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Register a new userA spin glass perspective on ferroic glasses
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David Sherrington
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A range of ferroic glasses, magnetic, polar, relaxor and strain glasses, are considered together from the perspective of spin glasses. Simple mathematical modelling is shown to provide a possible conceptual unification to back similarities of experimental observations, without considering all possible complexities and alternatives.
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As well as several different kinds of periodically ordered ferroic phases, there are now recognized several different examples of ferroic glassiness, although not always described as such and in material fields of study that have mostly been developed separately. In this chapter an attempt is made to indicate common conceptual origins and features, observed or anticipated. Throughout, this aim is pursued through the use of simple models, in an attempt to determine probable fundamental origins within a larger picture of greater complication, and analogies between systems in different areas, both experimental and theoretical, in the light of significant progress in spin glass understanding.
An argument that relaxor ferroelectricity in the isovalent alloy $mathrm {Ba(Zr}_{1-x}mathrm{Ti}_{x})mathrm{O}_3$ can be understood as an induced moment soft pseudo-spin glass on the B-ions of the $mathrm{ABO}_{3}$ matrix is extended to the experimentally paradigmic but theoretically more complex heterovalent relaxor $mathrm {Pb(Mg}_{1/3}mathrm{Nb}_{2/3}mathrm{)O}_3$ (PMN). It is argued that interesting behaviour of the onset of non-ergodicity, frequency-dependent susceptibility peaks and precursor nanodomains can be understood from analagous considerations of the B-ions, with the displacements of the Pb ions a largely independent, but distracting, side-feature. This contrasts with conventional conceptualizations.
Extensive experimental and numerical studies of the non-equilibrium dynamics of spin glasses subjected to temperature or bond perturbations have been performed to investigate chaos and memory effects in selected spin glass systems. Temperature shift and cycling experiments were performed on the strongly anisotropic Ising-like system {ising} and the weakly anisotropic Heisenberg-like system {AgMn}, while bond shift and cycling simulations were carried out on a 4 dimensional Ising Edwards-Anderson spin glass. These spin glass systems display qualitatively the same characteristic features and the observed memory phenomena are found to be consistent with predictions from the ghost domain scenario of the droplet scaling model.
Motivated by the mean field prediction of a Gardner phase transition between a normal glass and a marginally stable glass, we investigate the off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used as a model for colloidal or granular glasses. Deep inside the glass phase, we find that a sharp crossover pressure $P_{rm G}$ separates two distinct dynamical regimes. For pressure $P < P_{rm G}$, the glass behaves as a normal solid, displaying fast dynamics that quickly equilibrates within the glass free energy basin. For $P>P_{rm G}$, instead, the dynamics becomes strongly anomalous, displaying very large equilibration time scales, aging, and a constantly increasing dynamical susceptibility. The crossover at $P_{rm G}$ is strongly reminiscent of the one observed in three-dimensional spin-glasses in an external field, suggesting that the two systems could be in the same universality class, consistently with theoretical expectations.
The design of multi-functional BMGs is limited by the lack of a quantitative understanding of the variables that control the glass-forming ability (GFA) of alloys. Both geometric frustration (e.g. differences in atomic radii) and energetic frustration (e.g. differences in the cohesive energies of the atomic species) contribute to the GFA. We perform molecular dynamics simulations of binary Lennard-Jones mixtures with only energetic frustration. We show that there is little correlation between the heat of mixing and critical cooling rate $R_c$, below which the system crystallizes, except that $Delta H_{rm mix} < 0$. By removing the effects of geometric frustration, we show strong correlations between $R_c$ and the variables $epsilon_- = (epsilon_{BB}-epsilon_{AA})/(epsilon_{AA}+epsilon_{BB})$ and ${overline epsilon}_{AB} = 2epsilon_{AB}/(epsilon_{AA}+epsilon_{BB})$, where $epsilon_{AA}$ and $epsilon_{BB}$ are the cohesive energies of atoms $A$ and $B$ and $epsilon_{AB}$ is the pair interaction between $A$ and $B$ atoms. We identify a particular $f_B$-dependent combination of $epsilon_-$ and ${overline epsilon}_{AB}$ that collapses the data for $R_c$ over nearly $4$ orders of magnitude in cooling rate.
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