Nano-world of domains

posted Dec 29, 2009, 12:28 AM by Igor Lukyanchuk   [ updated Oct 27, 2010, 7:18 AM by Igor Lukyanchuk ]

The favorite  Landau sentence: "Nobody can cancel the Coulomb's law" is often overlooked in understanding of spontaneous polarization in  Ferroelectric materials that, paradoxically, should be completely destabilized by the backward depolarizing electrostatic field produced by the charge 4πρ=divP of the polarization surface breakdown. This puzzle is partially resolved in samples of >500nm where the unfavorable depolarizing field is screened by the free semi-conducting charges. Alternatively, the smaller samples are segregated onto up- and down- polarized domains, as was initially proposed  by Landau and Kittel for magnetic materials. This alternates the surface charge and vanishes the bulk depolarizing field.  

Current tendency of miniaturization of ferroelectric-based computer memories challenges the study of non-uniform polarization distribution in nano-samples. However the first-principle modeling by the ensemble of electrostatic dipoles is possible only for the very small systems < 50nm because of the non-local  Coulomb interaction.

So, how the surface of nano-device of realistic size of 50-500nm drives the polarization texture inside? To understand this we use the analytical approach of solution of nonlinear equations of  condensation to ferroelectric state coupled with electrostatic (Maxwell) equations. Such approach was proposed in early 80s by Chensky and Tarasenko but never explored after... Periodic domains, vortices, skyrmions and other exotic formations can be created inside of finite-size ferroelectric devices  by long-range Coulomb forces of surface. For sure they can be useful as the memory-units of future  memory devices. 

And this is not all !  Integration of ferroelectric elements into nano-electronic silicon environment again produces  the  polarization domains to compensate the interface-junction-created elastic stress. Surprisingly, the experimental    group from  Belfast and Cambridge reported that such ferro-elastic domains exist even inside of  samples with no interface. This discovery, confirmed by our modeling,  implies that the several-atom-thickness surface skin can trigger the intrinsic stress and  produce the drastic domain-structuring of device.

Figures: (a) Modeling of 3D vortices,  (b) Modeillng geometry of domain-structured nano-device  (c) Experimental discovery of ferroelastic domains in 3D nano-rod of BaTiO3  ( A.Schilling, M. Gregg, G. Catalan,and J. Scott )

Read more:

Domain-enhanced interlayer coupling in ferroelectric/paraelectric superlattices;

V. A. Stephanovich, I. A. Lukyanchuk, and M. G. Karkut; Phys. Rev. Lett.,  94 047601 (2005)

Ferroelectric domains in thin fims and superlattices: Results of numerical modeling

F. DeGuerville, M. ElMarssi, I. Luk'yanchuk, and L. Lachoche, Ferroelectrics, 359, 14, (2007)

Stability of vortex phases in ferroelectric easy-planes nano-cylinders
G. Pascoli L. Lahoche, I. Luk'yanchuk, Integrated Ferroelectrics, vol. 99,  60 (2008)

Universal Properties of Ferroelectric Domains
I.  Luk'yanchuk, L. Lahoche, A. Sene, Phys. Rev. Lett., 102, 147601 (2009) 

OrSuggestionigin of ferroelastic domains in free-standing single-crystal ferroelectric films  
I. Luk'yanchuk, A. Schilling, J.M. Gregg, et al., Phys. Rev. B 79, 144111 (2009) 

Effect of wall thickness on the ferroelastic domain size of BaTiO3,
G. Catalan, I. Luk'yanchuk, A. Schilling, J. M. Gregg, and J. F. Scott, Journ. of Mat. Sci. 44, 5307 (2009)

Light scattering in Quartz - the strongest in Nature

posted Dec 29, 2009, 12:25 AM by Igor Lukyanchuk   [ updated Jan 21, 2010, 2:09 AM ]

Modulated phase of  "Elongated triangles " (ELT)  discovered in 1996 by P.Saint-Gregoire and I.Luk'yanchuk in quartz can solve the 40-years problem of the anomalous light scattering at structural alpha-beta (a-b) transition at  T=847K, which is the strongest scattering known in crystalline materials. Since its discovery in 1956, this question was the subject of many controversies and is frequently erroneously treated in the classical books as manifistation of critical opalescence,  as was initially proposed by Nobel Laureate  V. Ginzburg. In fact, the scattering centers have the static nature that we  associated with microscopic blocs of the novel ELT.
Know already to the ancient jewelers and firstly studied by Le Chatelier in 1889 the a-b  transition was shown in 1975 to pass through the nonuniform incommensurate phase of "Equilateral triangles" (EQT) that exist within  interval of 1K and are clearly seen by means of Electron Microscopy. However these nanoscopic triangles do not change the global symmetry of Quartz and therefore are invisible to the light. That's why the discovery of the new, less symmetrical  ELT phase that lives within only 0.1K changes the situation! Having bi-axial symmetry the ferroelastic blocks of non-equilateral triangles have different optical indicatrices and therefore scatter the light.

Touching the history of Research  is the  very delicate issue. Discussing the problem of light scattering in quartz in the "International Light Scattering Conference in 1968,  Prof. G. Benedek from MIT has made the prognosis:
"There are many''old' '''and ''unstylish  fields of research which have again come to the center of attention as a result of the appearance of more modern experimental resources, new ideas ... Will all of this condition be enough to make work on the scattering of light again lead to great advances in the study of crystals? We shall know the answer to this question only in the future.'' 
Do we know the answer now ???

Read more:   A novel type of incommensurate phase in quartz: The elongated-triangle phase
P. Saint-Grégoire, E. Snoeck, C. Roucau, I. Luk'yanchuk, and V. Janovec; JETP Lett. 64, 410 (1996)

Dirac Fermions in Graphite

posted Dec 29, 2009, 12:15 AM by Igor Lukyanchuk   [ updated Dec 5, 2010, 12:58 PM by Igor Lukyanchuk ]

How realistic may be relativistic field models to describe  phenomena occurring in a condensed matter system ?  Such question should be particularly relevant for the systems  with massless Dirac fermions. The first unambiguous experim ental evidence for Dirac fermions occurrence in solids has  been reported by I.Lukyanchuk and Y.Kopelevich for graphite in 2004, one year before discovery of Dirac Fermions in graphite mono-layer (Graphene).  The identification of Dirac fermions became possible due to  phase-frequency analysis of quantum de Haas van Alphen and Shubnikov de Haas oscillations.  Actually, this method allows the efficient phase definition in any quantum oscillation phenomena and can be considered as a new tool in the condensed matter research. The identification of two-dimensional Dirac fermions in graphite undoubtedly makes this system a natural solid state laboratory to test predictions of relativistic theories of (2+1)-dimensional Dirac fermions.

Read more:
Phase analysis of quantum oscillations in graphite,
I. Luk'yanchuk, Y. Kopelevich, Phys. Rev. Lett., 93, 166402 (2004)
Dirac and normal fermions in graphite and graphene: Implications of the quantum Hall effect
I. A. Lukyanchuk and Y. Kopelevich, Phys. Rev. Lett., 97, 256801 (2006)
Lattice-induced double-valley degeneracy lifting in graphene by a magnetic field,
I. Luk'yanchuk and A. Bratkovsky; Phys. Rev. Lett., 100, 176404, (2008)
Searching for the Fractional Quantum Hall Effect in Graphite
Y. Kopelevich, B. Raquet, M. Goiran,... I. A. Lukyanchuk,.; et al., Phys. Rev. Lett., 103, 116802 (2009)

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