Session V8: Superconductivity: Spin Excitations and Ordering in Cuprates

Antiferromagnetism and superconductivity do not seem to coexist in Nd$_{2-x}$Ce$_x$CuO$_{4\pm\delta}$

High transition-temperature ($T_{\mathrm{c}}$) superconductivity develops near antiferromagnetic (AF) phases, and it is possible that magnetic excitations contribute to the superconducting (SC) pairing mechanism. In order to assess the role of antiferromagnetism, it is essential to understand the doping and temperature dependence of the two-dimensional AF spin correlations. The phase diagram is asymmetric with respect to electron and hole doping, and for the comparatively less-studied electron-doped materials, the AF phase extends much further with doping and it appears to overlap with the SC phase: the archetypical compound Nd$_{2-x}$Ce$_x$CuO$_{4\pm\delta}$ shows bulk superconductivity above $x \approx 0.13$, while evidence for AF order has been found up to $x\approx 0.17$. However, our inelastic magnetic neutron scattering measurements point to the distinct possibility that genuine long-range antiferromagnetism and superconductivity do not co-exist. The data reveal a magnetic quantum critical point where superconductivity first appears, consistent with an exotic quantum phase transition between the two phases. Our measurements also demonstrate that the pseudogap phenomenon in the electron-doped materials arises from a build-up of spin correlations, in agreement with recent theoretical proposals.   

New phase diagram of ideally flat CuO$_{2}$ plane: Cu-NMR study in Five-layered Cuprates

We report a systematic Cu-NMR study on Hg-, Tl-,Cu-based five-layered high-Tc cuprates. In underdoped HgBa$_{2}$Ca$_{4}$Cu$_{5}$O$_{y}$ (Hg-1245) with a Tc=72 K, the AFM order is detected with 0.1$\mu _{B}$ even at two outer planes (OP's) that are responsible for the onset of superconductivity (SC). This is the first microscopic evidence for the uniform mixed phase of AF and SC on a single CuO$_{2}$ [1]. Recently we found AFM insulating state at low temperatures in disordered fivelayered cuprate Cu-1245, whereas the carrier densities are similar to Hg-1245(OPT) where the AFM metallic state are realized in IP's[2]. This finding reinforces the phase diagram in which the AFM metallic phase exists between AFM insulator and SC states for the case of ideally-flat CuO$_{2}$ plane without disorder. [1] Mukuda et al., Phys. Rev. Lett. 96,087001 (2006) [2] Mukuda et al., J. Phys. Soc. Jpn., 75, No.12 (2006)   

High-Tc superconductivity and antiferromagnetism on self-doped high-Tc cuprate Ba$_{2}$Ca$_{3}$Cu$_{4}$O$_{8}$F$_{2}$

We report on the antiferromagnetism and high-Tc superconductivity in a F-substituted four-layered cuprate, composed of two outer and inner CuO$_{2 }$planes in a unit cell, Ba$_{2}$Ca$_{3}$Cu$_{4}$O$_{8}$F$_{2}$. Although a formal Cu valence is expected to be just +2.0 in the nominal composition, this is not a half-filled Mott insulator but a superconductor with Tc = 55K. Recently, it has been suggested that the origin of the superconductivity in this compound is self-doping by ARPES measurement [1] and band calculation [2], which means either outer or inner CuO$_{2}$ planes are hole-doped, and the others are electron-doped. From F-NMR study, we have confirmed magnetic order with T$_{N}$ = 100K, concluding the uniform mixing of superconductivity and magnetic order in a single CuO$_{2}$ plane. In addition, we have compared a three-layered compound Ba$_{2}$Ca$_{2}$Cu$_{3}$O$_{6}$F$_{2}$, which is also superconductor with Tc = 76K. We will introduce the unique magntic and superconducting phenomena in F-substituted cuprates from microscopic points of view. [1]Y. Chen, \textit{et al}., cond-mat/0611291 (2006) [2] W. Xie, et al., cond-mat/0607198 (2006)   

Effect of oxgyen ordering on the spin dynamics of YBa$_2$Cu$_3$O$_{6.5}$

We use inelastic neutron scattering to study the oxgyen disorder effect in electronic properties of YBCO 6.5. Previous work have shown when copper oxgyen chains in the YBCO 6.5 form ortho-II order, magnetic excitations in YBCO6.5 form a resonance around 33 meV and incommensurate spin flucutations below the resonance. In oder to study oxygen disorder effect on spin excitations of YBCO 6.5, we measured spin dynamics of detwinned Ortho-I YBCO (x=6.5) ($T_c$=48K), whose Cu-O chains are not well ordered. We find that oxygen disorder can have dramatic effect on spin dynamics of YBCO6.5. We discuss similarities and differences in spin dynamics in these two materials and their possible interpretation.   

Evolution of hourglass like magnetic excitation in underdoped La$_{1.90}$Sr$_{0.10}$CuO$_{4}$.

Recent neutron scattering studies have revealed similar ``hourglass-lik'' magnetic excitations in mono-layered La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ and bi-layered YBa$_{2}$Cu$_{3}$O$_{6.6}$. These results indicate that such hourglass-like dispersive excitations might be common to high-T$_{c}$ cuprates. To elucidate the interplay between the excitation and the superconductivity, we investigated the hole doping dependence of excitations. We performed inelastic neutron experiments for underdoped La$_{1.90}$Sr$_{0.10}$CuO$_{4 }$(T$_{c}$=29K) using chopper spectrometer PHAROS installed at Los Alamos National Laboratory. Clear four incommensurate peaks were observed at $\omega $=8meV and the incommensurability corresponds to $\sim $0.1 r.l.u., which is consistent with previous study. Around $\omega $=30meV, a single peak was observed at the antiferromagnetic magnetic zone center. This indicates that the hourglass-like excitations also exist in underdoped La$_{1.90}$Sr$_{0.10}$CuO$_{4}$ and that the saddle point becomes $\sim $30meV. For optimally doped La$_{1.84}$Sr$_{0.16}$CuO$_{4 }$(T$_{c}$ =38K), the saddle point is expected to correspond to 40meV or more, suggesting that the saddle point goes up with increasing hole doping. Moreover, we found that the slope of dispersion is almost same for La$_{1.90}$Sr$_{0.10}$CuO$_{4}$ and La$_{1.84}$Sr$_{0.16}$CuO$_{4}$. The reduction of energy at saddle point is recognized as a consequence of difference of incommensurability.   

Neutron Scattering in High-T$_c$ Cuprates: Two Component Spin-Fermion Model

Recent neutron scattering experiments reveal that the generic form of the magnetic excitations in the high-Tc cuprates has the so-called ``hour-glass'' form, in which both the quasi-elastic incommensurate (IC) excitations and the commensurate resonance peak show up at different excitation energies. We propose the two-component spin-fermion model having the local spin degrees of freedom and itinerant fermions. Our calculations of the dynamic spin correlation function both at normal and superconducting states explain the essential features of the hour-glass form of the neutron experiments.   

Inelastic neutron scattering study on spin excitations of Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$ ($T_c$=27.5K)

We use neutron scattering to study the evolution of spin excitations in electron doped Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$(PLCCO). For $T_c$ = 24 K PLCCO, Wilson et al. [Nature 442, 59 (2006)] have reported the presence of a resonance mode, a localized magnetic excitations coupled directly to the superconductivity in high-$T_c$ superconductors, similar to hole-doped superconductors such as YBa$_2$Cu$_3$O$_{6+\delta}$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and Tl$_2$Ba$_2$CuO$_ {6+\delta}$. Below the resonance are continuing of magnetic scattering with little temperature dependence. We show here our studies of the magnetic excitations on PLCCO ($T_c$=27.5K) with the highest $T_c$ reported in the literature. We confirm the presence of a resonance mode in this sample, and demonstrate that the low-energy magnetic scattering here is much different from the $T_c$=24 K PLCCO. Our results thus shed new light to the understanding of spin excitations in electron-doped copper oxides.   

Spin wave excitations in Nd2CuO4

In this talk we will present the inelastic neutron scattering results of spin wave excitations of the electron-doped superconductor parent compound Nd2CuO4 (NCO). We carried out our experiments on the HET time of flight spectrometer at the ISIS facility in England. Our work will complement previous studies on the parent compound of hole-doped superconductors, La2CuO4 (LCO). We are studying whether there is a difference between the magnetic exchange coupling of hole-doped and electron-doped superconductors. We have probed energies from 50 meV to above 300 meV in order to detemine the magnetic exchange coupling. We will present the results and discuss the similarities and differences between LCO and NCO.   

Incommensurate Spin Ordering and Excitations in Underdoped La$_{2-x}$Ba$_x$CuO$_4$

The diverse magnetic properties of the La$_{2-x}$(Sr,Ba)$_x$CuO$_4$ transition metal oxides may be tuned in a controllable way by doping with mobile holes. In one interpretation, the holes are believed to organise into correlated static or dynamic stripes. We report the first observation of static {\it incommensurate} spin ordering in underdoped La$_{2-x}$Ba$_x$CuO$_4$ (x$\sim $0.05, x=0.08) using neutron diffraction. Elastic collinear incommensurate peaks are observed below the superconducting transition (T$_C \sim $27 K) in La$_{2-x}$(Sr,Ba)$_x$CuO$_4$ (x=0.08). In marked contrast, diagonal satellite peaks have been observed at low temperature in positions rotated by 45$^\circ $ within the (HK0) plane for La$_{2-x}$(Sr,Ba)$_x$CuO$_4$ (x$\sim $0.05). Our neutron scattering results are compared with analogous studies on La$_{2-x}$Sr$_x$CuO$_4$ which indicate that such a rotation of the spin structure may be a generic feature of the underdoped La-214 cuprates.   

Spin and Charge Excitations in Checkerboards based on a Superstructure

Checkerboard patterns have been proposed to explain the real space structure observed in STM experiments on BSCCO and Na-CCOC. However, simple checkerboard patterns always give incommsensurate (IC) spin peaks rotated 45 degrees from the direction of the charge IC peaks, contrary to what is seen in neutron scattering. [1] Here, we study a more complicated checkerboard pattern which can resolve the low frequency inconsistency. Using spin wave theory, we explore the finite frequency response of this superstructure and find that the high energy response is inconsistent with neutron scattering results. In particular, there is no spin resonance peak. \newline \newline [1] D.X.Yao, E.W. Carlson and D.K.Campbell, Phys. Rev. B 73, 224525 (2006)   

Connecting spin and charge response in electron-doped cuprates

We perform a detailed analysis of angle-resolved photoemission data from electron-doped cuprates [1,2] in order to extract both the self-energy and the bare dispersion of the quasiparticles. The self-energy contains important information about the interactions among the quasiparticles. Taking the extracted bare quasiparticle dispersion as an input parameter we compute dynamical response functions employing a spin-fluctuation-based theory. In particular we estimate the dynamical spin susceptibility, which we then compare to recent inelastic neutron scattering data [3]. We obtain a resonance at the anti-ferromagnetic ordering wavevector $(\pi, \pi)$, whereas incommensurate spin excitations are mostly suppressed. Our approach provides a consistent theoretical description of both the spin and charge response in electron-doped cuprates. \newline \newline [1] H.~Matsui \textit{et al.}, Phys.~Rev.~Lett. \textbf{94}, 047005 (2005). \newline [2] H.~Matsui and T.~Takahashi, private communication. \newline [3] S.~D.~Wilson \textit{et al.}, Phys.~Rev.~B \textbf{74}, 144514 (2006).   

Local moment and inhomogeneous hyperfine interaction in the CuO$_2$ plane of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) single crystal by ${}^{17}$O NMR

The ${}^{17}$O NMR spectra of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) single crystals were measured in the magnetic field of 8 T from 4 K to 200 K. The linewidth of the oxygen in CuO$_2$ plane, O(1), was found to follow a Curie temperature dependence in the normal state, where the Curie coefficient decreases with the increase of $\delta$ oxygen in the crystal. In the superconductive state, it decreases with deceasing temperature, proportional to the decreasing Knight shift. This temperature dependence of the linewidth identifies the existence of local moment and inhomogeneous hyperfine interaction in the CuO$_2$ plane.   

Low-energy spin dynamics in La$_{1.95}$Sr$_{0.05}$CuO$_4$

The low energy part of spin fluctuation spectra $S({\bf q},E)$ of La$_{1.95}$Sr$_{0.05}$CuO$_4$ were measured using the cold neutron triple-axis spectrometer SPINS from 1.5 to 80 K. The incommensurate doublets of magnetic peaks show a tendency to move towards the commensurate (pi,pi) point with increasing energy, like the incommensurate quartets in (La,Ba)$_2$CuO$_4$ and other related cuprates. There is an energy-resolution limited ``central peak'' at $E=0$ below ~20K in the spectra $S({\bf q},E)$, likely due to the spin-glass transition [1]. The inelastic component has a different temperature dependence from the ``central peak'' and a detailed quantitative description of the data becomes available. The {\em local} spectra $S(E)$ behave in a manner closely resembling those of Li-doped La$_{2}$CuO$_4$ [2].\\ \,[1] Y. Chen et al., Phys. Rev. B {\bf 72}, 184401 (2005).\\ \,[2] W. Bao et al., Phys. Rev. Lett. {\bf 91}, 127005 (2003); Y. Chen et al., cond-mat/0408547.