Phase diagram of q1D cuprates Sr 14-x Ca x Cu 24 O 41 Tomislav Vuletić Zagreb, Naslov

T. Vuletić, B. Hamzić, S. Tomić Institut za fiziku, Zagreb Phase diagram of q1D cuprates Sr 14-x Ca x Cu 24 O 41 J. Akimitsu, T. Sasaki Dept. of Physics, Aoyama-Gakuin University, Tokyo, Japan T. Nagata Dept. of Physics, Ochanomizu University, Tokyo, Japan B. Gorshunov, P. Haas, M. Dressel 1. Physikalisches Institut, Universität Stuttgart Naslov

Sr 14-x Ca x Cu 24 O 41 (x = 0, 3, 9, 11.5) Ca-doped q1D cuprates Outline ₪ q1D cuprates, importance, motivation ₪ crystallographic structure ₪ distribution of holes ₪ dielectric spectroscopy, electrical transport ₪ we identified a low-temp. phase – charge density wave (CDW) ₪ CDW phase in the phase diagram of Sr 14-x Ca x Cu 24 O 41 ₪ CONCLUSION SlijedSlijed

Motivation Superconductivity under pressure (30-45 kbar) in Sr 0.4 Ca 13.6 Cu 24 O 41 Uehara et al., ₪ q1D cuprates – realization of hole- doped spin-ladders ₪ q1D cuprates – only superconducting cuprates without square-lattice layers ₪ spin-ladders: spin gap, short-range correlations ₪ doping spin-ladders with holes ₪ pairing of the holes  superconducting or CDW correlations Dagotto et al., M ot iv ac ij a

b=12.9 Å a=11.4 Å cCcC Chains: Ladders: c C =2.75 Å c L =3.9 Å 10·c C ≈7·c L ≈27.5 Å cLcL Crystallographic structure Sr 14-x Ca x Cu 24 O 41 A 14 Cu 2 O 3 laddersCuO 2 chains Kris tal Stru ktur a CuO 2 layer HTSC 2D cuprates 90 o - exchange, FM, J<0 180 o - superexchange, AF, J>0 Cu-O-Cu interaction on the ladders

Holes distribution... 7 Sr 2+ : Cu 3+ : Cu 2+ : O 2- : 40- ______________ Ø 7 Sr 2+ : Cu 2+ : O 2- : 42- ____________ Ø Cu 2 O 3 ladders CuO 2 chains ₪ Formal valence for copper ₪ 6 holes per f.u.  all on chains holes  O2p orbitalsCu 2+  spin ½ Sr 14 Cu 24 O 41, x=0 Stehiome trija stoichiometry  no dependence on Ca-doping Calculation of Madelung energy of the crystal  ₪ x=0 has an energy minimum when all 6 holes are on chains. ₪ on Ca-doping hole count on chains decreases Mizuno et al., 1997.

chains ladders ₪ NEXAFS (T=300K) near edge x-ray absorption fine structure Nücker et al., Holes distribution, experimentally... Nucker ₪ hole count on the ladders increases slightly (0.8  1.1) on Ca – doping Ca-doping ladders chains ₪ quantitative analysis – hole counts on different O2p sites ₪ different O2p orbital orientations  different polarized x-ray absorption

₪ quantitative analysis – hole counts on different O2p sites ladders chains Ca-doping Nucker ₪ different O2p orbital orientations  different polarized x-ray absorption Holes distribution, experimentally... ₪ NEXAFS (T=300K) near edge x-ray absorption fine structure Nücker et al., ₪ hole count on the ladders increases slightly (0.8  1.1) on Ca – doping

₪ Optical conductivity (T=300K) Osafune et al., Cu3d↔O2p x=0 x=3 x=6 x=10 x=11 HTSC cuprates (2D): ₪ analogous spectral weight transfer on hole doping q1D cuprates: ₪ Cu3d ↔ O2p peak spectral weight transferred to lower energies on Ca-doping ladders chains Cu3d ↔ O2p peak is related to holes localized on chains Osaf une ₪ hole count on the ladders increases (1  2.8) on Ca – doping

Kumagai et al., Cu NMR (T<300K) Spin ordering ₪ spin gaps induce the activated temperature dependence of the spin-lattice relaxation rate 1/T 1 ₪ spin gap appears on ladders below 250 K, on chains, below 70 K 1/T1akti vacija4 chains ladders

Kumagai et al., chains ladders 63 Cu NMR (T<300K) ₪ Ca-doping decreases spin gap on ladders, but not on chains Spin ordering Spinski procjep

Interacting antiferomagnetic dimers model: Spin ordering & charge localization on chains x=0... AF dimera 2cC2cC 3cC3cC ₪ T=5 -20 K Eccleston et al Regnault et al., Spin excitations were measured by inelastic neutron scattering ₪ T= 8.5 K Matsuda et al holes/10 sites 4cC4cC 2cC2cC 2cC2cC 2cC2cC

₪ T=5 0 K X-ray diffraction directly points to structural change related to charge-order Cox et al Spin ordering related to charge-order – holes are localized on chains AF dimera 2cC2cC 2cC2cC 5 šupljina/10 mjesta Spin ordering & charge localization on chains x=0...

Motoyama et al., ₪ x=0: insulating behavior ₪  : 2200K (300 K  80 K) ₪  c (300 K): 500 (cm) -1. ₪ x≠0: Ca–doped materials ₪  decreases ₪  c (300 K): increases ₪ x≥11 i T>50K : metallic conductivity Longitudinal dc resistivity Transport Nagata et al., x=11.5 ₪ x≥11.5 i T<12K, p=30-80 kbar : superconductivity

Sr 14-x Ca x Cu 24 O 41 –chains subsystem: T decreases – spin ordering according to AF dimer model Spin gap (independent of Ca-doping) Spin ordering ↔ charge order (localization of holes) Localized holes, do not contribute to electrical transport Sr 14-x Ca x Cu 24 O 41 – ladders subsystem: Singlet ground state – spins paired on rungs of the ladders Spin gap (decreases on Ca-doping) x=0: hole count on ladders different from zero x≠0: hole transfer on ladders increases Mobile holes, contribute to electrical transport MedjuSaz etak

 c - longitudinal resistivity Ca-doping: ₪  & T c decrease ₪ transition width T c /T c increases Holes transferred on ladders  single-particle electrical transport Insulator-insulator transition for x=0,3,9 Well defined: ₪ transition temp. T c ₪ activation energy  Exp:trans port

HP 4284A 2 complimentary techniques: Low frequencies (1mHz-100kHz) Very large resistances (up to 1 T  ) Lock-in V V+ V- SR-570 resistances (0.1 k  < 1 G  ), frequencies 20 Hz-1 MHz Dielectric spectroscopy Diel.tehni ka

Generalized Debye function Complex dielectric function ∞ Debye.fja

∞ Deby e.fja Complex dielectric function Generalized Debye function ₪ relaxation process strength  =  (0) -  ∞ ₪  0 – central relaxation time ₪ symmetric broadening of the relaxation time distribution 1 - 

Eps im eps re ₪ We analyze real & imaginary part of the dielectric function ₪ We fit to the exp. data in the complex plane ₪ We get the temp. dependence ,  0, 1-   re  im

Dep s vs T ₪ x=0,3,9: on decreasing temp. dielectric response appears suddenly ₪ response strength, , decreases gradually with temperature CORRESPONDENCE: Maximum in  T c determined from DC measurements.  – dielectric response strength

₪ characterization of the dielectric response  ∞ : relaxation time s »  qp = s  =10 5 »  qp =10 : strong dielectric response Dielectric relaxation in low-temp. phase we correlate with collective excitations of the Charge Density Wave on ladders 1-  : relaxation time distribution wider than Debye Activation in  0 = activation in DC resistivity   z ~  0

Fukuyama, Lee, Rice Phason: Elementary excitation associated with spatio-temporal variation of the CDW phase  (x,t) ₪ Periodic modulation of charge density ₪ Random distribution of pinning centers ₪ Local elastic deformations (modulus K ) of the phase  (x,t) ₪ Damping  ₪ Effective mass m *»1 ₪ External AC electric field E ex is applied Phason dielectric response governed by: free carrier screening, nonuniform pinning Phason CDW dielectric response

Littlew ood Max. conductivity close to the pinning frequency   pinned mode - transversal  0 - weak damping ==

Littlew ood Longitudinal mode is not visible in diel. response since it exists only for  =0! Low frequency tail extends to 1/  0 = strong damping  »  0 Screening: Max. conductivity close to the pinning frequency   pinned mode - transversal  0 - weak damping == Phason CDW dielectric response plasmon peak longitudinal

Littlew ood Experiments detect two modes == Nonuniform pinning of CDW gives the true phason mode a mixed character!  0 = Longitudinal response mixes into the low-frequency conductivity Phason CDW dielectric response

Low frequency mode: - Spectral weight mostly shifted to low-freq. mode ₪ standard CDW systems - Dielectric constant  = , independent of T ₪ q1d cuprates:  = 10 5   only holes on ladders condense into CDW ₪ q1d cuprates:  decreases with T   hole transfer back from ladders to chains:  0 changes - Characteristic relaxation time of the low-freq. mode  0 ~1/  z ₪ q1d cuprates: , activation energy equal for DC (  z ) & AC (  0 ) measurements Littlew ood Phason CDW dielectric response

  &  0 are related:  0 &  z – from our experiments  0 – carriers condensed in CDW (holes transferred to ladders = 1·10 27 m -3 = 1/6 of the total) m * - CDW condensate effective mass Sr 14-x Ca x Cu 24 O 41 Microwave conductivity measurements (cavity perturbation)  a peak at   =60 GHz  CDW pinned mode Kitano et al., CDW effective mass m *≈100 m* == 0=0=

Phase diagram of Sr 14-x Ca x Cu 24 O 41

Conclusion ₪ localized holes on chains do not contribute to el. transport ₪ mobile holes on ladders are responsible for el. transport ₪ x>9: CDW suppressed, HT insulating phase persists ₪ x≥11.5: external pressure suppresses HT insulating phase and establishes superconductivity ₪ phase transition from HT insulating to CDW phase (0≤x≤9) ₪ CDW develops on ladders (mobile holes) ₪ Ca-doping: graduallly suppresses CDW phase ( , T c decrease), increases disorder (T c /T c increases), increases dimensionality (  /T c falls of to 3.5)