NMR studies of cuprates pseudogap, correlations, phase diagram: past and future?

Transcription

1 NMR studies of cuprates pseudogap, correlations, phase diagram: past and future? P. Mendels NMR LPS, Orsay J. Bobroff PhD students: H. Casalta, L. Guerrin, S. ouazi Post-docs: T Ohno, A. Mahajan, A. Mac Farlane Oriented Crystallite Samples: J. Arabski, N. Blanchard 1, G. Collin, J.F. Marucco, V. Viallet F. Rullier Albenque Transport, SPEC (CEA, Saclay) Toulouse, LNCMP Single Crystal Samples: P. Lejay and D. Colson

2 Observation = Amazing Phenomena H. Alloul, Introduction to the Physics of Electrons in Solids Editions de l Ecole polytechnique English edition, Springer (to appear, december 2010)

3 NMR studies of cuprates : pseudogap, correlations, phase diagram: past and future? Magnetic spin susceptibilities in NMR : Usual metals and superconductors The case of cuprates: Singlet spin pairing Single spin fluid in the normal state Dynamic susceptibilities and spin lattice relaxation : Magnetic correlations in the phase diagram d- wave SC The pseudogap and questions on the phase diagram NMR as a local magnetic probe Pseudogap, MIT and disorder NMR and high field transport measurements SC Fluctuations and pseudogap Some answers about the phase diagram

4 Hyperfine Intercations - NMR Frequency Shifts Interactions between nuclear moments I and electronic moments s et l 2 r h γnγ e r r r v v s Dipolar ( I. r)( s. r ) Ηdd = I. s r r Ι r h 2 γnγ e r r Orbital Ηorb = I. l r3 Filled atomic shells : Contact c 8. ( ) 3 2 r π r n e I s r v Η = h γ γ δ Ηorb 0 ; Ηdd 0 Paramagnetic or diamagnetic compounds: r r + Η = h γ I ( B + r B L ΗT = ΗZ + Ηdd + Η r [ r r = < B ] L> + B < > < B r L BL L > χb 0 Mean field Linear response orb Insulators H orb Chemical shift (orbital currents) c n Frequency shift r. 0 BL ) Relaxation time Local measurement of the electronic susceptibility metals χ Pauli Knight shift (unpaired electrons)

5 Magnetic susceptibilities SQUID Measures Ion cores orbital Spin χ m α ( T ) = χ = χ dia dia + + [ ] orb s χ χ ( T ) + + i χ orb α χ i, α i, α NMR shift measures on each nuclear site i s α + always ( χ imp ) α =(x,y,z) i = atomic sites K i, α ( T ) = K dia i + K orb i, α + K s i, α ( T ) = K dia i + A orb i, α χ + orb i, α A s i, α χ s i, α ( T ) Local magnetic measurement on each nuclear site i

6 Knight Shift in Superconductors T c High T c cuprates YBCO 7 B 0 B 0// Ba CuO 2 conducting planes Cu Y O CuO 2 17 O NMR of the CuO 2 planes Vanishing of χ P in the superconducting state Cooper pairs are in a singlet state M. Takigawa et al PRL 1989

7 89 Y NMR shift in the metallic state H.A, T. Ohno and P. Mendels, PRL 1989 CuO 2 plane - ΔK K i dia orb orb s s, α ( T ) = K i + Ai, α χ i, α + Ai, α χ i, α ( T ) But transferred hyperfine couplings CuO 2 plane Local magnetic measurement

8 Sign of 89 Y NMR shift Negative sign comes from Y4d orbitals: core polarization pπ Y4d pσ Y4d Y4d Y4d Very weak OK So negative sign comes from pσ -Y4d hybridization

9 Is there an independent oxygen band at the Fermi level? H.A., T. Ohno and P. Mendels, PRL 1989 K (ppm) K s (T) = A χ s (T) does not change with hole doping A is driven by (Y4d-O2pσ) Cu(3d) covalency So there is no independent oxygen spin degree of freedom at E F

10 YBCO 6.63 K i Single spin fluid behaviour dia orb orb s s, α ( T ) = K i + Ai, α χ i, α + Ai, α χ i, α ( T ) M. Takigawa et al 1991, Y versus 17 O 63 Cu versus 17 O A single T dependence for K i,a (T): due to χ Cu (T) Notice: this allows determinations of the shift references for all nuclei

11 Phase Diagram and Band Structure There is a single spin fluid E O2pσ 3d 10 3d 9 NO!! Strong O2p -Cu 3d hybridization Magnetic correlations The holes steal spins from the copper hole background Zhang Rice spin singlets Cu3d -O2pσ n(e)

12 NMR studies of cuprates : pseudogap, correlations, phase diagram: past and future? Magnetic spin susceptibilities in NMR : Usual metals and superconductors The case of cuprates: Singlet spin pairing Single spin fluid in the normal state Dynamic susceptibilities and spin lattice relaxation : Magnetic correlations in the phase diagram d- wave SC The pseudogap and questions on the phase diagram NMR as a local magnetic probe Pseudogap, MIT and disorder NMR and high field transport measurements SC Fluctuations and pseudogap Some answers about the phase diagram

13 Physical Origin of the Spin Lattice Relaxation H Z = hγ S z.b 0 B 0 // z rf excitting field perturbation for H Z r B Transition probability L H r < B rf = hγ S.B 1 cosω r r > + B < B Relaxation: transverse components of the fluctuating field at the Larmor frequency L [ > ] = L L L 1 γ 2 n 1 T + L L t transitions if 1/2 H rf ( iω t) B 1 z = < B ( t) B (0) > exp dt Correlation function of the local field n -1/2-1/2 0 1/2 T 1 results from the coupling with the equilibrium fluctuations of the electron spins degrees of of freedom

14 1 T 1 2 2A = 2 h γ For a free electron gas χ (q, ω n ) is q independent up to k F χt ( ω ) = h γ e { n( EF ) + i π hω n ( EF )} 2 1 = A2 n E k T 2 ( F) 1 h π K= h 2 e A k Spin lattice relaxation in a free electron metal B T χ χt " ω = ( ω ) B T Aγe 2γ n( E 2 P F γeγ n n n n ) = ( ω ) χ "( q ω ) χ ", T n q T n logt 1 Al metal 27 Al NMR Τ 1 T= 1.85 sec. K TTK 1 2 = h π γ e γ 4 k B n 2 = S 0 Korringa law for a metal Thermometry log(1/t)

15 (T 1 T) Y Comparison of (T 1 T) -1 on 89 Y and 17 O OPT In YBCO 7 T 1 T is nearly constant on 17 O and 89 Y Like in a free electron metal UD In YBCO T T 1 K OPT Metallic like component UD 17 O

16 Distinct behaviour of (T 1 T) -1 on the Cu site: AF correlations (T 1 T) -1 Optimal T c 17 O 63 Cu In YBCO 7 T 1 T is nearly constant on 17 O but increases at low T for 63 Cu O and Y are insensitive to AF correlations while Cu probes them fully Increase of AF correlations at low T Even more for the underdoped case

17 T 1 for nuclei coupled to neighbouring sites Non local hyperfine coupling q dependence of the HF coupling A s, q) = A, exp( i q.r ) s O α ( O α 89 s Y A ( q) 8 D ( cosq a / 2 cosq / 2) 17 O 63 Cu A r i Y, α = α x ya s AO, α ( q) = 2 Cα cosqxa / 2 ( q) A + B cosq a i ( cosq a) s Cu, α = α 2 α x + y T 1 1 2k = 2 χ 2 B T A (q) " q, h γ 2 e q ( ω ) For Y and O, A(q) vanishes for q AF = (π/a,π/a) The AF fluctuations are filtered out by A(q) n / ω n χ " ( q, ω n ) Δq = π/ξ 60K YBCO 6.6 ξ(τ) is the AF correlation length probed by 63 Cu NMR ω 0 Neutron scattering (π/a,π/a) q

18 89 Y NMR shift Zn 2+ or Li + (no spin) substituted to Cu 2+ (spin 1/2) 89 Y n.n shift 89 Y main line shift 7 Li NMR shift Empty symbols: Zn 2+ Full symbols : Li + A. Mahajan, H.A PRL 1994; J. Bobroff, H. A. PRL, 1999 The spinless character of the impurity dominates the magnetic response

19 Spatial extent of the staggered moment S. Ouazi, J. Bobroff, H. A, PRB 2004 ξ imp (T) ξ imp ξ imp (T) varies smoothly with T and doping Review article: H.A, J. Bobroff, P. Hirschfeld and M. Gabay, RMP 2009

20 V 3 Sn 51 V NMR T 1 in the superconducting state (T 1 T) -1 /(T 1 T) -1 T=Tc Cuprates T c T 1 Korringa T c (0) /T s wave superconductor (T 1 T) -1 ~ exp (-Δ/k B T) for T<<T c T 1 minimum below T c (Hebel-Slichter peak in 1/ T 1) T 3 T/T c d wave superconductivity T 3 variation for T<<Tc

21 NMR studies of cuprates : pseudogap, correlations, phase diagram: past and future? Magnetic spin susceptibilities in NMR : Usual metals and superconductors The case of cuprates: Singlet spin pairing Single spin fluid in the normal state Dynamic suscptibilities and spin lattice relaxation : Magnetic correlations in the phase diagram d- wave SC The pseudogap and questions on the phase diagram NMR as a local magnetic probe Pseudogap, MIT and disorder NMR and high field transport measurements SC Fluctuations and pseudogap Some answers about the phase diagram

22 What about the origin of this T dependence? Large decrease (nearly full loss) of χ s (T) above T c Pseudogap in the electronic excitations Origin for K s H.A, T. Ohno and P. Mendels, PRL 1989

23 89 Y NMR shift 0.95 T m Phase Diagram and Pseudogap 0.91 T m Low T decrease of the susceptibility: opening of the pseudogap 0.64 T m T* Alloul et al,????

24 17 O NMR The drop of χ(τ) is generic of underdoped cuprates Hg1201 : one CuO 2 layer, J. Bobroff, H.A, PRL 1997 Can be used to estimate the hole doping! Bi2223 : three CuO 2 layers, A Trokiner et al, five CuO 2 layers Hg1245 Mukuda et al, JPSJ 2008

25 Knight Shift in underdoped YBCO K( 17 O) T c The large drop of χ s (T) above T c could be due to Cooper pair formation T c YBCO 7 T c being then due to phase coherence of these preformed pairs Bose Einstein condensation? Other scenarios competing magnetic orders RVB spin liquid YBCO 6.6 Stripes M. Takigawa et al PRB ddw order Orbital currents

26 Superconductivity in Bis 2 r 2 CaCu 2 O 8+x T c =95K PSEUDOGAP Niobium BCS C. Renner et al, PRL 1998 Underdoped cuprate

27 Superconducting fluctations in the normal state of cuprates Nernst effect La 2-x Sr x Cu O 4 Bi 2212 High field diamagnetism Wang et al, PRB 64 (2005) Wang et al, PRB 64 (2001) Precursor pairing?

28 underdoped Inhomogeneities in BiSCCO viewed by STM Cren et al,prl 84,147 (2000); Howald et al PRB (2001) DOS depends on the STM tip location : 2D maps of the gap magnitude Pan et al,nature 413, 282 (2001) Local distribution of hole doping optimal 560 A Lang et al,nature 412, 415 (2002)

29 La 2-x Sr x Cu O 4 Metal insulator transition MIT High field measurements Log T Y. Ando, G.S. Boebinger et al PRL 1995 G.S. Boebinger, Y. Ando et al PRL 1996 Insulating behaviour at optimal dpoping

30 Questions About the Phase Diagram Pseudogap: Preformed pairs? Phase transition? Crossover? Order parameter I M Strange metal? FL Transition to a Fermi liquid? SG MIT and Disorder? Pseudogap joins Tc curve or QCP??

31 NMR studies of cuprates : pseudogap, correlations, phase diagram: past and future? Magnetic spin susceptibilities in NMR : Usual metals and superconductors The case of cuprates: Singlet spin pairing Single spin fluid in the normal state Dynamic susceptibilities and spin lattice relaxation : Magnetic correlations in the phase diagram d- wave SC The pseudogap and questions on the phase diagram NMR as a local magnetic probe Pseudogap, MIT and disorder NMR and high field transport measurements SC Fluctuations and pseudogap Some answers about the phase diagram

32 89 Y NMR 1.0 T=120 K NMR Spectra: histograms of the hole content hole doping J. Bobroff, H.A, PRL 2002 Distribution of oxygen content oxygen doping y O 7 O O 6.6 O T=300 K hole doping P(y) Tc (K) O 7 O K (ppm) Detailed analysis of the spectra versus T The maximum distribution of hole content is much narrower than in Bi2212 (STM) or LSCO (RMN) seen on large samples (0.5g) likely of macroscopic origin 1.0 P (p) 0.5 O 6.6 Bi2212 LaSrCuO hole doping p O 7 YBaCuO 7 Distribution of hole content YBCO is very homogeneous Only weak charge disorder Tc (K)

33 Influence of defects on T c and on the pseudogap YBCO 6+x + 4%Zn YBCOZ 6+x No change of hole doping Y NMR shift Dilution effect on T N T* K s (%) pure Zn 2% Zn 4% T (K) No change of T* : the pseudogap is not sensitive to disorder Increase of the disordered magnetism range Large depression of T c H. Alloul, P. Mendels et al, PRL 67, 3140 (1991)

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35 Inflence of irradiation defects on transport properties 800 YBCO 6.6 #3 Δρ ρ (μω.cm) T (K) Same single crystal Δ T c The transition curves remain very sharp High energy (MeV) electron irradiation at low T Cu and O vacancies in the CuO 2 Planes Excellent control of defect content Homogeneous damage

36 Pulsed magnetic field facility in Toulouse B (tesla) ρ (μω.cm) High field suppresses SC reveals resistivity upturns 55T 0T YBCO 6.6 T c =25K t (sec) T (K) Disorder Induces MIT?

37 Δρ/ρ Irradiated YBCO (a) O -C 6.6 O -D 6.6 O -B 7 O -B 6.6 O -A1 6.6 A T /T dev Controlled disorder Δρ/ρ «Pure» low T c Cuprates (b) La Bi La Bi LaSr CuO 0.15 LaSr CuO T/T dev System Specific disorder reduces T c The upturns are quantitatively similar The disorder is not generic MIT is driven by disorder F. Rullier-Albenque, H. A. et al, EPL 2008.

38 The various cuprate families Phase diagram in the absence of disorder?? High quality single crystals?? SG and MIT are determined by disorder F. Rullier-Albenque, H. A. et al, EPL 2008.

39 NMR studies of cuprates : pseudogap, correlations, phase diagram: past and future? Magnetic spin susceptibilities in NMR : Usual metals and superconductors The case of cuprates: Singlet spin pairing Single spin fluid in the normal state Dynamic suscptibilities and spin lattice relaxation : Magnetic correlations in the phase diagram d- wave SC The pseudogap and questions on the phase diagram NMR as a local magnetic probe Pseudogap, MIT and disorder NMR and high field transport measurements SC Fluctuations and pseudogap Some answers about the phase diagram

40 Competing order Superconducting fluctuations and pseudogap Preformed pairs A new approach to determine SCF conductivity Total suppression of SC fluctuations with large fields F. Rullier-Albenque, H. A. et al, PRL 2007

41 Determination of T* and T c onset of SC Fluctuations T* and T c and σ SCF (T,H) can be measured in a single experiment H.A, F. Rullier-Albenque, EPL 2010 T* T* crosses T c at optimal doping The pseudogap cannot be the onset of pairing

42 The real phase diagram of cuprates YBa 2 Cu 3 O 6+x Irradiation defects decrease of T c and T c with disorder PG AF SCF SC SCF range does not change but increases with respect to T c Disordered H.A, F. Rullier-Albenque EPL 2010 F. Rullier-Albenque, H.A et al to be published

43 Some conclusions Magnetic spin susceptibilities in NMR : Singlet spin pairing Single spin fluid in the normal state The pseudogap is generic and robust to disorder Dynamic susceptibilities and spin lattice relaxation : Magnetic correlations up to the Optimal doping Metallic like at q=0, AF correlations for q=(π/a, π/a) d- wave SC The pseudogap and questions on the phase diagram Importance of disorder in the phase diagram MIT and SG phases governed by disorder SC Fluctuations and pseudogap SC Fluctuations follow Tc versus hole doping, remain with disorder A preformed pair scenario does not apply Pseudogap is intimately linked with magnetism (competing order?) NMR will be helpful to check possible models