Signatures of Anelastic Domain Relaxation in Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ Investigated by Mechanical Modulation of Resistivity

TL;DR

This study investigates anelastic domain relaxation in Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ using mechanical modulation of resistivity, revealing domain wall dynamics and their dependence on composition and strain.

Contribution

It introduces a novel AC mechanical deformation method to probe domain wall relaxation and provides quantitative analysis of activation energy and its strain dependence.

Findings

Peak in out-of-phase resistivity modulation in orthorhombic state

No phase lag in tetragonal composition, indicating domain motion effects

Activation energy decreases with increasing strain amplitude

Abstract

The resistive response of Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ to AC mechanical deformation is considered in the multi-domain state. This resistance change depends both upon the anelastic relaxation of domain walls and upon the relation between resistance and the domain wall configuration. Samples are adhered to the surface of a piezoelectric stack, which is driven by an AC voltage while the AC modulation of the sample resistance is measured. As the response time of electrons is faster than that of the lattice, the phase difference $\phi$ between the AC resistance modulation and the AC deformation of the piezoelectric is entirely due to anelastic relaxation effects in the sample. An expression is derived for relating $\phi$ to a sample's complex compliance, $J(\omega)$, in this experimental configuration. Measurements of Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ for x= (0.025, 0.052) reveal a peak in the out-of-phase resistivity modulation in the orthorhombic antiferromagnetic state well below the Ne\'el temperature $T_N$ and structural transition $T_S$. Meanwhile, for a composition that is tetragonal at all temperatures, x=0.07, the resistance modulation remains entirely in phase over the same temperatures, establishing domain motion as a probable cause of the observed effects in the samples that do undergo the tetragonal-to-orthorhombic transition. Fits are provided of $\tan\phi$ for a sample with x=0.025 for various amplitude excitations on the piezoelectric stack, from which the apparent activation energy $E_a$ for domain wall motion is found to decreases with increasing amplitude of the deformation along the $[110]_T$ axis. We find $\frac{dE_a}{d\varepsilon^0_{[110,110]_T}} = -1115\pm 196$ eV with $E_a = 9.09 \pm 0.74 \times 10^{-3}$ eV in the zero strain limit if we assume linearity over the entire range of strain amplitudes.