Topological excitations in nano- scale ferroelectrics ... · Igor Lukyanchuk. University of...
Transcript of Topological excitations in nano- scale ferroelectrics ... · Igor Lukyanchuk. University of...
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Igor LukyanchukUniversity of Picardie, France
Topological excitations in nano-scale ferroelectrics
Domains, vortices, skyrmions…
* Supported by H2020-ITN-NOTEDEV, H2020-RISE-ENGIMA
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What is Ferroelectric ?
Crystal with di-polar moment P
P-
-
-- --
+
Perovskite: PbTiO3
Pb
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Superlattice Technology: Laser ablation (1nm-1μm)
Result: Films … and Multilayers
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Nano-scale ?
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Periodic 180o Kittel domains
- were proposed by Landau & Lifshitz for ferromagnets in 1935
- were re-described by Kittel in 1946
and …
… were forgotten for ferroelectrics till 2000’s …
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180° Ferroelectric domainsIn theory…to minimize the energy of depolarization field E=-4πP
a
d
Mono-domain sample
Multi-domain sample
Depolarization energy :
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SrTiO3
PbTiO3
Kittel domains are formed in c-oriented ferroelectric films and superlattices…
… to minimize the depolarization field
VA Stephanovich, IA Luk’yanchuk, MG Karkut, PRL 94 , 047601 (2005)F De Guerville, I Luk’yanchuk, L Lahoche, M El Marssi Mat. Sci. & Eng. B 120, 16 (2005)IA Luk’yanchuk, L Lahoche, A Sené, PRL 102, 147601 (2009)
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Domain satellite !!!
Experimental confirmation
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PbTiO3
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Temperature Tc bulk
very thin film:only “soft”
F De Guerville, I Luk’yanchuk, L Lahoche, M El Marssi Mat. Sci. & Eng. B 120, 16 (2005)IA Luk’yanchuk, L Lahoche, A Sené, PRL 102, 147601 (2009)
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Soft domainsGradual profile of spontaneous polarization
is described by …
P(x,z) = A sn (k1x, m1) sn (k2z,m2)
thick domain wall
Polarization vanishes at the sample boundary
(Lukyanchuk et al. 2009)
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Hard (Kittel) domains, P=const
Soft domains, P=cos(kz)cos(qx)
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><<
>>>
P
Edep = P > Ecoerc
Landau Lifshitz paradox
Fractal branching
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“soft” spontaneous polarization, P0 (z-component)
+ induced depolarization field, E (smaller)
Very thin filmsSoft domain
solution of…
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“soft” spontaneous polarization, P0 (z-component)
+ induced depolarization field, E
= “vortices” of total polarization P=P0+χ Ε(new state of matter)
Very thin filmsSoft domain & vortex tubes
solution of…
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Negative capacitance
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Can capacitance be negative ???
but…
For two in-series capacitances
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for ultra-low-power nanoelectronics
Useful application
Device implementation: negative C
C: A. Cano and D. Jimenez, Appl. Phys. Lett. 97, 133509 (2010).
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Salahuddin, S. & Datta, S. Use of Negative Capacitance to Provide Voltage Amplification forLow Power Nanoscale Devices. Nano Lett. 8, 405-410 (2008).
Zhirnov, V. V. & Cavin, R. K. Negative capacitance to the rescue? Nature Nanotechnology 3,77-78 (2008).
A. Cano and D. Jimenez, Multidomain ferroelectricity as a limiting factor for voltage amplification in ferroelectric field-effect transistors, Appl. Phys. Lett. 97, 133509 (2010).
Krowne, C. M., Kirchoefer, S. W., Chang, W., Pond, J. M., & Alldredge, L. M. B. Examination of the possibility of negative capacitance using ferroelectric materials in solid state electronic devices. Nano letters, 11(3), 988-992. (2011).
Appleby, D. J. R., Ponon, N. K., Kwa, K. S. K., et al. Experimental Observation of NegativeCapacitance in Ferroelectrics at Room Temperature. Nano Lett. 14, 3864-3868 (2014).
Gao, W., Khan, A., Marti, X., Nelson, C., Serrao, C., Ravichandran, J., ... & Salahuddin, S. ( Room-temperature negative capacitance in a ferroelectric–dielectric superlattice heterostructure.Nano letters, 14(10), 5814-5819. 2014).
Khan AI, Chatterjee K, Wang B, Drapcho S, You L, Serrao, C, Bakaul SR, Ramesh R, and Salahuddin S. Negative capacitance in a ferroelectric capacitor.Nature Materials 14, 182–186 (2015).
Catalan, G., Jim´enez, D. & Gruverman, A. Negative capacitance detected. Nature Materials.14, 137-139 (2015)
IN FERROELECTRICS:
monodomain
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Temperature dependence ε(Τ) < 0 ∗
ε−1 (T)
Even in paraelectric state ε < 0
multidomain(pinned) DW
monodomain
multidomainfree DW
A. Sené, MSc Thesis (2007), PhD Thesis (2010)
P. Zubko, J.C. Wojdeł, M. Hadjimichael, S. Fernandez-Pena, A. Sené, I. Luk’yanchuk, J.-M. Triscone, J. Íñiguez, Nature, 534, 524 (2016)
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ε(Τ)<0 , direct experimental observation, 2016
Negative Capacitance in Multidomain Ferroelectric Superlattices, P. Zubko, J.C. Wojdeł, M. Hadjimichael, S. Fernandez-Pena, A. Sené, I. Luk’yanchuk, J.-M. Triscone, J. Íñiguez, Nature, 534, 524 (2016)
Domains are here !
X-ray
Satellite peak
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ε(Τ)<0 , ab-initio monte-carlo simulations, 2016 ( ibid. )
PbTiO3
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Why ε is negative?
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In external field, D = ε E
- opposite to P and D !!!
Intrinsic DW motion, Negative !!
εp
< 0A.M. Bratkovsky and A.P. Levanyuk, 2001A. Kopal, P. Mokry, J. Fousek T. Bahnık 1999
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THz dynamics of domain walls
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What is the dynamical dielectric response
ε(ω) ???
Domain dynamics in applied
E(t) = E0 cos (ωt)
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Dispersion ε(ω) for PTO layer
Re ε
Im ε
Principal result
Plasma resonance
Negative (!!) due to DW motion
Re ε
Im ε
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Different from ε(ω) in FIR of polar molecules, soft mode …
PbTiO3
Hlinka, J., Simon, E., Bogicevic, C., Karolak, F. & Janolin, P. E. Phys. Rev. B 84, 092104 (2011)
ε(ω)<0 at finite ω
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… Déjà vu plasma oscillations in metal
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Plasma resonance
In metal In ferroelectric with DW
moving DWs
Charge excess
At UV frequency At sub-THz frequency
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Electrodynamics
( plasmonics )
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DW plasma resonance
PZT, ab-initio: Q. Zhang, R. Herchig, I. Ponomareva 2011
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Model: harmonic oscillator
Deploarization restoring force
Kittel model + ab-initio
Soft Modedamping
Supplementary Information
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Dynamic response
With
andMaterial dependent !!!
Size dependent !!!
Supplementary Information
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Dispersion ε(ω) for PTO monolayer
Re ε
Im εPlasma resonance
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Dynamic permittivity of para / ferro superlattice:
with
“By design”
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PTO-STO superlattice: THz (NEZ) Metamaterial
Tuning of ε(ω) !!!
positive
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THz Optics, How to detect ???
Refractive index:
p-Reflectivity:
with
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Sub- and low THz Reflection-Absorbtion Spectroscopy (RAS)
Reflectance, p-polarization:
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Observation of Giant Sub THz rezonance at Brewster angle
Giant effect for superlattices x10 !!!
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Switching of Topological Structures in Ferroelectric nano-dots:
Domains, Vortices and Skyrmions
Electrostatics is important …
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Multibit Logic
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Stable states
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Uniform swith phase diagram, PbTiO3
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TOPLOGICAL ACCESS MEMORY (TAM)
- 3 Level: “yes”, “may be” “no”
- 4 Level: “yes”, “either yes or no ” “neither yes nor no”, no”
Towards non-deterministic and neuromorphic computing
Topology is strain- and temperature - tuneable
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Switching of Topological Structures in Ferroelectric nano-dots:
Domains, Vortices and Skyrmions
Electrostatics is important : Q=divP=0…
Confinement geometry
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Finite size samples with:
1D - easy axis polarization=> domains
2D - easy-plane polarization=> vortices
3D - sphere homotopy group S2=> skyrmions
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On the quantitative level: Anatomy of GL functional
Crystalline anisoropy(assumed to be weak…)
Strain-induced anisoropy(uniaxial, easy axis…)
Gradient of P induces the depolarization charge ρ=divP
Absolute value of P is involved Interaction with E
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NaNO2, 16x3nm
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Mathematics…phase field method
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Phase diagram, … different metastable states
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4-bit switching ….
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More details…
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PFM immage in PVDF-TrFE 50nm films
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Kirchhoff 1877 (Monatsb. Deutch. Acad.)Lorentz 1879 (Wied. Ann.)
Study of the real capacitor
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Fringing fieldBulk contribution
- Negative !- Nonlocal !
Energy of the real capacitor
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Another condition(opposite field)
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Most stable
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R
Ωf
Ωp
x
y
∂Ω1
∂Ω2
L
nferro
para
- Numerical- Analytic
P4(f)2 ∇π=ϕ∇(f)22
021
// P]-P)Pt[(4 ϕ−∇=∇ξ+πε −
)k(J)msinBmcosA( 1mmm ρθ+θΣ=Ψ
, (15)
θρ
ε+ρ
+θρ
ε+ρ
Σ=Φ msin])R
(KE
)Rk(J)k(JD[mcos])
R(
KE
)Rk(J)k(JC[ m
22
m//
2m
2mm
m22
m//
2m
2mm
, (16)
θρ
ε+ρ
+θρ
ε+ρ
Σ=ϕ msin])R
(KKF
)Rk(J)k(JD[mcos])
R(
KKE
)Rk(J)k(JC[ m
22
21
m//2m
2mm
m22
21
m//2m
2mm
)f(
, (17)
mmm
)p( )R)(msinHmcosG(ρ
θ+θΣ=ϕ.
Mathematics…
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radius
tem
pera
ture
K=1K=2
K=4
K=6
Vorticity
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Chiral skyrmions
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Polarization Switching in Ferrelectric Nanodot
Uniform switching
Domain nucleation
Polarization rotation
Very high coercive field (Landauer Paradox),because of the depolarization field
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Torsion instability
Low coercive field !
No depolarization charge, div P = 0 !!!
Linear stability analysis
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Further evolution: Skyrmion formation
Chiral (Bloch) Structure with divP=0
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Nonlinear equations with P-θ coupling
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CONCLUSION …
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“Topological Structures in Ferroic Materials” in International Institute of Physics, IIPNatal Brazil, June 2018
TOPO 2018
ORGANIZERS:José Antonio Eiras, University of Sao
Carlos, Brazil, Igor Lukyanchuk, University of
Picardie, France, Jan Seidel University of New South
Wales, Australia,
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8-10 International Workshops are selected per year
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Facilites:
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