A Lattice Litany for Transition Metal Oxides
Abstract
:1. Introduction
- (i)
- Structural phase transitionsNeutron and X-ray scattering in the 1970s were beginning to have sufficient resolution to suggest two low-frequency scattering components as the structural phase transition was approached: “central peaks” and ”soft modes.” Alex recognized the need for judicious experiments to probe different timescales [1] and was thereby able to separate phonon oscillations from slow cluster dynamics. This was powerful input to theory and simulation attempting to distinguish mean-field self-consistent phonon approximations from true critical behavior in double-well Landau–Ginzburg phase-transition theories. Advanced time-resolved experiments have now become essential tools in all classes of coupled charge–lattice–spin–orbital materials, including TMOs.
- (ii)
- Precursor StructureLocal structure measurements and inferences of the 1970/80s had relatively poor resolution (spectroscopy, NMR, diffuse scattering, etc.). However, Alex used them [1] to suggest that local distortions appear as precursor structure as Tc is approached in ferroelectric TMOs. Importantly, he showed that these precursors onset at temperatures significantly beyond critical regimes above and below Tc, and are tunable with strain, electric fields, etc. Fifty years later, I can suggest that many of these properties in TMOs and related materials are elastic microstructures. Indeed, as I discuss below, tuning phases and functions through elasticity is now emerging as an important focus in quantum materials [2].
- (ii)
- Quantum ParaelectricityUnlike, e.g., BaTiO3, SrTiO3 does not undergo a ferroelectric phase transition, but one can be induced with appropriate doping or pressure (strain). Alex understood the importance of this and advocated the concept of quantum tunneling between orientations (e.g., octahedral orientations), which had to be frozen out to stabilize a permanent ferroelectric state. He and others created the term “quantum paraelectric” to describe this situation and designed elegant experiments to probe the dynamics [2,3]. This concept now has many diverse analogs, including the internal dynamics of small polarons (below) and excitons, Kondo spin singlets, dynamic magnetism in Pu, and concepts for computational qubits such as Josephson junctions.
2. TMOs and Their Lattice
- Although the d-orbital (and even more so, the f-orbital) is indeed electronically localized, resulting in localization–delocalization electronic competition, it is also highly directional. This results in symmetry constrained unit cell structural distortions and a “network” competition for ground and metastable structural patterns (multiscale “landscapes”). This is not the case for extended and symmetrical (e.g., s) orbital materials, where dynamic screening dominates. The constraints are the origin of measured strongly anisotropic elastic constants in these materials, with intrinsically coupled configuration scales from unit cell to long-range, optic to acoustic—and hence high tunability by both local and global perturbations (doping, pressure, external fields).
- Neglecting or “integrating out” the oxygen degrees of freedom in TMOs and related materials is a significant over-simplification for many properties. The O polarizability and metal–O charge transfer (and associated bond length/buckling/rotation changes) must be treated explicitly [5]. Pioneers such as Heinz Bilz (Alex’s professional peer and colleague) appreciated this by augmenting “shell models” of the TMO electronic structure to capture effects of M–O charge transfer and polarizability [6]. We return to such “nonlinear shell models” below, including a successful prediction of the observed quantum paraelectric to ferroelectric transition in O18-doped SrTiO3.
- The electron–lattice coupling strength is typically not weak in TMOs. It may appear so if measured by conventional spatial averaging techniques. However, because of the delicate energy balances affecting electronic/magnetic orders, even rather weak average electron–lattice coupling can dominate globally and locally. We illustrate this with examples below. In addition, exotic (e.g., topological) singularities are usually energetically costly, and nature avoids or smooths them by engaging additional weaker degrees of freedom—as in dislocations, vortices, superconducting flux line cores, etc. Even when the globally averaged el-lattice strength is weak, it can be locally strong around dopants and defects. The formation of small (coupled spin–charge–lattice) polarons is an important example that we return to below. A finite densities of such polarons can order into secondary mesoscopic patterns (clumps, stripes, filaments, checkerboard phases, etc.) because of the long-range, directional elasticity noted above. Small polaron center-of-mass dynamics is very slow (because of Peierls–Nabarro lattice pinning), but unless dissipation is strong, their internal dynamics is a fundamental quantum tunneling property, and the internal charge oscillation is necessarily accompanied by non-adiabatic lattice (e.g., bond–length), and sometimes spin, oscillation. This coupled charge–lattice dynamics is familiar elsewhere, including quantum chemistry (e.g., [7]), “macroscopic quantum tunneling” [8], and perhaps also in the context of quantum paraelectric tunneling [9].
- Lattice anharmonicity is typically important in TMOs and assuming linear lattice dynamics is incomplete. Anharmonicity is the result of slaving among lattice, electronic, and magnetic degrees of freedom, proximity to a structural phase transition, impurities, interfaces, surfaces, etc. The M–O charge transfer is a particularly important source of nonlinear lattice dynamics. Among many interesting emergence and complexity consequences are multi-phonon bound states (“intrinsic local modes,” ILMs). Modern neutron scattering has indeed resolved modes outside linear phonon bands and attributed them to ILMs (e.g., [10]). Below, we will introduce ILMs embedded self-consistently in a sea of extended modes as a description of, e.g., relaxor ferroelectrics.
3. Small Polarons, Filamentary Landscapes, and Local Modes
4. Elasticity and Short–Long-Range Competitions
5. Hybridized Bands and more examples of Short–Long-Range Competitions
6. Conclusions and Discussion
- I have deliberately emphasized lattice, including elastic, effects in TMOs (and related d- and f- orbital materials) because these have often been under-represented in research on “strongly correlated” quantum matter. The recent workshop [2] is an encouraging community step. However, clearly, it remains to be understood when lattice, spin, charge, and orbital degrees of freedom individually dominate and then the others are slaved. There are likely to be classes of materials that should be so categorized in this fascinating collusion among degrees of freedom. This is a quantum mechanical adiabaticity question that must be addressed on appropriate spatial and temporal scales and, as with the importance of el–lattice coupling, not simply in terms of average properties. Functionality through charge, spin, and lattice at active interfaces, including between TMOs, is an important direction for applications (e.g., perovskite-based solar cells and detectors) [45,72]. Similarly, domain boundary engineering, e.g., in multiferroic materials [73], is a very attractive direction.
- The recent emphasis on quantum entanglement and the increasing recognition of geometry and topology in electronic and magnetic materials research raises important questions. For instance, (1) above in the context of when does the lattice simply renormalize parameters for quantum phases and when do topological lattice configurations act as the driving template for quantum mechanics? For example, this is an important issue in materials design for qubits and quantum information research.
- I have not focused here on high-temperature (HTC) mechanisms. The wonderful discovery of HTC in cuprates by Bednorz and Müller certainly propelled remarkable advances in synthesis, experimental, theoretical and simulation capabilities for complex electronic materials and whole new classes of materials have benefitted: multilayer TMOs [45], Dirac–Weyl materials, organic and heavy-fermions SCs, pnictides, multiferroics, over-doped HTC cuprates [74], etc. After these many years, a generally accepted theory of HTC remains elusive. Which of the multitude of measured perovskite features are directly relevant to the superconductivity mechanism has yet to be understood. However, much research falls into the framework of multiscale, coexisting charge-rich and charge-poor regions [29,75]. Inhomogeneous superconductivity is familiar, e.g., in granular superconductors. However, the possibility of inhomogeneity being an intrinsic template for the SC mechanism. For example, Reference [76] proposes micro (i.e., bond-length) strain (cf, Section 4) as a primary control parameter in cuprate SCs. The polaron patterns discussed above are also examples: precursors to CDWs and equilibria with multi-polaron (including bi-polaron) bound states. Such CDW-like phases embedded in various undoped broken-symmetry hosts are attractive scenarios, but the AF broken-symmetry host state is not unique. Rather, the main issue becomes: How do the charge-rich regions communicate? Magnetic, charge, and elastic fluctuations are all feasible [77]. There is accumulating evidence [29] for a checkerboard period-4 CDW-like configuration in cuprates. Various small perturbations can isolate such a specific periodicity for the ordering illustrated in Section 5 (e.g., [68]). However, qualitatively different origins are also interesting (e.g., [78]). The charge-transfer (polarizability) features of perovskites we have discussed lend themselves to W.A. Little’s scenario of enhanced SC from off-chain/plane polarizable material [79,80]. Finally, an intriguing consideration is that (correlated) percolating charged filaments organize fractally as doping increases, before finally over-packing and quantum melting. This would certainly be the optimal space filling to maximize percolating filamentary properties if those properties are desirable—e.g., for high Tc, as suggested for many years by J.C. Phillips [81].
Funding
Acknowledgments
Conflicts of Interest
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Bishop, A.R. A Lattice Litany for Transition Metal Oxides. Condens. Matter 2020, 5, 46. https://doi.org/10.3390/condmat5030046
Bishop AR. A Lattice Litany for Transition Metal Oxides. Condensed Matter. 2020; 5(3):46. https://doi.org/10.3390/condmat5030046
Chicago/Turabian StyleBishop, Alan R. 2020. "A Lattice Litany for Transition Metal Oxides" Condensed Matter 5, no. 3: 46. https://doi.org/10.3390/condmat5030046
APA StyleBishop, A. R. (2020). A Lattice Litany for Transition Metal Oxides. Condensed Matter, 5(3), 46. https://doi.org/10.3390/condmat5030046