan, J.F. Mitchell, and R. Fishman, Phys. Rev. B 103(18), 184413 (2021).

    Article  Google Scholar 

  38. R.S. Fishman, . Phys. Rev. B 103(21), 214440 (2021).

    Article  Google Scholar 

  39. J.D. Alzate-Cardona, D. Sabogal-Suárez, R.F.L. Evans, and E. Restrepo-Parra, J. Phys.: Condens. Matter 31(9), 095802 (2019).

    Google Scholar 

  40. M.D. Leblanc, J.P. Whitehead, and M.L. Plumer, J. Phys.: Condens. Matter 25(19), 196004 (2013).

    Google Scholar 

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Acknowledgements

Research at ORNL’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy (DOE).

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  1. Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    Zachary Morgan & Feng Ye

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  1. Zachary Morgan
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  2. Feng Ye
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Correspondence to Zachary Morgan.

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Morgan, Z., Ye, F. Toward Discord: Code for Simulating Continuous Spin Systems. JOM 74, 2338–2347 (2022). https://doi.org/10.1007/s11837-022-05273-5

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  • DOI: https://doi.org/10.1007/s11837-022-05273-5

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