Dynamics of polar nanodomains and critical behavior of the uniaxial relaxor SBN

Transcription

1 Dynamics of polar nanodomains and critical behavior of the uniaxial relaxor SBN W. Kleemann, Th. Braun, Angewandte Physik, Univ. Duisburg, Germany J. Banys, Physics Department, University of Vilnius, Lithuania Th. Granzow, Institut für Mineralogie, Universität zu Köln, Germany Z. Kutnjak, Jozef Stefan Institute, Ljubljana, Slovenia R. Pankrath, Fachbereich Physik, Universität Osnabrück, Germany Ce Charge disordered congruently melting tungsten bronze SBN61 Sr 0.61-x Ba 0.39 Nb 2 O 6 :(RE,TM) x RE=Ce,La,...; TM=Co,Cr,... 0 x 0.02 Random electric fields W. Kleemann et al., Fund. Phys. Ferroelectr. (Aspen) ed. R.E. Cohen, AIP Conf. Proc. 535 (2000) 26

2 Features of the 3D Random-Field Ising Model phase transition expected at T c ( robust against RFs ) spatial fluctuations of quenched random fields E i compete with thermal fluctuations of the order parameter modified critical behavior: new critical exponents 3d Ising 3d RFIM α (specific heat) Middleton, Fisher 2001 β (order parameter) Middleton, Fisher 2001 γ (dc susceptibility) Newman, Barkema 1996 ν (correlation length) Middleton, Fisher 2001 enhanced critical slowing-down: activated dynamic scaling τ = τ 0 exp[{t 0 /(T m - T c )} Θν ] instead of τ = τ 0 [(T m -T c )/T c ] -zν Fisher nm PFM image smearing of phase transition & formation of metastable domains Imry, Ma 1975; Villain 1985

3 Random-field induced polar nanodomains in a 2D model system kt/j=10 <N> = 2 RF distribution kt/j=0.6 <N>= 97 Random-field 4-state Potts model in d = 2 dimensions ( order ( local ( σ, σ ) H = J δ l lm σ l, m= ± Px, ± Py m parameter components) field components) + h γlσl, l 1 σl = σm δ ( σl, σm) = if 0 σl σm hγ l=± Ex, ± Ey kt/j= 1 <N> = 8 kt/j=0.8 <N> 25 kt/j=0.3 <N>=205 +P x -P x +P y -P y kt/j=0.2 <N>=206 H. Qian, L. Bursill, Int. J. Mod. Phys. B 10 (1996) 2027 coarse fluctuations of RFs

4 Fingerprint experiments of RFIM behavior of SBN61:Ce cluster formation optical second harmonic T>T c linear birefringence precursor critical slowing-down polydispersivelinear linear susceptibility activated dynamic scaling Θν = 1.1 new critical behavior linear susceptibility γ = RBIM 1.89 RFIM 97 Nb - NMR β = 0.14 linear birefringence β = 0.12 second harmonic generation (SHG) β = 0.14 pyroelectric current β = specific heat α 0 nanodomains piezoresponse scanning force microscopy (PFM) domain walls repoling, aging and memory effects creep and non-debye relaxation dynamic light scattering.

5 Dielectric permittivity at elevated frequencies 10 5 T = 320 K 340 K 360 K 380 K 400 K ε ' 10 4 domain walls & ionic conductivity ε" two dispersion steps T = 320 K 340 K 360 K 380 K 400 K nanoregions 10 2 ν min ν [Hz]

6 Distribution of relaxation times (unpoled SBN) g(τ) Tikhonov ε ( ω) = ε regularization of g( τ ) d lnτ + ε iωτ thermal shift of largest relaxation time τ max (T c +10K) T = 300 K τ [s]

7 Divergence of largest relaxation time log(τ/s) dynamic scaling of average relaxation time T c = 329.2±0.8 K -8 Θν = 1.08±0.04 τ = τ 0 exp [{T 0 /(T m -T c )} Θν ] τ 0 = 2.4x10-12 s, T 0 = K T c = K, Θν = 1.13 f 0 =6.6x10 10 Hz activated dynamic scaling 10-4 <τ> [s] Dec et al., EPL (2001) T m /T c T [K]

8 Order Parameter Criticality measured via NMR 93 Nb (I = 9/2) Spin-Spin relaxation time T 2 P/P T/T c Temperature (K) Blinc, Zalar, Lushnikov, WK et al. Phys. Rev. B 64 (2001) B = 9 T, ν L = 99,92 MHz 90 x - τ - 90 y Echo 1 T 2Q P = (1 P 0 P 2 ) 3 / 2 (1 T / Tc) Experiment (333< T < 349K): β = 0.14±0.03 Theory: β = 0.02± dim. Random-Field Ising Model (Middleton, Fisher 2001) ß

9 10 2. n ac - n th ac long-range order n (T c -T) 2β (a) (b) (c) T c - Linear Birefringence of SBN:Ce (revisited) (a) x = 0 β = 0.13 ± 0.01 (b) x = β = 0.12 ± 0.01 (c) x = β = 0.11 ± 0.01 T c + precursor nanodomains n <δp 2 > 1-tan -1 (ξq m )/(ξq m ) Ornstein-Zernike function Lehnen et al., EPJB (2000) Temperature [K]

10 Hyper Rayleigh scattering (SHG), revisited 1.2 SBN scattering geometry x(zz)x n = a(t c -T) 2β T c =332.22±0.03 Intensity I/I I/I 0 1 a=0.443±0.005 β=0.143±0.003 precursor nanodomains I ξ 2-η P. Lehnen (2001) 2β= data: Th. Braun (2004) T/T c Temperature [K]

11 Pyroelectric response and criticality of polarization polarization P (µc/cm 2 ) % poled 100% poled temperature T (K) polarization P (µc/cm ) p Granzow, Woike, WK et al., PRL 72 (2004) = pyroelectric response P β, where P = P0 (1 T / Tc ) T β(100% poled) = 0.13 RFIM β(1.5% poled) = d-Ising normalized polarization P/P(293 K) SBN:Cr 1.13 mol% 100% a.) 16% b.) 1.5% c.) 1E-5 1E-4 1E reduced temperature (1 - T/T ) C critical exponent β polarization P (20 C) (µc/cm )

12 Pyroelectric response and criticality of polarization Compensation of random fields by charges on head-tohead and tail-to-tail domains critical exponent β polarization P (20 C) (µc/cm 2 ) Crossover Analogy Dilute uniaxial antiferromagnets in a uniform magnetic field (DAFF Fishman, Aharony 1979) β =0.30±0.02 β = 0.14±0.02 (Fe 0.88 Zn 0.12 F 2 Belanger et al. 2002)

13 Specific heat anomaly of SBN61 ac calorimetry Z. Kutnjak et al. (submitted) non-ergodicity upon FC and upon ZFH/ZFC

14 Specific heat anomaly of SBN61 Z. Kutnjak, WK, et al., submitted C p = t -α± + Bt + C T= T/T c -1 Experiment: α ± = Simulations: α = DAFF systems: α 0 Theory: α =

15 Scaling relations of the critical exponents α = ± 0.02 (c p ) β = 0.14 ± 0.02 (NMR, LB, SHG, pyroelectric current) γ = 1.78 ± 0.05 (susceptibility, linear birefringence) Rushbrooke relation α+2β+γ = 2.04±0.05 Critical isotherm: δ =1+γ/β = 13.7 ± 0.05? how to overcome hysteresis? f=4x10-4 Hz T c T. Granzow (PhD Thesis 2003

16 Conclusion Ce dynamics of polar nanoregions and critical behavior qualify the uniaxial relaxor SBN Sr 0.61-x Ba 0.39 Nb 2 O 6 :(RE,TM) x to belong to the 3D Random Field Ising Model universality class (first ever realized ferroic RFIM!) open questions dynamics in the Terahertz region? (birth of the polar soft mode frequencies) critical T c? (critical exponent δ )