Jan Petzelt

Dielectric properties of Nb-doped (~1.5 at.%) rutile single crystals were studied in the 10-300 K temperature range (at frequencies below the MHz range down to 0.3 K) in a broad frequency range, including terahertz and infrared range, to understand the origin of its giant permittivity. The results were fitted, modelled and compared with those of the undoped rutile crystal measured in the terahertz and infrared ranges. The primary effect originates from the near-electrode depletion layer of lower conductivity compared to the bulk (surface barrier-layer capacitor effect), which causes a strong thermally activated relaxation in the MHz dielectric spectra. In the higher frequency range, the main difference between doped and undoped crystals is the presence of an overdamped microwave excitation (central mode) in the doped crystal for both polarizations, persisting down to 10 K and not thermally activated. This accounts for the previously reported increased permittivity values down to 2 K – where all lower-frequency relaxations are frozen – compared to undoped crystals. It also explains why our low-frequency permittivity at 0.3 K exceeds its THz value. In similar Nb-doped rutile single crystals it was quite recently ascribed [V. A. Dinh et al., Phys. Rev. B 114, 024112, (2026)] to microwave tunneling of molecular polarons. Polar phonons are affected only by a slightly increased damping.

Strontium titanate-based materials with ferroelectric or relaxor-like properties have drawn vast attention as polar dielectrics for electronics and telecommunications. Here, we study the lattice dynamics in sol–gel-derived Sr_1−1.5xBi_xTiO₃ thin films with x = 0.0053 and 0.167, deposited on Al₂O₃ substrates, using a variable-temperature far-infrared spectroscopy in a transmittance mode. Bi doping, known to induce a low-frequency dielectric relaxation in SrTiO₃ (ST) ceramics and films, due to off-centre dopant ion displacements generating electric dipoles, is shown to affect the polar phonon behaviour of thin films. We show that in weakly Bi-doped films, the low-frequency polar TO1 mode softens on cooling but less than in undoped ST. In heavily Bi-doped ST films, this mode displays no significant frequency variation with temperature from 300 to 10 K. The polar phonon behaviour of polycrystalline Bi-doped ST thin films is comparable with that of Bi-doped ST ceramics, which exhibit dielectric relaxations and harden soft-mode behaviour instead of the ferroelectric phase transition.

Herein, the properties of broadband dielectric spectra up to THz–infrared range of the (1 − x)BaTiO₃‐xBaZrO₃ (BZT‐x) solid solution are reviewed and complemented. This includes the proper ferroelectric (x = 0), diffuse ferroelectrics (0 < x ≤ 0.2), relaxor ferroelectrics (0.4 ≤ x ≤ 0.8), dipolar glasses (x > 0.8), and the normal dielectric (x = 1). The spectra are characterized by an overdamped central mode in the microwave range which weakens on cooling. Except for BaTiO₃, the soft mode and central mode do not soften appreciably and do not contribute substantially to the low‐frequency permittivity maximum. The most important dielectric contribution is brought by Cole–Cole relaxation assigned to hopping of Ti ions in the BaTiO₃ clusters, which obeys the Arrhenius law with a common activation energy for the whole relaxor range of E _a ≈ 181±17 meV and broadens on cooling as described by a temperature‐independent distribution of activation energies. It follows that the polar nanoregions within the BaTiO₃ clusters remain very small with temperature‐independent size and frozen boundaries, even if the Ti ions inside them are hopping. This differs from the usual lead‐containing relaxors, in which the polar nanoregions grow on cooling and follow the glass‐like freezing.

Giant permittivity (GP) materials are of interest as possible capacitors for energy storage. Ferroelectric and related homogeneous materials suffer from strongly temperature dependent dielectric properties. Therefore, within the last two decades, the interest has been focused to dielectric studies of various inhomogeneous GP materials, where the essential role was shown to be due to weak but inhomogeneous conductivity. Here we study, within the known models based on effective medium approximation, the broadband dielectric spectra of conducting core – less conducting shell structures, which are expected to be the most advantageous for revealing the GP effects. Examples of core–shell structures, in which the dielectric properties of both components are independent of frequency, are studied analytically and numerically within the generalized brick model. For the simple case of coated-spheres model the dielectric dispersion is of a single Debye-relaxation type and the optimal GP properties are for highly conducting cores and thinnest possible nonconducting and high-permittivity shells. For non-spherical core–shell particles the conditions for macroscopically isotropic composite are briefly discussed.

Recently, we have analyzed the complex infrared (IR) and terahertz (THz) response of the relaxor ferroelectric Pb(Mg_1/3Nb_2/3)O₃ (PMN) and suggested a new interpretation of the so-called intermediate temperature T^* ≈ 400 K, where the split soft phonon mode undergoes incomplete softening. IR-THz reflectivity was fitted using effective medium approximation, which describes the uniaxially anisotropic response of polar nanodomains (PNDs). It indicated that the response perpendicular to the local polarization undergoes a classical Cochran softening toward T^* with the extrapolated low-frequency permittivity obeying the Curie-Weiss (CW) law with T_C ≈ T^*. In this letter, we report analysis performed in a similar way on the published IR-THz response in closely related relaxor Pb(Mg_1/3Ta_2/3)O₃ and have revealed a similar behavior: The lowest-frequency phonon polarized perpendicularly to the local polarization of PNDs softens below ∼900 K according to the Cochran law and the corresponding low-frequency permittivity obeys the CW law with T_C = 340 K ≈ T^* and Curie constant C = 1.16 × 10⁵ K. This is comparable to similar parameters for PMN, T_C = 380 K ≈ T^* and C = 1.7 × 10⁵ K. This explains the high-temperature CW anomaly in the low-frequency dielectric response of both materials and strongly suggests that both relaxors undergo a local ferroelectric phase transition near T^* which induces a new polarization component perpendicular to the local random electric field.

Recently we have demonstrated that out-of-plane dielectric properties of polycrystalline SrTiO₃ (ST) films depend on the strain/stress induced by the substrates due to thermal expansion misfit. Here, we present a complementary infra-red (IR) spectroscopy investigation of the role of Al₂O₃ and MgO substrates on the lattice dynamics and in-plane dielectric properties of ST thin films also prepared by sol-gel. We verify that ST films deposited on Al₂O₃ substrates, being under a tensile stress, present the soft mode behaviour similar to that of ST single crystals, deviating just below 150 K. In contrast, ST films deposited on MgO substrates, being under compressive stress, have higher soft mode frequency from 10 to 300 K. It is thus proved that for polycrystalline ST films the intrinsic in-plane relative permittivity may be tuned through an induced stress state.

Microwave dielectric spectra of the relaxor ferroelectric PbMg_1/3Nb_2/3O₃ single crystals, (Nb + In) co-doped rutile ceramics, inhomogeneous conducting polyaniline pellets, composites of poly(ethylene terephthalate) and multi-walled carbon nanotubes were used for calculation of transmission and reflection spectra of the material slabs in the free space and estimation of absorbing and shielding properties of the materials. Studied high-permittivity high-loss materials with a strong and broad dielectric dispersion in the microwave range were shown to have a high potential for microwave shielding and absorbing applications. Broadband (two decades of frequency) 40 dB shielding and high attenuation constant were demonstrated in the microwave range.

Broadband dielectric spectra of dielectric-conductor nanocomposites of poly(ethylene terephthalate) with multiwalled carbon nanotubes (PET-xCNT) were used for calculation of their free-space shielding and absorbing parameters in the frequency range from 1 MHz to 1 THz. Revealed correlation of the composition and frequency dependent microwave dielectric and shielding/absorbing parameters allows determination of the CNT concentration range optimized for the shielding (x ≥ 0.4 vol%) and absorption (0.12 < x < 0.6 vol%) applications. Broadband (two frequency decades) 40 dB shielding, narrowband 30÷40 dB absorption and high attenuation constant up to 10⁴ neper/m were demonstrated.