Magnetoelastic coupling and microstructure dynamics associated with spin-orbit coupling in the ferrimagnetic/ferroelastic ordered double perovskite Ba2FeReO6

Strain coupling and relaxation dynamics associated with the ferrimagnetic/ferroelastic phase transition at ${T}_{c}\ensuremath{\approx}310\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ in double perovskite ${\mathrm{Ba}}_{2}{\mathrm{FeReO}}_{6}$ with a high degree of Fe/Re order have been investigated with resonant ultrasound spectroscopy through the temperature interval $\ensuremath{\sim}5--600\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and with applied magnetic field of up to $\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. Strain analysis using diffraction data from the literature is consistent with a Landau model of the transition as $Fm\overline{3}m{1}^{\ensuremath{'}}\ensuremath{\rightarrow}I4/m{m}^{\ensuremath{'}}{m}^{\ensuremath{'}}$, improperly ferroelastic, driven by a magnetic order parameter with symmetry ${\mathrm{\ensuremath{\Gamma}}}_{4}^{+}$. Ferroelastic shear strain of up to $\ensuremath{\sim}0.0015$ arises from spin/orbit coupling and is smaller than is typical of coupling with octahedral tilting. It provides the underlying cause of softening of the shear modulus observed over an interval of $\ensuremath{\sim}100\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ below ${T}_{\mathrm{c}}$, though with order/disorder rather than displacive character for the transition. Hysteretic effects suggest that precursor microstructures and mixed magnetic/ferroelastic domains below ${T}_{\mathrm{c}}$ depend on the thermal history of the sample and can evolve on a timescale of hours and days at room temperature. Elasticity data collected as a function of external magnetic field reveal that poled samples are slightly softer than those with multiple magnetic domains at 4 K. At 300 K there is a time-dependent viscous component of the response to the field that relates to the bulk modulus and, hence, to volume changes associated with magnetic ordering. A loss peak seen $\ensuremath{\sim}20--50\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ below ${T}_{\mathrm{c}}$ in AC magnetic measurements made at frequencies of $0.2--1\phantom{\rule{0.28em}{0ex}}\mathrm{kHz}$ yielded an activation energy $\ensuremath{\sim}0.4\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ and has been attributed to freezing of magnetic/ferroelastic domain walls. No equivalent loss peak was seen in the acoustic data measured at $\ensuremath{\sim}100--500\phantom{\rule{0.28em}{0ex}}\mathrm{kHz}$, however, implying that these domain walls are mobile in response to a dynamic magnetic field on a timescale of $\ensuremath{\sim}{10}^{\ensuremath{-}2}\text{--}{10}^{\ensuremath{-}3}\phantom{\rule{0.28em}{0ex}}\mathrm{s}$ but immobile in response to a dynamic stress field applied on a timescale of $\ensuremath{\sim}{10}^{\ensuremath{-}5}\text{--}{10}^{\ensuremath{-}6}\phantom{\rule{0.28em}{0ex}}\mathrm{s}$. Debye-like acoustic loss peaks at temperatures below $\ensuremath{\sim}100\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ yielded activation energies of $\ensuremath{\sim}0.02--0.1\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ and are discussed in terms of pinning/freezing of polarons. ${\mathrm{Ba}}_{2}{\mathrm{FeReO}}_{6}$ is a material with magnetoelastic and magnetoelectric heterogeneities that might be tuned by choice of thermal history and cation order.