IMSPEMAS 3 High-frequency dielectric spectroscopy in disordered ferroelectrics J. Petzelt Institute of Physics, Acad. Sci. Czech Rep., Prague Collaborators: Institute of Physics, Prague: V. Železný, S. Kamba (FT infrared), A. Pashkin, P. Kužel (timedomain THz spectroscopy), V. Bovtun, V. Porokhonskyy (HF dielectric spectroscopy), M. Savinov (LF dielectric spectroscopy), I. Rychetský (theory); B. Goshunov, M. Dressel (Univ. Stuttgart) BWO THz spectroscopy; A. Volkov, A. Pronin (IOFRAN Moscow) - BWO THz spectroscopy. J. Banys, J. Grigas (University of Vilnius) - MW measurements Many other collaborations providing the samples. Outline: Introduction Experimental techniques Dipolar glasses: RADP and DRADP Relaxors: PLZT and PMN Doped incipient ferroelectrics: KLT, KTN, SBiT Conclusions
Introduction: Displacive ferroelectrics (FE) ferroelectric as well as the paraelectric phase is well ordered. The dynamic nature of the FE transition is softening of the anomalously lowfrequency transverse polar phonon mode (FE soft mode SM, IR active) and instability of the paraelectric structure against this type of thermal vibrations at T C. No other anomalous dielectric dispersion is expected. Order-disorder FE in the paraelectric phase onesublattice ions move in a multi-minimum potential, which becomes single-minimum at low temperatures the crystal gradually order in the FE phase. The dynamic manifestation is a dielectric relaxation (Debye or close to Debye type) corresponding to the hopping of disordered ions in this multi-minimum potential, which undergoes critical slowing down at T C and gradually hardens and vanishes below T C. No additional phonon SM should exist. Many FE transitions reveal some features of both the pure types, i.e. partial softening of the phonon SM and appearance of the additional critical relaxation neat T C (central mode in inelastic scattering experiments).
Disordered FE remain structurally disordered down to low temperatures 3 main classes of disordered ferroelectrics: Dipolar glasses: important class is mixed FE-AFE crystals due to a frustration, very small and diffuse clusters are formed (size < 5 nm), which freeze-in at low T; Relaxor FE: high-permittivity compounds with a frozen structural disorder which prevents long-range FE ordering. Polar clusters typically 5-2 nm are formed at relatively high (so called Burns) temperature T d, whose polarization flipping slows down according to Vogel- Fulcher law; near and below the freezing Vogel-Fulcher temperature T f only the cluster boundaries fluctuate causing a very broad dielectric dispersion and losses. Doped incipient FE: depending on the doping level they may belong to both previous classes with some specific features (e.g. very high temperature of cluster formation).
Experimental techniques Broad-band dielectric spectroscopy (1 2 1 14 Hz): LF impedance analyzer HP4192A (1 Hz 1 MHz) HF impedance analyzer HP4291B (1 MHz 1.8 GHz) Waveguide measurements (8-12 and 3-4 GHz) Time-domain THz spectrometer based on fs laser (.15 2.5 THz, 5-8 cm -1 ) FTIR interferometer Bruker IFS 113v (.5-12 THz, 15 4 cm -1 ) All these techniques enable quantitative evaluation of the complex dielectric response function, mostly from 1 to 1 K. Backward-wave-oscillator (BWO) tunable monochromatic spectrometer (.1-1 THz, 3-33 cm -1 ) (University Stuttgart, General Physics Institute RAS Moscow) Raman and micro-raman spectrometer Inelastic neutron scattering (ILL Grenoble and LLB Saclay) Second-harmonic generation Differential scanning calorimetry
RADP and DRADP dipolar glasses Rb 1-x (NH 4 ) x H 2 PO 4 (RADP-x%) and Rb 1-x (ND 4 ) x D 2 PO 4 DRADP-x%) (glass for 3%<x<67%) is the best investigated dipolar glass for x 5% with very small clusters ( 2 nm) Phase diagram of DRADP-5: Glass (Vogel-Fulcher) temperature T g = 34 K ND 4 freezing temperature T f 12 K Cluster formation (Burns) temperature T d 22 K
Soft mode above T d can be well fitted with classically slowing-down Debye relaxation, which broadens below T d and changes gradually into Vogel-Fulcher (V-F) T- dependence
Single dispersion region (obeying Cole-Cole behaviour) for all T No sharp cluster walls (no separation of dynamics inside clusters and in the cluster-wall regions). Comparison with RADP-5: Large isotopic shift upwards of the soft-mode frequency; Stronger broadening of the dispersion on cooling; Frequency-independent losses at low T up to the mm range; Evidence for quantum tunneling?
PLZT and PMN relaxors (Pb 1-x La x )(Zr y Ti 1-y )O 3 (PLZT1(x/y/1-y)), x/65/35, 7<x<12, and PbMg 1/3 Nb 2/3 O 3 (PMN) are the beststudied relaxors. Our samples: PLZT 9.5/65/35 and 8/65/35 ceramics and PMN crystals Reflectivity 1..8.8.6.4 PMN fits THz 3 K.2 2 K. 2 4 6 8 1 Wavenumber (cm -1 ) Only the TO1 (soft) transverse optical phonon mode is T-dependent, but the softening tends to T d ( 62 K) and no anomaly appears near T f ( 22 K) or at maximum LF-permittivity temperature T m.
8 6 PLZT 8/65/35 PLZT 9.5/65/35 PMN Cochran fits ω s 2, cm -2 4 2 1 2 3 4 5 6 Temperature, K Phonon contribution to permittivity ε is not more than several hundreds and only above T d it probably contributes the full magnitude of ε.
12 1 ε' 8 6 4 3 K 36 K 4 K 43 K 52 K 3 K 36 K 4 K 43 K 52 K PLZT 8/65/35 3 25 2 15 1 ε'' 2 5 1 1 2 1 4 1 6 1 8 1 1 1 12 Frequency, Hz 1 1 2 1 4 1 6 1 8 1 1 1 12 1 14 Frequency, Hz Below T d a strong dispersion appears in the MW range which slows down according to the V-F law and broadens on cooling in previously annealed (above T d ) samples (this dispersion is pre-history sensitive). Below T f the dispersion becomes so broad that it results in frequency-independent loss spectra up to GHz or even higher range and corresponding (required by Kramers-Kronig relations) logarithmic dispersion of ε (ω).
25 2 15 B PLZT 9.5/65/35 PLZT 8/65/35 fits B = B (exp(dt)-1) 1 5 5 1 15 2 25 3 Temperature (K) The constant-loss level ε (ω) = (π/2)b(t) (so-called 1/f noise) decreases exponentially with decreasing T.
3 ε' 15 1 5 PMN f 1 Hz a 1.2 khz 11 khz 76 khz 1 MHz 3 MHz 1 MHz 3 MHz 1 MHz 3 MHz 1 GHz 1.8 GHz 42 GHz f b 25 2 15 1 ε'' 5 1 2 3 4 5 6 7 Temperature, K 1 2 3 4 Temperature, K
6 4 ε' 2 8 23 K ε'' 4 21 K a 16K 11 K 23 K 22 K 21 K 2 K 18 K 16 K 14 K 11 K 1 K 1 2 1 4 1 6 1 8 1 1 1 12 Frequency, Hz b 15 1 ε' 5 3 2 ε'' 1 23 K 23 K 25 K 27 K 29 K 27 K 25 K PMN 29 K c 39 K 39 K 1 2 1 4 1 6 1 8 1 1 1 12 Frequency, Hz d Also for PMN, the constant loss behaviour is nicely seen below 2 K.
Doped KTaO 3 : KTaO 3 : Li (KLT) and KTaO 3 :Nb (KTN) KLT: ε / 45 4 35 3 25 2 15 1 5 7 (K 1-X Li X )TaO 3 x = 6% 1 2 3 Temperature, K 1 Hz 1.2 khz 11 khz 1 khz 1MHz 1 MHz 1 MHz 1.64 GHz THz ε // 6 5 4 3 2 1 1.2 khz 11 khz 1 khz 1 MHz 1 MHz 1 MHz 1.64 GHz 5 1 15 2 25 Temperature, K
Li + ions (substituting K + ions) are off-centre because of smaller radius (r(li + ) =.68 Å, r(k + ) = 1.3 Å) sitting at 6 positions among which the Li + ions hop; Two relaxations appear which broaden on cooling obeying the Arrhenius law. At higher doping the RT relaxation reaches up to the THz range. Striking TO1 mode hardening to Li concentration. 1 9 K 1-x Li x TaO 3 Soft-mode frequency (cm -1 ) 8 7 6 5 4 3 x = x =.6% x = 1.6% x = 4.3% x = 6% 2 5 1 15 2 25 3 Temperature (K) Strong HF and MW dispersion expected also in KTN (tails are seen into THz range), but details are not yet known.
KTN: Nb 5+ ions (substituting Ta 5+ ) have the same radius as Ta 5+ (.72 Å), but their positions are still under debate. For higher doping nano-clusters are formed with Nb displaced along (111), in both PE as well as FE phase dipolar glass picture rather than usual FE transition; TO1 mode is somewhat softer than in pure KTO, since Nb ions show more tendency to ferroelectricity than Ta (KNbO 3 is a high T c FE unlike KTaO 3 ); TO1 frequency is practically independent of Nb concentration in the range of 1-2% Nb obeying the Cochran law above 4 K. At low T, differences appear among various types of experiments. 9 8 Soft mode frequency (cm -1 ) 7 6 5 4 3 2 1 ω ΤΟ = A [2 (T-T c )] 1/2 T c = 27 K ω ΤΟ = A (T-T c )1/2 KTO (Klein, INS 1996) KTN x = 2.2% (IR) KTN x = 1.8% (IR) KTN x = 1.2% (Chou INS 199) KTN x = 2% (Kugel HRM 1984) 5 1 15 2 25 3 Temperature (K)
Doped SrTiO 3 : Sr 1-1.5x Bi x TiO 3 (SBiT-x%) ceramics Bi 3+ substituted for Sr 2+ is aliovalent dopant Charge compensation by creation of Sr vacancy in the vicinity of two Bi ions; No phase transitions seen above 1 K up to 2% of Bi; Bi 3+ radius (.96 Å) is smaller than that of Sr 2+ (1.12 Å), nevertheless, the lattice parameter increases Bi concentration; Free space for Bi off-centre rattling forming nuclei for dynamic polar clusters; Dramatic hardening of the TO1 soft-mode frequency on Bi doping influence of strong local fields. 14 13 12 Soft-mode frequency (cm -1 ) 11 1 9 8 7 6 5 4 3 2 Sr 1-1.5x Bi x TiO 3 1 5 1 15 2 25 3 Temperature (K) %.67% 2.67% 8% 13.3% 16.7%
In SBiT a complex dielectric dispersion up to THz range appears consisting of 4 relaxation regions of different origins. The highest one near 1 cm -1 is not thermally activated (activation of acoustic phonons with wavelengths corresponding to the cluster sizes), the lowest one is connected with O vacancies since it can be annealed away, and the intermediate ones are connected with the cluster dynamics. CONCLUSIONS Common features to all disordered FE: Considerable damping of all IR modes down to low T; Soft mode does not soften completely and below T d does not account for the whole permittivity; Pronounced dielectric dispersion below the polar phonon range (possibly consisting of several relaxation regions), which softens, broadens and usually weakens on cooling, but remains present down to the lowest T. The details of this dispersion (which is basically due to the polar-cluster dynamics) are very sample and pre-history dependent and so far cannot be calculated theoretically;
Characteristic differences among the classes of disordered FE: Subtle problem, because the number of studied systems is still very limited, but our so far experience shows that: - in dipolar glasses there is only one dispersion region below non-anomalous polar phonons which indicates very smeared and small clusters; - in relaxors the lowest polar phonon hardens on cooling below T d, which characterises the dynamics inside the clusters (local FE transition), whereas the additional dispersion characterises the dynamics in cluster boundaries; the T m temperature has no physical relevance; - in doped incipient ferroelectrics the additional dispersion below phonon range is more complex consisting of several relaxation regions depending on the dopant type and concentration and surviving up to high T. The analogy of T d is so far unknown, but obviously it lies at very high T (determined by the activation energy of the hopping ions).