J. D. Thompson with Tuson Park, Zohar Nussinov, John L. Sarrao Los Alamos National Laboratory and Sang-Wook Cheong Rutgers University

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1 Dielectric Glassiness in Hole-Doped but Insulating Cuprates and Nickelates J. D. Thompson with Tuson Park, Zohar Nussinov, John L. Sarrao Los Alamos National Laboratory and Sang-Wook Cheong Rutgers University Outline: Introduction--the materials and their response to doped holes Dielectric properties of these materials - evidence for charge glassiness - relation to spin glassiness Perspective Complex Behavior in Correlated Electron Systems, Lorentz Center, 25

2 The materials / Ni 2+ Parent compounds La 2 CuO 4 and La 2 NiO 4 - crystallize in tetragonal K 2 NiF 4 structure type but orthorhombically distort at reduced temperatures - Mott insulators - antiferromagnetic with T N 3 K Hole doping on La or Cu sites -Sr 2+ for La 3+ 1 hole/sr -Li 1+ for Cu 2+ 1 hole/li hole doping La 2-x Sr x CuO 4 unconventional superconductivity but also strange metallic and other complex states that arise from competing Coulomb, kinetic, magnetic, etc. interactions Temperature Strange metal

3 Holes in La 2 Cu 1-x Li x O 4 : basics J. L. Sarrao et al., PRB 54, 1214 (1996) structure: same effect on global crystal structure as Sr substitution for La magnetic order: T N for 3% holes, essentially the same as for hole doping with Sr transport: in contrast, neither metallic nor superconducting

4 Holes in La 2 Cu 1-x Li x O 4 : complex spin states Spin freezing T N T N T N B. J. Suh et al., PRL 81, 2791 (1998) R. H. Heffner et al., Physica B , 65 (22) spin freezing into a glassy state at low T by µsr and NQR similar to Sr doping an intrinsic response to doped holes and NOT a disorder effect analysis of NRQ phase separation of holes to boundaries of hole-free regions; magnetic properties controlled by the collective response of doped holes and dynamics of mobile hole-rich stripes (similar to stripey inhomogeneities in Sr-doped nickelate)

5 Holes in La 2 Cu 1-x Li x O 4 : complex spin dynamics at higher doping W. Bao et al., PRL 91, 1275 (23) '' for T>5K, dynamical susceptibility scales as χ ( ω) / χπ = f ( hω / kbt ) i.e., ω/t scaling as expected for quantum-critical fluctuations, but below 5K, '' χ ( ω) / χ, χ determined by a characteristic energy scale π = g( hω / Γ ) Γ 1 mev (11 K) consistent with expectations of a 2D quantum-disordered (spin-liquid) system resulting spin-phase diagram: AFM + spin glass for x < x c ; beyond x c, quantum critical fluctuations at high T, followed by a quantum-disordered and eventually spin-glass ground state What is happening in the charge channel??

6 Probing the charge degrees of freedom dielectric constant measurements: simple for non-metals, charge equivalent to spin susceptibility La 2 CuO 4+x introduction of mobile holes from excess oxygen: clear evidence for spin-charge coupling T N C. Y. Chen et al., PRL 63, 237 (1989) G. Cao et al. PRB 47, 1151 (1993) very large dielectric constant at low T ( 1 4 ) in La 2 CuO 4+x with holes (x>) and about 1 2 with few or no holes also phase separation for x>, with one phase metallic and weakly superconducting; compromises dielectric measurement

7 Dielectric response of La 2 Cu 1-x Li x O 4 (x=.23) ε' ε'' T. Park et al., PRL 94, 172 (25) 1 khz 1 khz 5 khz γ = 1.49E9 = 18 K α = T (K) generally good description of data possible role of polar defects large dielectric constant (~1 4 ) and frequency dependent relaxational behavior at low temperatures possible model: proposed to account for similar dielectric responses of presumed colossal dielectric CaCu 3 Ti 4 O 12 (Ramirez et al.,cond-mat/29498) i) isolated, structurally defected unit cells relax between equivalent configurations at a rate: γ=γ exp(- /T), where is an energy barrier. ii) dielectric function in this model given by: ε ε( ω, T ) = αγ 1 iω + γ where α is a dimensionless parameter that depends on defect concentration and the polarizability of defect

8 Evidence for charge glassiness in La 2 Cu 1-x Li x O 4 (x=.23) ε'' Hz 1 khz 1 khz 1 khz 5 khz β = ε' same data as previous slide, now plotted as imaginary vs. real part of ε with temperature as implicit variable scaling as found for glassy systems ' ε ε ' ' ε ε 1 = (1 + iωτ ) τ : relaxation time; ε : zero-frequency real part of dielectric constant; ε : limiting real part of dielectric constant as ω β solid curve: fit to equation with a single parameter β=.9 (β=1 simple Debye relaxation) deviation from universal arc arising from additional contribution to ε (ε dc = σ dc /ωε ); more prominent at low frequencies and high temperatures, where conductivity is higher

9 Dipole freezing temperature in La 2 Cu 1-x Li x O 4 (x=.23) 15 La 2 Cu 1-x Li x O 4 (x=.23) 1 khz θ = βπ / 2 T f ε'' 1 5 θ ε' glass-like charge (dipole) response analogous to glass response for spins randomly oriented dipoles freeze at T f divergence of relaxation time (ωτ ) " ' ' Davidson-Cole equation in polar co-ordinates: ωτ = tan( θ / β ), tanθ = ε /( ε ε ) as ωτ, linear relation between ε and ε, with an angle θ=βπ/2 T f : highest temperature to which linear relationship holds (close to temp. where ε peaks)

10 Frequency dependence of freezing temperature in La 2 Cu 1-x Li x O 4 (x=.23) 1M glass transition temperature T implied by nonzero freezing temperature T f as ω 1k frequency (Hz) 1k 1k 1 freezing temperature exp (-E / k B T) exp {-E / k B (T-T )} (T - T ) n fits to T f (ω): Activated or Arrhenius behavior: τ(t) = exp(e/k B T) rather poor fit freezing of hopping holes is not the origin T f (K) Vogel-Fulcher (VF) increase: τ(t) = exp [E/k B (T-T )] popular form to describe glass formers gives better fit, with E=25K and T =3.5K power-law form: τ(t) = a(t-t ) - n best fit, with T =5 K and n=3.2 power-law form consistent with a critical slowing down for critical scaling n=νz, where correlation length ξ (T-T ) -ν and correlation time τ ξ z if T, e.g. by pressure or doping, then Davidson-Cole and similar expressions for glass formers are naturally consistent with quantum-critical scaling of the dielectric constant

11 Similar dielectric responses in La 2-x Sr x NiO 4 (x=1/3) ε' ε" (a) (b) 1 khz 1 khz 5 khz T (K) 1 Hz 1 khz 1 khz 1 khz 5 khz β = ε' γ = 4 x 1 1 = 538 K α =.987 T. Park et al., PRL 94, 172 (25) frequency(hz) 1k 1k 1k 1 La 1.66 Sr.33 NiO 4 (T-T ) n ε'' T (K) dielectric response also consistent with defect model, but with γ and about an order of magnitude larger than in Li-doped cuprate shift of T f to higher temperatures comparably good fit to Davidson-Cole form, with β=.75 power-law form: τ(t) = a(t-t ) - n best fit, with T =17 K and n La 1.66 Sr.33 NiO 4 1 khz θ = βπ / 2 θ ε' T f

12 Inhomogeneities in Sr-doped nickelate Stripe schematic predicted [e.g., V. J. Emery; J. Zaanen] and found experimentally [e.g., J. M. Tranquada et al; S-W. Cheong et al; P. D. Hatton et al] that doped holes in nickelates form antiphase domain walls separating undoped, antiferromagnetic regions for x=1/3, stripes on the sample surface correlated over long distances ( >1 unit cells) but disordered or correlated over much shorter distances in the bulk (P. D. Hatton et al., Physica B, 318, 289 (22)) similar electronic inhomogeneities in Sr-doped cuprates (S. A. Kivelson et al., RMP 75, 121 (23)) Is the dielectric response of both due to stripe defects or glassiness? Difficult to distinguish defect versus glass behavior, but given high defect concentration (x=1/3) in nickelates, unlikely that isolated defect model is appropriate

13 Perspective competing long and short range interactions, e.g., Coulomb and magnetic exchange, common in complex oxides intrinsically heterogeneous states, of which stripe phases are one particular example tendency toward spatial ordering of phases frustrated by long range interactions and/or quenched disorder observed phenomena independent of added impurity (in-plane Li for Cu in the cuprate and out-of-plane Sr for La in the nickelate) quenched disorder a secondary consideration glassiness self-generated due to an exponentially large number of metastable states, as proposed by Schmalian and Wolynes (PRL 85, 836 (2))? does not rely on quenched disorder assumes system is uniformly frustrated with competition on different length scales solution of model Hamiltonian rugged energy landscape of metastable states characteristic energy barrier E [TS c (T)] -1, where S c is the configurational entropy of the system; implies a Vogel- Fulcher dependence of the relaxation time τ(t) exp [ E/k B (T-T )]

14 Additional considerations roles of anisotropy and partial spin freezing implied by inelastic neutron scattering in.6-li doped cuprate (Y. Chen et al., cond-mat/53167) dynamic magnetic structure factor S(q,E) consistent with the sum of 3D, quasi-3d and 2D components with corresponding spectral weights I i = dqdes i (q,e) peak in I 3D at glass temperature, but I quasi-3d continues to increase spins with 2D correlations remain fluctuating to 1.5 K, i.e. remain in a spin-liquid state with characteristic energy of 1 mev distinctly different from conventional glasses in which fluctuations freeze out below T g possible interpretation provided by spin-shard model (O.P. Suskov and A. H. Casto Neto (cond-mat/54234)

15 Summary an intrinsic, collective response of doped holes (no dielectric anomaly in holefree La 2 CuO 4 ) to competing interactions that produce mesoscale spin/charge inhomogeneities dielectric response and glassy charge dynamics not specific to stripes, which are common in nickelates but not conclusively seen in Li-doped cuprate probably not a conventional spin or charge glass qualitative, zeroth-order interpretation provided by a model of self-generated glassiness relevance to strange metallic phase in the HTS cuprates? Temperature Strange metal C. Panagopoulos and V. Dobrosavljevic, cond-mat/41111

16 Spin freezing in La 2 Cu 1-x Li x O 4 and La 2-x Sr x NiO 4 1.2x x1-6 La 2-x Sr x NiO 4 1.1x La 1.67 Sr.33 NiO 4 χ (arb. units) 3.x1-6 1.x1-3 9.x x1-6 La 2 Cu 1-x Li x O 4 ZFC FC 2.x T (K) C/T (mj/mol K 2 ).1.5 'excess' entropy T (K) evidence for spin-glass behavior from dc magnetization: irreversibility in field-cooled and zero-field cooled and peak in ZFC data excess entropy at low temperature consistent with emergence of a glassy phase deviation temperature is comparable to charge-glass temperature

17 Relationship between spin and charge freezing χ ac (emu) 4.x x1-6 3.x T (K) 1 La 1.67 Sr.33 NiO 4 La 2-x Sr x NiO T (K) charge glass spin glass 2 Hz 1 Hz 1 khz 1 khz weak, frequency-dependent feature in ac magnetic susceptibility, as expected for spin freezing charge freezing at T greater than spin freezing inhomogeneous charge dynamics responsible for spin glassiness? similar hierarchy of scales found in La 1.94 Sr.6 CuO 4 (M.-H.Julien et al, PRL 83, 64 (1999)) 1 1k 1k 1k 1M frequency (Hz)