Polarization-dependent near-field phonon nanoscopy of oxides: ${\mathrm{SrTiO}}_3, {\mathrm{LiNbO}}_3$, and ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3$

Resonant infrared near-field optical spectroscopy provides a highly material-specific response with subwavelength lateral resolution of $\sim 10\mathrm{nm}$. Here, we report on the study of the near-field response of selected paraelectric and ferroelectric materials, i.e., ${\mathrm{SrTiO}}_3, {\mathrm{LiNbO}}_3$, and ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3$, showing resonances in the wavelength range from 13.0 to $15.8\mu \mathrm{m}$. We investigate these materials using scattering scanning near-field optical microscopy in combination with a tunable mid-infrared free-electron laser. Fundamentally, we demonstrate that phonon-induced resonant near-field excitation is possible for both $p$- and $s$-polarized incident light, a fact that is of particular interest for the nanoscopic investigation of anisotropic and hyperbolic materials. Moreover, we exploit that near-field spectroscopy, as compared to far-field techniques, bears substantial advantages such as lower penetration depths, stronger confinement, and a high spatial resolution. The latter permits the investigation of minute material volumes, e.g., with nanoscale changes in crystallographic structure, which we prove here via near-field imaging of ferroelectric domain structures in ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3$ thin films.

Figure 1

Far- and near-field response of a model material having a single phonon resonance with a TO mode at $20.0\mu \mathrm{m}$ and a LO mode at $13.3\mu \mathrm{m}$: (a) Simplified sketch of the s-SNOM setup, consisting of sample and tip. Note the definition of $p$- and $s$-polarized light. (b) Far-field reflectivity $R$ at the phonon resonance and (c) real and imaginary parts of the permittivity ${\epsilon }^{\prime }$ and ${\epsilon }^{\prime \prime }$. (d), (g) Permittivity for a smaller wavelength regime from $13.0–16.5\mu \mathrm{m}$ (see box in c), matching (e), (f) and (h), (i). (e), (h) Calculated near-field signal NF as a function of tip-sample distance $h$ and wavelength $\lambda$; in (e) and (f) the illuminating light is $p$ polarized, in (h) and (i) it is $s$ polarized. For comparison, NF is normalized to the maximum value for $p$ polarization. (f), (i) Spectra for tip-sample distances of $h=0$, 30, and 60 nm corresponding to the dashed lines in (e) and (h). Please note that the same figure layout is used for experimental results reported in Figs. 2, 3, 4.

Figure 2

Far- and near-field response of strontium titanate (STO): (a) Sketch of the experimental near-field setup. (b) Measured far-field reflectance $R$ [35] in comparison to literature data [87]. (c), (d), (g) Overview and detailed view of real and imaginary parts of the permittivity ${\epsilon }^{\prime }$ and ${\epsilon }^{\prime \prime }$, calculated using literature data [87]. The wavelength regime from $13.2–16.0\mu \mathrm{m}$ in (d)–(i) is marked with a box in (c). (e), (f), (h), (i) Near-field signal NF measured for different tip-sample distances $h$ and wavelengths $\lambda$; in (e) and (f) the illuminating light is $p$ polarized, in (h) and (i) it is $s$ polarized. (f), (i) Spectra for tip-sample distances of $h=0$, 30, and 60 nm corresponding to the dashed lines in (e) and (h). For clear comparison with theory, the figure is arranged according to Fig. 1. As expected, STO shows an enhanced near-field signal within the reststrahlenband around $\lambda \approx 15\mu \mathrm{m}$.

Figure 3

Far- and near-field responses of lithium niobate (LNO): (a) Sketch of the experimental near-field setup. (b) Measured far-field reflectance $R$ in comparison to literature data [90]. (c), (d), (g) Overview and detailed view of real and imaginary parts of the permittivity ${\epsilon }^{\prime }$ and ${\epsilon }^{\prime \prime }$, calculated using literature data [90]. The wavelength regime from $12.0–14.5\mu \mathrm{m}$ in (d)–(i) is marked with a box in (c). (e), (f), (h), (i) Near-field signal NF measured for different tip-sample distances $h$ and wavelengths $\lambda$; in (e) and (f) the illuminating light is $p$ polarized, in (h) and (i) it is $s$ polarized. (f), (i) Spectra for tip-sample distances of $h=0$, 30, and 60 nm corresponding to the dashed lines in (e) and (h). For LNO, the near-field resonance occurs around $12.5–14.5\mu \mathrm{m}$.

Figure 4

Far- and near-field responses of lead zirconate titanate (PZT): (a) Sketch of the experimental near-field setup. (b) Measured far-field reflectance $R$ in comparison to thin-film reflectance calculated using phonon data of PZT [83] and STO (substrate) [90] with ${\epsilon }_{\infty }$ of PZT taken from Ref. [92]. (c), (d), (g) Overview and detailed view of real and imaginary parts of the permittivity, ${\epsilon }^{\prime }$ and ${\epsilon }^{\prime \prime }$, calculated using literature data [83, 92]. The wavelength regime from $13.5–16.3\mu \mathrm{m}$ in (d)–(i) is marked with a box in (c). (e), (f), (h), (i) Near-field signal NF measured for different tip-sample distances $h$ and wavelengths $\lambda$; in (e) and (f) the illuminating light is $p$ polarized, in (h) and (i) it is $s$ polarized. (f), (i) Spectra for tip-sample distances of $\mathrm{h}=0$, 30, and 60 nm corresponding to the dashed lines in (e) and (h). For PZT, the near-field resonance occurs around $15.0–16.5\mu \mathrm{m}$.

Figure 5

Ferroelectric domain structure of PZT thin film obtained via complementary methods: (b) Out-of-plane (oop) PFM amplitude map showing high/low response for $c/a$ domains, respectively. The same domain structure is observable in both the $p$- (c) and $s$-polarized (d) near-field images. When changing the wavelength from ${\lambda }_1=15.3\mu \mathrm{m}$ (top quarter) to ${\lambda }_2=15.8\mu \mathrm{m}$ (lower three quarters), the domain contrast is characteristically reversed for both polarizations. In order to enable usage of the same color scale, the obtained signals are multiplied by a constant factor shown in the white boxes. The domain structure shown in (b)–(d) is evidently decoupled from the topography (a), which was measured simultaneously to (d). (a)–(d) Depict the same sample area; scale bar in (a).