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We performed muon-spin-rotation/-relaxation measurements to investigate the magnetic behavior of ${T}^{\ensuremath{'}}$-type ${\mathrm{Eu}}_{2}{\mathrm{CuO}}_{4}$ (ECO), which is the parent compound of electron-doped cuprate superconductors, and the effects of oxygen-reduction annealing on its magnetism. In as-sintered (AS) ECO, we clarified the development of magnetic correlations upon cooling below ${T}_{\mathrm{N}1}$ (= 265 K) as well as the coexistence of a dominant fluctuating spin state and partially ordered spin state in the temperature range between $\ensuremath{\sim}150$ K and ${T}_{\mathrm{N}1}$. Upon further cooling, uniform long-range magnetic order was observed below ${T}_{\mathrm{N}2}=110$ K, which is close to the ordering temperature of 115 K in ${T}^{\ensuremath{'}}$-type ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ (LCO) [Phys. Rev. B 82, 180508(R) (2010)]. For oxygen-reduction-annealed ECO, a similar ordering sequence with the same ${T}_{\mathrm{N}2}$ was observed but without the partially ordered spin state. Therefore, the fluctuating spin state over a wide temperature range and a ${T}_{\mathrm{N}2}$ less than the N\'eel temperature (${T}_{\mathrm{N}2}\ensuremath{\approx}{T}_{\mathrm{N}1}$) in T-type LCO are common features of the ${T}^{\ensuremath{'}}$-type parent ${R}_{2}{\mathrm{CuO}}_{4}$ ($R\mathrm{CO}$, $R$: rare-earth ion). The origin of the partially ordered spin state in AS ECO is discussed from the viewpoint of chemical defect. Furthermore, we discuss the roles of electron doping and repairing defect in the observed effect of annealing on the magnetism of ${T}^{\ensuremath{'}}$-type $R\mathrm{CO}$.

We report the inverse Laplace transform analysis of the $^{139}\mathrm{La}$ nuclear spin-lattice relaxation rate $1/{T}_{1}$ (${\mathrm{ILTT}}_{1}$ analysis) in charge-ordered ${\mathrm{La}}_{1.885}{\mathrm{Sr}}_{0.115}{\mathrm{CuO}}_{4}$ (${T}_{\mathrm{charge}}\ensuremath{\simeq}80$ K, ${T}_{c}\ensuremath{\simeq}{T}_{\mathrm{spin}}^{\mathrm{neutron}}=30$ K), and shed light on its magnetic inhomogeneity. We deduce the probability density function $P(1/{T}_{1})$ of the distributed $1/{T}_{1}$ (i.e., the histogram of distributed $1/{T}_{1}$) by taking the inverse Laplace transform of the experimentally observed nuclear magnetization recovery curve $M(t)$. We demonstrate that spin freezing sets in in some domains precisely below the onset of charge order at ${T}_{\mathrm{charge}}$, but their volume fraction grows only gradually toward ${T}_{c}$. Nearly a half of the sample volume exhibits properties expected for canonical high-${T}_{c}$ cuprates without charge order even near ${T}_{c}$. Our findings explain why charge order does not suppress ${T}_{c}$ of ${\mathrm{La}}_{1.885}{\mathrm{Sr}}_{0.115}{\mathrm{CuO}}_{4}$ as significantly as in ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_{4}$.

We investigate the interplay between the lattice, charge, and spin dynamics in charge-ordered high ${T}_{c}$ cuprate ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_{4}\phantom{\rule{4pt}{0ex}}({T}_{c}=4\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ based on the inverse Laplace transform (ILT) analysis of the $^{139}\mathrm{La}$ nuclear spin-lattice relaxation rate $1/{T}_{1}$ (dubbed ${\mathrm{ILTT}}_{1}$ analysis hereafter). A major thrust of the ${\mathrm{ILTT}}_{1}$ analysis is that one can deduce the probability density function $P(1/{T}_{1})$ of distributed $1/{T}_{1}$. We demonstrate that $1/{T}_{1}^{\text{lm}}$, defined as the log mean (i.e., the center of gravity on a logarithmic scale) of $P(1/{T}_{1})$, can be well approximated by $1/{T}_{1}^{\text{str}}$ deduced from the phenomenological stretched fit; however, $P(1/{T}_{1})$ can provide much richer insight into how the lattice, charge, and spin fluctuations and their distribution develop near and below the long-range charge order at ${T}_{\text{charge}}\ensuremath{\sim}54\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Upon entering the charge-ordered state, a divergent increase of $1/{T}_{1}^{\text{lm}}$ toward the spin ordering at ${T}_{\text{spin}}^{\ensuremath{\mu}\text{SR}}\ensuremath{\simeq}35\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ is accompanied by an asymmetric broadening of $P(1/{T}_{1})$. Even deep inside the charge-ordered state, $1/{T}_{1}$ at a gradually diminishing fraction of $^{139}\mathrm{La}$ sites continues to slow down as temperature is lowered, as expected for canonical superconducting ${\mathrm{CuO}}_{2}$ planes without enhanced spin fluctuations. The fraction of such canonical $^{139}\mathrm{La}$ sites almost disappears by $\ensuremath{\simeq}40\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. In contrast, nearly half of the $^{139}\mathrm{La}$ sites in ${\mathrm{La}}_{1.885}{\mathrm{Sr}}_{0.115}{\mathrm{CuO}}_{4}\phantom{\rule{4pt}{0ex}}({T}_{\text{charge}}\ensuremath{\simeq}80\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ still exhibit the canonical behavior without enhanced spin fluctuations even near its ${T}_{c}=31\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. These contrasting behaviors explain why superconductivity in ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_{4}$ is more strongly suppressed than in ${\mathrm{La}}_{1.885}{\mathrm{Sr}}_{0.115}{\mathrm{CuO}}_{4}$ despite the lower onset temperature of the charge order.

Compelling efforts to improve the critical temperature $({T}_{c})$ of superconductors have been made through high-pressure application. Understanding the underlying mechanism behind such improvements is critically important; however, much remains unclear. Here we studied ortho-III ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.73}$ (YBCO) using x-ray scattering under hydrostatic pressure (HP) up to $\ensuremath{\sim}6.0\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. We found the reinforced oxygen order of YBCO under HP, revealing an oxygen rearrangement in the Cu-O layer, which evidently shows the charge-transfer phenomenon between the $\mathrm{Cu}{\mathrm{O}}_{2}$ plane and Cu-O layer. Concurrently, we also observed no disorder-pinned charge-density-wave signature in $\mathrm{Cu}{\mathrm{O}}_{2}$ plane under HP. This indicates that the oxygen rearrangement modifies the quenched disorder state in the $\mathrm{Cu}{\mathrm{O}}_{2}$ plane. Using these results, we appropriately explain why pressure condition can achieve higher ${T}_{c}$ compared with the optimal ${T}_{c}$ under ambient pressure in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$. As an implication of these results, finally we have discussed that the change in disorder could make it easier for ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ to undergo a transition to the nematic order under an external magnetic field.

$^{139}\mathrm{La}$ NMR is suited for investigations into magnetic properties of ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$-based cuprates in the vicinity of their magnetic instabilities, owing to the modest hyperfine interactions between $^{139}\mathrm{La}$ nuclear spins and Cu electron spins. We report comprehensive $^{139}\mathrm{La}$ NMR measurements on a single-crystal sample of high-${T}_{c}$ superconductor ${\mathrm{La}}_{1.885}{\mathrm{Sr}}_{0.115}{\mathrm{CuO}}_{4}$ in a broad temperature range across the charge and spin order transitions $({T}_{\mathrm{charge}}\ensuremath{\simeq}80$ K, ${T}_{\mathrm{spin}}^{\mathrm{neutron}}\ensuremath{\simeq}{T}_{c}=30$ K). From the high-precision measurements of the linewidth for the nuclear spin ${I}_{z}=+1/2$ to $\ensuremath{-}1/2$ central transition, we show that paramagnetic line broadening sets in precisely at ${T}_{\mathrm{charge}}$ due to enhanced spin correlations within the ${\mathrm{CuO}}_{2}$ planes. Additional paramagnetic line broadening ensues below $\ensuremath{\sim}35$ K, signaling that Cu spins in some segments of ${\mathrm{CuO}}_{2}$ planes are on the verge of three-dimensional magnetic order. A static hyperfine magnetic field arising from ordered Cu moments along the $ab$ plane, however, begins to develop only below ${T}_{\mathrm{spin}}^{\ensuremath{\mu}SR}=15--20$ K, where earlier muon spin rotation measurements detected Larmor precession for a small volume fraction $(\ensuremath{\sim}20%)$ of the sample. Based on the measurement of $^{139}\mathrm{La}$ nuclear-spin-lattice relaxation rate $1/{T}_{1}$, we also show that charge order triggers enhancement of low-frequency Cu spin fluctuations inhomogeneously; a growing fraction of $^{139}\mathrm{La}$ sites is affected by enhanced low-frequency spin fluctuations toward the eventual magnetic order, whereas a diminishing fraction continues to exhibit a behavior analogous to the optimally superconducting phase even below ${T}_{\mathrm{charge}}$. These $^{139}\mathrm{La}$ NMR results corroborate our recent $^{63}\mathrm{Cu}$ NMR observation that a very broad, anomalous winglike signal gradually emerges below ${T}_{\mathrm{charge}}$, whereas the normally behaving, narrower main peak is gradually wiped out [T. Imai et al., Phys. Rev. B 96, 224508 (2017)]. Furthermore, we show that the enhancement of low-energy spin excitations in the low-temperature regime below ${T}_{\mathrm{spin}}^{\mathrm{neutron}}\phantom{\rule{4pt}{0ex}}(\ensuremath{\simeq}{T}_{c})$ depends strongly on the magnitude and orientation of the applied magnetic field.

Until recently, many authors remained skeptical about the presence of charge order in superconducting cuprates. As early as 1999, Hunt $e\phantom{\rule{0}{0ex}}t$ $a\phantom{\rule{0}{0ex}}l$. [Phys. Rev. Lett. 82, 4300] demonstrated that superconducting La${}_{1.885}$Sr${}_{0.115}$CuO${}_{4}$ (T${}_{c}$=30 K) shares nearly identical, peculiar NMR anomalies observed at the charge order transition of Nd codoped La${}_{1.48}$Nd${}_{0.4}$Sr${}_{0.12}$CuO${}_{4}$ (suppressed T${}_{c}$=6 K). In particular, ${}^{63}$Cu NMR signals gradually disappear in the charge ordered state. Where did the wiped out ${}^{63}$Cu NMR signals go? The authors here take full advantage of advancements in the instrumental technologies of NMR over the last two decades, and finally solve this mystery.

We investigate electronic excitations in ${\mathrm{La}}_{2\ensuremath{-}x}{(\mathrm{Br},\mathrm{Sr})}_{x}{\mathrm{CuO}}_{4}$ using resonant inelastic x-ray scattering (RIXS) at the oxygen $K$ edge. RIXS spectra of the hole-doped cuprates show clear momentum dependence below 1 eV. The broad spectral weight exhibits positive dispersion and shifts to higher energy with increasing hole concentration. Theoretical calculation of the dynamical charge structure factor on oxygen orbitals in a three-band Hubbard model is consistent with the experimental observation of the momentum and doping dependence, and therefore the momentum-dependent spectral weight is ascribed to intraband charge excitations which have been observed in electron-doped cuprates. Our results confirm that the momentum-dependent charge excitations exist on the order of the transfer energy ($t$), and the broad spectral line shape indicates damped and incoherent character of the charge excitations at the energy range in the doped Mott insulators.

Physical review / B covering condensed matter and materials physics 95(16), 165108(2017). doi:10.1103/PhysRevB.95.165108, Unrevealing local magnetic and electronic correlations in the vicinity of charge carriers is crucial in order tounderstand rich physical properties in correlated electron systems. Here, using high-energy optical conductivity(up to 35 eV) as a function of temperature and polarization, we observe a surprisingly strong spin polarizationof the local spin singlet with enhanced ferromagnetic correlations between Cu spins near the doped holesin lightly hole-doped $La_{1.95}Sr_{0.05}Cu_{0.95}Zn_{0.05}O_4$. The changes of the local spin polarization manifest stronglyin the temperature-dependent optical conductivity at ∼7.2 eV, with an anomaly at the magnetic stripe phase(∼ 25 K), accompanied by anomalous spectral-weight transfer in a broad energy range. Supported by theoreticalcalculations, we also assign high-energy optical transitions and their corresponding temperature dependence,particularly at ∼2.5, ∼8.7, ∼9.7, ∼11.3, and ∼21.8 eV. Our result shows the importance of a strong mixture ofspin singlet and triplet states in hole-doped cuprates and demonstrates a new strategy to probe local magneticcorrelations using high-energy optical conductivity in correlated electron systems., Published by Inst., Woodbury, NY

Inelastic neutron scattering measurements of magnetic excitations in hole-doped high-${T}_{c}$ cuprates ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ ($x=0$ and 0.075) have been performed over a wide temperature range of 5--500 K extending beyond the pseudogap temperature of $\ensuremath{\sim}360$ K for $x=0.075$. For $x=0$, the two-dimensional spin-wave excitations at low temperatures are thermally robust and the dispersion is slightly softened on heating up to $T=400$ K. For $x=0.075$, the spin-wave-like excitations in the upper part of the hourglass-shaped dispersion remain at $T=300$ K. However, further heating above $T=400$ K induces a broad ridge centered at $(1/2,1/2)$; thereby the hourglass-shaped dispersion becomes blurred above the pseudogap temperature. The localized spin nature of magnetic excitations below ${T}^{*}$ suggests that the pseudogap is related to the proximity to a Mott insulator rather than being a precursor of Cooper pairs.

In superconducting copper oxides, some Cu-O bond-stretching phonons around 70 meV show anomalous giant softening and broadening of electronic origin, and electronic dispersions have large renormalization kinks near the same energy. These observations suggest that phonon broadening originates from quasiparticle excitations across the Fermi surface and the electronic dispersion kinks originate from coupling to anomalous phonons. We measured the phonon anomaly in underdoped ($x=0.05$) and overdoped ($x=0.20$ and 0.25) La${}_{2\ensuremath{-}x}$Sr${}_{x}$CuO${}_{4}$ by inelastic neutron and x-ray scattering with high resolution. Combining these and previously published data, we found that doping dependence of the magnitude of the giant phonon anomaly is very different from that of the ARPES kink, i.e., the two phenomena are not connected. We show that these results provide indirect evidence that the phonon anomaly originates from novel collective charge excitations as opposed to interactions with electron-hole pairs. Their amplitude follows the superconducting dome so these charge modes may be important for superconductivity.

Electronic band dispersions in copper oxide superconductors have kinks around 70 meV that are typically attributed to coupling of electrons to a bosonic mode. We performed angle-resolved photoemission spectroscopy experiments on overdoped cuprate high temperature superconductors to test the relationship between the superconducting transition temperature and electron-bosonic mode coupling. Remarkably, the kinks remain strong in the heavily overdoped region of the doping phase diagram of La${}_{2\ensuremath{-}x}$Sr${}_{x}$CuO${}_{4}$, even when the superconductivity completely disappears. This unexpected observation is incompatible with the conventional picture of superconductivity mediated by the sharp bosonic modes that are responsible for the kink unless extra doping strongly suppresses their $d$-wave projection but not the overall spectral weight. Our results favor pairing mediated by a very broad electronic spectrum or an unconventional mechanism without pairing glue.

Neutron-scattering experiments reveal that a diagonal spin modulation, which is a one-dimensional modulation rotated away by $45\ifmmode^\circ\else\textdegree\fi{}$ from that in the superconducting phase, occurs universally across the insulating spin-glass phase in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4} (0.02l~xl~0.055).$ This establishes an intimate relation between the magnetism and the transport properties in the high-temperature copper oxide superconductors. Furthermore, it is found that the charge density per unit length estimated using a charge stripe model is almost constant throughout the phase diagram, even when the modulation rotates away by $45\ifmmode^\circ\else\textdegree\fi{}$ at the superconducting boundary. However, at the lowest values for x the density changes approaching 1 hole/Cu as in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}.$ Magnetic excitation spectra suggest that magnetic correlations change from incommensurate to commensurate at $\ensuremath{\omega}\ensuremath{\sim}7 \mathrm{meV}$ and $T\ensuremath{\sim}70 \mathrm{K},$ indicating a characteristic energy for the incommensurate structure of 6--7 meV.

We report the results of an extensive elastic neutron-scattering study of the incommensurate (IC) static spin correlations in ${\mathrm{La}}_{1.95}{\mathrm{Sr}}_{0.05}{\mathrm{CuO}}_{4},$ which is an insulating spin glass at low temperatures. Recent work by Wakimoto et al. has revealed the presence of new two-dimensional satellite peaks in ${\mathrm{La}}_{1.95}{\mathrm{Sr}}_{0.05}{\mathrm{CuO}}_{4}$ at positions rotated by $\ensuremath{\sim}45\ifmmode^\circ\else\textdegree\fi{}$ in reciprocal space from those found in superconducting samples. The present neutron-scattering experiments on the same $x=0.05$ crystal employ a narrower instrumental Q resolution and thereby have revealed that the crystal has only two, rather than four, orthorhombic twins at low temperatures with relative populations of $2:1.$ This has made possible the precise characterization of the IC elastic peaks around $(1,0,0)$ and $(0,1,0)$ (orthorhombic notation) in each domain separately. We find that, in a single twin, only two satellites are observed at $(1,\ifmmode\pm\else\textpm\fi{}{0.064,L)}_{\mathrm{ortho}}$ and $(0,1\ifmmode\pm\else\textpm\fi{}{0.064,L)}_{\mathrm{ortho}},$ that is, the modulation vector is only along the orthorhombic ${b}^{*}$ axis. This demonstrates unambiguously that ${\mathrm{La}}_{1.95}{\mathrm{Sr}}_{0.05}{\mathrm{CuO}}_{4}$ has a one-dimensional rather than two-dimensional static diagonal spin modulation at low temperatures, consistent with certain stripe models. From the L dependence we conclude that the spin correlations are predominantly two dimensional. We have also reexamined the $x=0.04$ crystal that previously was reported to show a single commensurate peak. By mounting the sample in the $(H,K,0)$ zone, we have discovered that the $x=0.04$ sample in fact has the same IC structure as the $x=0.05$ sample. The incommensurability parameter $\ensuremath{\delta}$ for $x=0.04$ and 0.05, where $\ensuremath{\delta}$ is the distance from $(1/2,1/2)$ in tetragonal reciprocal lattice units, follows the linear relation $\ensuremath{\delta}\ensuremath{\simeq}x.$ These results demonstrate that the insulator to superconductor transition in the underdoped regime $(0.05l~xl~0.06)$ in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ is coincident with a transition from diagonal to collinear static stripes at low temperatures thereby evincing the intimate coupling between the one-dimensional spin density modulation and the superconductivity.

We have performed resonant inelastic x-ray scattering (RIXS) near the Cu-K edge on cuprate superconductors La(2-x)Sr(x)CuO(4), La(2-x)Ba(x)CuO(4), La(2-x)Sr(x)Cu(1-y)Fe(y)O(4) and Bi(1.76)Pb(0.35)Sr(1.89)CuO(6+d), covering underdoped to heavily overdoped regime and focusing on charge excitations inside the charge-transfer gap. RIXS measurements of the 214 systems with Ei = 8.993 keV have revealed that the RIXS intensity at 1 eV energy transfer has a minimum at (0,0) and maxima at (0.4pi, 0) and $(0, 0.4pi) for all doping points regardless of the stripe ordered state, suggesting that the corresponding structure is not directly related to stripe order. Measurements with Ei = 9.003 keV on metallic La(1.7)Sr(0.3)CuO(4) and Bi(1.76)Pb(0.35)Sr(1.89)CuO(6+d) exhibit a dispersive intra-band excitation below 4 eV, similar to that observed in the electron-doped Nd(1.85)Ce(0.15)CuO(4). This is the first observation of a dispersive intra-band excitation in a hole doped system, evidencing that both electron and hole doped systems have a similar dynamical charge correlation function., 7 pages, 7 figures

Inelastic neutron scattering experiments have been performed on lightly-doped La$$_{1.96}$$Sr$$_{0.04}$$CuO$$_{4}$$, which shows diagonal incommensurate spin correlations at low temperatures. We previously reported that this crystal, with a single orthorhombic domain, exhibits the ``hourglass" dispersion at low energies [Phys. Rev. Lett. 101, 197001 (2008)]. In this paper, we investigate in detail the energy evolution of the magnetic excitations up to 65 meV. It is found that the anisotropic excitations at low energies, dispersing only along the spin modulation direction, crossover to an isotropic, conical dispersion that resembles spin waves in the parent compound La$_2$CuO$$_{4}$$. The change from two-fold to full symmetry on crossing the waist of the hourglass reproduces behavior first identified in studies of underdoped YBa$_2$Cu$_3$O$$_{6+x}$$. We discuss the significance of these results.

Systematic inelastic neutron scattering studies have been performed on La${}_{1.85}$Sr${}_{0.15}$Cu${}_{1\ensuremath{-}y}$Ni${}_{y}$O${}_{4}$ in order to elucidate the microscopic mechanism of magnetic Ni impurity doping effects on spin dynamics and superconductivity. In contrast to Zn doping, which precipitates static or quasistatic spin correlations around dopant, Ni doping remarkably reduces ${E}_{\mathrm{comme}}$, the minimum energy of the upward branch of the hourglass-shaped magnetic dispersion where a commensurate magnetic peak is observed. Ni doping at $y\ensuremath{\sim}0.04$ further reduces ${E}_{\mathrm{comme}}$ to zero energy and broadens the distribution of ${E}_{\mathrm{comme}}$, corresponding to the appearance of the normal state at base temperature ($T\ensuremath{\sim}4$ K) as well as the broadening of the superconducting transition.

We have observed the bulk Fermi surface (FS) in an overdoped (x=0.3) single crystal of La2?xSrxCuO4 by using Compton scattering. A two-dimensional (2D) momentum density reconstruction from measured Compton profiles yields a clear FS signature in the third Brillouin zone along [100]. The quantitative agreement between density functional theory (DFT) calculations and momentum density experiment suggests that Fermi-liquid physics is restored in the overdoped regime. In particular the predicted FS topology is found to be in good accord with the corresponding experimental data. We find similar quantitative agreement between the measured 2D angular correlation of positron annihilation radiation (2D-ACAR) spectra and the DFT-based computations. However, 2D-ACAR does not give such a clear signature of the FS in the extended momentum space in either the theory or the experiment.

Purely local experimental probes of many copper oxide superconductors show that their electronic states are inhomogeneous in real space. For example, scanning tunneling spectroscopic imaging shows strong variations in real space, and according to nuclear quadrupole resonance (NQR) studies, the charge distribution in the bulk varies on the nanoscale. However, the analysis of the experimental results utilizing spatially averaged probes often ignores this fact. We have performed a detailed investigation of the doping dependence of the energy and linewidth of the zone-boundary Cu-O bond-stretching vibration in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ by inelastic neutron scattering. Both our results as well as previously reported angle-dependent momentum widths of the electronic spectral function detected by angle-resolved photoemission can be reproduced by including the same distribution of local environments extracted from the NQR analysis.

Inelastic neutron scattering experiments have been performed on lightly doped La{sub 1.975}Sr{sub 0.025}CuO{sub 4}, which contains a hole concentration slightly higher than the critical concentration for three-dimensional long-range antiferromagnetic order. We previously found that the magnetic excitation spectrum in the insulating phase with a diagonal incommensurate spin modulation has similarities to that in the superconducting regime, where the spin modulation is bond parallel. In this study, we investigate the excitations in detail around E{sub cross}, at which the excitations become most nearly commensurate. It is found that both the magnitude and the anisotropy of the momentum width of the excitations change abruptly at E{sub cross}. Our experimental results suggest that the magnetic excitations rising from the pair of (diagonally) incommensurate wave vectors merge at E{sub cross} into isotropic excitations.

By performing time-of-flight neutron scattering measurements on a large sample of single crystals of Sr${}_{2}$RuO${}_{4}$, we studied the detailed structure of the imaginary part of the dynamic spin susceptibility over a wide range of phase space. In the normal state at $T=5$ K, strong incommensurate (IC) peaks were clearly observed around ${\mathbf{Q}}_{\mathrm{c}}=(0.3,0.3)$ up to at least $\ensuremath{\hbar}\ensuremath{\omega}=80$ meV. In addition, our data also show strong magnetic fluctuations that exist on the ridges connecting the IC peaks around the $(\ensuremath{\pi},\ensuremath{\pi})$ point rather than around the $\ensuremath{\Gamma}$ point. Our results are consistent with the semi-mean-field random phase approximation calculation for a two-dimensional Fermi liquid with a characteristic energy of 5.0 meV. Furthermore, the IC fluctuations were observed even at room temperature.

We present a combined analysis of neutron scattering and photoemission measurements on superconducting FeSe{sub 0.5}Te{sub 0.5}. The low-energy magnetic excitations disperse only in the direction transverse to the characteristic wave vector (1/2,0,0) whereas the electronic Fermi surface near (1/2,0,0) appears to consist of four incommensurate pockets. While the spin resonance occurs at an incommensurate wave vector compatible with nesting, neither spin-wave nor Fermi-surface-nesting models can describe the magnetic dispersion. We propose that a coupling of spin and orbital correlations is key to explaining this behavior. If correct, it follows that these nematic fluctuations are involved in the resonance and could be relevant to the pairing mechanism.

We use inelastic neutron scattering to study the temperature dependence of magnetic excitations (for energies up to 100 meV) in the cuprate La1.875Ba0.125CuO4. This compound exhibits stripe order below a temperature of �50 K; previous measurements have shown that the magnetic excitations of the stripe-ordered phase have an hour-glass-like dispersion, with a saddle point at � 50 meV. Here we compare measurements in the disordered phase taken at 65 and 300 K. At energies on the scale of kBT , there is substantial momentum-broadening of the signal, and the low-energy incommensurate features can no longer be resolved at 300 K. In contrast, there is remarkably little change in the scattered signal for energies greater than kBT . In fact, the momentum-integrated dynamic susceptibility is almost constant with temperature. We suggest that the continuity of higher-energy magnetic excitations is strong evidence for dynamic stripes in the high-temperature, disordered phase. We reconsider the nature of the magnetic dispersion, and we discuss the correspondences between the thermal evolution of magnetic stripe correlations with other electronic properties of the cuprates.

The reflectivity $R(\ensuremath{\omega})$ of both the $ab$ plane and the $c$ axis of two single crystals of ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125\ensuremath{-}y}{\mathrm{Sr}}_{y}\mathrm{Cu}{\mathrm{O}}_{4}$ has been measured down to $5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, using coherent synchrotron radiation below $30\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. For $y=0.085$, a Josephson plasma resonance is detected at $T⪡{T}_{c}=31\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in the out-of-plane ${R}_{c}(\ensuremath{\omega})$, and a far-infrared peak (FIP) appears in the in-plane optical conductivity ${\ensuremath{\sigma}}_{ab}(\ensuremath{\omega})$ below $50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, where nonstatic charge ordering (CO) is reported by x-ray scattering. For $y=0.05$ $({T}_{c}=10\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, below the ordering temperature ${T}_{\mathit{CO}}$, a FIP is again observed in ${\ensuremath{\sigma}}_{ab}(\ensuremath{\omega})$. The FIP then appears to be an infrared signature of CO, either static or fluctuating, as reported in previous work on the La-Sr cuprates.

Inelastic neutron-scattering experiments were performed on ${A}_{3}{\mathrm{Cu}}_{3}{(\mathrm{P}{\mathrm{O}}_{4})}_{4}$ ($A=\mathrm{Ca}$, Sr, and Pb), which consists of one-dimensional array of linear copper spin trimers. It was found that the magnetic excitations are well described by the linear Heisenberg antiferromagnetic spin trimer model, in which the main interaction is the nearest-neighbor intratrimer interaction and the weak next-nearest-neighbor intratrimer and intertrimer interactions are expected. The intratrimer coupling constants are determined to be 9.45(3), 10.04(3), and 9.13(2) meV for ${A}_{3}{\mathrm{Cu}}_{3}{(\mathrm{P}{\mathrm{O}}_{4})}_{4}$ with $A=\mathrm{Ca}$, Sr, and Pb, respectively. The other interactions were found to be very small.

The nature of charge stripe order and its relationship with structural phase transitions were studied using synchrotron x-ray diffraction in ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}\phantom{\rule{0.2em}{0ex}}(0.05\ensuremath{\leqslant}x\ensuremath{\leqslant}0.10)$. For $x=0.05$, as temperature increased, incommensurate superlattice peaks associated with the charge order disappeared just at the structural phase transition temperature, ${T}_{d2}$. However, for $x=0.075$ and 0.09, the superlattice peaks still existed as a short range correlation even above ${T}_{d2}$, indicating a precursor of charge ordering. Furthermore, temperature dependences of the superlattice peak intensity, correlation length, and incommensurability for $x=0.05$ are different from those for $x=0.075$ and 0.09. These results suggest that the transition process into the charge stripe order strongly correlates with the order of the structural phase transitions. A quantitative comparison of the structure factor associated with the charge order have been also made for all the samples.

We present a neutron scattering study of stripe correlations measured on a single crystal of La$_{1.875}$Ba$_{0.125}$CuO$_{4}$. Within the low-temperature-tetragonal (LTT) phase, superlattice peaks indicative of spin and charge stripe order are observed below 50 K. For excitation energies $\hbar\omega\le12$ meV, we have characterized the magnetic excitations that emerge from the incommensurate magnetic superlattice peaks. In the ordered state, these excitations are similar to spin waves. Following these excitations as a function of temperature, we find that there is relatively little change in the {\bf Q}-integrated dynamical spin susceptibility for $\hbar\omega\sim10$ meV as stripe order disappears and then as the structure transforms from LTT to the low-temperature-orthorhombic (LTO) phase. The {\bf Q}-integrated signal at lower energies changes more dramatically through these transitions, as it must in a transformation from an ordered to a disordered state. We argue that the continuous evolution through the transitions provides direct evidence that the incommensurate spin excitations in the disordered state are an indicator of dynamical charge stripes. An interesting feature of the thermal evolution is a variation in the incommensurability of the magnetic scattering. Similar behavior is observed in measurements on a single crystal of La$_{1.875}$Ba$_{0.075}$Sr$_{0.050}$CuO$_{4}$; maps of the scattered intensity in a region centered on the antiferromagnetic wave vector and measured at $\hbar\omega=4$ meV are well reproduced by a model of disordered stripes with a temperature-dependent mixture of stripe spacings. We discuss the relevance of our results to understanding the magnetic excitations in cuprate superconductors.

Lattice distortions associated with charge stripe order in 1/8 hole-doped La 1 . 8 7 5 Ba 0 . 1 2 5 - x Sr x CuO 4 are studied using synchrotron x-ray diffraction for x=0.05 and x=0.075. The propagation wave-vector and charge order correlation lengths are determined with a high accuracy, revealing that the oblique charge stripes in orthorhombic x=0.075 crystal are more disordered than the aligned stripes in tetragonal x=0.05 crystal. The twofold periodicity of lattice modulations along the c axis is explained by long-range Coulomb interactions between holes on neighboring CuO 2 planes.

Low-energy magnetic excitations of chromium have been reinvestigated with a single-${\mathit{Q}}_{\ifmmode\pm\else\textpm\fi{}}$ crystal using neutron scattering techniques. In the transverse spin-density-wave phase a well-defined magnetic excitation is found around $(0,0,1)$ with a weak dispersion perpendicular to the wave vector of the incommensurate structure. The magnetic excitation has an energy gap of $\ensuremath{\omega}\ensuremath{\simeq}4\mathrm{meV}$ at $(0,0,1),$ which exactly corresponds to the Fincher excitation previously studied only along the incommensurate wave vector.

We have investigated the magnetism and the superconductivity of the electron-doped ${\mathrm{Pr}}_{1\ensuremath{-}x}{\mathrm{LaCe}}_{x}{\mathrm{CuO}}_{4}$ by means of zero-field muon spin rotation/relaxation and magnetic susceptibility measurements. At low temperatures, a well-defined muon spin rotation free from the effect of rare-earth moments was observed for samples with $xl~0.08$ corresponding to the antiferromagnetic (AF) order of Cu spins. Bulk superconductivity was identified in a wide Ce concentration range of $0.09l~xl~0.20$ with a maximum transition temperature of 26 K. Abrupt appearance of the superconducting (SC) phase at $x\ensuremath{\sim}0.09$ is concomitant with a destroy of the AF ordered phase, indicating the competitive relation between two phases. Possible relation between the wide SC phase and the lattice spacing is discussed.

Neutron-scattering experiments were performed to study the magnetic-field effect on the electron-doped cuprate superconductor ${\mathrm{Nd}}_{1.86}{\mathrm{Ce}}_{0.14}{\mathrm{CuO}}_{4},$ which shows the coexistence of magnetic order and superconductivity. The $(\frac{1}{2}\frac{3}{2}0)$ magnetic Bragg intensity, which originates from the order of both the Cu and Nd moments at low temperatures, shows no magnetic-field dependence when the field is applied perpendicular to the ${\mathrm{CuO}}_{2}$ plane up to 10 T above the upper critical field. This result is significantly different from that reported for the hole-doped cuprate superconductors, in which the quasistatic magnetic order is noticeably enhanced under a magnetic field.

The magnetization in a lightly doped La 2 - x Sr x CuO 4 (x=0.018) single crystal was measured. Spin-flop transition was clearly observed in the hole-doped antiferromagnetically ordered state under increasing magnetic fields perpendicular to the CuO 2 plane. In the spin-glass phase below 25 K, the spin-flop transition becomes broad but the step in the magnetization curve associated with the transition remains finite at the lowest temperature. We show in this report that, at low temperature, the homogeneous antiferromagnetic order is disturbed by the redistribution of holes, and that the spatial variance of the local hole concentration around x=0.018 increases.

The effects of the application of a magnetic field on the diagonal stripe spin-glass phase is studied in lightly doped La 2 - x Sr x CuO 4 (x=0.014 and 0.024). With increasing magnetic field, the magnetic elastic intensity at the diagonal incommensurate (DIC) positions (1,′∈,0) decreases as opposed to the increase seen in superconducting samples. This diminution in intensity with increasing magnetic field originates from a spin reorientation transition, which is driven by the antisymmetric exchange term in the spin Hamiltonian. On the other hand, the transition temperature, the incommensurability, and the peak width of the diagonal incommensurate correlations are not changed with magnetic field. This result suggests that the magnetic correlations are determined primarily by the charge disproportionation and that the geometry of the diagonal incommensurate magnetism is also determined by effects-that is, stripe formation-which are not purely magnetic in origin. The Dzyaloshinskii-Moriya antisymmetric exchange is nevertheless important in determining the local spin structure in the DIC stripe phase.

We report the results of elastic neutron-scattering measurements performed on -hole-doped La 1 . 8 7 5 Ba 0 . 1 2 5 - x Sr x CuO 4 single crystals with x=0.05, 0.06, 0.075, and 0.085. In the low-temperature less-orthorhombic[(LTLO), Pccn symmetry] phase, the charge-density-wave (CDW) and spin-density-wave (SDW) wave vectors were found to tilt in a low-symmetric direction with one-dimensional anisotropy in the CuO 2 plane, while they were aligned along the high-symmetry axis in the low-temperature tetragonal (P4 2 /ncm symmetry) phase. The coincident direction of two wave vectors suggests a close relation between CDW and SDW orders. The SDW wave vector systematically deviates from the Cu-O bond direction in the LTLO phase upon Sr substitution and the tilt angle in the LTLO phase is smaller than that in the low-temperature orthorhombic phase (Bmab symmetry) with comparable in-plane orthorhombic distortion. These results demonstrate a correlation between the corrugated pattern of the CuO 2 plane and the deviations.

The Hall coefficient in the low-temperature tetragonal phase and the midtemperature orthorhombic phase of ${\mathrm{La}}_{1.88\ensuremath{-}y}{\mathrm{Y}}_{y}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}$ $(y=0,0.04)$ single crystals is measured under high magnetic fields up to 9 T in order to investigate the detailed behavior of the transport properties at low temperatures in the stripe phase. When the superconductivity is suppressed by high magnetic fields, the Hall coefficient has negative values in low temperatures, and the temperature region of the negative values spreads as increasing magnetic fields. This result indicates that the Hall coefficient in the stripe phase around $x=0.12$ is a finite negative value, not zero.

The hole concentration dependence of the magnetic correlations is studied in very lightly doped ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ $(xl0.02),$ which shows coexistence of a three-dimensional antiferromagnetic long-range-ordered phase and a spin-glass phase at low temperatures. It is found that the spin-glass phase in the coexistence region also shows a diagonal spin modulation as in the pure spin-glass phase in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ $(0.02l~xl~0.055).$ Below $x\ensuremath{\sim}0.02$ the diagonal stripe structure is the same as that in $x\ensuremath{\sim}0.02$ with a volume fraction almost proportional to hole concentration, suggesting that electronic phase separation of the doped holes occurs so that some regions with hole concentration ${c}_{h}\ensuremath{\sim}0.02$ and the rest with ${c}_{h}\ensuremath{\sim}0$ are formed. To our best knowledge, this represents the most direct observation to date of electronic phase separation in lightly doped antiferromagnets. Such phase separation has been predicted by a number of theories.

An elastic neutron scattering study has been performed on several single crystals of La$_{2-x}$Sr$_{x}$CuO$_{4}$ for {\it x} near the lower critical concentration {\it x$_{c}$} for superconductivity. % In the insulating spin-glass phase ({\it x} = 0.04 and 0.053), the previously reported one-dimensional spin modulation along the orthorhombic {\it b}-axis is confirmed. % Just inside the superconducting phase ({\it x} = 0.06), however, two pairs of incommensurate magnetic peaks are additionally observed corresponding to the spin modulation parallel to the tetragonal axes. % These two types of spin modulations with similar incommensurabilities coexist near the boundary. % The peak-width $\kappa$ along spin-modulation direction exhibits an anomalous maximum in the superconducting phase near {\it x$_{c}$}, where the incommensurability $\delta$ monotonically increases upon doping across the phase boundary. % These results are discussed in connection with the doping-induced superconducting phase transition., Comment: 9pages, 9figures