The preparation and properties of PPMO single crystals were reported elsewhere [B. Padmanabhan et al., J. Magn. Magn. Mater. 307 (2006) 288; Phys. Rev. B 75 (2007) 024419. In Pr1-xPbxMnO3, the Curie temperature Tc and the temperature of the metal-insulator transition, TMI do not coincide, and metallic conductivity occurs in the paramagnetic state in parts of the phase diagram, a phenomenon uncommon to mixed valence manganites. The figure shows the temperature dependence of magnetization (M) and resistivity (ρ) at selected magnetic fields of a PPMO sample. The magnetoresistance, [ρ(H)–ρ(0)]/ρ(0), is found to be ~90% close to TMI and at a field of 9 T. From the maximum change in slope of the M vs. T curve, Tc ~ 210 K was estimated which is distinctly lower than the corresponding TMI ≈ 255 K [47]. The scaling analysis near the critical temperature indicated in addition that the underlying magnetic transition is a conventional one, with short-range Heisenberg-like critical exponents. This study emphasizes the presence of additional frustrated couplings which intercepts the formation of long-range order. Deviation of the susceptibility from the Curie-Weiss law above Tc and history-dependent transport properties [R.-W. Li et al., Phys. Rev. B 71 (2005) 092407] suggest the presence of small magnetic metallic clusters above Tc that form percolating metallic paths in the paramagnetic metallic state upon reducing T. Note that evidence for the formation of localized ~1.2 nm magnetic clusters above Tc in another mixed valent manganite has earlier been found by small-angle neutron scattering measurements [J. M. DeTeresa et al., Nature 386 (1997) 256]. We also note the sharpness of the resistive transition which can be inferred from the logarithmic derivative of the resistivity, (dρ/dT)/(ρ/T), cf. figure above. Such a sharp metal-insulator transition is indicative of a largely strain-free sample.

For the tunneling studies a STM (Omicron Nanotechnology) under ultra high vacuum conditions (p ≤ 10-10 mbar) was utilized at numerous fixed temperatures, 30 K ≤ T ≤ 300 K, mostly in the vicinity of Tc and TMI. Since crystals with perovskite structure do not cleave easily, preparing a clean surface for STM studies is a challenge. Just before inserting the crystal into the UHV chamber, we scraped the surface inside isopropanol to rip off some part of it. This preparation gave locally cleaved surfaces on a length scale of micrometers. STM was conducted using tungsten tips, and typically 0.3 nA for the current set point and 0.8 V for the sample bias voltage, V. This implies that we probed the unoccupied density of states (DOS) of PPMO. In order to check on the quality of the tunneling contacts the dependence of the tunneling current I on relative tip-sample distance z was repeatedly measured throughout the experiments. The exponential dependence of I(z) yielded typical values of the effective work function Φ ~ 1.5 eV confirming excellent vacuum tunnel barriers. Topography often showed terraces with step heights (~0.4 nm) close to the unit cell extension which indicates a <100> surface of the pseudocubic perovskite crystal. To map the surface electronic state, we carried out thousands of STS measurements at 30 K ≤ T ≤ 300 K and—for each T—at different locations on the sample surface. Typically, an area of 50×50 nm2 with a lateral resolution of 1 nm (2500 pixels) was investigated. Tunneling current I and differential conductance, G = dI/dV, were measured simultaneously while ramping V from –1 to +1 V. An average of 2500 G-V curves taken at representative T are shown in figure (a) at the right. At T < TMI ≈ 255 K, the G-V curves display metallic behavior with a finite value of G0 signifying a finite DOS at the Fermi energy EF. In contrast, at 300 K the G-V curve around V = 0 is indicative of a semiconducting gap. The strong asymmetry of the G curves at T ≤ TMI and their severe change beyond TMI point at a strongly modified DOS at TMI. For quantifying the STS results and their temperature evolution, the local G0 is presented in color-coded conductance maps, figures (b)–(e) at the right, with the color scale covering 0 ≤ G0 ≤ 0.64 nS. These conductance maps represent slopes of individual I-V curves at V→0. The homogeneity of the local DOS at EF can be inferred from the corresponding histograms, figures (g)–(j), presenting the frequency of the observed G0 values within the conductance maps in the same color code. A sharp distribution of G0 at 30 K confirms a homogeneous electronic phase at low T < Tc. Similarly, the conductance map at 300 K (in the insulating regime) is also highly homogeneous [figure (e)], with most of the G0 values very close to zero [figure (j) and inset].

Most interestingly, as T is raised through Tc and approaches TMI ≈ 255 K inhomogeneities start to develop at a length scale of 2–3 nm, as seen in the above figures (c) and (d) at the right. A few of the I–V curves taken at T = 199 K are shown in above figure (f). These curves reveal both metallic and insulating behavior at different points on the surface. A bimodal distribution of G0 at 199 K is clearly visible in figure (h), with two maxima in G0 frequency located at similar G0-values as for low and high T, respectively. The increasing weight at G0→0 while retaining a peak at G0 ~ 0.3 nS provides a direct observation of coexisting insulating and conducting regions and hence, nanometer-scale phase separation as well as a growth of the former with T. Importantly, this phase separation does not persist deep into the ferromagnetic state in this compound. At T < 177 K, no indication of the insulating phase is found. Notably, this temperature coincides with the onset of constancy in (dρ/dT)/(ρ/T) below the dip near Tc (red dashed line in the first figure). In the figure at the right, the G0 values (green crosses) of the main peak in the histograms are plotted in dependence on temperature. This peak shifts to lower conductance values as T is increased and, importantly, an increasing weight at G0→0 is observed for T ≥ 199 K. The existence of a finite number of instances with G0 ≅ 0, i.e. of insulating areas, at and above 199 K is marked by blue triangles in the figure. We observe a drastic change in the G0 distribution when cooling below 260 K: the conducting areas appear then to immediately dominate the histograms. This temperature coincides with the rapidly changing bulk property ρ(T) near TMI (see figure at the right) which indicates that our STS results are not dominated by surface effects.

However, the distributions near T_MI [cf. above figure 2(h), (i)] are significantly broadened compared to both, low T (30 K) and high T = 300 K > T_MI. The sharp distribution at T = 300 K clearly indicates that these broad distributions of G0 at intermediate T reflect a sample property rather than an instrumental influence. The T dependences observed in STS arise mainly from a strongly changing DOS of PPMO at these temperatures. This change of electronic properties can be explained by the release of lattice distortions around T_MI, when immobilized polaronic carriers become successively mobile producing spatially inhomogeneous conductance distributions. The positive temperature coefficient of resistance observed above T_c can be explained by electronic transport through percolating metallic regions. Moreover, the inhomogeneities due to phase separation may directly influence the DOS on a local scale: nanometer-size particles are known for a modified DOS with respect to the bulk.

By comparing topography and conductance maps taken over identical areas we could exclude that the phase separation is directly correlated with topography. Moreover, scans over areas of 20×20 nm² with a lateral resolution of 0.4 nm exhibit similar sizes of the individual phases as in case of 50×50 nm² scans. Non-identical trace and retrace maps reveal a slow glassy dynamics of the electronic states and confirm that the phase separation observed here is not due to static chemical disorder.

Our findings are distinct from previous experimental results where PS was seen on a (sub-)micrometer scale and persisted deep into metallic regime. It remains an open question, whether the particular properties of PPMO with a metallic paramagnetic state for T_c< T < T_MI are responsible for the clear observation of nanometer-scale phase separation and its confinement to this temperature range, and whether the result can be generalized to other mixed valence manganites. Further, the specific pattern of electronic inhomogeneity in the local surface DOS is certainly affected by unavoidable intrinsic disorder, induced by random chemical substitutions and/or surface effects. In addition, disorder effects due to size differences between A-site Pr³⁺ and Pb²⁺ ions may play a role. However, the observed nanometer-scale phase separation is not a simple and fixed result of static chemical disorder, as can be inferred from the homogeneity of the electronic properties deep in the metallic state (low T) as well as in the insulating one (300 K). Hence, in order to resolve the relevance of disorder effects on PS and the associated length scale, similar spatially resolved STS studies on different manganites are called for.