Giant domain wall response of highly twinned ferroelastic materials

Abstract

Many ferroelastic crystals display at sufficiently low measurement frequencies a huge elastic softening below Tc which is caused by domain wall motion. Materials range from perovskites to iron based superconductors and shape memory materials. We present a model -based on Landau-Ginzburg theory including long range elastic interaction between needle shaped ferroelastic domains -to describe the observed superelastic softening. The theory predicts that the domain wall contribution to the elastic susceptibility is different for improper and proper ferroelastic materials. A test of the theory against experimental data on SrTiO3, KMnF3, LaAlO3, La1−xNdxP5O14 and NH4HC2O4· 1 2 H2O yields excellent agreement.The macroscopic response of materials depends often on structures spanning a broad range of length and time scales. Examples of such inhomogeneous structures are precursor clusters near structural phase transitions, domains and domain walls, interfaces at first order displacive or reconstructive phase transitions, etc. They have been reported in a wide range of functional materials. Prominent cases are the enhancement of piezoelectric response [1] of nanotwinned BaTiO 3 for domain thickness below 50 nm, or the giant piezoelectric effect in ferroelectric relaxors [2] due to the high mobility of polar nanoregions [3]. Generally, domains and domain boundaries in ferroic crastals can act as structural elements for creating novel functional devices [4]. The usefulness of domain boundaries in Domain Boundary Engineering depends on the time scale of their response. Static or pinned domain boundaries can be used as functional units since they can host functional properties (ferroelectric, superconducting, etc.) which are absent in the bulk [5]. Mobile domain boundaries can lead to giant macroscopic responses, depending on the frequency of the changing external field.In the present work we will focus on ferroelastic materials, which depending on the type of coupling between the primary order parameter η and the strains ε can be classified as proper, pseudo proper, improper or coelastic ones [6]. Very often ferroelastic crystals consist of a large number of domains which are separated by domain boundaries [7]. Due to mechanical compatibility these domain boundaries should be planar with well defined orientation. However, in real crystals very often needle or dagger shaped domains appear [6]. There are still many open questions, e.g. concerning the stability of ferroelastic domains, their motion under an applied dynamic stress, the observed domain freezing [8] at sufficiently low temperature, etc.Understanding the macroscopic behaviour of multidomain crystals is important for technological applications as well as for the interpretation of seismic signals of our Earth, since domain wall motion influences the low frequency elastic and anelastic behaviour of minerals at seismic frequencies (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20). In recent years we have performed quite detailled low frequency (0.1-...

Electronic nematic susceptibility of iron-based superconductors

“…However, the experimental data obtained at lower stress are much too small in comparison to this model for temperatures T < T s . These anomalously low values of the Young's modulus below T s likely arise from the 'superelastic' behaviour of the twinned samples, which is due to domain wall motion and typically found in ferroelastic materials [105,112,113]. The effect can be understood by considering two kinds of structural domains, + -type domains which are elongated along [110] and −type type domains which are shortened along this direction.…”

Symmetry breaking in hexagonal and cubic polymorphs of BaTiO3

“…Figure 3shows elastic modulus and associated tanδ as a function of temperature for h-BTO samples. Transition from the hexagonal paraelectric-paraelastic phase into orthorhombic paraelectric-ferroelastic phase is clearly visible around 220 K. The transition is characterized by a large softening56 of the material possibly related to formation of ferroelastic domains below…”

Multiferroic (ferroelastic/ferromagnetic/ferrimagnetic) aspects of phase transitions in RCo2Laves phases

“…A linear baseline, as an approximation for a small intrinsic softening effect, has been subtracted so as to ascribe the remaining 'excess' to motion of twin walls. According to Harrison and Redfern [46] and Schranz et al [48] this excess should scale with q 2 if the number of ferroelastic twin walls does not vary with temperature. The observation of (excess compliance) 2 ∝ temperature (figure 9) is then consistent with the tricritical character deduced from the strain variation in figure A.1 (e 2 t ∝ q 4 ∝ (T c − T )).…”

“…On this basis, it has been assumed that the contribution of intrinsic effects to the observed softening of the shear modulus would be correspondingly smaller for NdCo 2 . Following the approach of Harrison and Redfern [46] and Schranz et al [48], data from figure 5 have been replotted as 1/ f 2 , which scales with the elastic compliance, in figure 9. A linear baseline, as an approximation for a small intrinsic softening effect, has been subtracted so as to ascribe the remaining 'excess' to motion of twin walls.…”