OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 7 — Jul. 1, 2014
  • pp: 1416–1426

Diffraction by a frustrated system: the triangular Ising antiferromagnet

Chunhong Yoon and Rick P. Millane  »View Author Affiliations


JOSA A, Vol. 31, Issue 7, pp. 1416-1426 (2014)
http://dx.doi.org/10.1364/JOSAA.31.001416


View Full Text Article

Enhanced HTML    Acrobat PDF (3569 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Expressions are derived for diffraction by the triangular Ising antiferromagnet, a disordered lattice system consisting of two kinds of scatterer and exhibiting geometric frustration. Analysis of the expressions shows characteristics of the diffraction patterns, including the presence of Bragg and diffuse diffraction, superlattice reflections, and their behavior with temperature. These characteristics are illustrated by numerical simulations. The results have application to diffraction imaging of disordered systems.

© 2014 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(110.7440) Imaging systems : X-ray imaging

ToC Category:
Diffraction and Gratings

History
Original Manuscript: January 23, 2014
Revised Manuscript: April 2, 2014
Manuscript Accepted: April 7, 2014
Published: June 10, 2014

Citation
Chunhong Yoon and Rick P. Millane, "Diffraction by a frustrated system: the triangular Ising antiferromagnet," J. Opt. Soc. Am. A 31, 1416-1426 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-7-1416


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. M. Woolfson, An Introduction to X-ray Crystallography, 2nd ed. (Cambridge University, 1997).
  2. T. R. Welberry, Diffuse X-Ray Scattering and Models of Disorder (Oxford University, 2004).
  3. S. T. Bramwell, S. G. Carling, C. J. Harding, K. D. M. Harris, B. M. Kariuki, L. Nixon, and I. P. Parkin, “The anhydrous alums as model triangular-lattice magnets,” J. Phys. Condens. Matter 8, L123–L129 (1996). [CrossRef]
  4. D. Davidovic, S. Kumar, D. H. Reich, J. Siegel, S. B. Field, R. C. Tiberio, R. Hey, and K. Ploog, “Magnetic correlations, geometrical frustration, and tunable disorder in arrays of superconducting rings,” Phys. Rev. B 55, 6518–6540 (1997). [CrossRef]
  5. R. F. Wang, C. Nisoli, R. S. Freitas, J. Li, W. McConville, B. J. Cooley, M. S. Lund, N. Samarth, C. Leighton, V. H. Crespi, and P. Schiffer, “Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands,” Nature 439, 303–306 (2006). [CrossRef]
  6. Y. Qi, T. Brintlinger, and J. Cumings, “Direct observations of the ice rule in artificial kagome spin ice,” Phys. Rev. B 77, 094418 (2008). [CrossRef]
  7. E. Mengotti, L. J. Heyderman, A. F. Rodríguez, A. Bisig, L. Le Guyader, F. Nolting, and H. B. Braun, “Building blocks of an artificial kagome spin ice: photoemission electron microscopy of arrays of ferromagnetic islands,” Phys. Rev. B 78, 144402 (2008). [CrossRef]
  8. S. Ladak, D. E. Read, G. K. Perkins, L. F. Cohen, and W. R. Branford, “Direct observation of magnetic monopole defects in an artificial spin-ice system,” Nat. Phys. 6, 359–363 (2010). [CrossRef]
  9. Y. Han, “Geometric frustration in buckled colloidal monolayers,” Nature 456, 898–903 (2008). [CrossRef]
  10. P. K. Luther and J. M. Squire, “Three-dimensional structure of the vertebrate muscle A-band. II. The myosin filament superlattice,” J. Mol. Biol. 141, 409–439 (1980). [CrossRef]
  11. C. H. Yoon, “Image analysis and diffraction by the myosin lattice of vertebrate muscle,” Ph.D. thesis (University of Canterbury, 2008).
  12. T. R. Welberry, A. P. Heerdegen, D. C. Goldstone, and I. A. Taylor, “Diffuse scattering resulting from macromolecular frustration,” Acta Crystallogr. B67, 516–524 (2011). [CrossRef]
  13. M. Bretz, “Ordered helium films on highly uniform graphite—finite size effects, critical parameters, and the three-state Potts model,” Phys. Rev. Lett. 38, 501–505 (1977). [CrossRef]
  14. A. N. Berker, S. Ostlund, and F. A. Putnam, “Renormalization-group treatment of a Potts lattice gas for krypton adsorbed onto graphite,” Phys. Rev. B 17, 3650–3665 (1978). [CrossRef]
  15. J. L. Jacobsen and H. C. Fogedby, “Monte Carlo study of correlations near the ground state of the triangular antiferromagnetic Ising model,” Phys. A 246, 563–575 (1997). [CrossRef]
  16. R. Liebmann, Statistical Mechanics of Periodic Frustrated Ising Systems (Springer-Verlag, 1986).
  17. A. P. Ramirez, “Geometric frustration: magic moments,” Nature 421, 483 (2003). [CrossRef]
  18. A. P. Ramirez, “Geometrically frustrated matter—magnets to molecules,” MRS Bull. 30, 447–451 (2005). [CrossRef]
  19. M. Harris, “The eternal triangle,” Nature 456, 886–887 (2008). [CrossRef]
  20. G. H. Wannier, “Antiferromagnetism: the triangular Ising net,” Phys. Rev. 79, 357–364 (1950). [CrossRef]
  21. J. Stephenson, “Ising-model spin correlations on the triangular lattice,” J. Math. Phys. 5, 1009–1024 (1964). [CrossRef]
  22. J. Stephenson, “Ising-model spin correlations on the triangular lattice. III. Isotropic antiferromagnetic lattice,” J. Math. Phys. 11, 413–419 (1970). [CrossRef]
  23. D. J. Wojtas and R. P. Millane, “The two-point correlation function for the triangular Ising antiferromagnet,” Phys. Rev. E 79, 041123 (2009). [CrossRef]
  24. W. J. Stroud and R. P. Millane, “Cylindrically averaged diffraction by distorted lattices,” Proc. R. Soc. London Ser. A 452, 151–173 (1996). [CrossRef]
  25. E. Rastelli, S. Regina, and A. Tassi, “Monte Carlo simulations on a triangular Ising antiferromagnet with nearest and next-nearest interactions,” Phys. Rev. B 71, 174406 (2005). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited