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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)