Microscopic origin of dimensionality-dependent ultrafast polaron redressing in perovskite versus layered manganites

In ultrafast optical pump-probe experiments on paramagnetic manganites, the sub-picosecond recovery of the transient reflectivity is the redressing of a photoexcited carrier into its Jahn-Teller polaronic ground state. Measurements on the 3D perovskite La $_{0.7}$ Ca $_{0.3}$ MnO $_3$ and the quasi-2D Ruddlesden-Popper bilayer (a layered perovskite) La $_{1.4}$ Sr $_{1.6}$ Mn $_2$ O $_7$ find that this redressing is slower in the quasi-2D compound — the opposite of what finite-phonon-mass Holstein-polaron theory predicts — and the microscopic origin (layered crystal-field $e_g$ splitting, quantum confinement, modified lattice dynamics, or in-plane short-range ferromagnetic spin correlations above $T_C$ ) remains undetermined. The problem is to construct a dimension-sensitive microscopic dynamical model that couples Jahn-Teller/Holstein polaron energetics with fully dynamical (finite-phonon-mass) lattice degrees of freedom and spin-dependent double-exchange hopping, quantitatively reproduces the measured temperature-dependent relaxation time $\tau(T)$ of both compounds in the paramagnetic insulating phase, and identifies the dominant mechanism of the dimensionality dependence.

Background

Colossal-magnetoresistance (CMR) manganites — mixed-valence manganese oxides such as La $_{0.7}$ Ca $_{0.3}$ MnO $_3$ — owe their physics to the interplay of three ingredients. Double exchange is the ferromagnetic transport mechanism: an $e_g$ electron hops between Mn ions with an amplitude $t_{ij}=t\cos(\theta_{ij}/2)$ set by the angle between neighboring local $t_{2g}$ core spins, which are tied to the itinerant electron's spin by Hund's-rule coupling. The Jahn-Teller (JT) effect is the coupling of the Mn $^{3+}$ $e_g$ orbital degeneracy to distortions of the surrounding MnO $_6$ oxygen octahedron. Their combination produces polarons: quasiparticles in which the charge carrier is self-trapped by the lattice distortion it induces. Above the Curie temperature $T_C$ , CMR manganites are paramagnetic insulators whose carriers form small JT polarons; below $T_C$ double exchange prevails and the compound becomes a ferromagnetic metal.

In an ultrafast optical pump-probe experiment, a femtosecond laser pulse momentarily liberates a carrier from its polaronic self-trapping and a delayed probe pulse monitors the transient reflectivity. The sub-picosecond recovery observed above $T_C$ is attributed to polaron redressing: the relaxation of the photoexcited electron back into its polaronic ground state with phonon emission. This is a direct dynamical probe of the electron-phonon coupling that static probes (transport, neutron/x-ray diffuse scattering, optical conductivity) infer only indirectly.

J. Lee et al. (2016) compared $\tau(T)$ in 3D perovskite La $_{0.7}$ Ca $_{0.3}$ MnO $_3$ (LCMO; $T_C\approx 250$ K) and the quasi-2D bilayer La $_{1.4}$ Sr $_{1.6}$ Mn $_2$ O $_7$ (bilayered LSMO; 3D ordering at $T_C\approx 90$ K), the latter consisting of MnO $_2$ bilayers separated by insulating (La,Sr) $_2$ O $_2$ rock-salt blocks so that the electronic structure is quasi-two-dimensional. The key observation is that redressing is slower in the quasi-2D compound throughout the paramagnetic phase. This contradicts the standard microscopic picture. In the Emin-Holstein adiabatic scaling of the polaron energy — an approximation to the Holstein model, the minimal model of a charge carrier coupled locally to optical phonons, that treats the lattice as static (zero phonon mass) — with $E(R)=T_e/R^2 - V_S^{int}/(2R^d)$ for a polaron of radius $R$ in $d$ dimensions, no 2D bound state exists at all; and the refined calculation of Ku, Trugman and Bonča (Phys. Rev. B 65, 174306 (2002)), which includes a finite phonon mass, shows that a 2D polaronic bound state does exist but carries a smaller energy barrier between polaronic and free-electron ground states than in 3D, so the 2D redressing time was expected to be shorter. The authors discuss two candidate resolutions: in-plane short-range ferromagnetic correlations that persist well above $T_C$ in the bilayer (a magnetization plateau between 90 and 250 K, and neutron pair-distribution-function evidence — scattering measurements of instantaneous interatomic distances — for double-exchange processes far above the 3D ordering temperature), and the crystal-field splitting of the $e_g$ levels by the lower symmetry of the layered structure, which competes with JT splitting and was neglected in their analysis. They state that a full treatment of lower-dimensionality effects — quantum confinement and crystal-field changes — is beyond the scope of their paper, call for the same measurements on thin-film manganites, and conclude that a new model is needed in which the polaron redressing time is governed by the dimensionality of the electronic structure and the presence of spin correlations above $T_C$ . A fully quantitative account of this process is still missing: existing exact treatments of polaron formation and relaxation dynamics (Ku and Trugman, Phys. Rev. B 75, 014307 (2007); Golež, Bonča, Vidmar and Trugman, Phys. Rev. Lett. 109, 236402 (2012)) solve the spinless single-polaron Holstein problem and do not include double-exchange spin physics, layered crystal fields, or a comparison to the measured manganite $\tau(T)$ .

Problem Statement

Construct a predictive, dimension-sensitive microscopic dynamical model of polaron redressing in manganites — coupling Jahn-Teller/Holstein polaron energetics with a fully dynamical (finite-phonon-mass) lattice, spin-dependent double-exchange hopping $t_{ij}=t\cos(\theta_{ij}/2)$ , the layered-structure crystal-field splitting of the $e_g$ levels, and short-range in-plane ferromagnetic spin correlations above $T_C$ — and use it to determine the microscopic origin of the observed slower polaron redressing (apparently stronger electron-phonon coupling) in quasi-2D La $_{1.4}$ Sr $_{1.6}$ Mn $_2$ O $_7$ relative to 3D La $_{0.7}$ Ca $_{0.3}$ MnO $_3$ . The model must quantitatively reproduce the measured temperature-dependent sub-picosecond relaxation time $\tau(T)$ of both compounds in the paramagnetic insulating phase, and its mechanism conclusion — identifying which ingredient(s) among crystal-field $e_g$ splitting, quantum confinement, modified lattice dynamics, and spin correlations above $T_C$ dominate the dimensionality dependence — must be testable against targeted experiments such as probe-photon-energy-dependent, thin-film, or spin-correlation-controlled ultrafast measurements.

References

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