Generality and defect-mediated screening of anisotropic domain-wall conductance in improper ferroelectric hexagonal manganites

In hexagonal rare-earth manganites ($h$-RMnO$_3$), ferroelectric domain walls show an orientation-dependent electrical conductance that varies continuously with the angle between the wall normal and the ferroelectric polarization. The originating 2012 study established this on ErMnO$_3$ and left two unresolved microscopic questions: whether the orientation-conductance relation holds across the other members of the hexagonal-manganite series (and how it depends on rare-earth species, stoichiometry and bulk carrier density), and what the energetics, concentrations, formation mechanisms and kinetics of the defect-assisted charge compensation that stabilizes head-to-head walls are, together with their consequences for the long-term stability and field-driven dynamics of the wall conductance. Later work has generalized the theory across the family, identified the carrier types at charged walls, and quantified oxygen-defect segregation and migration, but a systematic experimental verification across the series and a quantitative microscopic account of head-to-head wall compensation remain open.

Background

Hexagonal rare-earth manganites $h$-RMnO$_3$ (R = Y, In, and the rare earths Sc, Dy–Lu) are improper ferroelectrics: their spontaneous polarization $P_z$ along the hexagonal $c$-axis is a by-product of a unit-cell-tripling trimerization distortion of the MnO$_5$ bipyramids, not of a polar instability of the lattice itself. Because the primary order parameter is structural, the ferroelectric domain pattern is fixed by topology: six trimerization-antiphase/ferroelectric domains meet in the well-known cloverleaf vortices, and this protected structure forces the coexistence of domain walls whose polarization meets head-to-head or tail-to-tail. At such walls the normal component of the polarization jumps, producing a sheet of bound charge ($2P_z\cos\alpha$ per unit area, with $\alpha$ the angle between the wall normal and $P_z$, so that $\alpha = 0^\circ$ is a head-to-head wall with positive bound charge and $\alpha = 180^\circ$ a tail-to-tail wall with negative bound charge), so these are called charged domain walls; in conventional proper ferroelectrics they are normally avoided because of the divergent electrostatic cost. Early scanning-probe work on YMnO$_3$ (Choi et al., Nature Materials 2010) had found interlocked structural and ferroelectric walls to be insulating, and Eliseev et al. (Phys. Rev. B 2011) had predicted spatially inhomogeneous equilibrium conductivity around charged walls in uniaxial ferroelectric semiconductors. In BaTiO$_3$, Sluka et al. (Nature Communications 2013) later showed a quasi-free-electron gas at charged walls, and Zuo et al. (J. Appl. Phys. 2014) modeled charge compensation at head-to-head and tail-to-tail walls — proper-ferroelectric counterparts in which screening is carried by free carriers rather than by bound lattice defects. The key experiment is Meier, Seidel, Cano et al., Nature Materials 11, 284–288 (2012): combining conductive atomic force microscopy (c-AFM, which maps local current injected by a biased tip) with piezoresponse force microscopy (PFM, which maps the polarization pattern), they measured the conductance of individual walls in ErMnO$_3$ as a continuous function of wall angle. Since ErMnO$_3$ is a p-type semiconductor, tail-to-tail walls (negative bound charge) are screened by the readily available mobile holes and are more conductive than the bulk, while head-to-head walls (positive bound charge) would need electrons, which are scarce; the authors argued that screening there 'can only be achieved by bound charges such as cation vacancies, which do not contribute to conductance', so head-to-head walls are less conductive than the bulk. First-principles calculations on the analogous compound YMnO$_3$ attributed the extra enhancement at hole-accumulating walls to the fact that holes enter the broad O(2p)–Mn(3d) valence band with low effective mass, whereas electrons at head-to-head walls would be confined to a narrow Mn $d_{z^2}$ band. Two aspects of this picture were left open by the paper itself and define the present problem. First, the authors state that they 'choose ErMnO$_3$ as our model hexagonal manganite, although we expect similar behaviour in the other members of the series' — a conjecture, not a demonstration, and the wall conductance is expected to be sensitive to rare-earth species, stoichiometry (oxygen interstitials and cation vacancies set the p-type carrier density) and to the bulk carrier density $n_0$ (the unperturbed mobile-carrier density set by this defect chemistry) that sets the nonlinear screening length, i.e. the distance over which the wall's bound sheet charge is compensated by mobile carriers. Second, the compensating defects at head-to-head walls were invoked qualitatively: their microscopic energetics, equilibrium concentrations, formation and migration mechanisms, and kinetics were not established, nor was their influence on the long-term stability and the dynamical response of the wall conductance under applied fields. Subsequent work has advanced both strands without closing them: first-principles studies of charged walls in YMnO$_3$, InMnO$_3$ and YGaO$_3$ (Småbråten et al., 2018) gave family-level design rules; interstitial oxygen was identified as the source of p-type conductivity in the family (Skjærvø et al., 2016); electron inversion layers at charged walls of ErMnO$_3$ were imaged and field-switched (Mundy et al., 2017); Hall-effect and Kelvin-probe measurements established high-mobility p-type carriers at tail-to-tail walls and directly n-type, non-ohmic head-to-head walls in p-type ErMnO$_3$ (Turner et al., 2018; McCartan et al., 2024); low-temperature electrostatic force microscopy revealed partially uncompensated bound charges with different screening behavior for positively and negatively charged walls (Schoenherr et al., 2019); and segregation enthalpies of oxygen vacancies/interstitials and their voltage-driven migration and splitting into interstitial-rich (p-type) and vacancy-rich (n-type) regions were quantified (Schultheiß et al., 2020; Wang et al., 2019; He et al., 2025) — mostly at nominally neutral walls or in the bulk, not as a quantitative compensation model for charged walls across the series.

Problem Statement

Establish, at the microscopic level, the origin and material dependence of the anisotropic domain-wall conductance in improper ferroelectric hexagonal manganites, continuing directly from the 2012 ErMnO$_3$ experiment. The problem has two jointly supporting strands with one common objective — a quantitative, transferable account of what sets charged-wall conductance in this family. (1) Series generality: experimentally determine whether the continuous orientation dependence of wall conductance (head-to-head least conductive, tail-to-tail most conductive, roughly an order of magnitude between them, superimposed on carrier accumulation/depletion and band-structure effects) occurs in the other members of the $h$-RMnO$_3$ series (the family-wide claim assessed experimentally on at least three members spanning the light-to-heavy rare-earth range, each with characterised stoichiometry and carrier density), and quantify how the relation depends on the rare-earth species, on stoichiometry (oxygen interstitials, cation vacancies, deliberate doping), and on the bulk carrier density that enters the nonlinear screening of the wall bound charge. (2) Defect-assisted screening: identify and quantify the microscopic compensation mechanism at head-to-head domain walls in these p-type semiconductors — the defect species involved (e.g., cation vacancies, oxygen-related defects, electron accumulation forming an inversion layer), their formation energetics, equilibrium concentrations, formation and migration kinetics, and their mobility — and determine how this compensation controls the long-term stability and the dynamical response of the wall conductance under applied electric fields, including under field-driven wall motion. Because the two strands share one objective, the account must relate the measured wall conductance (and its angle dependence) quantitatively to the identified compensation mechanism and hold across the family.

References

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