NMR evidence for spatial correlations between spin and charge order in (La,Eu) 2-x Sr x CuO 4 Nicholas Hans-Joachim Grafe, Los Alamos National Laboratory Markus Hücker, Brookhaven National Laboratory Bernd Büchner, Leibniz Instit ü t, Dresden "The STM and neutron scattering experiments have broadened our knowledge of high-T c materials, but it's not clear how their separate findings are related to one other. Only when several different techniques are brought to bear on the same material will researchers get some insight into how the spin and charge structures influence one other." -- Physics Today, Sept. 2004

Evidence for Spin Inhomogeneity Inelastic NS in La 2-x Sr x CuO 4 ( R. Birgeneau et al. ): dynamic incommensurate AF correlations K. Yamada et al., PRB (98) Elastic / Inelastic NS in La 2-x-y RE y Sr x CuO 4 and La Ba CuO 4 ( Tranquada et al.): LTT phase stabilizes static incommensurate AF below T N ~ 50K and spin excitations suggestive of 1D spin ladders J. Tranquada et al., Nature 375, 561 (95) J. Tranquada et al., Nature 429, 534 (04)

Evidence for Charge Inhomogeneity STM ( Kapiltunik et al., Davis et al., Yazdani et al. )- inhomogeneous surface states in Bi 2 Sr 2 CaCuO 8-x and Ca 2-x Na x CuO 2 Cl 2 : modulations of LDOS at length scales ~ 4a 0 T. Hanaguri et al., Nature 430, 1001 (04) Cu NQR in La 2-x Sr x CuO 4 ( Imai et al.): Local hole doping variations at nm level P. M. Singer et al., PRL 88, (02) O NMR in La 2-x Sr x CuO 4 ( Haase, Slichter et al. ): Spatial variations of local spin susceptibility and local EFG J. Haase et al., J. Supercond. 13, 723 (00)

NMR as Probe of Spin and Charge Zeeman Interaction - alignment in external field ~ eV (5 mK) Hyperfine Interaction - alignment with electron spin ~ eV Quadrupolar Interaction - alignment with EFG ( Q,  ~ eV

Rare-Earth Co-doping and LTT La 1.8-x Eu 0.2 Sr x CuO 4 H.-H. Klau  et al., PRL (2000) Superconductivity suppressed Glassy spin freezing in LTT phase  SR H.-H. Klau  et al., Hyperfine Int. (2000) M. Braden, unpublished (1999) INS

Spin Response in LTT phase NMR N. Curro et al., PRL (2000) ESR V. Kataev et al., PRB 55, 3394 (97) M. Hucker., Ph. D. Thesis (1999) Susceptibility dominated by Van Vleck term from Eu 3+ and from CuO 2 plane La NMR, Cu NMR,  SR and Gd ESR dominated by glassy spin fluctuations

Oxygen NMR in Cuprates Hyperfine coupling at O site is to the two nearest neighbor Cu spins Vanishes for AF correlations (Filtered out by form factor)  /2 Cu O

Quadrupolar Splitting Frequency Satellite Splitting proportional to local EFG, c +3/2 +1/2 -1/2 -3/2 -5/2 5/2 17 O NMR in La 1.8-x Eu 0.2 Sr x CuO 4 allows one to probe the EFG in the limit of slow spin dynamics

Oxygen Electric Field Gradient 2p 6 does not create an EFG at the nucleus, but 2p 5 does La 2-x Sr x CuO 4 La 1.8-x Eu 0.2 Sr x CuO 4 T > 150K EFG is a direct measure of the number of holes in the O 2p orbital

NMR Spectra on Aligned Powder powder sample necessary to enrich with 17 O Aligned and mixed with epoxy Enriched and non-enriched spectra are subtracted

Spectra From the planar O spectra, we observe: T dependent Knight shift Magnetic broadening below 20K Strongly T dependent c ! La 1.67 Eu 0.2 Sr 0.13 CuO 4

Temperature Dependence EFG is strongly temperature dependence below T ~ 60K Never been seen previously in superconducting cuprates Effective number of holes at the O sites has decreased!

Missing Signal Intensity Some of the oxygen sites do not contribute to signal: remaining sites experience reduced hole doping Where do the holes go? x=0.13 x=0.20 O Intensity La Intensity

NEXAFS and O hole doping J. Fink et al., J. Elec. Spec (1994) La 1.8-x Eu 0.2 Sr x CuO 4 X-ray absorption fluorescence spectroscopy of the O 1s  2p transition: intensity proportional to number of holes in oxygen 2p orbitals No observable change of holes in 2p orbitals of LESCO!

Implications of NEXAFS and NMR Breadth of the local hole distribution increases at low temperatures for both LTO and LTT For LTT, an unknown mechanism wipes-out regions of high hole doping What is this mechanism? T > T q T < T q

Hyperfine Field and Wipeout P(T 1 -1 ) ln(T 1 -1 ) Detection window set by spectrometer - maximum d etectable T 1 -1 La NMR 1 T1T1 ~ H hyp 2  Site H hyp (kOe/  B ) La~ 1 Cu~ 100 O ~ 0-50 PRL (2000) LaCu

Hyperfine Fields at Oxygen O Cu H hyp ~ 0 O Cu O H hyp ~ large 1 T1T1 ~ H hyp 2  ~ large These sites wiped-out! 1 T1T1 ~ H hyp 2  

Spin Density Modulation O Cu O O S(r)S(r) H hyp ~  S( r ) T 1 -1 is largest near nodes of S(r): wiped out The NMR signal showing reduced hole concentration comes from regions far from nodes! Is hole concentration correlated with the nodes?

Charged Domain Walls Charged Domain-Walls: Zaanen et al. (PRB (89)) Bishop et al. (cond-mat/ ) Hyperfine fields wipe out regions of high hole density Spatial correlation between n p ( r ) and  S( r )

Checkerboard Topology 1D stripes: 25% of signal is lost Site-centered checkerboard: 38% lost Experiment: ~ 50% lost Random disorder: r 0 ~ 15 Å

An Interesting Question LTOLTT Conventional Picture of Stripe Pinning: Why is the width of the local doping distribution the same in both La 2-x Sr x CuO 4 and La 1.8-x Eu 0.2 Sr x CuO 4, and there are no dramatic changes at T LT ? Perhaps the charge inhomogeneity is already set in at a high temperature Small fluctuations (local phonons – Bishop) give rise to spin fluctuations that are gapped and exhibit glassy behavior in the LTT phase T LT

Glassy Behavior Inhomogeneity remains spatially disordered Gives rise to slow spin (and possibly charge) fluctuations

In-plane Doping: La 2 Cu 1-x Li x O 4 Li 1+ in-plane doping ~ Zn 2+ & hole No incommensurate splitting Curie-Weiss susceptibility from FM response surrounding Li sites Holes “bound” to Li sites J. L. Sarrao et al., PRB (1996)

NMR in La 2 Cu 1-x Li x O 4 La NMR O Suh et al., PRL (98)Park et al., PRL (05) Glassy spin and charge dynamics O spectra show large magnetic broadening, possibly changes in EFG as well Zn impurity in YBCO Julien et al., PRL (2000)

Summary O NMR observes a distribution of local charges, that is spatially correlated with the local spin density The LTT structure suppresses spin fluctuations, rather than “pins” stripes The spin fluctuations must be important for superconductivity The stripe “template” may exist at high temperatures, and the spin and charge fluctuations observed are only excitations associated with this heterogeneity

Resistivity