Tuning of dielectric properties of SrTiO${}_3$ in the terahertz range

Tuning of the dielectric permittivity spectra of strontium titanate (SrTiO${}_3$) single crystals in an external electric field is investigated between 90 and 300 K by means of terahertz time-domain spectroscopy. Application of the electric bias leads to an appreciable tuning of the permittivity observed up to room temperature both in the parallel and perpendicular directions to the bias field. The observed behavior is interpreted in terms of soft-mode hardening due to the anharmonic character of its potential. No additional low-frequency relaxation mode was observed. A weak temperature dependence of the anharmonic coefficients was found in agreement with previously published low-temperature data.

Figure 1

Schematic illustration of the two experimental geometries used: (a) Perpendicular geometry; nanocrystalline tin oxide electrodes; and (b) parallel geometry; the bias is applied by using interdigitated metallic electrodes. $A$ $=$ 40 μm: period of the electrode structure; $l$ $=$ 15 μm: distance between electrode fingers.

Figure 2

Electrostatic simulation of the electric-field distribution near the air-STO interface ($x$ $=$ 0). (a) Arrows: electric-field distribution; colors: electrostatic potential distribution. (b) Squared value of the bias field components $E_{z,\mathrm{avg}}$ and $E_{x,\mathrm{avg}}$ averaged over 1-μm-thick slices in the $x$ direction parallel to the surface. The simulation is done for an electrostatic potential of ±1 V on the electrodes.

Figure 3

Experimental wave forms and spectra obtained with a 100-μm-thick STO crystal in the perpendicular geometry: (a) Time-domain wave forms, 120 K; (b) Fourier transformations of the wave forms, 120 K; (c) time-domain wave form measured at 250 K with the first echo; here the field-induced tuning is visible for the echo (its displacement to shorter time delays with applied voltage corresponds to a field-induced reduction of the permittivity).

Figure 4

Dielectric permittivity of a 100-μm-thick STO crystal at 120 K. Unbiased permittivity (solid line) is approximated using an underdamped harmonic oscillator model (Ref. 15). The electric-field-induced permittivity was calculated from the experimental wave forms. Full symbols represent results of the tuning using the parallel geometry; crosses and empty symbols represent results obtained in the perpendicular geometry.

Figure 5

Relative field-induced changes in the complex dielectric function obtained for the perpendicular geometry. (a) and (b) $E_{\mathrm{bias}}$ $=$ 40 kV/cm, varying $T$; (c) and (d) $T$ $=$ 150 K, varying the bias field. Symbols: Experimental data. Lines: Fits by an underdamped harmonic oscillator.

Figure 6

Electric-field-induced hardening of the soft mode in the perpendicular geometry at several temperatures. The symbols represent the fits of the experimental spectra using a harmonic oscillator model (17); the lines represent fits of the soft-mode behavior at each temperature by using Eq. (21).

Figure 7

Relative field-induced changes in the complex dielectric function in the parallel geometry. (a) and (b) $E_{\mathrm{bias}}$ $=$ 40 kV/cm, varying $T$; (c) and (d) $T$ $=$ 150 K, varying the bias field. Symbols: Experimental data. Lines: Fits by an underdamped harmonic oscillator.

Figure 8

Electric-field-induced hardening of the soft mode in the parallel geometry at several temperatures. Symbols are obtained from the fits of the experimental spectra by a harmonic oscillator model (17); lines represent fits of the soft-mode behavior at each temperature by using Eq. (22).

Figure 9

Resulting anharmonic parameters ${\beta }_{\perp }$ and ${\beta }_{\parallel }$ as functions of temperature (solid symbols) and ${\beta }_{\parallel }$ taken from Ref. 6 (open symbols).