Temperature dependent percolation mechanism for conductivity in ${{\rm{Y}}}_{0.63}$ ${\mathrm{Ca}}_{0.37}$TiO₃ revealed by a microstructure study

The top panel of figure 1 shows microscope images of a ${{\rm{Y}}}_{0.63}$ ${\mathrm{Ca}}_{0.37}$TiO₃ single crystal at T = 10 K in three different orientations, i.e. facing a (001), (010), and (100) surface of the material, respectively, with respect to the orthorhombic Pbnm symmetry. For each of these different orientations, specific patterns of bright and dark regions appear which show a preferred direction. As a result, the whole sample surface partitions in stripe-like patterns with a width of the order of 10–20 μm. While on the (100)-surface, these stripes extend across the whole field of view of several hundreds of μm, on the other two surfaces they form disconnected islands of one kind with extensions of the order of 100–200 μm within a background of the other kind. The bottom panel of figure 1 shows the evolution of the pattern with temperature from 100 K to room temperature for the (001)-surface. Comparing figures 1(a) and (d), it is seen, that islands of brighter areas exist at 10 K, which grow upon heating, while their shape is mainly maintained even at 100 K. Upon further heating a growth of these islands in a and b directions of the sample continues. However, this growth starts to take place more rapidly, so that these islands start to connect in a and b directions at ∼140 K. Furthermore, at ∼150 K, bright stripes evolving in b direction start to occur within the dark background. The width of these sub-stripes is $\sim 5\,\mu {\rm{m}}$ and the distance between the stripes is ∼20 μm. Finally, the brighter areas consisting of the former islands and the evolving stripes continue to grow and form a connected network as it is shown in figure 1(e) for 170 K.

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The contrast between bright and dark areas continuously weakens above 100 K and eventually becomes insignificant at room temperature. However, by artificially enhancing the contrast of the microscope images, the different areas can be shown to still exist at 296 K, as shown in figure 1(f).

A noteworthy observation is the fact that the bright areas invariably show up in the same positions after several temperature cycles. Given the exceptionally high doping level, it seems likely to assume chemical inhomogeneity of the material to be the reason for this pattern. Additionally, the microscope images show temperature hysteresis of the surface fractions in the same temperature region as reported in the resistivity data. Remarkable is, however, the unusually large length scales in the range of many tens to hundreds of μm, i.e.several orders of magnitude larger than what had previously been reported [14].

In order to investigate the electronic properties of the different areas observed in the microscope images, spatially resolved photoelectron spectroscopy measurements have been carried out at T = 110 K. The inset in figure 2(a) shows the Ti 3d spectral weight for two different sites on the sample, denoted as 'A' and 'B'. As the blowup in the main panel reveals, the spectra especially differ in a narrow region close to the Fermi level, with 'B' being slightly more conducting than 'A'.

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Figure 2(b) shows a map of a $200\,\mu {\rm{m}}\times 70\,\mu {\rm{m}}$ area of the sample with a pixel size of $1\,\mu {{\rm{m}}}^{2}$. The sample surface was oriented in [001]-direction and fractured before the measurement to get a clean surface. For each pixel, a full spectrum in the energy range as shown in the inset of figure 2(a) has been taken. Photoemission intensity variations due to surface roughness etc have been corrected for by normalizing each spectrum to unity. The map shows the integrated intensity in a narrow energy window around the Fermi level, i.e.the region where the spectra from sites 'A' and 'B' vary, as color values. Thus, more conducting regions appear bright and red in the figure in contrast to the insulating blue ones. The map reveals a similar domain pattern of stripes with a separation of $\approx 20\,\mu {\rm{m}}$ as had been observed in the microscope images. Furthermore, a smaller scale stripe formation is recognizable. The widths and distances between these sub-stripes are of the order of $\sim 1\,\mu {\rm{m}}$. Stripe-like features are also observed in the photoemission spectral weights of the O $2p$ band which is a natural consequence of the hybridization with the Ti $3d$, and presumably related to a rigid band shift. The presumption based on the microscope observations, that the origin of the stripe pattern might be chemical inhomogeneity, appears to be in line with the results of the photoelectron spectroscopy.

Various Raman investigations on ${{\rm{Y}}}_{1-x}$Ca_xTiO₃ are available in the literature, showing that the Raman spectra are quite different between insulating (x < 0.33) and metallic (x > 0.39) samples at low temperatures [18, 19]. However, the phonon energies at room temperature do not change significantly by doping. This suggests, that mode assignments on YTiO₃ can be transferred to our doped material [19]. Phonon mode calculations are available for the perovskitelike YMnO₃ [20]. As the Ti³⁺/Mn³⁺ ions do not participate in the Raman active modes, no significant shift in the mode energies due to their different masses are expected. Table 1 shows the phonon energies for YMnO₃, both lattice dynamical calculations (LDC) and experimentally observed values compared to the experimentally obtained values for YTiO₃ [19]. This shows that there is indeed a good overall agreement in energies of both materials. Finally, the Raman shifts of ${{\rm{Y}}}_{0.63}$ ${\mathrm{Ca}}_{0.37}$TiO₃ obtained in this work from fits of the Raman spectra are also listed in table 1. This comparison allows an explicit mode assignment of the observed phonon peaks. The Raman active modes for ${{\rm{Y}}}_{0.63}$ ${\mathrm{Ca}}_{0.37}$TiO₃ in Pbnm symmetry are assumed to be ${\rm{\Gamma }}=7{A}_{g}+5{B}_{1g}+7{B}_{2g}+5{B}_{3g}$. The Wyckoff positions are 4(c) for both Y and O1, 4(a) for Ti, and 8(d) for O2. But only Y, O1 and O2 yield Raman active modes. The Raman scattered light corresponding to A_g-modes retains the polarization of the incoming light, refereed to in experiment as parallel polarization, while for the ${{\rm{B}}}_{1g}$−, B_2g−, and ${{\rm{B}}}_{3g}$-modes, the polarization changes with the Raman process, thus these are observed in cross polarized geometry. The phase transition from Pbnm to P2₁/n preserves the total number of modes, because the primitive cell is the same in both phases and inversion symmetry is not broken. However, this transition leads to a redistribution of orthorhombic B_g-modes to monoclinic A_g ones. Therefore, the polarization dependence of the Raman modes can be used to identify the crystallographic phase of the material. Figure 3(a) shows the Raman spectra in c(aa)$\bar{{\rm{c}}}$ geometry at 10 K, obtained from two different spots on the sample, corresponding to distinct phases, as described above in the optical microscopy section. Significant differences are visible in the spectral weights and peak positions of the Raman spectra obtained from the bright and dark phases, respectively, see figure 1(a). The energy regions at ∼310, ∼390 and ∼640 cm⁻¹, denoted as P1, P2, and P3, respectively, exhibit the most prominent differences between the two phases. As reported in Tsurui et al (2004) [19], the modes P1 and P2 are fingerprints of Raman spectra obtained from conducting samples with doping level $x\gt 0.39$, while P3 is only visible for doping levels $x\lt 0.39$, thus belonging to the insulating phase. Therefore, the Raman spectra allow us to identify the darker areas of the sample in figure 1(a), as the LTO phase, represented by P1 and P2, and the brighter areas as the LTM phase, represented by P3. Figures 3(b) and (c) show the temperature dependence of the spectra for spatially fixed positions in conducting and insulating regions, respectively, in the range from 10 K to room temperature. Of particular interest is the feature P3, which is strongest in the insulating domain at 10 K. The polarization geometry and the calculated frequencies from the literature suggest that the feature consists of the ${{\rm{B}}}_{2g}(1)$ breathing mode and of other bond-stretching modes. These become Raman active in parallel polarization in the monoclinic phase and show a strong temperature dependence. Note, that the structural distortions, the modulation of the Ti–O bond distances, associated with orbital and charge ordering, are remarkably strong in these titanates [15], which may explain the strong signal of the P3 feature as well as the strong temperature dependence.

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Table 1.  Calculated and experimentally obtained phonon modes of YMnO₃ [20], YTiO₃ [19], and the LTM phase of ${{\rm{Y}}}_{0.63}$ ${\mathrm{Ca}}_{0.37}$TiO₃ measured at 10 K in $c({aa})\bar{c}$ geometry, respectively. The Raman shifts are given in units of cm⁻¹.

Mode	YMnO3	YMnO3	YTiO3	${{\rm{Y}}}_{0.63}$ ${\mathrm{Ca}}_{0.37}$TiO3
	Calc.	Exp.	Exp.	LTM—phase
Ag(7)	104	151	145
Ag(5)	147	188	168
Ag(2)	223	288	273
Ag(6)	304	323	314	294
Ag(4)	407	396	417	394
Ag(3)	466	497	446	457
Ag(1)	524	518	512	532
B1g(7)	137	151	142
B1g(5)	162	220	219
B1g(4)	285	317	306
B1g(6)	393	341	328
B1g(3)	470	481	487
B1g(2)	583	537	521
B1g(1)	617	616	643
B2g(5)	145	178	151
B2g(4)	363	336	284
B2g(3)	390		366	342
B2g(2)	476		452	494
B2g(1)	610		678	637
B3g(5)	181	205	162
B3g(3)	288	284	303
B3g(4)	342	384
B3g(2)	413		485
B3g(1)	593		644	593

Following the temperature evolution of P3 from room temperature to 10 K, the peak weight continuously increases and saturates between 100 K and 150 K, see figure 4. Such a saturation behavior is also observed for the static G-type distortion pattern associated with the charge and orbital order of the LTM phase [15]. This similarity in saturation behavior indicates, that the ${{\rm{B}}}_{2g}(1)$ modes become ${{\rm{A}}}_{1g}$ modes, which correspond to the static distortions of the LTM phase. As the unit cell volumes of LTO and LTM phases differ, strain plays an important role in the phase separated state, which has been reported in TEM measurements: [14] it has been observed that especially the LTO phase is highly strained in contrast to the LTM phase, which will favor phase separation.

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The Raman spectra in the conducting domain show an abrupt change between 150 K and 180 K. This is especially seen in the peak weights of P1 and P2, shown as black and red curves in figure 4. Both modes require a description by an asymmetric Fano lineshape in the fits, which may hint to an enhanced coupling of the charge carriers to the phonon modes P1 and P2.

At room temperature, the spectra in the different regions of the material are almost identical, in agreement with the observation that in the microscope images the contrast between them is barely detectable.