Microscopic driving force and phase diagram of current-induced polaron melting and ordering in colossal-electroresistance manganites

In the narrow-bandwidth manganite Pr$_{1-x}$Ca$_x$MnO$_3$ (PCMO), electric current drives a disordering transition of a long-range-ordered Jahn–Teller-polaron solid directly observed by in-situ transmission electron microscopy (Jooss et al., PNAS 2007). The transition is not purely thermal — electric fields up to 10$^{10}$ V/m without current produce no disordering, and full reordering of the polaron solid requires reversal of the current sign — yet the microscopic driving force for the coherent motion of ordered-polaron domains at the onset of disordering has never been identified. Since 2007, subsequent work has attributed pulse-induced resistance changes to interfacial polaron localization, established oxygen-vacancy migration as a key defect-mediated switching channel, converged device-level modeling on valence-change mechanisms, and contested the Zener-polaron ground state itself via neutron spin-wave and resonant x-ray studies — but no work discriminates the thermal, non-thermal-current, and defect-mediated mechanisms behind the current-induced solid–liquid transition, and the cooperative polaron phase diagram beyond it (current-driven dynamic polaron ordering, and the connection to magnetic-field-induced colossal magnetoresistance) remains uncharacterized.

Background

Doped rare-earth manganites Re$_{1-x}$A$_x$MnO$_3$ (Re a rare-earth, A an alkaline-earth cation) are mixed-valence perovskite oxides famous for colossal magnetoresistance (CMR) — drops in electrical resistivity by orders of magnitude under a magnetic field. Their physics arises from a competition between the double-exchange interaction (ferromagnetic hopping of $e_g$ electrons — the conduction-active Mn $3d$ orbitals — between Mn$^{3+}$ and Mn$^{4+}$ sites, favored by parallel Mn spins) and the Jahn–Teller (JT) effect (a lattice distortion that lowers the energy of a degenerate electronic state by removing its symmetry), together with strong on-site Coulomb repulsion. When electron–lattice coupling dominates, a charge carrier can become self-trapped in the lattice distortion it induces; this composite excitation is a small polaron (an electron dressed by phonons, with a large effective mass and thermally activated hopping transport).

Near half doping ($x \approx 0.5$) many manganites form charge- and orbital-ordered insulating states. The classical Goodenough picture is the CE-type order, in which Mn$^{3+}$/Mn$^{4+}$ charges alternate in checkerboard fashion and the $e_g$ orbitals order in zigzag ferromagnetic chains. An alternative proposal by Daoud-Aladine et al. (Phys. Rev. Lett. 89, 097205 (2002)) based on neutron diffraction of Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ is the Zener polaron: instead of site-centered charges, an electron localizes on a Mn–O–Mn dimer, forming a ferromagnetic pair (a 'ferromagnetic dimer') embedded in an antiferromagnetic background. Whether half-doped manganites realize site-centered CE order, Zener polarons, or an intermediate dimerized state remains disputed (see below), and the distinction matters because Zener-polaron order breaks inversion symmetry and can be ferroelectric.

Pr$_{1-x}$Ca$_x$MnO$_3$ (PCMO) is a narrow-bandwidth manganite that stays insulating and charge-ordered over a wide doping range. Beyond CMR it exhibits colossal electroresistance (CER): its resistance changes by large factors under electric current or field, a property relevant to resistive random-access memory (RRAM) and memristive devices. Jooss, Wu, Beetz, Klie, Beleggia, Schofield, Schramm, Hoffmann and Zhu (Proc. Natl. Acad. Sci. USA 104, 13597 (2007)) combined high-resolution transmission electron microscopy (TEM), electron diffraction, Lorentz microscopy of electric domains, and in-situ transport with a piezo-controlled metal tip. They reported: (i) static long-range ordering of JT polarons forming a 'polaron solid' — a new charge- and orbital-ordered state with noncentrosymmetric (odd-parity) cooperative JT distortions, implying ferroelectricity coexisting with antiferromagnetic order (multiferroicity); and (ii) a current-induced polaron solid–liquid transition underlying the CER: at a threshold field $E_c \approx 0.5 \times 10^5$ V/m with applied current, the ordered superstructure first moves coherently through the crystal over seconds to minutes and then dissolves into a polaron-disordered phase, accompanied by a large drop of the polaron hopping activation barrier. Crucially, control experiments with fields up to $10^{10}$ V/m but zero current produced no change, ruling out a purely field-driven mechanism; and after current switch-off the ordered state does not spontaneously recover — a sign reversal of the current is required — ruling out a purely thermal (Joule-heating) mechanism, since latent-heat release would demand undercooling rather than reversed current. The transition persists over a remarkably wide window, $80\,\mathrm{K} \le T \le 300\,\mathrm{K}$ and $0.3 \le x \le 0.5$.

The paper's closing discussion states that these observations are only first steps toward a much richer cooperative polaron phase diagram, possibly including transitions from small self-trapped polarons to current-driven dynamic polaron ordering with long-range electron–lattice interaction, and that the current-induced polaron reorganization could be a clue to the magnetic-field-induced metallic state, where double exchange may enhance long-range electron–lattice coupling. Candidate non-thermal mechanisms for the transition include spin-transfer torque, carrier injection, and local electric-field gradients; later work added a further candidate, migration of oxygen vacancies under bias. One important development since 2007 is that the Zener-polaron interpretation of the ordered state itself has been contested: full spin-wave spectra of Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ (Ewings et al., Phys. Rev. B 94, 014405 (2016)) and of the bilayer Pr(Ca,Sr)$_2$Mn$_2$O$_7$ (Johnstone et al., Phys. Rev. Lett. 109, 237202 (2012)) are incompatible with strongly bound ferromagnetic dimers and favor CE-type coupling, while resonant x-ray scattering (García-Fernández et al., Phys. Rev. Lett. 103, 097205 (2009)), first-principles theory (Barone et al., Phys. Rev. B 83, 233103 (2011)), nanocrystalline PCMO multiferroicity (Shukla et al., Phys. Rev. B 90, 245126 (2014)), and the Jooss group's own microscopy and density-functional theory (DFT) calculations (Wu et al., Phys. Rev. B 76, 174210 (2007); Sotoudeh et al., Phys. Rev. B 95, 235150 (2017)) support or assume Zener-polaron-type order. This controversy postdates the 2007 paper and concerns the identification of the ordered phase whose current-induced melting and reordering is at issue; the mechanism question arises under either interpretation of the ordered phase.

Problem Statement

Identify the microscopic mechanism by which electric current drives the order–disorder transition of the long-range polaron-ordered (Zener-polaron-type charge- and orbital-ordered) state in Pr$_{1-x}$Ca$_x$MnO$_3$, and characterize the cooperative polaron phase diagram beyond the initially observed solid–liquid transition. Concretely: (i) determine the driving force for the coherent motion of the ordered-polaron domains at the onset of current-induced disordering — discriminating between Joule heating, specific non-thermal current effects (such as spin-transfer torque, carrier injection, or local electric-field gradients), and defect-mediated channels such as oxygen-vacancy migration — in a way that explains why electric field alone (up to $10^{10}$ V/m at zero current) produces no disordering while current flow at $E_c \approx 0.5\times10^5$ V/m does, and why full reordering of the polaron solid requires reversal of the current sign; and (ii) map the current–temperature–doping phase diagram of the cooperative polaron states across the observed window ($80\,\mathrm{K} \le T \le 300\,\mathrm{K}$, $0.3 \le x \le 0.5$), establishing whether current-driven dynamic polaron ordering with long-range electron–lattice interaction exists, and whether the same reorganization of Jahn–Teller modes underlies the magnetic-field-induced colossal magnetoresistance and how the double-exchange interaction modifies the polaron dynamics. The two parts are jointly required and belong to the same open problem: (i) is the central, narrowly posed sub-question, resolved by naming a specific driving force that accounts for both control-experiment constraints; (ii) extends it to the cooperative polaron phase diagram, which — because the existing data do not fix that diagram — is characterized as an explicit proposed phase diagram with its discriminating tests rather than as an experimentally established result. The structural controversy over the nature of the ordered phase — microscopy and DFT evidence supporting Zener-polaron-type ordering versus counter-evidence from neutron spin-wave and resonant x-ray studies (see Background) — postdates the source paper and is unresolved context for identifying the state whose melting is to be explained.

References

1. Ch. Jooss, L. Wu, T. Beetz, R. F. Klie, M. Beleggia, M. A. Schofield, S. Schramm, J. Hoffmann, Y. Zhu, 'Polaron melting and ordering as key mechanisms for colossal resistance effects in manganites', Proc. Natl. Acad. Sci. USA 104, 13597–13602 (2007). DOI: 10.1073/pnas.0702748104, https://doi.org/10.1073/pnas.0702748104
2. A. Daoud-Aladine, J. Rodríguez-Carvajal, L. Pinsard-Gaudart, M. T. Fernández-Díaz, A. Revcolevschi, 'Zener Polaron Ordering in Half-Doped Manganites', Phys. Rev. Lett. 89, 097205 (2002). DOI: 10.1103/PhysRevLett.89.097205, https://doi.org/10.1103/PhysRevLett.89.097205
3. Lijun Wu, R. F. Klie, Yimei Zhu, Ch. Jooss, 'Experimental confirmation of Zener-polaron-type charge and orbital ordering in Pr$_{1-x}$Ca$_x$MnO$_3$', Phys. Rev. B 76, 174210 (2007). DOI: 10.1103/PhysRevB.76.174210, https://doi.org/10.1103/PhysRevB.76.174210
4. Ch. Jooss, J. Hoffmann, J. Fladerer, M. Ehrhardt, T. Beetz, Lijun Wu, Yimei Zhu, 'Electric pulse induced resistance change effect in manganites due to polaron localization at the metal-oxide interfacial region', Phys. Rev. B 77, 132409 (2008). DOI: 10.1103/PhysRevB.77.132409, https://doi.org/10.1103/PhysRevB.77.132409
5. S. Schramm, J. Hoffmann, Ch. Jooss, 'Transport and ordering of polarons in CER manganites PrCaMnO', J. Phys.: Condens. Matter 20, 395231 (2008). DOI: 10.1088/0953-8984/20/39/395231, https://doi.org/10.1088/0953-8984/20/39/395231
6. M. García-Fernández, U. Staub, Y. Bodenthin, V. Scagnoli, V. Pomjakushin, S. W. Lovesey, A. Mirone, J. Herrero-Martín, C. Piamonteze, E. Pomjakushina, 'Orbital Order at Mn and O Sites and Absence of Zener Polaron Formation in Manganites', Phys. Rev. Lett. 103, 097205 (2009). DOI: 10.1103/PhysRevLett.103.097205, https://doi.org/10.1103/PhysRevLett.103.097205
7. Paolo Barone, Silvia Picozzi, Jeroen van den Brink, 'Buckling-induced Zener polaron instability in half-doped manganites', Phys. Rev. B 83, 233103 (2011). DOI: 10.1103/PhysRevB.83.233103, https://doi.org/10.1103/PhysRevB.83.233103 (arXiv:1103.4804)
8. Zhaoliang Liao, Peng Gao, Xuedong Bai, Dongmin Chen, Jiandi Zhang, 'Evidence for electric-field-driven migration and diffusion of oxygen vacancies in Pr$_{0.7}$Ca$_{0.3}$MnO$_3$', J. Appl. Phys. 111, 114506 (2012). DOI: 10.1063/1.4724333, https://doi.org/10.1063/1.4724333
9. G. E. Johnstone, T. G. Perring, O. Sikora, D. Prabhakaran, A. T. Boothroyd, 'Ground state in a half-doped manganite distinguished by neutron spectroscopy', Phys. Rev. Lett. 109, 237202 (2012). DOI: 10.1103/PhysRevLett.109.237202, https://doi.org/10.1103/PhysRevLett.109.237202 (arXiv:1210.7108)
10. M. Scherff, J. Hoffmann, B. Meyer, T. Danz, Ch. Jooss, 'Interplay of cross-plane polaronic transport and resistive switching in Pt–Pr$_{0.67}$Ca$_{0.33}$MnO$_3$–Pt heterostructures', New J. Phys. 15, 103008 (2013). DOI: 10.1088/1367-2630/15/10/103008, https://doi.org/10.1088/1367-2630/15/10/103008
11. Vinay Kumar Shukla, Soumik Mukhopadhyay, Kalipada Das, A. Sarma, I. Das, 'Direct experimental evidence of multiferroicity in a nanocrystalline Zener polaron ordered manganite', Phys. Rev. B 90, 245126 (2014). DOI: 10.1103/PhysRevB.90.245126, https://doi.org/10.1103/PhysRevB.90.245126 (arXiv:1412.7723)
12. Zhi-Hong Wang, Q. H. Zhang, G. Gregori, G. Cristiani, Y. Yang, X. Li, L. Gu, J. R. Sun, B.-G. Shen, H.-U. Habermeier, 'Control of charge order melting through local memristive migration of oxygen vacancies', Phys. Rev. Materials 2, 054412 (2018). DOI: 10.1103/PhysRevMaterials.2.054412, https://doi.org/10.1103/PhysRevMaterials.2.054412
13. R. F. Mamin, J. Strle, D. A. Bizyaev, R. V. Yusupov, V. V. Kabanov, D. Mihailovic, A. A. Bukharaev, 'Magnetic field control of electric-field-induced local domain growth in manganites', Ferroelectrics 499, 143–149 (2016). DOI: 10.1080/00150193.2016.1167509, https://doi.org/10.1080/00150193.2016.1167509
14. R. A. Ewings, T. G. Perring, O. Sikora, D. L. Abernathy, Y. Tomioka, Y. Tokura, 'Spin excitations used to probe the nature of the exchange coupling in the magnetically ordered ground state of Pr$_{0.5}$Ca$_{0.5}$MnO$_3$', Phys. Rev. B 94, 014405 (2016). DOI: 10.1103/PhysRevB.94.014405, https://doi.org/10.1103/PhysRevB.94.014405 (arXiv:1501.01148)
15. Mohsen Sotoudeh, Sangeeta Rajpurohit, Peter Blöchl, Daniel Mierwaldt, Jonas Norpoth, Vladimir Roddatis, Stephanie Mildner, Birte Kressdorf, Benedikt Ifland, Christian Jooss, 'Electronic structure of Pr$_{1-x}$Ca$_x$MnO$_3$', Phys. Rev. B 95, 235150 (2017). DOI: 10.1103/PhysRevB.95.235150, https://doi.org/10.1103/PhysRevB.95.235150 (arXiv:1610.07548)
16. Max Buczek, Zoe Moos, Alexander Gutsche, Stephan Menzel, Regina Dittmann, 'Pr$_{1–x}$Ca$_x$MnO$_3$-Based Memristive Heterostructures: Basic Mechanisms and Applications', Chem. Rev. 125, 6156–6202 (2025). DOI: 10.1021/acs.chemrev.4c00813, https://doi.org/10.1021/acs.chemrev.4c00813
17. A. Dehning, E. Janetta, C. Hausmann, C. Flathmann, J. Hoffmann, Ch. Jooss, 'Anisotropic colossal electro-resistance effect in epitaxial layered Pr$_{0.5}$Ca$_{1.5}$MnO$_4$ films', Appl. Phys. Lett. 127, 161902 (2025). DOI: 10.1063/5.0285380, https://doi.org/10.1063/5.0285380
18. J. Sacanell, A. G. Leyva, P. Levy, 'Electrical current effect in phase-separated La$_{5/8-y}$Pr$_y$Ca$_{3/8}$MnO$_3$: Charge order melting versus Joule heating', J. Appl. Phys. 98, 113708 (2005). DOI: 10.1063/1.2136787, https://doi.org/10.1063/1.2136787