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Christos Panagopoulos

Christos Panagopoulos. Laboratory for E lectronic P hase C ontrol in A dvanced M aterials. Complex quantum materials:. The electronic degrees of freedom become pre-organised much like in colloids

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Christos Panagopoulos

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  1. Christos Panagopoulos Laboratory for Electronic Phase Control in Advanced Materials

  2. Complex quantum materials: • The electronic degrees of freedom become pre-organised much like in colloids • The resulting systems are intermediate between an electron liquid and an electron crystal • We can alter matter with tuning of relevant parameters at T=0 Utilise phase competition: Although in doped CES the dominating interactions occur at [eV] energies, the competition of phases is at low energies. Hence, minute perturbations cause large responses

  3. Low dimensional systems at the border between being Metals – Insulators – SC’s Transition Metal Oxides: Using charge carrier doping asQuantum Tuning Parameter Insulating Delocalised Metallic High-Tc Superconducting

  4. La2CuO4 La Cu Each ion has a free spin. At T=0 these spins exhibit AF Order: No overall spontaneous magnetisation

  5. Cu-O Planes Other Layers 350 metallic Non-metallic Temperature (K) AF SC 0 30 Carrier concentration (%) La-Cu-O La2-xSrxCuO4 hole motion is frustrated and low energy dynamics come into play Néel ordered

  6. Muon depolarisation 0.8 0.8 1.2 1.2 0 0 0.4 0.4 time (ms) Muon Spin Relaxation (106 - 109 Hz) mm=200me K.E.=4 MeV Spin J=1/2, Local probe of low energy dynamics: The magnetic moments of the muons rotate around the local magnetic fields whose distribution is reflected in the frequency and relaxation of the muon precession. B B r r Muon depolarisation time (ms) In-homogeneously ordered magnet Uniform long range ordered magnet Fast fluctuating moments

  7. (>500MeV) mm=200me K.E.=4 MeV When a muon decays it emits a positron preferentially along the direction of its spin. By measuring the anisotropic distribution of the decay positrons from a bunch of muons deposited at the same conditions we determine the statistical average direction of the spin polarisation of the muon ensemble

  8. x = 0.04 T = 0.8 K 0 0.5 1 1.5 Phys Rev B 67, R220502(2003) 60, 14617(1999) 72, 014536 (2005) La2-xSr2+xCuO4 La2-xSrxCuO4 x = 0.01 T = 4 K 0.2 x = 0.01 T = 2 K 0.1 0.15 Temperature (K) 0.0 0.5 1.5 0 1 0.5 1.5 Carrier concentration Muon depolarisation x = 0.09 T = 0.4 K 0.2 0.1 microseconds

  9. Kiefl et al PRL ‘89 YBCO6.04 YBa2Cu3O6+x Extended magnetic order YBCO6.27 Niedermayer et al PRL ‘98 X = 0.15; p=0.08 YBCO6.5 Carrier concentration time (ms)

  10. 40 AF Correlation length (Å) 20 Phys Rev B 67, R220502(2003) R. Birgeneau et al PRB ‘88 60, 14617(1999) 0 72, 014536 (2005) doping 0.025 La2-xSr2+xCuO4 x = 0.01 T = 2 K Temperature (K) 0.15 0 1 0.5 1.5 0.10 x = 0.03 T = 1 K Carrier concentration La2-xSrxCuO4 Muon depolarisation 0 0.5 1 1.5 x = 0.08 T = 60 mK 0.8 1.2 0 0.4 microseconds

  11. 40K 109 Hz Muon depolarisation 8K 106 Hz time (ms) La2-xSrxCuO4 (x=0.06) Extended magnetic order Carrier concentration CP et al., Physica C ‘00 (M2S Houston) CP et al., Phys. Rev. B 66, 064501 (2002)

  12. 40K 109 Hz Muon depolarisation 8K 106 Hz time (ms) La2-xSrxCuO4 (x=0.06) Extended order Extended magnetic order Carrier concentration CP et al., Physica C ‘00 (M2S Houston) CP et al., Phys. Rev. B 66, 064501 (2002)

  13. In such a system: FCdata Edwards-Anderson OP q(T)~(Tg-T)b; Tg=10K, b0.8 PM phase Freeze order Freezing implies time reversal, rotational & translational symmetry breaking in the Cu-O planes. La2-xSrxCuO4 (x=0.03) accompanied by a non-unique OP: i.e., We have a large number of degenerate thermodynamic states with the same macroscopic properties but different microscopic configurations Such a system would possess a wide distribution of relaxation times C.P. et al., Phys Rev B 72, 014536 (2005)

  14. Edwards-Anderson OP q(T)~(Tg-T)b; Tg=10K, b0.8 101 T<Tg H increase (0.2-6 T) 100 q / | t |b H=0.04-55 kG H//ab q ~ (H2)b/f 10-1 T>Tg 10-2 10-2 103 108 H2 / | t |f (G2) Moment after setting field to zero q(T, H)=[(c0 + C/T) – c(T, H)] / (C/T) Using t=(T – Tg)/ Tg and a scaling fn. F(z): SG-OP: q(T, H) = |t|b F (H2 / |t|f ) b, g = f-b are critical exponents. When F (z0) = const. (t<0); q~ tb and b (=0.8) is estimated from the slope in a log-log plot of q (at T<Tg) versus t in the limit of zero field. Similarly using F (z∞)=zb/f, f is determined from the dependence of q on Tg from the relation q(Tg, H) = (H2)b/f. The slope then gives b/f = 0.165 or f=4.2.

  15. 8 10 12 14 16 ac-susceptibility using miniature coils: Sensitivity: 10-8 emu La2-xSrxCuO4 (x=0.03)

  16. Charge involvement: Doping the parent AFI causes a distribution of charge and spin. Due to competition between interactions the system would display meta-stable states also in the charge sector

  17.  The charge would wander collectively between many local minima i.e., relaxation times Noise due to uncorrelated fluctuators • As the inelastic scattering time grows with lowering T multiple scattering effects would give rise to conductivity fluctuations which would grow with lowering T. La2-xSrxCuO4 (x=0.03) T - independent fractional changes Time (seconds) Where   denotes the time average I. Racevic, D. Popovic, T. Sasagawa, G. Jelbert & C.P. (preprint)

  18. AF domains • Distribution of charge & spin • Glassy dynamics occur at different temperature for spin & charge • Relaxor behaviour  cooperative charge dynamics presence of correlated charge-ordered regions

  19. Hysteresis subloops T = 200 mK La2-xSrxCuO4 (x=0.03) Resistance Magnetic field (Tesla) I. Racevic, D. Popovic, T. Sasagawa & C.P. (preprint)

  20. Gz(t) = A1exp(- l1t) + A2exp(- (l2t)b) + A3 ; A1=0 at high-T Changes happen in bursts of energy just like indicating the system doesn't like intermediate strained arrangements

  21. Changes happen in bursts of energy just like indicating the system doesn't like intermediate strained arrangements Carrier concentration

  22. AF domains • Distribution of charge & spin • Glassy dynamics occur at different temperature for spin & charge • Relaxor behaviour  cooperative charge dynamics presence of correlated charge-ordered regions

  23. Tweed vs T The tweed modulates on a length scale of a few atomic spacings. Thinking about the competition between different regions which at a given temperature do or do not want to transform to the deformed martensite phase, we saw a clear analogy to the frustration found in spin glasses. Different regions along the fibres in the tweed pattern had to transform in concert, leading to frustration.

  24. STM: a charge-probe Tweed: The two colours reflect the two martensitic variants (tall-and-skinny vs. short-and-fat). All materials parameters in our model are determined from independent experimental measurements in FePd alloys, except for the coupling to impurities. There are long–ranged correlations in the two diagonal directions, but only short–ranged correlations horizontally and vertically. Ca1.9Na0.1CuO2Cl2 , T=100mK, High-resolution STM -topograph of the cleaved CaCl plane. T. Hanaguri et al.,Nature, 430, 1001 (2004)

  25. x=0.00 T=8K 0.15 0 Do the slow density fluctuations persist when more carriers are added ? 0.5 1.5 x=0.03 T=1K Kiefl et al PRL ‘89 20 YBCO6.44 ? 0 0.5 1 1.5 Muon depolarisation x=0.08 T=60 mK Extended magnetic order 10 Niedermayer et al PRL ‘98 0.8 1.2 0 0.4 [0.08] Carrier concentration (%) time (ms) Fluctuations would increase due to dynamics accompanied by the added carriers Also as the fluctuations increase, quantum fluctuations may replace the thermal fluctuationsat zero temperature and hence suppress the frozen glassy-like state

  26. 109 Hz 4 K 0.8 K Muon depolarisation 106 Hz 0.04 K time (ms) Extended magnetic order Low energy Spin fluctuations Carrier concentration (%) CP et al., Phys Rev B 66, 064501 (2002) CP et al., Phys Rev B 69, 144510 (2004)

  27. With 5% Zn Muon depolarisation Muon depolarisation Carrier concentration (%) C.P. et al., Phys Rev B 66, 064501(2002) Phys Rev B 69, 144510(2004)

  28. G. Boebinger et al. PRL ’96 0.8 Resistivity (mOhm-cm) 0.4 Spin-charge fluctuations 100 0 200 Temperature (K) Carrier concentration (%) C.P. et al., Phys Rev B 72, 014536 (2005)

  29. 20 1/l2(0) [mm-2] 10 Carrier concentration (%) C.P. et al., Phys. Rev. Lett. 81, 2336 (1998) Phys Rev B 60, 14617 (1999) Phys Rev B 66, 064501 (2002) Phys Rev B 67, R220502 (2003) Phys. Rev. B 72, 014536 (2005)

  30. 40 30 AF Correlation length (Å) 20 10 R. Birgeneau et al., PRB ‘98 20 20 Spin-charge density fluctuations Extended magnetic order 1/l2(0) [mm-2] 10 10 Carrier concentration (%) Carrier concentration (%)

  31. 20 Extended magnetic order 1/l2(0) [mm-2] Spin-charge density fluctuations 10 Carrier concentration (%) If the native electronic “relaxor-state” is the parent state from which SC emerges, then further to the magnetic interactions associated with the magnetic instability, the spin-charge density fluctuations may induce an additional attractive quasiparticle interaction This would suggest the presence of 2-SC domes each centred at different points …

  32. C.P. in preparation(2006) 350 50 mW-cm Y-Ba-Cu-O Ca-Y-Ba-Cu-O 80 mW-cm La-Sr-Cu-O 150 mW-cm 300 mW-cm La-Ba-Cu-O TC Temperature (K) Extended magnetic order density fluctuations 30 0 Carrier concentration (%) Superconductivity maxima seem to track changes associated with the magnetic and density fluctuations

  33. SC

  34. CeRhIn5 10 Temperature Temperature (K) TN TC SC 0 40 Pressure (kbar) • (@Tc max) = 3 mW-cm • M. Niklas et al., JPCM 13, L905 (2001)

  35. CeRhIn5 TN Temperature (K) TC 2 0 40 Pressure (kbar) TN CeCu2Si2 TC 2 Temperature (K) 0 40 Pressure (kbar) • (@Tc max) = 10 mW-cm • B. Bellarbi et al., PRB 30, 1182 (1984) • (@Tc max) = 3 mW-cm • M. Niklas et al., JPCM 13, L905 (2001)

  36. CeRhIn5 TN Temperature (K) TC 2 0 40 Pressure (kbar) Yuan et al., Science 302, 2104 (2003) Holmes et al., PRB 69, 024508 (2004) TN CeCu2Si2 TC 2 Temperature (K) 0 40 Pressure (kbar) CeCu2(Si1-xGex)2 2 TN Temperature (K) TC TC 0

  37. 350 YBaCuO TC 0 30 Carrier concentration (%) TN CeCu2Si2 TC 2 Temperature (K) Temperature (K) Separation into low-density (HF) and high-density (intermediate valence) domains, populated by heavy and light carriers ? 0 40 Pressure (kbar) LaBaCuO CeCu2(Si1-xGex)2 2 TN Temperature (K) Temperature (K) TC TC TC 0 30 0

  38. The similarity between d & f electron systems suggests TC may be set by the characteristic temperature of magnetic and density fluctuations. This tends to be below 100 K in the f-electron systems but higher in the HTS cuprates HTS: quasi-2D, shortx 350 La-Ba-Cu-O CeCu2(Si1-xGex)2 2 Temperature (K) Temperature (K) TC TC 0 30 0 Carrier concentration (%) Pressure

  39. Ghost of Superconductivity on a Fall Day Phys Rev B 69, 144508 (2004) Phys Rev B 72, 024528 (2005) Phys Rev Lett 96, 047002 (2006) 300 AF Temperature (K) EMO Spin-charge DF’s HTSC 0 30 Carrier Concentration

  40. General issues involved: • Science of emergent complex states::We looked at issues such as self organisation, dynamical phase transitions and quantum fluctuations between competing ground states. • Functionality:Because charge, spin, lattice & orbital degrees of freedoms are active, we observed large responses to small perturbations. This has lead to highly responsive functions. • Quantum control:We tuned relevant parameters and altered matter: AFI  EMO  DF’s  HTS

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