Elastic relaxations associated with the Pm\bar 3 m –R\bar 3 c transition in LaAlO₃: II. Mechanisms of static and dynamical softening

Abstract

Brillouin spectra have been collected in situ at temperatures up to ∼1000 K for different crystallographic directions from two single crystal plates of LaAlO(3) perovskite. Elastic moduli derived from these, together with heat capacity, spontaneous strain and Raman data from the literature, have then been used to calibrate the coefficients in a classical Landau free energy expansion for the second order [Formula: see text] phase transition at T(c) = 817 K. The static strain/order parameter coupling model provides a quantitative description of elastic softening between room temperature and ∼700 K, but from ∼700 K up to T(c) additional elastic softening correlates with the development of a central peak in the Brillouin spectra. The presence of quasi-elastic scattering, which reaches maximum intensity ∼5-15 K below T(c), implies a strong dynamical component to the phase transition. Relaxation times estimated from the width of the central peak are of the order of ∼10-100 ps and appear to be more or less constant between ∼700 and 800 K, which is consistent with an intrinsic origin associated with phonon density fluctuations. Central peak width variations and an irregular pattern of acoustic velocity variations in a 20 K temperature interval below T(c) are interpreted in terms of flipping of clusters of tilted octahedra between different ⟨111⟩, ⟨011⟩ and ⟨001⟩ tilt axes. The additional softening beyond that expected from the classical strain/order parameter coupling model can be understood in terms of coupling of acoustic modes with the central peak mode(s).

Multiferroic (ferroelastic/ferromagnetic/ferrimagnetic) aspects of phase transitions in RCo2Laves phases

“…[1,[27][28][29][30] and references therein). The coupling behaviour will still be correctly described and the general phenomenology will also be essentially the same, however, so generalities which follow from earlier work on displacive systems [23][24][25][26][31][32][33][34] still apply. If the excess free energy is dominated by the second-and fourth-order terms, such that the expansion can be truncated to exclude sixth-order terms, only the tetragonal and rhombohedral structures can be stable.…”

“…These relationships have the same form as for octahedral tilting transitions associated with the R point of the Brillouin zone of perovskites [23][24][25][26]. Solutions to (2) give the different possible equilibrium magnetic structures in table 1, which includes all possible combinations of the non-zero order parameter components.…”

“…For a tricritical transition the amount of softening is expected to reduce non-linearly with falling temperature. In SrTiO 3 , the symmetry-breaking shear strain reaches ∼0.001 and the softening of the shear modulus is ∼20% [23], while equivalent strains and softening values are up to ∼ − 0.003, ∼ − 0.002 and ∼40%, ∼25% for LaAlO 3 and SrZrO 3 , respectively [24,38,43]. Rather than reducing with falling temperature, as would be expected for classical order parameter relaxation in response to an induced strain, however, the amount of softening of the shear modulus of NdCo 2 increases with falling temperature.…”

“…This pattern and magnitude of softening is more reminiscent of superelastic softening due to displacement of ferroelastic twin walls, as seen in low frequency experiments on SrTiO 3 [44], KMn 1−x Ca x F 3 [45] and LaAlO 3 [46]. There are insufficient data available to quantify fully the extent of the intrinsic softening of individual shear elastic constants due to the strain/order parameter coupling in NdCo 2 , but smaller effects would generally be expected for magnetic ordering than for displacive transitions because the inverse susceptibility, χ −1 , scales approximately with the excess entropy, S, through the value of the Landau A coefficient (B/B * ≈ 1 in equation (6)), which Landau theory gives as S = − [23,24,47], in comparison with A∼11.5 J mol −1 K −1 expected for the simplest case of order/disorder where S = −R ln 2 at q = 1. On this basis, it has been assumed that the contribution of intrinsic effects to the observed softening of the shear modulus would be correspondingly smaller for NdCo 2 .…”

Elastic and anelastic relaxation behaviour of perovskite multiferroics I: PbZr0.53Ti0.47O3 (PZT)–PbFe0.5Nb0.5O3 (PFN)

“…These models have been tested for PZTFN6 but neither provides a quantitative fit to the precursor softening. Additional softening not due to classical strain/ order parameter coupling might alternatively be considered in terms of coupling of acoustic modes with a central peak mode, as seen, for example, below the cubic-rhombohedral octahedral tilting transition in LaAlO 3 [144]. A central peak mode has been seen in Brillouin spectra from single crystals of Pb(Zr 0.55 Ti 0.45 )O 3 and Pb(Zr 0.58 Ti 0.42 )O 3 by Kim et al [74] and has relaxation times in the range *1-3 ps.…”