In Situ Analysis of Ferroelastic Domains in LaAlO₃

Akin to their sister ferroics (e.g ferroelectrics and ferromagnetics), ferroelastics are characterised by regions of differently orientated states (domains), separated by domain walls, that form when cooled below a critical temperature (T_C) in order to reduce its inherent free energy¹. Domain walls are of particular interest, exhibiting unique properties on the nanoscale from the bulk, such as (super-conductivity in an insulating medium. When an external field is applied, domains can further nucleate, annihilate or become mobile in response to the stimuli, presenting unique possibilities for active-adaptable devices.<br/><br/>Temperature and stress are examples of such stimuli and are capable of switching the domain structure, a mechanism that mediates many of the functional properties utilised applications such as memory devices, switches and sensors. The understanding of how the domains behave in response to externally applied fields is critical to the development of advanced applications such as neuromorphic computing²; based on the jerky mobility of domain walls, and by extension domains, in materials with ferroelastic components. These discrete jerks emit elastic fields that can destabilise surrounding structures and trigger a cascade of switching events known as avalanches.<br/><br/>Mean-field theory continues to be successfully employed in the characterisation of avalanches³ by predicting the power-law distribution of jerks in the form, g(x)dx ~ x^-εdx whereby g(x) describes the probability (g) of a jump (x) and the energy critical exponent (ε) which is fundamental for classifying switching behaviours, taken from the maximum-likelihood method. The values attained for these critical exponents are independent of the systems’ microscopic properties and exhibit no characteristic time or size scales. This allows for such systems to be ordered into different universal classes, thus garnering insight into more intractable systems that demonstrate the same statistical behaviour, such as the crackling of sweet wrappers and tectonic activity⁴.<br/>This study builds upon work conducted on bulk LaAlO₃ (LAO), which tested the effect of the sample aspect ratio (AR) on the dynamical domain behaviour as it was heat cycled (HC) past T_C (~545°C) and back to room temperature under closed atmospheric conditions. <i>In situ</i> transmission optical imaging confirmed a divergence in dynamical behaviour during the cool down from T_C in relation to a change of AR, between a i) low AR (~1:1) which remained largely stable throughout and resembled its RT patterning at high temperatures, and ii) a higher AR (~1.8) which demonstrated a global reconfiguration premeditated by a cascading domain wall front. This was further characterised with a pixel by pixel mean-field analysis that showed a constant integrated critical exponent value throughout the low aspect ratio sample and critical exponent mixing in the higher aspect ratio sample, which had not been identified in literature prior.<br/>Here we complement the bulk studies by investigating ferroelastic domain dynamics at the microscale, utilising a LAO lamella of varying aspect ratios. These samples were HC <i>in situ</i> under different atmosphere including vacuum. The results here presented highlight the inherent differences in domain dynamics as a function of AR at the macro and microscale, which is fundamental for the advancement of active adaptable devices.<br/>¹ G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, Reviews of Modern Physics <b>84</b> (1), 119 (2012).<br/>² Ekhard K. H. Salje, APL Materials <b>9</b> (1), 010903 (2021).<br/>³ Blai Casals, Guillaume F. Nataf, and Ekhard K. H. Salje, Nature Communications <b>12</b> (1) (2021).<br/>⁴ James P. Sethna, Karin A. Dahmen, and Christopher R. Myers, Nature <b>410</b> (6825), 242 (2001).