The electric susceptibility comes from polarizability in the
誘電応答 The electric susceptibility comes from polarizability in the material.
分極 ex. NO 2
誘電LOSS
The Damped Forced Oscillator 共鳴型 A damped forced oscillator is a harmonic oscillator experiencing a sinusoidal force and viscous drag. We must add a viscous drag term: The solution is now: The electron still oscillates at the light frequency, but with an amplitude and a phase that depend on the relative frequencies.
LST relation Lorentz oscillator model
Band picture
Torelance factor KNb. O 3 ABO 3 La. Al. O 3 Li. Nb. O 3 Li. Ta. O 3 KTa. O 3 Pb. Ti. O 3 Cd. Ti. O 3 0. 8 Ilmenite Structure Ca. Ti. O 3 Sr. Ti. O 3 Ba. Ti. O 3 1. 0 Torelance factor 0. 9 Distorted Cubic Perovskite Structure
Torelance factor KNb. O 3 La. Al. O 3 ABO 3 Li. Nb. O 3 Li. Ta. O 3 KTa. O 3 Pb. Ti. O 3 Cd. Ti. O 3 0. 8 Ilmenite Structure Ca. Ti. O 3 Sr. Ti. O 3 Ba. Ti. O 3 1. 0 Torelance factor 0. 9 Distorted Cubic Perovskite Structure
量子常誘電性 ーSr. Ti. O 3を例にして • Typical Perovskite type dielectric. • Quite large e (>10000 below 10 K). • Quantum-paraelectric (T<37 K).
Barrett formula Generally permittivity is well described by the Barrett formula which one can obtain in the mean field approximation treating the ionic polarizability quantum mechanically: where T 1 = 84 K (saturation temperature), T 0 = 38 K (Curie-Weiss temperature), C = 9 · 104 K (Curie constant) in STO.
Quantum paraelectricity 伊藤(東 大 )による
Li dope effect in KTO
Isotope effect on dielectricity 東 大 伊藤ら 例えば、
臨界タンパク光 混合液体系(Binary Liquid system)の例 温度計 Hexane(C6H14) : Methanol(CH3OH) = 6 : 4 (in mol ) ~ 5 : 1 (in volume) Hexane-rich phase 2成分の界面 Methanol-rich phase
Partially Miscible Binary Systems hexane and methanol n n Begin with pure A (left side of graph). Only have one phase. As B is added: n Below the saturation limit, there will only be one phase n Above the saturation limit, there will be two phases. n n n Mole fraction of methanol, In this diagram, the composition of one of the phases is a’ and the composition of the other phase is a”. Eventually enough B is added such that A is actually dissolved in B and you once again only have one phase. Above Tuc (the upper critical temperature), the two liquids are miscible in all proportions. n No phase separation occurs.
Power spectrum of the scattering wave • Wiener-Khinchin theorem エルゴード性が成り立つときは アンサンブル平均になる。
火星の夕焼けーMie散乱 NASA MARS PATHFINDER
Hyper-Raman spectrum in KTO By Inoue, K.
Hyper-Raman と Ramanの比較
動的マイクロドメイン J. Hemberger, Phys. Rev. B 52 (1995), 13159.
Random配置と位置→角度mapping SHG散乱の角度依存性のsimulation
動的マイクロドメイン J. Hemberger, Phys. Rev. B 52 (1995), 13159.
Absorption edge of Sr. Ti. O 3 Above TC=105 K Cubic phase High temperature phase (Cubic) Urbach rule Strong electron-phonon interaction STE probably exist.
Temperature dependence of decay 30 K t – 2 dependence indicates bimolecular reaction process. Hopping lifetime t Distribution function G(t) is derived using Inv. Laplace tr.
可視光物性 局在 Thermal Activation Life Time Distribution G(t) 43 me. V Tunneling Electron Trap STE Hole Trap t=1. 45 ms
Cole-cole plot in photo-irradiated KTO
Reflection Spectrum of Sr. Ti. O 3 O(2 p)→Ti(3 d) O(2 p)→Sr(5 s) 価電子帯の底 Ti(3 d) 価電子帯のトップ O(2 p) E 0 UVSOR BL-1 Bにて測定
Absorption edge of Sr. Ti. O 3 Below TC=105 K Tetragonal phase ・Indirect bandgap Eg=3. 14 e. V (low temperature) ・Free Excitonnの吸収 なし
Temperature dependence of luminescence intensity アレニウスプロット ・単一の熱消光の式
Decay of luminescence Non-exponential shape Tunneling of localized e-and h+ pairs?
Temperature dependence of lifetime distribution Weighted mean lifetime <t> is defined as
Lifetime of STE Under high excitation densities, the integrated emission intensity increases in proportional to the excitation power but fast-lifetime component grows non-linearly. h+ e Directly e- h+ e- e- h+ Direct formation of STE with lifetime oft=1. 45 ms. Long lifetime ---- hopping process
Photo-induced absorption After 30 min. irradiation of 400 nm with 1 m. J/cm 2. Photo-induced absorption band in mid-gap
Persistent spectral hole burning Two components • Persistent spectral hole burning → Inhomogeneous broadening of the band, Ghole~1. 5 GIR. • Decreasing of absorption in → Homogeneous broad band whole range.
The origin of absorption band From photoemission measurements in n and p-type Sr. Ti. O 3, electron and hole density of states (DOS) appears in the middle of the band gap. Eg EF • e- has Ti 3 d character. • h+ is trapped as O 23 are reported. Localized electron and hole as small polaron observed in photo-induced absorption T. Higuchi et al. : Phys. Rev. B 57 6978 (1998) 局在
Barrett formula and its deviation Slater’s theory of Ba. Ti. O 3 (Description of Ti ion behavior within mean field approximation) Quantum mechanical treatment Barrett formula T 0: Curie temperature T 1: Quantum effect temperature M: Parameter Barrett formula gives a seemingly good fit, but it shows some deviation.
Ferroelectric phase transition and “Soft-mode” Ferroelectric phase transiton Curie Point Ba. Ti. O 3 type Cubic perovskite structure ( T >393 K ) Ba O Ba Ti O Ti Ferro Para TO 1 mode (Slater’s mode) TO 1 mode softening causes ferroelectric phase transition in Ba. Ti. O 3. LST relation Static permittivity Soft-mode frequency
What is THz time-domain spectroscopy (THz-TDS)? Fourier analysis Measured THz waveform Complex Fourier components (which can be reduced to amplitude and phase. ) By THz-TDS, We can determine the complex dielectric constant without the help of Kramers-Kronig analysis.
Generation and detection of THz Generation (Dipole radiation) THz pulse In. As Detection (Electro-optic effect) D 1 EO-crystal(Zn. Te) Lorentz force D 2 (110) Scanning e- THz field h+ fs IR pulse Surface depletion field Probe pulse (001)
N 2 purge BOX Cryostat B=1 T THz wave EO-crystal In. As(emitter) Delay Mode-Locked Ti: Sapphire Laser 80 MHz 80 fs 810 nm THz-TDS
Experimental Setup Sensitivity: If transmitted THz electric field becomes 1/3000, we can observe it. Range of bandwidth: 0. 3 THz~2. 5 THz Sample B(1 T) Nominally pure crystal of KTa. O 3 (100) 50μm thick Off-Axis Parabolic Mirror Emitter In. As f=200 N 2 -gas Purge Box d nce a l Ba ector t De THz Pulse Sample f=100 Cryostat 80 k. Hz Lock-in Amplifier To PC GLP EO-crystal Zn. Te λ/4 AOM GLP BS f=300 Mode-Locked Ti: Sapphire Laser 80 fs, 810 nm, 720 m. W f=1000 Time Delay
How is the complex refractive index obtained? sample Complex transmission coefficient (from experiment) Above two expressions are equated and solved. Complex transmission coefficient (from theory) is obtained!!
Experimental results Temperature dependence of transmitted waveform l. Retardation (Phase shift) increased l. Decrease of intensity ( Reflection and Absorption) and increased Relation between and ※The origin of horizontal axis has determined by the interference of the laser pulses, one of which is for the THz emittion and the other one is for detection.
The obtained dispersion In low temperature, l. Increasing dispersion l. Dispersion with a steep slope A single Lorentz Model Soft-mode is observed! Fitting parameters Ω 0 : Mode frequency γ 0 : Damping ε 0 : Static dielectric constant u. We assumed .
Soft mode frequency and damping Comparison with hyper Raman (HRS)* (* H. Vogt and H. Uwe : Phys. Rev. B 29(1984)1030) l. Mode frequency (Ω 0: left) is in excellent agreement with that of hyper Raman scattering(HRS). l. Damping (γ 0: right) is in good agreement with HRS below 50 K but above 50 K it proportionally increases.
Static permittivity Permittivities by THz-TDS and 100 Hz AC measurement “ε0” obtained by THz-TDS is in excellent agreement with the permittivity of 100 Hz.
Temperature dependence of damping Assumption Population of interaction phonon : Planck distribution T 0=99 K (~2. 1 THz) C=0. 46 “C” is independent of T. l. Impurities, defects, etc. l. Quantum fluctuation?
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