Abstract
Intrinsic heterogeneity, from nano- to meso- scales, of lattice/charge/spin variables, is common in complex oxides such as cuprates and manganites, that have strain-based ferroelastic transitions. We summarize our viewpoint that the central player is the power-law, anisotropic, strain-strain force that lies concealed in the apparently innocuous St. Venant compatibility constraint, namely the maintenance of lattice integrity, under strain texturing induced by charges and spins, that act as ‘local stresses’ and ‘local transition temperatures’
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Dagotto, (Ed.) Nanoscale Phase Separation and Colossal Magnetoresistance, Springer (2003).
A.R. Bishop, S.R. Shenoy and S. Sridhar (Eds.) Intrinsic Multiscale Structure and Dynamics in Complex Electronic Oxides, World Scientific (2003).
A. Bianconi, N.L. Saini, A. Lanzara, M. Missori, T. Rosetti, H. Oyanagi, H. Yamguchi, K. Oka and T. Ito, Phys. Rev. Lett. 76, 3412 (1996); E.S. Bozin, G.H. Kwei, H. Takagi and S.J.L. Billinge, Phys. Rev. Lett. 84, 5856 (2000); K.M. Lang, V. Madhavan, J.E. Hoffman, E.W. Hudson, H. Eisaki, S. Uchida and J.C. Davis, Nature 415, 412 (2002).
Y. Huang, I.M. Palstra, S.W. Cheong and B. Batlogg, Phys. Rev. B 52, 15046 (1995)
M. Faeth, S. Friesen, A.A. Menovsky, Y. Tomloka, J. Aarts and J.A. Mydosh, Science 285, 1540 (1999).
Y. Ando in Ref. S.R. Shenoy and S. Sridhar (Eds.) Intrinsic Multiscale Structure and Dynamics in Complex Electronic Oxides, World Scientific (2003) [2].
S.R. Shenoy, T. Lookman, A. Saxena and A. R. Bishop, Phys. Rev. B 60, R12537 (1999).
T. Lookman, S. R. Shenoy, K.O. Rasmussen, A. Saxena and A.R. Bishop, Phys. Rev. B, 67, 024114 (2003); T. Lookman, S. R. Shenoy, K.O. Rasmussen, A. Saxena and A.R. Bishop, J. de Physique IV, ICOMAT-02 Proc. (2003).
K.O. Rasmussen, T. Lookman, A. Saxena, A.R. Bishop, R. C. Albers and S.R. Shenoy, Phys. Rev. Lett. 87, 055704 (2001).
A.R. Bishop, T. Lookman, A. Saxena and S.R. Shenoy, Europhysics Lett. 63, 289 (2003).
S.R. Shenoy, T. Lookman, A. Saxena and A.R. Bishop, in Ref. [2].
A. Saxena, T. Lookman, A.R. Bishop and S.R. Shenoy, in Ref. S.R. Shenoy and S. Sridhar (Eds.) Intrinsic Multiscale Structure and Dynamics in Complex Electronic Oxides, World Scientific (2003) [2]; D.M. Hatch, T. Lookman, A. Saxena and S.R. Shenoy, Phys. Rev. B 68, 104105 (2003).
A.J.C. Barre de Saint-Venant in C.L.M.H. Navier, Resume’ des Lecons sur l’Application de la Mechanique (Dunod, Paris, 1864).
S.F. Borg, Fundamentals of Engineering Elasticity, Second edn. 1990, World Scientific.
M. Baus and R. Lovett, Phys. Rev. Lett. 65, 1781 (1990); 67, 406 (1991); Phys. Rev. A 44, 1211 (1991).
S. Kartha, J.A. Krumhansl, J.P. Sethna and L.K. Wickham, Phys. Rev. B 52, 803 (1995)
The ‘normalization’ factors are chosen so that for e 1,e 2 in 2D \( (E_{xx} 2 + E_{yy} 2)/2 = 1; \) or for e 3 in 3D, \( (4E_{xx} 2 + E_{yy} 2 + E_{zz} 2)/6 = 1 \), at \( |E_{xx} | = |E_{yy} | = |E_{zz} | = 1 \).
A.E. Jacobs, Phys. Rev. B 52, 6327, (1995).
This direct method yields the same results as the Lagrange multiplier method for finding the kernel introduced in Ref. J.A. Krumhansl, J.P. Sethna and L.K. Wickham, Phys. Rev. B 52, 803 (1995) [16] for the square-rectangle case, and used for kernels in 2D and 3D in Refs. [7–12].
In Fig. 8 of Ref. S. R. Shenoy, K.O. Rasmussen, A. Saxena and A.R. Bishop, Phys. Rev. B, 67, 024114 (2003) [8], different nearly-degenerate textured states evolved under relaxational dynamics are shown. In scores of such relaxations, we have found a uniform state only once, for a particular initial-state random seed.
L. Vasiliu-Doloc, S. Rosenkranz, R. Osborn, S.K. Sinha, J.W. Lynn, J. Mesot, O.H. Seeck, G. Preost, A.J. Fedro and J.F. Mitchell, Phys. Rev. Lett. 83, 4393 (1999); S. Shimomura, N. Wakabayashi, H. Kuwahara and Y. Tokura, Phys. Rev. Lett. 83, 4389 (1999); Z. Islam, X. Liu, S.K. Sinha, J.C. Lang, S.C. Moss, D. Haskel, G. Srajer, P. Wochner, D.R. Lee, D.R. Haeffner and U. Welp, Phys. Lett. 93, 157008 (2004).
A.R. Bishop, T. Lookman, A. Saxena and S.R. Shenoy, cond-mat/0304198.
Ch. Renner, G. Aeppli, B-G. Kim, Y-A. Soh, and S.W. Cheong, Nature 416, 518 (2002); S.J.L. Billinge in Ref [2].
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Shenoy, S.R., Lookman, T., Saxena, A., Bishop, A.R. (2006). Structural Symmetry, Elastic Compatibility, and the Intrinsic Heterogeneity of Complex Oxides. In: Bianconi, A. (eds) Symmetry and Heterogeneity in High Temperature Superconductors. NATO Science Series II: Mathematics, Physics and Chemistry, vol 214. Springer, Dordrecht . https://doi.org/10.1007/1-4020-3989-1_9
Download citation
DOI: https://doi.org/10.1007/1-4020-3989-1_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3987-4
Online ISBN: 978-1-4020-3989-8
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)