Size Effects in Ferroelectrics (and some reference to ferroics in general) Marty Gregg Queen s University Belfast

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1 Size Effects in Ferroelectrics (and some reference to ferroics in general) Marty Gregg Queen s University Belfast Outline: Basics of ferroelectricity Critical correlation volume, superparaelectricity and relaxors Influence of boundaries I: strain coupling Influence of boundaries II: depolarising fields Strain and depolarisation effects on ferroelectric domains Size effects on dynamics of ferroelectrics permittivity and switching Ferroelectrics develop reversible electrical polarisation when electric field is applied Field Up Field Down Polarization Voltage Important fundamental features which point to a strong sensitivity to size: Ferroelectricity traditionally described as a cooperative effect below a critical volume ferroelectricity is not thought to be sustained expect ferroelectricity to be destabilised as size is reduced; Critical correlation volume, superparaelectricity and relaxors Even without consideration of boundaries, size effects in ferroelectrics are expected Development of polarisation involves, in most cases, physical distortion of the unit cell strain and polarisation are therefore coupled. Surface / interfacial strain and strain clamping has a major influence; Dipolar nature means that discontinuities / boundaries / surfaces can be charged the field between charged surfaces opposes the dipole formation depolarising fields increase when surfaces are close together. Large group of dipoles aligned significant energy payoff associated with alignment Small group of dipoles energy payoff associated with alignment comparable with thermal energy Certainly at finite temperature, tension between energy reduction of ordering (enthalpic term) and energy reduction from increased entropy leads to a critical volume at which superparaelectricity is possible (similarly with superparamagnetism) Do Superparaelectric systems exist? Optical and electrical behaviour of relaxor electroceramics Cross superparaelectric rationalisation (L. E. Cross Ferroelectrics 76, 24 (987) Cross describes idea that local nanoregions develop superparaelectric polarisation, and within each nanoregion the direction of polarisation is thermally flipping between sets of possible orientations; G. A. Smolenski et al. Sov. Phys. Solid State (96) and other works noted broad peak in permittivity with temperature, not sharp Curie anomaly seen in conventional ferroelectrics proposed Diffuse Phase Transition caused by material having heterogeneous clusters with distribution of Curie temperatures. Did NOT account for frequency dispersion on low T side of permittivity peak Optical studies by Burns and Dacol PRB and Sol. State Comms (983) show while linear measured polarisation (P) is zero at RT, mean of P 2 is nonzero!! Suggests local polar regions which are randomly oriented either in time or space (or both) Explains permittivity response: on cooling thermal excitation decreases such that progressively polar orientations can be controlled by applied field (permittivity initially increases on cooling); eventually, the temperature lowers to the point where timescales required for responding to external field become an issue for some of the superparaelectric polar clusters explains peak in permittivity AND low T frequency dispersion

2 Freezing of the superparaelectric At even lower temperatures the polar nanoclusters are unable to respond to a small external field even in infinite time, and a frozen state develops often called a glass. Colla et al. PRL (995) notes freezing to a glass state, and the fieldinduced ferroelectric state that can be induced by d.c. fields. Now behaviour understood by random field random bond (RFRB) models of nanoscale heterogeneity (see Blinc et al. PRL 83, 424, (999) for example); Any direct evidence of polar nanoclusters Relaxor electroceramics classical case of Pb(Mg /3 Nb 2/3 )O 3 Early critical observations: N. de Mathan et al. JPCM (99) observed PMN on cooling no complete breaking of cubic symmetry BUT at 5K clear diffuse broadening consistent with local symmetry breaking (implied polar distortion in regions ~0nm in diameter). Possible model of structure after T. R. Shrout and J. Fielding, Proc. IEEE Ultrasonics Symp, 2, 7 (990) other direct microscopy studies also clearly point to existence of local (polar) nanoregions. More recent work see Jeong et al. PRL (2005) Influence of boundaries I: Strain coupling Pertsev Phase Diagrams Inherent importance of strain coupling is undeniable manifested in bulk through shapeconserving twins / 90 o domains, BUT..in thin film geometries, particularly those in which misfit strain between film and substrate is small and film thicknesses are less than needed to form misfit dislocations. This recognised in classic phenomenological work by N. A. Pertsev et al. Pertsev and coworkers suggest new phase diagrams for epitaxial thin film ferroelectrics that are clamped to single crystal substrates. Work progressed by others involved in LandauGinzburgDevonshire free energy descriptions of ferroelectrics e.g. Ban and Alpay JAP (2002) / (2003). Experimental testing of Pertsev ideas Under tensile strain? Substrates and thin film electrode systems which induce compressive epitaxial strain relatively easy to make. Some early reports of straincoupled stabilisation of cphase (consistent with Pertsev) e.g. Sinnamon et al APL (2002), but most impressive demonstration found in Haeni et al. Nature (2004) Central idea that strain clamping / strain coupling causes alterations in phase transition behaviour very evident in recent work. 2

3 Strain coupled transition behaviour in nanoscale systems with many interfaces ferroelectric superlattices Strain coupled enhanced polarisation in superlattices Strain coupling in BTO / STO superlattices responsible for development of inplane polarisation in STO at room temperature seen by Rios et al. JPCM (2003), and rationalised by atomistic simulations by Johnston et al PRB (2005) Also watch for work by Dawber and Triscone on superlattice coupling effects Influence of boundaries II: depolarising fields Suspected effects of the depolarising field Progressive loss of ferroelectricity (if no domain formation considered) ve charged surface P E ve charged surface Existence of surfaces which do not offer any charge compensation create voltage and field which opposes the polarisation responsible for the charge in the first place. As distances between surfaces decreases the charge density on the faces is largely unchanged hence depolarisation field dramatically increases in nanoscale objects. Equivalent modelling with acknowledgement of surface effects What about suppression of ferroelectricity in experiment? Shaoping Li et al. Phys. Lett. A 22 (996) Vendik and Zubko JAP (2000) In thin films of PbTiO 3, while Tc is progressively suppressed with reduced thickness ferroelectricity persists. Above figure (Fong et al. PRL 2006) relates to compensating surfaces, but similar in noncompensating conditions with formation of domains holding stability of ferroelectricity (see next overhead). 3

4 Other experimental observations thin films and nanowires SPMwritten bits surprisingly stable when very small indeed in nanowires and thin film media Yun et al. Nanoletters (2002) nonaxial remanent polarisation stable at RT on 2nm single crystal BaTiO 3 nanowire Streiffer et al. PRL (2002) thin film PbTiO 3 Tc suppressed, but RT ferroelectricity remains. Depolarisation field effects negated by 80 o domains Tybell et al. PRL (2002) SPM outofplane switching in thin film PZT FE stability down to ultrananoscale in isolated islands is less clear Strain and depolarisation effects on ferroelectric domains Islands cut from thin films by FIB (Ganpule et al. APL 999) show ferroelectric response down to ~00nm diameter Islands examined by Roelofs et al. APL (2002) suggest loss of ferroelectricity below diameter ~20nm ve charged surface P E ve charged surface Domains minimise the macroscopic manifestation of the depolarising field Shape contraint at surfaces and boundaries induces 90 o domain formation Domains can also form in order to accommodate macroscopic shape constraints shape compensating domains Basic phenomenological physics for domain periodicities variation with size Electrostatic energy associated with free surface d F = Uw γ w Total domain wall energy d w 80 o domains Under equilibrium: F d = 0 = U γ 2 w w 2 d w = γ U Kittel, Phys. Rev. 70, 965 (946); Zhirnov, Sov. Phys. JETP 35, 822 (959); Mitsui & Furuichi, Phys. Rev. 90, 93 (953); Roytburd, Phys. Status Solidi A 37, 329 (976). 4

5 Study domains imaged by STEM in BaTiO 3 slabs of controlled thickness (cut with FIB) Find Kittel s law obeyed across 6 orders of magnitude a 200 nm b 0.25 Å c 0.0 Å 90 o domains Region for selected area diffraction {0} domain walls, Period in this case ~50nm from both real space and reciprocal space measurements Schilling et al., PRB (2006) log 0 [domain period (nm)] 0 5 Mitsui's data on Rochelle Salt (gradual cooling) Mitsui's data on Rochelle Salt (sudden cooling) Schilling's data on BaTiO 3 Streiffer's data on PbTiO 3 F α Streiffer's data on PbTiO 3 F β Dumas's data on Co Sparks's data on Ni Wu's data on LSMO log 0 [thickness (nm)] Kittel s law W=kd /2 holds for ferroics across 6 orders of mag. Constant of proportionality similar within each ferroic subgroup. Schilling et al., APL (2006) Ferroelectric columns / wires / picture frames Stripe domains; Domain periodicity response sensitive to additional size constraint (being thin in more than one dimension) 300nm x z d y d x Domain period (λ) (nm) lamellae columns (Thickness) /2 (nm) /2 Kittel: y Gradient of plot / 2 w = γ d U U / 2 Flux / Field Closure Domains in Ferroelectric Nanodots C. Kittel, Rev. Mod. Phys., 2, 54 (949) ~5nm Modelling of ferroelectric dots and nanowires 200nm ~0nm Naumov et al. Nature, 432, 737 (2004) and J. F. Scott, Nature Materials, 4, 3 (2005) Fu and Bellaiche PRL, 9, (2003) 5

6 Ferroic Vortices in Minerals Vortex core observations in Ferromagnets Shinjo et al. Science, 289, 930 (2000) Harrison et al., PNAS, 99, 6556 (2002) Wachowiak et al., Science, 298, 577 (2002) N. D. Mermin, Rev. Mod. Phys., 5, 59 (979) More complex morphologies ferroelectric solenoids? Suggests nanoscale ferroelectric solenoid Wachowiak et al., Science, 298, 577 (2002) E Gorbatsevich & Kopaev, Ferroelectrics, 6, 32 (994) and J. F. Scott, Nature Materials, 4, 3 (2005) 250nm Toroidal Nanoscale Ferroelectrics Domain imaging clearly shows no evidence of vortices down to ~00nm Secondary electron images generated by Gaion primary beam on FIB 200nm 200nm 5 μm Conventional {0} oriented domain walls, with predictable periodicities. Need to push dimensions down below that achievable with FIB alone or look at systems in which polar rotation is easier (MPB systems or relaxors below T f ). 6

7 Ferroelectric nanorings made by TEM sectioning PZTinternally coated nanoporous alumina Rings using latex sphere templates Nanosphere deposition Polystryene Zhu et al., APL 89, 2293 (2006) rings made, but not yet evidence of vortex domains Metal deposition Ar Ion milling Removal of spheres Aizpurua et al., PRL 90, 5740 (2003) Nanorings PZT nanoring arrays Size effects on dynamics of ferroelectrics permittivity and switching Move from bulk / single crystal to thin film results in dramatic collapse in lowfield permittivity, smearing of Curie anomaly, and apparent migration of Curie peak mainly to lower temperatures: Shaw et al. APL (999), also Parker et al. APL (2002) 300nm As yet no evidence of vortex domain formation Reduction in permittivity rationalised by series capacitance dead layer Origin of the series capacitance? Possibilities: C. A. Mead, PRL, 6, 545 (96) (i) Distinct layer of low permittivity in the ferroelectric layer Inverse capacitance Parasitic Series Capacitance C eff = C bulk K (ii) Electronic structure of ferroelectricelectrode interface Schottky barriers etc. (iii) Polarisation suppression at interface (Vendik JAP 2000) (iv) Progressive hardening of polarisationrelated softmodes (Sirenko et al. Nature 2000) (v) Capacitive effect due to nonideal field screening WITHIN the electrode (see work by Dawber) Film Thickness 7

8 What does experiment tell us about origin of series capacitance? Classical work by Basceri et al. JAP one of the earliest attempts to identify the electrical characteristics of the series cap component. Broadly temperature independent; bias field tends to reduce the influence of the series capacitance Physical extent of any distinct layer if in the ferroelectric? Work by Sinnamon et al. APL 200: considers IF a distinct layer of lower permittivity exists within the ferroelectric at the ferroelectricelectrode boundary, then on continuing to reduce the thickness of thin film capacitors, eventually reach a point where the entire structure is composed of the low permittivity layer. At this point the series capacitor model must break down does it? Dashed line is series cap model fitted to data for thin film capacitors >70nm in thickness. Other capacitor structures down to 7.5nm lie on the same function therefore series cap still holds, and any deadlayer must be of total thickness <7.5nm. Recently extended by McAneney to <5nm. Coercive field increases with decreases in film thickness Kay and Dunn (962) Perimeter switching effects Taken from Dawber et al. JPCM (2003) Kinetics of switching dependent on the perimeter of the micro / nano capacitor (Samsung PZT FRAM processing?) 8