Parabolic temporal profiles of non-spanning avalanches and their importance for ferroic switching

Abstract

Computer simulation of a ferroelastic switching process shows avalanche formation with universal averaged temporal avalanche profiles, where J(t) is the avalanche "amplitude" at time t. The profiles are derived for the three most commonly used "jerk"-singularities, namely, the total change of the potential energy U via J(t) = (dU(t)/dt)2, the energy drop J(t) = -dU/dt, and the stress drop J(t) = -dτxy/dt. The avalanches follow, within the time resolution of our modeling, a universal profile J(t)/Jmax = 1 - 4(t/tmax - 0.5)2 in the a-thermal regime and the thermal regime. Broadening of the profiles towards a 4th order parabola arises from peak overlap or peak splitting. All profiles are symmetric around t/tmax = 0.5 and are expected to hold for switching processes in ferroic materials when the correlations during the avalanche are elastic in origin. High frequency applications of ferroic switching are constrained by this avalanche noise and its characteristic temporal distribution function will determine the bandwidth of any stored or transmitted signal.