Session T21: Magnetic Ordering and Dynamics in Cuprates

Two Dimensional Incommensurate and Three Dimensional Commensurate Magnetic Order and Fluctuations in $La_{2-x}Ba_{x}CuO_{4}$

We present neutron scattering measurements on single crystals of $La_{2-x}Ba_{x}CuO_{4}$, with $0 \leq x \leq$ 0.035. These experiments reveal the evolution of the magnetism: from a three dimensional (3D) commensurate (C) antiferromagnet, with a relatively high T$_{N}$, to a two dimensional (2D) incommensurate (IC) antiferromagnet with finite range static correlations, with relatively low effective T$_{N}$s. At low temperatures, the 2D IC magnetism co-exists with the 3D C magnetism for Ba concentrations as low as x = 0.0125. We find that 3D C magnetism disappears by x = 0.025; consistent with the limit of x $\sim$ 0.02 observed in the sister family of doped Mott insulators $La_{2-x}Sr_{x}CuO_{4}$. We construct a phase diagram based on magnetic order parameter measurements, which displays much of the complexity of standard high temperature superconductivity phase diagrams discussed in the literature. Analysis of high energy-resolution inelastic neutron scattering shows the low energy dynamic susceptibility to fall off with temperature on a scale much higher than the effective 2D IC T$_{N}$s in the sample. This effect is such that appreciable dynamic 2D IC magnetic fluctuations inhabit much of the ``pseudogap'' regime of the phase diagram.   

Novel magnetic excitations in the high-temperature superconductor HgBa$_{2}$CuO$_{4+ \delta }$

We report on the observation of novel magnetic excitations in the pseudogap phase of the cuprate superconductor HgBa$_{2}$CuO$_{4+\delta }$ (Hg1201) using neutron scattering, and on their relationship with antiferromagnetic (AF) fluctuations. Following polarized neutron diffraction experiments that demonstrated a novel (q=0) magnetic order in the pseudogap phase [B. Fauqu\'{e} \textit{et al.} PRL 96, 197001 (2006); Y. Li \textit{et al.}, Nature 455, 372 (2008)], our inelastic measurements revealed two weakly-dispersive magnetic excitation branches in Hg1201 [Y. Li \textit{et al.}, Nature 468, 283 (2010), and preprint]. These excitations are observed in the pseudogap phase and appear to be associated with the q=0 magnetic order. In our optimally-doped sample, the magnetic resonance occurs at the dispersion maximum of the higher-energy branch. In under-doped Hg1201, the two excitation branches exhibit local intensity maxima at q$_{AF}$, and we find evidence for an hourglass dispersion associated with the lower branch. These results reveal a profound connection between the novel excitations and the conventional AF fluctuations.   

Stripe order in La$_{2-x}$Ba$_{x}$CuO$_{4}$ in high magnetic fields

The observation of enhanced spin stripe order in the vortex cores of La$_{2-x}$Sr$_{x}$CuO$_{4}$ has been a landmark experiment that revealed the intimate connection between superconductivity and incommensurate antiferromagnetism. Only recently we have observed a corresponding field dependence of the spin and, more importantly, of the charge stripe order in La$_{2-x}$Ba$_{x}$CuO$_{4}$. Here we present our recent results from neutron diffraction, x-ray diffraction, and torque measurements in high magnetic fields. These helped us to establish the field versus temperature and doping phase diagrams for spin and charge order, and to further corroborate the stripe model as the more appropriate description than for example spiral and vortex states.   

Pressure study of local tilts and their correlation to stripe order in single crystal La$_{1.875}$Ba$_{0.125}$CuO$_{4}$

The strong Tc suppression in LaBaCuO at x=0.125 is widely believed to be related to formation of static stripes, at least partially driven by a strong electron-lattice coupling in a low temperature tetragonal (LTT) phase (Tranquada et al., Nature 375, 561 (1995)). A recent high-pressure experiment appears to challenge this view as it was observed that static stripe order persists to pressures higher than required to induce LTT to HTT transition (Hucker et al., PRL 104, 057004 (2010)). We carried out high-pressure La K-edge polarized XAFS measurements in LaBaCuO (x=0.125) single crystals in a diamond anvil cell to probe local CuO6 tilts. We observe that the local tilts remain LTT-like at high pressure, even though the macroscopic structure is HTT. The results suggest a significant order-disorder component to this pressure-induced phase transition, whereby the local LTT tilts remain present in the local scale but disorder over long range resulting in HTT symmetry seen by diffraction. The result may help explain why the stripe order is largely unaffected by the LTT to HTT pressure-induced transition. Work at Argonne (BNL) is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357 (DE-AC02-98CH10886).   

Gutzwiller Charge and Magnetic Phase Diagrams of Cuprates

We extend our previous analysis of the magnetic phase diagram of the cuprates to look for charge instabilities, either purely electronic or involving electron-phonon coupling, employing Gutzwiller approximation GA+RPA calculations of the Hubbard model. In the absence of phonons we find an overscreening instability for large doping at $(\pi ,\pi)$. In the presence of electron-phonon coupling, we find a rich response to Fermi surface nesting, very similar to the magnetic case, and in this case the instability criterion can be formulated as a generalized Stoner criterion. In the hole-doping regime, where evidence exists for a nonmagnetic (stripe) pseudogap, we find competing instabilities. Since the same susceptibility peaks are present for both spin and charge excitations, differences in preferred $q$-vectors arise from the $q$-dependence of the interaction $U_{eff,q}$.   

The impact of incommensurate bond centered density waves in underdoped cuprates

We study the particle-particle channel and the particle-hole channel of the valence bond fluctuations away from half filling in cuprates. Based on strong-coupling analysis of the t-J model, we argue that the superexchange interaction J induced incommensurate bond centered density wave order is the driving mechanism for the pseudogap state. We show that the interplay between the incommensurate bond centered density wave instability and the intrinsic electronic inhomogeneity in real cuprates materials is responsible for the observed pseudogap phenomena.   

Two-component electron fluid and pseudogap asymmetry in underdoped high-Tc cuprate superconductors

Evidence from NMR of a two-component spin system in the cuprate high-Tc superconductors is shown to be paralleled by similar evidence from the total electronic entropy so that a two-component quasiparticle fluid is implicated. We propose that this two-component behavior arises from reconstruction of the energy-momentum dispersion into two branches in the pseudogap regime. If correct then it follows that single-component electronic behavior will be recovered when the pseudogap closes in the overdoped regime. We illustrate this by calculating the spin susceptibility using the resonating valence bond spin liquid model developed by Yang, Rice and Zhang, finding excellent agreement with the NMR results. In addition, we find that the particle-hole asymmetric pseudogap of this model accounts for both the large thermoelectric power, and the downturn in resistivity observed in underdoped cuprates.   

Spin excitations in a layered antiferromagnetic metal

The proximity of antiferromagnetic order in high-temperature superconducting materials is considered a possible clue to the electronic excitations which form superconducting pairs. Here we study the transverse and longitudinal spin excitation spectrum in a one-band model in the pure spin density wave (SDW) state and in the coexistence state of SDW and superconductivity. We start from a Stoner insulator which is similar to the case of cuprate parent compounds. By changing the chemical potential and the SDW order parameter, we study the evolution of the spectrum with different Fermi surfaces, such as the one with only hole pockets, with only electron pockets and with pockets of both types. We also compute the spin excitations in the coexistence of the AF and d-wave superconductivity, motivated by electron-doped cuprates.   

Coexistence of Superconductivity and Magnetic Order in RuGd$_2$Sr(Cu$_{1-x}$Fe$_x$)$_2$O$_8$ probed by $^{99}$Ru and $^{57}$Fe M\"{o}ssbauer Effects

RuGd$_2$Sr$_2$Cu$_2$O$_8$ develops magnetic order at about 137K and becomes a superconductor at lower temperatures(T$_{SC} \sim$ 40K). T$_{SC}$ decreases with increasing Fe doping in RuGd$_2$Sr$_2$(Cu$_{1-x}$Fe$_x$)$_2$O$_8$ and is zero by $x=.03$. We measure the $^{99}$Ru and $^{57}$Fe M\"{o}ssbauer Effects for x=0, 0.1, 0.2, and 0.3. The $^{57}$Fe M\"{o}ssbauer spectra(MS) show that there are two different Fe sites at 4.2K with very similar hyperfine magnetic fields, $H_{hyper}\sim 48$ T. However $H_{hyper}$ goes to zero at $\sim$half the Fe sites in a temperature range between 30K and 40K in superconducting and non-superconducting samples. There is no significant change in $H_{hyper}$ in the $^{99}$Ru MS in this temperature range. We conclude that the Fe sites whose $H_{hyper}$ does not change are in the magnetically ordered RuO planes. We assume that the Fe's which see the transition between 30K and 40K are in the CuO planes and investigate how this transition arises.   

NMR Studies of the pseudogap in BSCCO-2212

We present O-17 NMR measurements on a single crystal of overdoped BSCCO-2212 (T$_{c}$= 82K). As a function of temperature we measure the planar oxygen's: resonance linewidths, Knight shift (K), electronic field gradient (EFG), and spin lattice relaxation rate (1/T1) along each principle axis. Our analysis shows that their temperature dependence can be explained by a suppression of the density of states in the pseudogap region T $<$ T$^{\ast }$ = 94K.   

$^{17}$O and $^{199}$Hg NMR measurements of HgBa$_2$CuO$_{4+y}$ single crystals

The high superconducting transition temperature and the simple tetragonal structure of HgBa$_2$CuO$_{4+y}$ (Hg1201) makes this material an ideal candidate to study unconventional superconductivity in the cuprates[1]. Nuclear magnet resonance has been performed on Hg1201 single crystals which have been annealed in an $^{17}$O atmosphere to various dopings. Preliminary results of the NMR spectra and relaxation of both $^{17}$O and $^{199}$Hg are presented. Narrow linewidths allow for the resolution of both $^{17}$O lattice sites and a doping dependent $^{199}$Hg spectral splitting[2]. This work is supported by \textbf{DOE/BES: DE-FG02-05ER46248} and the NHMFL by NSF and the State of Florida.[1] N. Bari\u{s}i\'{c} \textit{et al}, PRB \textbf{78}, 054518 (2008) [2] J. Haase \textit{et al}, arXiv:1110.601v1 (2011)   

Magnetic susceptibility analysis on Zn-doping in the high $T_{c}$ superconductor YBa$_{2}$Cu$_{3}$O$_{7}$

Localized magnetic moments are known to destroy superconductivity in conventional superconductors. In the case of YBa$_{2}$Cu$_{3}$O$_{7}$ (YBCO), the nonmagnetic ion Zn has a very strong impact on suppressing the superconducting transition temperature ($T_{c})$. YBCO loses all superconductivity when only 10\% of the Cu is substituted with Zn.\footnote{R. E. Walstedt et al. Phys. Rev. B, \textbf{48}, 10646 (1993)} In this project, we have investigated the magnetic susceptibility for a number of Zn doping levels in samples with the nominal composition YBa$_{2}$(Cu$_{1-x}$Zn$_{x}$)$_{3}$O$_{7}$. We observe the development of Curie-Weiss paramagnetism for some Zn compositions, and will address whether the associated paramagnetic moments might cause magnetic pair-breaking.   

Observable NMR signal from orbital current order in YBCO

Assuming, as suggested by recent neutron scattering experiments, that a broken symmetry state with orbital current order occurs in the pseudo-gap phase of the cuprate superconductors, we show that there must be associated equilibrium magnetic fields at various atomic sites in the unit cell, which should be detectable by NMR experiments.   

Numerical study of magnetic excitations probed by photon spectroscopies in families of high-temperature superconductors

Magnetic excitation in high-temperature superconductors has been a topic of cutting edge research for many years. In photon spectroscopies, single- and two-magnon excitations can be created and measured efficiently using techniques such as resonant inelastic x-ray scattering and optical Raman scattering. We present numerical studies of the magnetic excitations for different families of high-temperature superconductors, including both copper and iron based superconductors. These magnetic excitations and their dispersions provide important information in understanding the magnetic properties of these materials.