How polaron dynamics control the magnitude of colossal magnetoresistance in ferromagnetic manganites

Maschek et al. (Phys. Rev. B 93, 045112 (2016)) showed that La $_{0.7}$ Sr $_{0.3}$ MnO $_{3}$ , the prototypical weakly magnetoresistive ferromagnetic manganite, is in fact a polaronic metal hosting dynamic CE-type polarons with lifetime $\tau\approx 1$ ps, and proposed that the strength of colossal magnetoresistance (CMR) scales with the inverse polaron lifetime rather than with electron-phonon coupling strength. The open problem posed by that work, still unresolved after a decade of follow-up studies, is to determine quantitatively how polaron dynamics control CMR: (i) a systematic, quantitative comparison of quasielastic polaron scattering - energy-integrated intensity, lifetime, and correlation length - across manganite compounds spanning the range of CMR magnitudes, including establishing whether La $_{0.7}$ Ca $_{0.3}$ MnO $_{3}$ possesses a polaronic-metallic ground state at low temperature; (ii) realistic theories of polaron dynamics incorporating temporal and spatial fluctuations that reproduce the measured scattering observables and predict whether, and if so how, polaron mobility (and the other candidate polaron quantities) controls magnetoresistance; and (iii) a quantitative account of whether phase separation and percolation of charge-ordered regions explain the sudden increase of quasielastic intensity at the Curie temperature. Follow-up work (2018-2026) tested the proposed lifetime-CMR correlation within the La $_{1-x}$ Sr $_{x}$ MnO $_{3}$ family, compared La $_{0.7}$ Ca $_{0.3}$ MnO $_{3}$ with LSMO near $T_C$ , produced first Langevin-dynamics theories of quasielastic spectral weight, and reframed the controlling quantity as a distortion diffusion rate - but none of the three linked questions is resolved.

Background

Colossal magnetoresistive (CMR) manganites are perovskite oxides La $_{1-x}$ A $_{x}$ MnO $_{3}$ (A = Ca, Sr, Ba) in which a ferromagnetic metallic ground state gives way, on warming, to a paramagnetic phase; near the Curie temperature $T_C$ an applied magnetic field lowers the resistivity dramatically - by roughly a factor of 10 in Sr-doped compounds and up to 1000-fold in Ca-doped ones. The carriers are $e_g$ electrons moving between mixed-valent Mn $^{3+}$ (Jahn-Teller active, with one $e_g$ electron) and Mn $^{4+}$ sites. 'Double exchange' (Zener's mechanism, whereby $e_g$ electron hopping is favored by ferromagnetic alignment of the Mn spins) explains the metallic ferromagnetism, but Millis, Littlewood, and Shraiman showed it cannot by itself explain the large resistivity above $T_C$ ; the standard theory of Millis, Shraiman, and Mueller attributes the excess resistivity to the dynamic Jahn-Teller (JT) effect - coupling of the $e_g$ electron to Mn-O bond distortions - so that the amplitude of the lattice distortion controls how strongly resistivity rises above $T_C$ , and compounds with stronger electron-phonon coupling (EPC) should show larger magnetoresistance.

A polaron is a charge carrier together with its self-induced lattice distortion; in manganites the relevant distortions are local JT oxygen displacements, and short-range polaron correlations occur at the wave vector $\mathbf{q}_{CE}\approx (1/4,1/4,0)$ (pseudocubic notation) characteristic of 'CE-type' charge-and-orbital order, the canonical Mn $^{3+}$ /Mn $^{4+}$ arrangement of half-doped manganites. In inelastic neutron scattering (INS) and inelastic x-ray scattering (IXS), dynamic polarons produce a quasielastic (QE) response: a Lorentzian centered at zero energy transfer whose energy half-width $\Gamma$ gives the polaron lifetime $\tau=\hbar/\Gamma$ and whose momentum width gives the inverse spatial correlation length $\xi$ .

Because La $_{0.7}$ Sr $_{0.3}$ MnO $_{3}$ (LSMO) has the highest $T_C\approx 350$ K of these compounds but only modest magnetoresistance, it was long treated as an almost pure double-exchange metal with weak electron-lattice coupling. Diffuse scattering then revealed large lattice distortions at $T_C$ (Weber et al., 2013), and Maschek et al. (2016), combining INS and IXS, found LSMO to be a 'polaronic metal': transverse acoustic phonons soften and broaden strongly on heating through $T_C$ , and a QE component from dynamic CE-type polarons with $\tau\approx 1$ ps appears already in the ferromagnetic phase between about 200 K and $T_C$ and is strongly enhanced above $T_C$ , while the resistivity stays metallic. Comparing with the layered manganite La $_{1.2}$ Sr $_{1.8}$ Mn $_{2}$ O $_{7}$ - which has a polaron-metallic ground state and roughly a hundred times stronger magnetoresistance - the authors proposed that the strength of magnetoresistance scales with the inverse polaron lifetime, i.e. with polaron mobility, not with the strength of EPC. In La $_{0.7}$ Ca $_{0.3}$ MnO $_{3}$ (LCMO), by contrast, the paramagnetic phase above $T_C$ is a polaronic insulator with static polarons; short-range polaron correlations are known to persist into its ferromagnetic phase (Dai et al., 2000; Zhang et al., 2001), yet whether its low-temperature ground state is polaronic-metallic was, in the source paper, 'not established or ruled out'.

The source paper explicitly leaves open: (i) a systematic quantitative comparison of polaron scattering intensity and dynamics across different manganites and how the differences correlate with the magnitude of CMR; (ii) whether LCMO possesses a polaronic-metallic ground state at low temperature; and (iii) realistic theories of polaron dynamics including temporal (lifetime) and spatial (correlation length) fluctuations that predict how polaron mobility controls magnetoresistance, going beyond existing theories that emphasize static distortion amplitudes; and it advances, in its discussion and without quantitative demonstration, the related interpretation (iv) that phase-separation scenarios - coexisting charge-ordered and ferromagnetic metallic domains, with nucleation and percolation at $T_C$ - account for the observed sudden increase of QE intensity at $T_C$ .

Problem Statement

Determine, quantitatively and across the CMR manganite family, how polaron dynamics control the magnitude of colossal magnetoresistance. The source paper (Maschek et al., Phys. Rev. B 93, 045112 (2016)) explicitly leaves three linked questions open for future work and, in its discussion, advances a phase-separation/percolation interpretation of the sharp quasielastic intensity increase at $T_C$ without testing it quantitatively; these four linked items jointly serve one scientific objective and are consolidated here into three deliverables (with the La $_{0.7}$ Ca $_{0.3}$ MnO $_{3}$ ground-state question folded into the cross-compound benchmark):

Cross-compound scattering benchmark. Establish, under comparable conditions and with energy and momentum resolution sufficient to extract them, the energy-integrated quasielastic intensity, the lifetime $\tau$ , and the correlation length $\xi$ of CE-type polaron correlations as functions of temperature through $T_C$ , in manganite compounds spanning the range of CMR magnitudes - from weakly magnetoresistive La $_{1-x}$ Sr $_{x}$ MnO $_{3}$ to strongly magnetoresistive La $_{1-x}$ Ca $_{x}$ MnO $_{3}$ and the layered La $_{1.2}$ Sr $_{1.8}$ Mn $_{2}$ O $_{7}$ - and establish which of these observables, if any, correlates with the magnitude of CMR. The comparison is built from the resolved values reported in the cited literature - the La $_{1-x}$ Sr $_{x}$ MnO $_{3}$ ( $x = 0.2, 0.3$ ) comparison (ref. 2), the La $_{0.7}$ Ca $_{0.3}$ MnO $_{3}$ -versus-La $_{0.7}$ Sr $_{0.3}$ MnO $_{3}$ comparison (ref. 3), and the layered La $_{1.2}$ Sr $_{1.8}$ Mn $_{2}$ O $_{7}$ study (ref. 7) - together with, for the compounds whose polar lifetimes remain resolution-limited, the measurement that would resolve them. A necessary constituent is determining whether La $_{0.7}$ Ca $_{0.3}$ MnO $_{3}$ possesses a polaronic-metallic ground state at low temperature, which the source states has 'not been established or ruled out'.
Realistic dynamical theory. Develop models of polaron dynamics that include temporal (lifetime/diffusion) and spatial (correlation-length) fluctuations, reproduce the measured dynamical observables ( $\tau$ , $\xi$ , QE intensity, and their temperature dependences), and predict whether, and if so how, polaron mobility (and the other candidate polaron quantities) controls magnetoresistance - going beyond existing theories that emphasize static distortion amplitudes.
Mechanism of the $T_C$ anomaly. Clarify quantitatively whether phase-separation scenarios - coexisting charge-ordered and ferromagnetic metallic domains, with nucleation and percolation of charge-ordered regions at $T_C$ - account for the observed sudden increase of QE intensity at $T_C$ , or whether another mechanism (such as the onset of cooperative diffusive motion of quasistatic lattice distortions proposed by later work) is responsible.

Deliverables 1 and 3 supply the phenomenological benchmark and the transition-mechanism test that any account of CMR must satisfy; deliverable 2 is the theoretical account that must reproduce them and predict transport. All three deliverables are jointly required: a complete answer identifies and quantifies the polaron quantity that controls the magnitude of CMR - if such a quantity exists, otherwise it establishes and explains the absence of such a correlation - and resolves the mechanism of the sudden increase of quasielastic intensity at $T_C$ , supported jointly by the cross-compound data and by a model validated against both scattering and transport measurements.

References

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