Conductivity Contrast and Tunneling Charge Transport in the Vortexlike Ferroelectric Domain Patterns of Multiferroic Hexagonal ${\mathrm{YMnO}}_3$

We deduce the intrinsic conductivity properties of the ferroelectric domain walls around the topologically protected domain vortex cores in multiferroic ${\mathrm{YMnO}}_3$. This is achieved by performing a careful equivalent-circuit analysis of dielectric spectra measured in single-crystalline samples with different vortex densities. The conductivity contrast between the bulk domains and the less conducting domain boundaries is revealed to reach up to a factor of 500 at room temperature, depending on the sample preparation. Tunneling of localized defect charge carriers is the dominant charge-transport process in the domain walls that are depleted of mobile charge carriers. This work demonstrates that, via equivalent-circuit analysis, dielectric spectroscopy can provide valuable information on the intrinsic charge-transport properties of ferroelectric domain walls, which is of high relevance for the design of new domain-wall-based microelectronic devices.

Figure 1

Temperature dependence of (a) ${ϵ}^{\prime }$ and (b) ${\sigma }^{\prime }$ of sample 1 with silver-paint contacts measured for various frequencies under cooling (open symbols). The solid line in (a) shows ${ϵ}^{\prime }(T)$ at 1 Hz for the same sample, using sputtered platinum contacts. The dotted line in (a) roughly indicates the separation of relaxations 1 and 2 showing up at low and high temperatures, respectively. The two horizontal dashed lines in (a) indicate the capacitances (divided by the empty capacitance $C_0$) of the two insulating regions used for the fits of the frequency-dependent data (Fig. 2). The closed circles in (a) represent ${ϵ}_{\text{bulk}}^{\prime }$ as resulting from these fits; the corresponding dashed line is a guide for the eyes. The closed circles in (b) show the bulk dc conductivity as determined from the fits. The line in (b) is a fit of ${\sigma }_{\text{bulk}}$ with the Arrhenius law [cf. Fig. 3]. The inset in (a) shows ${ϵ}^{\prime }(T)$ at 1 Hz, measured at the first heating run and the subsequent cooling run.

Figure 2

(a) ${ϵ}^{\prime }$ and (b) ${\sigma }^{\prime }$ spectra of sample 1. The solid lines in (a) and (b) are fits using the equivalent circuit indicated in (a) (see the text), simultaneously performed for ${ϵ}^{\prime }(\nu )$ and ${\sigma }^{\prime }(\nu )$. The dotted line in (b) connects the shoulders arising from relaxation 1.

Figure 3

(a) Schematic sample cross section (not to scale) indicating bulk, SBLC, and IBLC regions, where the IBLCs arise from the DWs (this picture is somewhat oversimplified, as only part of the DWs have low conductivity [4]). (b) Arrhenius representation of the bulk dc conductivity and apparent layer conductivities (conductances multiplied by the bulk geometry factor $d/A$) of sample 1 as obtained from the fits shown in Fig. 2. (c) Bulk dc conductivity and true layer conductivities calculated as described in the text. (d) The same as (c) but using a representation that linearizes $\sigma (T)$ for variable range hopping. The solid lines in (b)–(d) are linear fits; the dashed lines are guides to the eye.

Figure 4

Bulk dc conductivity and true layer conductivities of the annealed samples 1a (a) and 2 (b), deduced from the equivalent-circuit analysis as described in the text. The solid lines in both frames are linear fits; the dashed lines are guides to the eye. At the right side of the figures, PFM images of the $ab$ sample surfaces are shown.