Session B11: Magnetic Properties of Cuprate Superconductors

Disappearance of antiferromagnetic spin excitations in overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$

We have used time-of-flight neutron spectroscopy to study magnetic excitations, for energies up to $\sim $100 meV, in overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x$ = 0.25 and 0.30 [1]. Comparison of spectra integrated over the width of an antiferromagnetic Brillouin zone demonstrates that the magnetic scattering at intermediate energies, 20$<\omega <$100 meV, progressively decreases with overdoping. Previous work has shown that the low-energy magnetic excitations also disappear with overdopoing [2]. This strongly suggests that the magnetism is a vestige of the parent antiferromagnet; spatial segregation of the doped holes, as in the stripe picture, provides a natural way for this to occur. Both the magnetism and superconductivity disappear as the system becomes a homogeneous metal. [1] S. Wakimoto \textit{et al}., Phys. Rev. Lett. \textbf{98}, 247003 (2007). [2] S. Wakimoto \textit{et al}., Phys. Rev. Lett. \textbf{92}, 217004 (2007).   

Spin Susceptibility of Underdoped Cuprates: Insight from Stripe-Ordered $\bf La_{1.875}Ba_{0.125}CuO_4$

The low-temperature decrease of the bulk magnetic susceptibility in underdoped high-temperature superconductors has commonly been cited as evidence for a pseudogap; however, the interpretations range from a Fermi-liquid perspective, with the susceptibility being proportional to the density of free carriers, to strong coupling pictures, with the susceptibility resulting from antiferromagnetic correlations among local moments. Analysis of the susceptibility of a particular cuprate, the stripe ordered $\rm La_{1.875}Ba_{0.125}CuO_4$, sheds new light on this remarkable system and puts tight constraints on possible interpretations. The recently discovered magnetic transition in high magnetic fields will also be discussed.\newline [1] M. H\"ucker, G. D. Gu, J. M. Tranquada, cond- mat/0503417v2.\newline [2] Q. Li, M. H\"ucker, G. D. Gu, A. M. Tsvelik, J. M. Tranquada, Phys. Rev. Lett. 99, 067001 (2007).   

Magnetic correlations on full chains of ortho-II YBCO6.5

We propose that the $^{63}$Cu NMR line shape of chain Cu in YBCO6.5 Ortho-II samples may be explained by assuming induced magnetization due to oxygen vacancies and strong correlations in the chain. The model consists of CuO chains coupled to CuO2 plane with Hubbard correlations treated in unrestricted Hartree-Fock approxmiation, which induce magnetic moments around oxygen chain vacancies. The broadening and shift of NMR main line is consistent with increased chain magnetization at low temperature. Tunneling between chains and the plane induces magnetization on the planar coppers as well, which gives rise to quasi-1D like spin correlations in the plane.   

Normal state magnetic susceptibility measurements in underdoped YBa$_2$Cu$_3$O$_{7-\delta}$

Motivated by the observation of staggered magnetic moments by Fauqu\'e\textit{ et al.} [Phys. Rev. Letters 96, 197001 (2006)] using neutron diffraction in underdoped YBa$_2$Cu$_3$O$_{7-\delta}$, we have measured the magnetization of fourteen underdoped YBa$_2$Cu$_3$O$_{7-\delta}$ samples under 1 T from $T_C$ to 400 K. The oxygen contents are ranging from 6.43 to 7.00, and the critical temperatures $T_C$ from about 30 K to 91 K. We present here high resolution susceptibility data corresponding to a sensitivity of $10^{-8}$ $\mu_B$ per Cu atom. We separate the different contributions to the magnetization. We find: i) a small ferromagnetic contribution, visible at all temperatures within our range of measurement and consistent with a few ppm of $Fe_30_4$, ii) A ``1/T'' paramagnetic contribution attributed to a few percent of free Cu ions, iii) The contribution of the ``pseudogap'' which gives a susceptibility increasing with temperature excepted in the optimally doped samples where the susceptibility is flat as expected for Pauli paramagnetism. We discuss the physical implications of this contribution in light of experiments from Fauqu\'e \textit{et al}.   

The Persistence of High-Frequency Spin Fluctuations in Overdoped Superconducting La$_{2-x}$Sr$_{x}$CuO$_{4}$ ($x$=0.22)

The wavevector and energy dependence of the spin fluctuations in overdoped superconducting La$_{1.78}$Sr$_{0.22}$CuO$_4$ ($T_c$=26~K) were investigated up to high energy (160~meV) by inelastic neutron scattering. Overdoping was found to suppress the strong magnetic response $\chi^{\prime\prime}(\mathbf{q},\omega)$ present in optimally doped La$_{2-x}$Sr$_{x}$CuO$_4$ which is peaked near 50~meV. The magnetic excitations were less dispersive than in the optimal compound and incommensurate at all energies investigated. Overdoping did not appear to weaken the high-frequency $E\ge 100$~meV response, suggesting that significant antiferromagnetic exchange couplings persist well into the overdoped part of the cuprate phase diagram.   

Conditions for magnetically induced singlet d-wave superconductivity on the square lattice

It is expected that at weak to intermediate coupling, d-wave superconductivity can be induced by antiferromagnetic fluctuations. However, one needs to clarify the role of Fermi surface topology, density of states, pseudogap, and wave vector of the magnetic fluctuations on the nature and strength of the induced d-wave state. To this end, we study the generalized phase diagram of the two-dimensional half-filled Hubbard model as a function of interaction strength $U/t$, frustration induced by second-order hopping $t^{\prime }/t$, and temperature $T/t$. In experiment, $U/t$ and $t^{\prime }/t$ can be controlled by pressure. We use the two-particle self-consistent approach (TPSC), valid from weak to intermediate coupling. D-wave superconductivity can be induced by magnetic fluctuations but only if they are near commensurate wave vectors and not too close to perfect nesting conditions where the pseudogap becomes detrimental to superconductivity. For given $U/t$ there is thus an optimal value of frustration $t^{\prime}/t$ where the superconducting $T_c$ is maximum. The symmetry d$_{x^{2}-y^{2}}$ vs d$_{xy}$ of the superconducting order parameter depends on the wave vector of the underlying magnetic fluctuations in a way that can be understood qualitatively from simple arguments.   

Finite size effects in NMR $T_2$ relaxation by vortex vibrations

Nuclear magnetic resonance measurements are a powerful probe of electronic behavior in superconductors, but a precise understanding of all relaxation mechanisms is required to draw accurate conclusions. A previous calculation of the rate of transverse relaxation in the cuprate superconductor YBa$_2$Cu$_3$O$_{7-\delta}$ based on an overdamped elastic model of vortex motions predicted relaxation rates orders of magnitude slower than those observed in experiments, despite strong experimental evidence pointing to vortex vibrations as the dominant relaxation mechanism. Here the finite size of the powder grains is explicitly included in the calculation, and we find that both the relaxation rate and the time dependence of the recovery seen in the experiments can be accounted for. The dependence of the relaxation rate on the size and shape of the samples is explored.   

Evolution of the spin dynamics in electron-doped high-transition temperature superconductor Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$( Tc=24K, 27K)

We use both polarized and unpolarized neutron scattering to study spin excitations in electron doped cuprates Pr$_{0.88} $LaCe$_{0.12}$CuO$_{4-\delta}$(Tc=24K, 27K). We determine the dynamic susceptibility and its temperature dependence for energes between 0.5meV to 30meV in these samples. Our results show that the spectral weight of optimal doped PLCCO (27K) around resonance energy region ($\sim$10meV) is much stronger than that of the slightly underdoped 24K PLCCO. We also demonstrate that using polarized neutrons are necessary to isolate magnetic scattering from nonmagnetic processes. A determination of the evolution of spin excitations in PLCCO as the system is tuned from nonsuperconducting to superconducting states is important to our understanding of the role of magnetism in high-Tc superconductivity.   

Incompatibility of Checkerboard Patterns with the Resonance Peak in Cuprate Superconductors

Checkerboard patterns have been proposed to explain STM experiments on the cuprates BSCCO and Na-CCOC. However, simple checkerboard patterns are inconsistent with neutron scattering data, since they have low energy incommsensurate spin peaks rotated $45^o$ from the direction of the charge peaks.[1] Recently, more complicated checkerboard patterns have been proposed in order to reconcile this conflict. In this work, we have studied modulated checkerboards by using spin wave theory and analyzed noncollinear checkerboards as well. We find that the high energy response of the modulated checkerboards is inconsistent with neutron scattering results, since they fail to exhibit a resonance peak at ($\pi,\pi$), which has recently been shown to be a universal feature of cuprate superconductors. Furthermore, noncollinear checkerboards also lack a resonance peak. [2] However, stripe patterns naturally exhibit a resonance peak consistent with neutron scattering data. References: [1] D. X. Yao, E. W. Carlson and D. K. Campbell, Phys. Rev. B 73, 224525 (2006) [2] D. X. Yao and E. W. Carlson, arXiv:0708.1966   

High field, low temperature 17O Knight shift in an underdoped High-Tc cuprate: La(2-x)Sr(x)CuO(4) for x =0.115, 0.15

We use high magnetic fields ($>$30T) to suppress the superconducting Tc in order to investigate the normal state NMR properties of La(2-x)Sr(x)CuO(4) (LSCO) at low temperatures. Recent studies have shown glassy behavior and incommensurate spin-waves in LSCO, which has been discussed as evidencing a stripe ordered picture at low temperatures in the under-doped regime. We use 17O NMR as a local probe of the electron density on the planar oxygens. 17O Knight shift and linewidth were obtained over a wide temperature range in the normal state for under-doped (x=0.115) and optimally doped (x=0.15) LSCO.   

Static Magnetic Order in Underdoped HgBa$_{2}$CuO$_{4+\delta }$

It is believed by many that understanding the pseudogap phase is essential to understanding the mechanism of high-transition-temperature superconductivity. Here we present the first experimental identification, by polarized neutron diffraction, of an exotic magnetic order in the HgBa$_{2}$CuO$_{4+\delta }$ (Hg1201), which is considered the model high-Tc material with (i) simple tetragonal structure, (ii) large spacing between the CuO$_{2}$ planes, and (iii) the highest Tc among all single-layer compounds [1]. The order parameter develops below a characteristic temperature T$_{mag}$ that nicely agrees with the pseudogap temperature T* determined by DC transport. Our result is highly consistent with the previous work by B. Fauque \textit{et al. }on the bi-layer compound YBCO [2], and can be interpreted within an orbital-current picture that breaks time-reversal symmetry but preserves discrete translational symmetry. The magnitude and the orientation of the magnetic moments of the current loops are experimentally investigated. 1. X. Zhao \textit{et al.}, Adv. Mat. \textbf{18}, 3243 (2006). 2. B. Fauque \textit{et al.}, PRL \textbf{96}, 197001 (2006).   

Quantum Spin Excitations through the metal-to-insulator crossover in YBa$_2$Cu$_3$O$_{6+y}$

We use inelastic neutron scattering to study the temperature dependence of the spin excitations of a detwinned superconducting YBa$_2$Cu$_3$O$_{6.45}$ ($T_c=48$ K). In contrast to earlier work on YBa$_2$Cu$_3$O$_{6.5}$ ($T_c=58$ K), where the prominent features in the magnetic spectra consist of a sharp collective magnetic excitation termed ``resonance'' and a large ($\hbar\omega\approx 15$ meV) superconducting spin gap, we find that the spin excitations in YBa$_2$Cu$_3$O$_{6.45}$ are gapless and have a much broader resonance. Our detailed mapping of the spin excitations along the $a^\ast$- axis direction reveals a dispersion consistent with the ``hourglass'' like dispersion near the resonance, but the spin excitations are isotropic at lower energies. Since a fundamental change in the low-temperature normal state of YBa$_2$Cu$_3$O$_{6+y}$ when superconductivity is suppressed takes place at $y\sim0.5$ with a metal-to-insulator crossover (MIC), where the ground state transforms from a metallic to an insulating-like phase, our results suggest a clear connection between the large change in spin excitations and the MIC.   

Magnetic excitations in the high-temperature superconductors HgBa$_{2}$CuO$_{4+\delta }$ and Nd$_{1.845}$Ce$_{0.155}$CuO$_{4}$

We report inelastic neutron scattering results for the magnetic excitations in hole-doped HgBa$_{2}$CuO$_{4+\delta }$ (Hg1201) and electron-doped Nd$_{2-x}$Ce$_{x}$CuO$_{4+\delta }$ (NCCO). The magnetic resonance mode has been observed previously in the superconducting state of several hole-doped systems. Recently, this mode has also been claimed to be present in the electron-doped compounds. We found in underdoped Hg1201 (T$_{c}\sim $85 K) the resonance-like feature appearing at rather high energy of 57(2)meV. Surprisingly, the dynamic susceptibility enhancement appears below the pseudogap temperature T$^{\ast }$ and shows no anomaly at T$_{c}$. Unlike recent reports for optimally-doped NCCO and (Pr,La,Ce)$_{2}$CuO$_{4+\delta }$, we found no evidence for a resonance mode in NCCO (x=0.155) in the 7-12 meV range. Instead, we identify two lower-energy features. One is associated with spectral weight redistribution below T$_{c}$ due to the electronic gap 2$\Delta $, the other already present in normal state is likely associated with the significant spin correlations in the electron-doped cuprates.