Domain boundary engineering – recent progress and many open questions

Some domain boundaries contain functionalities which do not exist in the bulk. Typical examples are (super-) conducting twin walls in WO₃, highly conducting walls in BiFeO₃ and in structural interfaces between SrTiO₃ and LaAlO₃, and ferroelectric walls in CaTiO₃. The emerging field of ‘Domain Boundary Engineering’ endeavors to generate such functional interfaces in a multitude of materials for applications in device materials. Some of the recent successes are reviewed together with suggestions for further research.     

On the thickness of domain walls in ferroelectrics and ferroelastics

Ferroelastic and ferroelectric domain walls are commonly described by wall profiles of the tanh(x/w)-type. We argue that this profile is still a good approximation if higher-order gradient energies are considered. Such energies are relevant for phase transitions close to structural incommensurations and also for phase transitions with dominant elastic interactions. Their effect on the wall profile is to influence the effective wall thickness. Positive gradient energies tend to widen domain walls beyond the values predicted in classic Landau-Ginzburg theory.     

Fluctuations and some strain related interaction mechanisms in structural phase transitions

Materials which undergo structural phase transitions with bilinear coupling between the spontaneous strain (e ^sp _i ) and the thermodynamic order parameter (Q) of the type λ_i e ^sp _i Q show characteristic fluctuation pattern at T > T _c. Snapshots of such pattern show tweedlike structures with butterfly shaped structure factors. Some experimental fluctuation patterns are reviewed and compared with the theoretical predictions.

At T ≤ T_c , characteristic microstructures often include structural twinning. The relevant energy expressions for order/disorder systems are recalled and their contribution to thermodynamic fluctuations are described. It is anticipated that some of the physical mechanisms may play a role also in improper ferroelastics with coupling of the type λ_i e ^sp _i Q ² _k where Qk is a component of a degenerate order parameter Q = {Qk}.     

Specific heat and latent heat of KMnF3 ferroelastic crystal

The specific heat and the heat flux exchanged by a single crystal of KMnF₃ have been measured simultaneously while cooling the sample at constant rate of 0·06 K/h through the phase transition at T ₀= 186 K. The phase transition is weakly first order and close to a tricritical point. The temperature dependence at T185 K of the excess specific heat and the excess entropy follow very well the predictions of a Landau potential at a tricritical point.     

Geometrical coupling between inhomogeneous strain fields: Application to fluctuations in ferroelastics

The compatibility conditions of elasticity theory are applied to the calculation of strain fluctuations in ferroelastic materials. A ferroelastic transition with an acoustic phonon mode instability and an order-disorder transition with striction are considered in the framework of the Landau-Ginzburg functional. Anisotropy of strain correlation functions and their critical behaviour in the symmetric phase near the transition point are analysed and compared with the results of the Ornstein-Zernike theory of fluctuations. Characteristic shape of the correlation functions (“butterflies”) are predicted.     

The effect of clamped and free boundaries on long range strain coupling in structural phase transitions

In ferroelastic structural phase transitions, the atomic ordering in one cell creates a local strain field which is propagated elastically throughout the material, resulting in an effective or indirect coupling J(R _ij ) between the ordering in cells i and j. With free boundaries on the sample, the J(R _ij ) contains a Zener-Eshelby term J _Z of infinite range, which largely determines the transition temperature T _c. The present paper shows what happens when the boundaries are clamped. On cooling from a high temperature an anomaly takes place at more or less the same temperature as the phase transition for free boundaries. Cooling results in an irregular pattern of domains with positive and negative order parameter whose long range strains cancel. Two cases are distinguished. In the “tweed” case coherent domain boundaries form easily and result in fine lamellar domains. When coherent domain boundaries are not possible (the “non-Sapriel”) case, larger less regular domains are formed. In either case the macroscopic net strain adds up to zero.     

Domain wall conductivity in La-doped BiFeO3

The transport physics of domain wall conductivity in La-doped bismuth ferrite (BiFeO3) has been probed using variable temperature conducting atomic force microscopy and piezoresponse force microscopy in samples with arrays of domain walls in the as-grown state. Nanoscale current measurements are investigated as a function of bias and temperature and are shown to be consistent with distinct electronic properties at the domain walls leading to changes in the observed local conductivity. Our observation is well described within a band picture of the observed electronic conduction. Finally, we demonstrate an additional degree of control of the wall conductivity through chemical doping with oxygen vacancies, thus influencing the local conductive state.     

Order-parameter coupling in the improper ferroelectric lawsonite

Low-temperature specific heat and thermal expansion measurements are used to study the hydrogen-based ferroelectric lawsonite over the temperature range 1.8 K ≤ T ≤ 300 K. The second-order phase transition near 125 K is detected in the experiments, and the low-temperature phase is determined to be improper ferroelectric and co-elastic. In the ferroelectric phase T ≤ 125 K, the spontaneous polarization P(s) is proportional to (1) the volume strain e(s), and (2) the excess entropy ΔS(e). These proportionalities confirm the improper character of the ferroelectric phase transition. We develop a structural model that allows the off-centering of hydrogen positions to generate the spontaneous polarization. In the low-temperature limit we detect a Schottky anomaly (two-level system) with an energy gap of Δ ～ 0.5 meV.     

The electrooptic effect in NH4IO3

The static electrooptic coefficients of NH₄IO₃ at room temperature are r₄₃ = 4.9, r₆₁ = 1.0, r₁₂n²₁ ? r₃₂n³₃ = 59.6, r₂₂n³₂ ? r₃₂n³₃ = 116.8 [ X 10^-12m/V]. The electrooptic effect depends on temperature and shows two ph ase transitions at 82.5°C and near 120°C.