Order–disorder, ferroelasticity and mobility of domain walls in multiferroic Cu–Cl boracite

C M Fernandez-Posada,C Cochard,M A Carpenter,R W Whatmore,J M Gregg

doi:10.1088/1361-648x/abcb0f

Abstract

Domain walls in Cu–Cl boracite develop as a consequence of an improper ferroelastic, improper ferroelectric transition, and have attracted close interest because some are conductive and all can be mechanically written and repositioned by application of an electric field. The phase transition and its associated dynamical properties have been analysed here from the perspective of strain and elasticity. Determination of spontaneous strains from published lattice parameter data has allowed the equilibrium long-range order parameter for F 3c → Pca21 to be modelled simply as being close to the order–disorder limit. High acoustic loss in the cubic phase, revealed by resonant ultrasound spectroscopy, is consistent with the presence of dynamical microdomains of the orthorhombic structure with relaxation times in the vicinity of ∼10−5–10−6 s. Low acoustic loss in the stability field of the orthorhombic structure signifies, on the other hand, that ferroelastic twin walls which develop as a consequence of the order–disorder process are immobile on this time scale. A Debye loss peak accompanied by ∼1% elastic stiffening at ∼40 K is indicative of some freezing of defects which couple with strain or of some more intrinsic freezing process. The activation energy of ⩾∼0.01–0.02 eV implies a mechanism which could involve strain relaxation clouds around local ferroelectric dipoles or freezing of polarons that determine the conductivity of twin walls.

Highlights

Boracites form an extensive family of compounds with general formula M3B7O13X, where M is a divalent metal and X is generally a halogen [1, 2]
Domain walls in Cu–Cl boracite develop as a consequence of an improper ferroelastic, improper ferroelectric transition, and have attracted close interest because some are conductive and all can be mechanically written and repositioned by application of an electric field
Low acoustic loss in the stability field of the orthorhombic structure signifies, on the other hand, that ferroelastic twin walls which develop as a consequence of the order–disorder process are immobile on this time scale

Summary

Introduction

Boracites form an extensive family of compounds with general formula M3B7O13X, where M is a divalent metal and X is generally a halogen [1, 2]. Equation (A1) is a Landau expansion in one order parameter, q, including coupling with polarisation, P, and symmetry breaking shear strains, et and e6, of the form λPq2, λetq2and λe6q2 It follows that P, et, e6 are expected to vary with q2 and, that the transition is improper ferroelectric, improper ferroelastic. As set out in the appendix, neither of the standard Landau solution for a weakly first order transition, representing a displacive limit, or the standard Bragg–Williams solution [32], representing an order/disorder limit, reproduces the temperature dependence of q2 It turns out, that only a small modification of the Bragg–Williams equation is needed to provide a satisfactory representation of the experimental data, apart from in the temperature interval immediately below the transition point where dynamical effects may still be important. The magnitudes of strains coupled with the order parameter vary up to a few % [appendix figure A1(b)] and are comparable with the strains which accompany octahedral tilting transitions in perovskites [34, 35]

Sample description and experimental details

Elasticity and anelasticity at high temperatures

Elasticity and anelasticity at low temperatures

DC and AC magnetism

A Landau expansion obtained using the software package