Ferroelasticity, anelasticity and magnetoelastic relaxation in Co-doped iron pnictide: Ba(Fe0.957Co0.043)2As2.

The hypothesis that strain has a permeating influence on ferroelastic, magnetic and superconducting transitions in 122 iron pnictides has been tested by investigating variations of the elastic and anelastic properties of a single crystal of Ba(Fe0.957Co0.043)2As2 by resonant ultrasound spectroscopy as a function of temperature and externally applied magnetic field. Non-linear softening and stiffening of C 66 in the stability fields of both the tetragonal and orthorhombic structures has been found to conform quantitatively to the Landau expansion for a pseudoproper ferroelastic transition which is second order in character. The only exception is that the transition occurs at a temperature (T S ≈ 69 K) ~10 K above the temperature at which C 66 would extrapolate to zero ([Formula: see text] ≈ 59 K). An absence of anomalies associated with antiferromagnetic ordering below T N ≈ 60 K implies that coupling of the magnetic order parameter with shear strain is weak. It is concluded that linear-quadratic coupling between the structural/electronic and antiferromagnetic order parameters is suppressed due to the effects of local heterogeneous strain fields arising from the substitution of Fe by Co. An acoustic loss peak at ~50-55 K is attributed to the influence of mobile ferroelastic twin walls that become pinned by a thermally activated process involving polaronic defects. Softening of C 66 by up to ~6% below the normal-superconducting transition at T c ≈ 13 K demonstrates an effective coupling of the shear strain with the order parameter for the superconducting transition which arises indirectly as a consequence of unfavourable coupling of the superconducting order parameter with the ferroelastic order parameter. Ba(Fe0.957Co0.043)2As2 is representative of 122 pnictides as forming a class of multiferroic superconductors in which elastic strain relaxations underpin almost all aspects of coupling between the structural, magnetic and superconducting order parameters and of dynamic properties of the transformation microstructures they contain.

Strain relaxation behaviour of vortices in a multiferroic superconductor.

The elastic and anelastic properties of a single crystal of Co-doped pnictide Ba(Fe0.957Co0.043)2As2 have been determined by resonant ultrasound spectroscopy in the frequency range 10-500 kHz, both as a function of temperature through the normal-superconducting transition (T c ≈ 12.5 K) and as a function of applied magnetic field up to 12.5 T. Correlation with thermal expansion, electrical resistivity, heat capacity, DC and AC magnetic data from crystals taken from the same synthetic batch has revealed the permeating influence of strain on coupling between order parameters for the ferroelastic (Q E) and superconducting (Q SC) transitions and on the freezing/relaxation behaviour of vortices. Elastic softening through T c in zero field can be understood in terms of classical coupling of the order parameter with the shear strain e 6, λe 6 [Formula: see text], which means that there must be a common strain mechanism for coupling of the form λ [Formula: see text] Q E. At fields of ~5 T and above, this softening is masked by Debye-like stiffening and acoustic loss processes due to vortex freezing. The first loss peak may be associated with the establishment of superconductivity on ferroelastic twin walls ahead of the matrix and the second is due to the vortex liquid-vortex glass transition. Strain contrast between vortex cores and the superconducting matrix will contribute significantly to interactions of vortices both with each other and with the underlying crystal structure. These interactions imply that iron-pnictides represent a class of multiferroic superconductors in which strain-mediated coupling occurs between the multiferroic properties (ferroelasticity, antiferromagnetism) and superconductivity.

Elastic and anelastic relaxation behaviour of perovskite multiferroics II: PbZr0.53Ti0.47O3 (PZT)-PbFe0.5Ta0.5O3 (PFT).

Elastic and anelastic properties of ceramic samples of multiferroic perovskites with nominal compositions across the binary join PbZr0.53Ti0.47O3-PbFe0.5Ta0.5O3 (PZT-PFT) have been assembled to create a binary phase diagram and to address the role of strain relaxation associated with their phase transitions. Structural relationships are similar to those observed previously for PbZr0.53Ti0.47O3-PbFe0.5Nb0.5O3 (PZT-PFN), but the magnitude of the tetragonal shear strain associated with the ferroelectric order parameter appears to be much smaller. This leads to relaxor character for the development of ferroelectric properties in the end member PbFe0.5Ta0.5O3. As for PZT-PFN, there appear to be two discrete instabilities rather than simply a reorientation of the electric dipole in the transition sequence cubic-tetragonal-monoclinic, and the second transition has characteristics typical of an improper ferroelastic. At intermediate compositions, the ferroelastic microstructure has strain heterogeneities on a mesoscopic length scale and, probably, also on a microscopic scale. This results in a wide anelastic freezing interval for strain-related defects rather than the freezing of discrete twin walls that would occur in a conventional ferroelastic material. In PFT, however, the acoustic loss behaviour more nearly resembles that due to freezing of conventional ferroelastic twin walls. Precursor softening of the shear modulus in both PFT and PFN does not fit with a Vogel-Fulcher description, but in PFT there is a temperature interval where the softening conforms to a power law suggestive of the role of fluctuations of the order parameter with dispersion along one branch of the Brillouin zone. Magnetic ordering appears to be coupled only weakly with a volume strain and not with shear strain but, as with multiferroic PZT-PFN perovskites, takes place within crystals which have significant strain heterogeneities on different length scales.

Strain behavior and lattice dynamics in Ni50Mn35In15.

The lattice dynamics in the polycrystalline shape-memory Heusler alloy Ni50Mn35In15 have been studied by means of resonant ultrasound spectroscopy (RUS). RUS spectra were collected in a frequency range 100-1200 kHz between 10 and 350 K. Ni50Mn35In15 exhibits a ferromagnetic transition at 313 K in the austenite phase and a martensitic transition at 248 K accompanied by a change of the magnetic state. Furthermore it displays a paramagnetic to ferrimagnetic transition within the martensitic phase. We determined the temperature dependence of the shear modulus and the acoustic attenuation of Ni50Mn35In15 and compared it with magnetization data. Following the structural softening, which accompanies the martensitic transition as a pretransitional phenomenon, a strong stiffening of the lattice is observed at the martensitic magneto-structural transition. Only a weak magnetoelastic coupling is evidenced at the Curie temperatures both in austenite and martensite phases. The large acoustic damping in the martensitic phase compared with the austenitic phase reflects the motion of the twin walls, which freezes out in the low temperature region.

Elastic and magnetoelastic relaxation behaviour of multiferroic (ferromagnetic + ferroelectric + ferroelastic) Pb(Fe0.5Nb0.5)O3 perovskite.

Resonant Ultrasound Spectroscopy has been used to characterize elastic and anelastic anomalies in a polycrystalline sample of multiferroic Pb(Fe(0.5)Nb(0.5))O(3) (PFN). Elastic softening begins at ~550 K, which is close to the Burns temperature marking the development of dynamical polar nanoregions. A small increase in acoustic loss at ~425 K coincides with the value of T(*) reported for polar nanoregions starting to acquire a static or quasi-static component. Softening of the shear modulus by ~30-35% through ~395-320 K, together with a peak in acoustic loss, is due to classical strain/order parameter coupling through the cubic → tetragonal → monoclinic transition sequence of ferroelectric/ferroelastic transitions. A plateau of high acoustic loss below ~320 K is due to the mobility under stress of a ferroelastic microstructure but, instead of the typical effects of freezing of twin wall motion at some low temperature, there is a steady decrease in loss and increase in elastic stiffness below ~85 K. This is attributed to freezing of a succession of strain-coupled defects with a range of relaxation times and is consistent with a report in the literature that PFN develops a tweed microstructure over a wide temperature interval. No overt anomaly was observed near the expected Néel point, ~145 K, consistent with weak/absent spin/lattice coupling but heat capacity measurements showed that the antiferromagnetic transition is actually smeared out or suppressed. Instead, the sample is weakly ferromagnetic up to ~560 K, though it has not been possible to exclude definitively the possibility that this could be due to some magnetic impurity. Overall, evidence from the RUS data is of a permeating influence of static and dynamic strain relaxation effects which are attributed to local strain heterogeneity on a mesoscopic length scale. These, in turn, must have a role in determining the magnetic properties and multiferroic character of PFN.