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Controlling chiral magnetic domains in a multiferroic material is promising for applications in spintronics or data storage devices. The authors study the electric-field driven relaxation of multiferroic domains in NaFeGe${}_{2}$O${}_{6}$ as a function of temperature and electric field over several decades in time. An astonishingly simple combination of an Arrhenius-like temperature dependence with a Merz law for the electric-field dependence describes the relaxation times with only two parameters, indicating that multiferroic relaxation is essentially determined by domain-wall motion.

The structural distortion and magnetoelastic coupling induced through commensurate magnetism has been investigated by neutron diffraction in structurally related ${\mathrm{MnWO}}_{4}$ and $\mathrm{NaFe}{({\text{WO}}_{4})}_{2}$. Both systems exhibit a competition of incommensurate spiral and commensurate spin up-up-down-down ordering along the magnetic chains. In the latter commensurate phases, the alternatingly parallel and antiparallel arrangement of ${\mathrm{Fe}}^{3+}$ or ${\mathrm{Mn}}^{2+}$ moments leads to sizable bond-angle modulation and thus to magnetic dimerization. For $\mathrm{NaFe}{({\text{WO}}_{4})}_{2}$ this structural distortion has been determined to be strongest for the low-field up-up-down-down arrangement, and the structural refinement yields a bond-angle modulation of $\ifmmode\pm\else\textpm\fi{}1.15(16)$ degrees. In the commensurate phase of ${\mathrm{MnWO}}_{4}$, superstructure reflections signal a comparable structural dimerization and thus strong magneto-elastic coupling different to that driving the multiferroic order. Pronounced anharmonic second- and third-order reflections in the incommensurate and multiferroic phase of ${\mathrm{MnWO}}_{4}$ result from tiny commensurate fractions that can depin multiferroic domains.

The magnon dispersion of ferromagnetic SrRuO_{3} was studied by inelastic neutron scattering experiments on single crystals as a function of temperature. Even at low temperature the magnon modes exhibit substantial broadening pointing to strong interaction with charge carriers. We find an anomalous temperature dependence of both the magnon gap and the magnon stiffness, which soften upon cooling in the ferromagnetic phase. Both effects trace the temperature dependence of the anomalous Hall effect and can be attributed to the impact of Weyl points, which results in the same relative renormalization in the spin stiffness and magnon gap.

Triplet pairing in Sr_{2}RuO_{4} was initially suggested based on the hypothesis of strong ferromagnetic spin fluctuations. Using polarized inelastic neutron scattering, we accurately determine the full spectrum of spin fluctuations in Sr_{2}RuO_{4}. Besides the well-studied incommensurate magnetic fluctuations, we do find a sizable quasiferromagnetic signal, quantitatively consistent with all macroscopic and microscopic probes. We use this result to address the possibility of magnetically driven triplet superconductivity in Sr_{2}RuO_{4}. We conclude that, even though the quasiferromagnetic signal is stronger and sharper than previously anticipated, spin fluctuations alone are not enough to generate a triplet state strengthening the need for additional interactions or an alternative pairing scenario.

The low energy magnetic excitations spectra of the pristine and doped quasi-one-dimensional spin chains cuprates $\mathrm{SrCu}{\mathrm{O}}_{2}$ have been investigated by inelastic neutron scattering. The momentum-integrated magnetic dynamical structure factor yields a constant integrated intensity with regard to energy in the pure compound, while it shows a strong decay, at low energies, in the compounds doped with nonmagnetic impurities, namely, $\mathrm{SrC}{\mathrm{u}}_{0.99}{\mathrm{M}}_{0.01}{\mathrm{O}}_{2}$ (with $M=\mathrm{Zn}$ or Mg) and $\mathrm{S}{\mathrm{r}}_{0.99}\mathrm{L}{\mathrm{a}}_{0.01}\mathrm{Cu}{\mathrm{O}}_{2}$ ($\mathrm{C}{\mathrm{u}}^{+}$ carrying $S=0$ created within the chains). These results evidence the opening of a spin pseudogap in the two-spinon continuum of $\mathrm{SrCu}{\mathrm{O}}_{2}$ upon doping, stemming from disruptions of the spin chains by quantum impurities.

The magnon dispersion of ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$ has been studied by polarized and unpolarized neutron scattering experiments on crystals containing 0, 1, and 10% of Ti. Ti is inserted in order to enable the growth of large, partially detwinned crystals. One percent of Ti has a negligible impact on structural and magnetic properties. Also for 10% Ti content magnetic properties still change very little, but the insulating phase is stabilized up to at least 700 K and structural distortions are reduced. The full dispersion of transverse magnons studied for 1% Ti substitution can be well described by a conventional spin-wave model with interaction and anisotropy parameters that agree with density functional theory calculations. Spin-orbit coupling strongly influences the magnetic excitations, as it is most visible in large energies of the magnetic zone-center modes arising from magnetic anisotropy. Additional modes appear at low energy near the antiferromagnetic zone center and can be explained by a sizable magnetic moment of 0.11 Bohr magnetons, which the density functional theory calculations find located on the apical oxygens. The energy and the signal strength of the additional branch are well described by taking into account this oxygen moment with weak ferromagnetic coupling to the Ru moments.

Inelastic neutron scattering experiments on Sr_{2}RuO_{4} determine the spectral weight of the nesting induced magnetic fluctuations across the superconducting transition. There is no observable change at the superconducting transition down to an energy of ∼0.35 meV, which is well below the 2Δ values reported in several tunneling experiments. At this and higher energies magnetic fluctuations clearly persist in the superconducting state. Only at energies below ∼0.3 meV can evidence for partial suppression of spectral weight in the superconducting state be observed. This strongly suggests that the one-dimensional bands with the associated nesting fluctuations do not form the active, highly gapped bands in the superconducting pairing in Sr_{2}RuO_{4}.

We use neutron scattering to study magnetic excitations near the antiferromagnetic wave vector in the underdoped single-layer cuprate HgBa_{2}CuO_{4+δ} (superconducting transition temperature T_{c}≈88 K, pseudogap temperature T^{*}≈220 K). The response is distinctly enhanced below T^{*} and exhibits a Y-shaped dispersion in the pseudogap state, whereas the superconducting state features an X-shaped (hourglass) dispersion and a further resonancelike enhancement. A large spin gap of about 40 meV is observed in both states. This phenomenology is reminiscent of that exhibited by bilayer cuprates. The resonance spectral weight, irrespective of doping and compound, scales linearly with the putative binding energy of a spin exciton described by an itinerant-spin formalism.

By comprehensive neutron diffraction measurements we have studied the magnetic structure of aegirine $({\mathrm{NaFeSi}}_{2}{\mathrm{O}}_{6})$ in and above its multiferroic phase. Natural aegirine exhibits two magnetic transitions into incommensurate magnetic order with a propagation vector of ${\stackrel{P\vec}{k}}_{\mathrm{inc}}=(0,\ensuremath{\sim}0.78,0)$. Between 9 and 6 K, we find a transverse spin-density wave with moments pointing near the $c$ direction. Below 6 K, magnetic order becomes helical and spins rotate in the $ac$ plane. The same irreducible representation is involved in the two successive transitions. In addition, the ferroelectric polarization $\stackrel{P\vec}{P}$ appearing along the $b$ direction cannot be described by the most common multiferroic mechanism but follows $\stackrel{P\vec}{P}\ensuremath{\propto}{\stackrel{P\vec}{S}}_{i}\ifmmode\times\else\texttimes\fi{}{\stackrel{P\vec}{S}}_{j}$. Synthetic ${\mathrm{NaFeSi}}_{2}{\mathrm{O}}_{6}$ does not exhibit the pure incommensurate helical order but shows coexistence of this order with a commensurate magnetic structure. By applying moderate pressure to natural aegirine, we find that the incommensurate magnetic ordering partially transforms to the commensurate one, underlining the nearly degenerate character of the two types of order in ${\mathrm{NaFeSi}}_{2}{\mathrm{O}}_{6}$.

We present a comprehensive study on ${\mathrm{PrCaFeO}}_{4}$ using macroscopic methods, neutron and x-ray diffraction, as well as inelastic neutron scattering. One polycrystalline and two single-crystal samples were investigated exhibiting structural phase transitions from a high-temperature tetragonal phase to an intermediate orthorhombic phase (space group $Bmeb$) at $510{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ (783 K). At approximately 240 K a second structural phase transition takes place into the space group $Pccn$ where the tilt axis of the ${\mathrm{FeO}}_{6}$ octahedra changes from the [100] to the $\ensuremath{\langle}110\ensuremath{\rangle}$ directions. Due to strong diffuse scattering at high temperatures neutron powder diffraction can only safely state that ${T}_{N}$ is above 330 K. ${\mathrm{PrCaFeO}}_{4}$ exhibits a magnetic spin-flop phase transition where the magnetic moments turn from the $b$ axis to the $c$ axis upon cooling. However, the transition temperatures and the width of this magnetic transition are strikingly different between the investigated samples, suggesting a strong influence from the real structure. Indeed, a significant difference in the oxygen content was deduced by single-crystal x-ray diffraction. The magnon dispersion was studied by inelastic neutron scattering revealing a nearest-neighbor interaction comparable to that in ${\mathrm{LaSrFeO}}_{4}$ but with smaller anisotropy gaps. A clear interlayer dispersion was observed resulting from the structural distortions and the relief of geometrical frustration due to the orthorhombic splitting.

Inelastic neutron scattering techniques have been used to study the field-induced multiferroic transition and the temperature dependence of magnetic excitations in ${\text{TbMnO}}_{3}$. The significant changes in the spin-wave spectra across the field-induced transition perfectly agree with a rotation of the cycloidal spiral plane and with efficient pinning in the commensurate high-field phase. Further analysis of the $\mathbf{Q}$ dependence allows the identification of an electromagnon in the multiferroic high-field phase whose energy and polarization precisely matches previous infrared data. This and the zero-field temperature dependence of a zone-center magnon, which exactly agrees with that of an optically detected excitation, document that the inverse Dzyaloshinskii-Moriya interaction induces an electromagnon hybrid excitation in ${\text{TbMnO}}_{3}$.

We present an inelastic neutron scattering study on single-crystalline LiFeAs devoted to the characterization of the incommensurate antiferromagnetic fluctuations at $\mathbf{Q}=(0.5\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta},0.5\ensuremath{\mp}\ensuremath{\delta},{q}_{l})$. Time-of-flight measurements show the presence of these magnetic fluctuations up to an energy transfer of 60 meV, while polarized neutrons in combination with a longitudinal polarization analysis on a triple-axis spectrometer prove the pure magnetic origin of this signal. The normalization of the magnetic scattering to an absolute scale yields that magnetic fluctuations in LiFeAs are by a factor of 8 weaker than the resonance signal in nearly optimally Co-doped ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$, although a factor of 2 is recovered due to the split peaks owing to the incommensurability. The longitudinal polarization analysis indicates weak spin-space anisotropy with a slightly stronger out-of-plane component between 6 and 12 meV. Furthermore, our data suggest a fine structure of the magnetic signal most likely arising from superposing nesting vectors.

As in ${{\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}\mathrm{O}}_{6+x}$ and ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{8+\ensuremath{\delta}}$, the pseudogap state in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ is characterized by the existence of an intra-unit-cell magnetic order revealed by polarized neutron scattering technique. We report here a supplementary set of polarized neutron scattering measurements for which the direction of the magnetic moment is determined and the magnetic intensity is calibrated in absolute units. These data allow a close comparison between bilayer systems ${{\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}\mathrm{O}}_{6+x}$ and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ and raise important questions concerning the range of the magnetic correlations and the role of disorder around optimal doping.

Commensurate antiferromagnetic ordering has been observed in the superconducting high-$Tc$ cuprate ${\rm YBa_{2}Cu_{3}O_{6.5}}$ (${\rm T_{c}}$=55 K) by polarized and unpolarized elastic neutron scattering. The magnetic peak intensity exhibits a marked enhancement at $T_{c}$. Zero-field $\mu $SR experiments demonstrate that the staggered magnetization is not truly static but fluctuates on a nanosecond time scale. These results point towards an unusual spin density wave state coexisting with superconductivity.

The influence of magnetic ( $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$) and nonmagnetic ( $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) impurities on the spin dynamics of an optimally doped high temperature superconductor is compared in ${\mathrm{YBa}}_{2}({\mathrm{Cu}}_{0.97}{\mathrm{Ni}}_{0.03}{)}_{3}{\mathrm{O}}_{7}$ ( ${T}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}80\mathrm{K}$) and ${\mathrm{YBa}}_{2}({\mathrm{Cu}}_{0.99}{\mathrm{Zn}}_{0.01}{)}_{3}{\mathrm{O}}_{7}$ ( ${T}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}78\mathrm{K}$). In the Ni-substituted system, the magnetic resonance peak (which is observed at ${E}_{r}\ensuremath{\simeq}40\mathrm{meV}$ in the pure system) shifts to lower energy with a preserved ${E}_{r}/{T}_{c}$ ratio while the shift is much smaller upon Zn substitution. By contrast Zn, but not Ni, restores significant spin fluctuations around 40 meV in the normal state. These observations are discussed in the light of models proposed for the magnetic resonance peak.

We report a comprehensive polarized and unpolarized neutron scattering study of the evolution of the dynamical spin susceptibility with temperature and doping in three underdoped single crystals of the \YBCO{6+x} high temperature superconductor: \YBCO{6.5} (Tc = 52 K), \YBCO{6.7} (Tc = 67 K), and \YBCO{6.85} (T_c = 87 K). Theoretical implications of these data are discussed, and a critique of recent attempts to relate the spin excitations to the thermodynamics of high temperature superconductors is given.

We report first inelastic neutron scattering measurements in the normal state of Sr_2RuO_4 that reveal the existence of incommensurate magnetic spin fluctuations located at ${\bf q}_0=(\pm 0.6\pi/a, \pm 0.6\pi/a, 0)$. This finding confirms recent band structure calculations that have predicted incommensurate magnetic responses related to dynamical nesting properties of its Fermi surface.

The magnetic excitation spectrum of a YBa2Cu3O7 crystal containing 0.5% of nonmagnetic (Zn) impurities has been determined by inelastic neutron scattering. Whereas in the pure system a sharp resonance peak at E . 40 meV is observed exclusively below the superconducting transition temperature Tc, the magnetic response in the Zn-substituted system is broadened significantly and vanishes at a temperature much higher than Tc. The energy-integrated spectral weight observed near q › sp, pd increases with Zn substitution, and only about half of the spectral weight is removed at Tc. [S0031-9007(99)08563-4]

We present elastic and inelastic neutron scattering data on LaSrFeO$_4$. We confirm the known magnetic structure with the magnetic moments lying in the tetragonal basal plane, but contrarily to previous reports our macroscopic and neutron diffraction data do not reveal any additional magnetic phase transition connected to a spin reorientation or to a redistribution of two irreducible presentations. Our inelastic neutron scattering data reveals the magnon dispersion along the main-symmetry directions [0 $\xi$ 0] and [$\xi$ -$\xi$ 0]. The dispersion can be explained within linear spin-wave theory yielding an antiferromagnetic nearest-neighbour interaction parameter $J_{1}=7.4(1)$ meV and a next-nearest neighbour interaction parameter $J_{2}=0.4(1)$ meV. The dispersion is gapped with the out-of-plane anisotropy gap found at $\Delta_{out}=5.26(2)$ meV, while evidence is present that the in-plane anisotropy gap lies at lower energies, where it cannot be determined due to limited instrument resolution., Comment: 9 pages, 11 figures

Inelastic-neutron-scattering measurements have been performed to determine the imaginary part of the dynamical susceptibility, \ensuremath{\chi}\ensuremath{''}(Q,\ensuremath{\omega}), of a ${\mathrm{YBa}}_{2}$(${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$${\mathrm{Zn}}_{\mathit{y}}$${)}_{3}$${\mathrm{O}}_{6.97}$ sample exhibiting a superconducting transition at ${\mathit{T}}_{\mathit{c}}$=69 K. Zinc substitution induces striking modifications of the energy dependence of \ensuremath{\chi}\ensuremath{''}(Q,\ensuremath{\omega}) but magnetic fluctuations remain peaked at the antiferromagnetic wave vector, ${\mathit{Q}}_{\mathrm{AF}}$, at all investigated energies. In the superconducting state of the zinc-free compound, \ensuremath{\chi}\ensuremath{''}(Q,\ensuremath{\omega}) is restricted to a narrow energy range, \ensuremath{\Elzxh}\ensuremath{\omega}=33--47 meV, displaying a spin gap at ${\mathit{E}}_{\mathit{G}}$=33 meV and a resonant enhancement at ${\mathit{E}}_{\mathrm{\ensuremath{\tau}}}$=39 meV, both features vanishing upon heating up above ${\mathit{T}}_{\mathit{c}}$. In the y=0.02 substituted sample in the superconducting state, there is still an energy band in the range 32--47 meV but no clear resonance, and a signal is now observed in the low energy range, though the line shape of \ensuremath{\chi}\ensuremath{''}(Q,\ensuremath{\omega}) indicates some reminiscence of the spin gap of the pure compound. \textcopyright{} 1996 The American Physical Society.

Inelastic-neutron-scattering experiments have been performed to study the spin-excitation spectrum in the overdoped regime of the high-${\mathit{T}}_{\mathit{c}}$ superconducting system ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6+\mathit{x}}$, x=0.97. All the observed magnetic fluctuations are peaked at the antiferromagnetic wave vector. In the superconducting state, the magnetic response is restricted over a limited energy range (\ensuremath{\Elzxh}\ensuremath{\omega}=33\char21{}46 meV). The imaginary part of the magnetic susceptibility is characterized by two contributions defined by different q widths and different temperature dependences. A resonant contribution, which displays a narrower q width, appears to be connected with superconductivity. The two contributions can be accounted for in the framework of the t-t\ensuremath{'}-J model in the presence of superconductivity. The main new feature in the overdoped regime is the partial disappearance of magnetic correlations for temperatures above the superconducting temperature. \textcopyright{} 1996 The American Physical Society.

Polarized elastic neutron scattering measurements have been performed in the bilayer copper oxide system ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$, providing evidence for an intra-unit-cell magnetic order inside the pseudogap state. That shows time reversal symmetry breaking in that state as already reported in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ through dichroism in circularly polarized photoemission experiments. The magnetic order displays the same characteristic features as the one previously reported for monolayer ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}}$ and bilayer ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+\mathit{x}}$, demonstrating that this genuine phase is ubiquitous of the pseudogap of high temperature copper oxide materials.

The incommensurate stripelike magnetic ordering in two single-layered manganites, Nd0.33Sr1.67MnO4 and Pr0.33Ca1.67MnO4, is found to exhibit an hourglasslike excitation spectrum very similar to that seen in various cuprates superconductors, but only for sufficiently short correlation lengths. Several characteristic features of an hourglass dispersion can be identified: enhancement of intensity at the merging of the incommensurate branches, rotation of the intensity maxima with higher energy transfer, and suppression of the outward-dispersing branches at low energy. The correlation length of the magnetic ordering and the large ratio of intra- to interstripe couplings are identified as the decisive parameters causing the hourglass shape of the spectrum.

Magnetic correlations in superconducting LiFeAs were studied by elastic and by inelastic neutron-scattering experiments. There is no indication for static magnetic ordering, but inelastic correlations appear at the incommensurate wave vector ($0.5\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta},0.5\ensuremath{\mp}\ensuremath{\delta},0$) with $\ensuremath{\delta}\ensuremath{\sim}0.07$ slightly shifted from the commensurate ordering observed in other FeAs-based compounds. The incommensurate magnetic excitations respond to the opening of the superconducting gap by a transfer of spectral weight.

Spin-polarized neutron diffraction experiments have revealed an unusual $q=0$ magnetic order in the model high-temperature superconductor HgBa${}_{2}$CuO${}_{4+\ensuremath{\delta}}$ (Hg1201) below the pseudogap temperature ${T}^{*}$ [Y. Li et al., Nature (London) 455, 372 (2008)]. Together with results for the structurally more complex compound YBa${}_{2}$Cu${}_{3}$O${}_{6+\ensuremath{\delta}}$ (YBCO) [B. Fauqu\'e et al., Phys. Rev. Lett. 96, 197001 (2006); H.A. Mook et al., Phys. Rev. B 78, 020506 (2008)], this establishes the universal existence of a genuine novel magnetic phase in underdoped cuprates with high maximal ${T}_{\mathrm{c}}$ (above 90 K at optimal doping). Here we report a systematic study of an underdoped Hg1201 sample (${T}_{\mathrm{c}}=75$ K), the result of which is consistent with the previously established doping dependence of the magnetic signal. We present an assumption-free analysis of all the data available for Hg1201. Depending on how the hole concentration is estimated, comparison with the results for YBCO leads to different scenarios for the competition between the $q=0$ magnetic order and the spin-density-wave order found in heavily underdoped YBCO.

We report inelastic neutron-scattering experiments on single crystals of Nd${}_{1\ensuremath{-}x}$Sr${}_{x}$MnO${}_{3}$ with $x=0.5$ and $x=0.49$. The spin-wave dispersion in the charge-, orbital-, and spin-ordered state in Nd${}_{0.5}$Sr${}_{0.5}$MnO${}_{3}$ exhibits a strongly anisotropic stiffness. The sign of the anisotropy is characteristic for the site-centered model for charge and orbital ordering in half doped manganites. Within this model, linear spin-wave theory yields a perfect description of the experimental dispersion. In the ferromagnetic metallic state of Nd${}_{1\ensuremath{-}x}$Sr${}_{x}$MnO${}_{3}$ with $x=0.49$ and $x=0.50$ magnetic excitations exhibit nearly the same magnon dispersion. High intense signals near the zone boundary over a wide energy level overlap with a sharp spin-wave dispersion, which can be described with a Heisenberg model including nearest-neighbor interactions.

We report a polarized neutron-scattering study of the orbital-like magnetic order in strongly underdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.45}$ and ${\mathrm{YBa}}_{2}({\mathrm{Cu}}_{0.98}{\mathrm{Zn}}_{0.02}){}_{3}{\mathrm{O}}_{6.6}$. Their hole-doping levels are located on both sides of the critical doping ${p}_{\mathrm{MI}}$ of a metal-insulator transition inferred from transport measurements. Our study reveals a drop down of the orbital-like order slightly below ${p}_{\mathrm{MI}}$ with a steep decrease of both the ordering temperature ${T}_{\mathrm{mag}}$ and the ordered moment. Above ${p}_{\mathrm{MI}}$, substitution of quantum impurities does not change ${T}_{\mathrm{mag}}$, whereas it lowers significantly the bulk ordered moment. The modifications of the orbital-like magnetic order are interpreted in terms of a competition with electronic liquid crystal phases around ${p}_{\mathrm{MI}}$. This competition gives rise to a mixed magnetic state in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.45}$ and a phase separation in ${\mathrm{YBa}}_{2}({\mathrm{Cu}}_{0.98}{\mathrm{Zn}}_{0.02}){}_{3}{\mathrm{O}}_{6.6}$.

By inelastic neutron scattering, we have analyzed the magnetic correlations in the paramagnetic metallic region of the series Ca${}_{2\ensuremath{-}x}$Sr${}_{x}$RuO${}_{4}$, $0.2\ensuremath{\leqslant}x\ensuremath{\leqslant}0.62$. We find different contributions that correspond to two-dimensional ferromagnetic fluctuations and to fluctuations at incommensurate wave vectors ${Q}_{1}^{\mathrm{IC}}=(0.11,0,0)$, ${Q}_{2}^{\mathrm{IC}}=(0.26,0,0)$, and ${Q}_{\ensuremath{\alpha}\ensuremath{\beta}}^{\mathrm{IC}}=(0.3,0.3,0)$. These components constitute the measured response as a function of the Sr concentration $x$, of the magnetic field, and of the temperature. A generic model is applicable to metallic Ca${}_{2\ensuremath{-}x}$Sr${}_{x}$RuO${}_{4}$ close to the Mott transition, in spite of their strongly varying physical properties. The amplitude, characteristic energy, and width of the incommensurate components vary only slightly as functions of $x$, but the ferromagnetic component depends sensitively on concentration, temperature, and magnetic field. While ferromagnetic fluctuations are very strong in Ca${}_{1.38}$Sr${}_{0.62}$RuO${}_{4}$ with a low characteristic energy of 0.2 meV at $T=1.5$ K, they are strongly suppressed in Ca${}_{1.8}$Sr${}_{0.2}$RuO${}_{4}$, but reappear upon the application of a magnetic field, and form a magnon mode above the metamagnetic transition. The inelastic neutron scattering results document how the competition between ferromagnetic and incommensurate antiferromagnetic instabilities governs the physics of this system.

We report an inelastic-neutron-scattering and muon-spin-relaxation study of the effect of 2% spinless (Zn) impurities on the magnetic order and dynamics of YBa(2)Cu(3)O(6.6), an underdoped high-temperature superconductor that exhibits a prominent spin pseudogap in its normal state. Zn substitution induces static magnetic order at low temperatures and triggers a large-scale spectral-weight redistribution from the magnetic resonant mode at 38 meV into uniaxial, incommensurate spin excitations with energies well below the spin pseudogap. These observations indicate a competition between incommensurate magnetic order and superconductivity close to a quantum critical point. Comparison to prior data on La(2-x)Sr(x)CuO(4) suggests that this behavior is universal for the layered copper oxides and analogous to impurity-induced magnetic order in one-dimensional quantum magnets.

We present a neutron-scattering study of the static and dynamic spin correlations in the underdoped high-temperature superconductor YBa2Cu3O6.45 in magnetic fields up to 15 T. The field strongly enhances static incommensurate magnetic order at low temperatures and induces a spectral-weight shift in the magnetic-excitation spectrum. A reconstruction of the Fermi surface driven by the field-enhanced magnetic superstructure may thus be responsible for the unusual Fermi surface topology revealed by recent quantum-oscillation experiments.

Magnetic correlations in Ti-substituted ${\text{Sr}}_{3}{({\text{Ru}}_{1\ensuremath{-}x}{\text{Ti}}_{x})}_{2}{\text{O}}_{7}$ have been studied by elastic and inelastic neutron-scattering techniques. Below transition temperatures of the order of 20 K, the samples with 7.5 and 10% of Ti content exhibit an incommensurate spin-density wave ordering with a propagation vector ${\mathbf{q}}_{\mathbf{i}\mathbf{c}}=(0.24,0.24,0)$, which does not reflect the dominant magnetic instabilities in pure ${\text{Sr}}_{3}{\text{Ru}}_{2}{\text{O}}_{7}$. Strong inelastic correlations near ${\mathbf{q}}_{\mathbf{i}\mathbf{c}}$ were found to persist in ${\text{Sr}}_{3}{({\text{Ru}}_{1\ensuremath{-}x}{\text{Ti}}_{x})}_{2}{\text{O}}_{7}$ far above the magnetic ordering; they become gapped in the ordered state.

Spin correlations in La2-xSrxCoO4 (0.3 0.3 exhibits incommensurate spin ordering with the modulation closely following the amount of doping. These incommensurate phases strongly resemble the stripe phases observed in cuprates and nickelates, but incommensurate magnetic ordering appears only at larger Sr content in the cobaltates due to a reduced charge mobility.

We have studied incommensurate spin ordering in single-crystal underdoped ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4}$ with $x\ensuremath{\sim}0.08$, 0.05, and 0.025 using neutron-scattering techniques. Static incommensurate magnetic order is observed in the ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4}$ ($x=0.05$ and 0.025) compounds with ordering wave vectors which are rotated by $45\ifmmode^\circ\else\textdegree\fi{}$ about the commensurate (0.5,0.5,0) position, with respect to that in the superconducting $x=0.08$ material. These spin modulations are one dimensional in the $x=0.05$ and 0.025 samples, with ordering wave vectors lying along the orthorhombic ${b}^{\ensuremath{\ast}}$ direction. Such a rotation in the orientation of the static spin ordering as a function of increasing Ba doping, from diagonal to collinear, is roughly coincident with the transition from an insulating to a superconducting ground state and is similar to that observed in the related ${\text{La}}_{2\ensuremath{-}x}{\text{Sr}}_{x}{\text{CuO}}_{4}$ system. This phenomenon is therefore a more generic property of underdoped La-214 cuprates.

Polarized beam neutron-scattering measurements on a highly perfect crystal of ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{6.6}$ show a distinct magnetic transition to a different phase with an onset at about 235 K, the temperature expected for the pseudogap transition. The moment is found to be about $0.1{\ensuremath{\mu}}_{B}$ for each sublattice and has a correlation length of at least $75\text{ }\text{\AA{}}$. We found the critical exponent for the magnetic neutron intensity to be $2\ensuremath{\beta}=0.37\ifmmode\pm\else\textpm\fi{}0.12$. This is the proper range for the class of transition that has no specific-heat divergence possibly explaining why none is found at the pseudogap transition.

The magnetic correlations in the charge and orbital ordered manganite ${\text{La}}_{1/2}{\text{Sr}}_{3/2}{\text{MnO}}_{4}$ have been studied by elastic and inelastic neutron scattering techniques. Out of the well-defined charge exchange (CE)-type magnetic structure with the corresponding magnons, a competition between CE-type and ferromagnetic fluctuations develops. Whereas ferromagnetic correlations are fully suppressed by the static CE-type order at low temperature, elastic and inelastic CE-type correlations disappear with the melting of the charge-orbital order at high temperature. In its charge-orbital disordered phase, ${\text{La}}_{1/2}{\text{Sr}}_{3/2}{\text{MnO}}_{4}$ exhibits a dispersion of ferromagnetic correlations, which remarkably resembles the magnon dispersion in ferromagnetically ordered metallic perovskite manganites.

We report a neutron scattering study of the spin excitation spectrum in the superconducting state of the slightly overdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ system $({T}_{c}=87\phantom{\rule{0.3em}{0ex}}\mathrm{K})$. We focus on the dispersion of the resonance peak in the superconducting state that is due to a $S=1$ collective mode. The measured spin excitation spectrum bears a strong similarity to the spectrum of the ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ system for a similar doping level (i.e., $x\ensuremath{\sim}0.95\ensuremath{-}1$), which can be described as intersecting upward- and downward-dispersing branches. A close comparison of the threshold of the electron-hole spin flip continuum, known from angle resolved photoemission measurements in the same system, indicates that the magnetic response in the superconducting state is confined, in both energy and momentum, below the gapped Stoner continuum. In contrast to ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$, the spin excitation spectrum is broader than the experimental resolution. In the framework of an itinerant-electron model, we quantitatively relate this intrinsic energy width to the superconducting gap distribution observed in scanning tunneling microscopy experiments. Our study further suggests a significant in-plane anisotropy of the magnetic response.

The magnetic excitations in Ca 1.8 Sr 0.2 RuO 4 were studied across the metamagnetic transition and as a function of temperature using inelastic neutron scattering. At low temperature and low magnetic field the magnetic response is dominated by a complex superposition of incommensurate antiferromagnetic fluctuations. Upon increasing the magnetic field across the metamagnetic transition, paramagnon and finally well-defined magnon scattering is induced, partially suppressing the incommensurate signals. The high-field phase in Ca 1.8 Sr 0.2 RuO 4 , therefore, has to be considered as an intrinsically ferromagnetic state stabilized by the magnetic field.

The lattice dynamics in ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ has been studied by inelastic neutron scattering combined with shell-model calculations. The in-plane bond-stretching modes in ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ exhibit a normal dispersion in contrast to all electronically doped perovskites studied so far. Evidence for strong electron phonon coupling is found for $c$-polarized phonons suggesting a close connection with the anomalous $c$-axis charge transport in ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$. The role of this electron-phonon coupling in the superconducting pairing remains, however, a challenging open issue.

Resonant magnetic modes with odd and even symmetries were studied by inelastic neutron scattering experiments in the bilayer high-${T}_{c}$ superconductor ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+y}$ over a wide doping range. The threshold of the spin excitation continuum in the superconducting state, deduced from the energies and spectral weights of both modes, is compared with the superconducting $d$-wave gap, deduced from electronic Raman scattering in the ${B}_{1g}$ symmetry on the same samples. Above a critical doping level of $\ensuremath{\delta}\ensuremath{\simeq}0.19$, both mode energies and the continuum threshold coincide. We find a simple scaling relationship between the characteristic energies and spectral weights of both modes, which indicates that the resonant modes are bound states in the superconducting energy gap, as predicted by the spin-exciton model of the resonant mode.

The magnon dispersion in the charge, orbital, and spin ordered phase in La1/2Sr3/2MnO4 has been studied by means of inelastic neutron scattering. We find excellent agreement with a magnetic interaction model based on the CE-type superstructure. The magnetic excitations are dominated by ferromagnetic exchange parameters revealing a nearly one-dimensional character at high energies. The strong ferromagnetic interaction in the charge or orbital ordered phase appears to be essential for the capability of manganites to switch between metallic and insulating phases.

One of the leading issues in high-$T_C$ superconductors is the origin of the pseudogap phase in underdoped cuprates. Using polarized elastic neutron diffraction, we identify a novel magnetic order in the YBa$_2$Cu$_3$O$_{6+x}$ system. The observed magnetic order preserves translational symmetry as proposed for orbital moments in the circulating current theory of the pseudogap state. To date, it is the first direct evidence of an hidden order parameter characterizing the pseudogap phase in high-$T_C$ cuprates., 3 figures

The compound TlCuCl3 represents a model system of dimerized quantum spins with strong interdimer interactions. We investigate the triplet dispersion as a function of temperature by inelastic neutron scattering experiments on single crystals. By comparison with a number of theoretical approaches we demonstrate that the description of Troyer, Tsunetsugu, and Wuertz [Phys. Rev. B 50, 13515 (1994)] provides an appropriate quantum statistical model for dimer spin systems at finite temperatures, where many-body correlations become particularly important., 4 pages, 4 figures, to appear in Physical Review Letters

Detailed neutron scattering measurements of ${\mathrm{Y}\mathrm{B}\mathrm{a}}_{2}{\mathrm{C}\mathrm{u}}_{3}{\mathrm{O}}_{6.95}$ found that the resonance peak and incommensurate magnetic scattering induced by superconductivity represent the same physical phenomenon: two dispersive branches that converge near 41 meV and the in-plane wave vector ${\mathbf{q}}_{\mathrm{A}\mathrm{F}}=(\ensuremath{\pi}/a,\ensuremath{\pi}/a)$ to form the resonance peak. One branch has a circular symmetry around ${\mathbf{q}}_{\mathrm{A}\mathrm{F}}$ and quadratic downward dispersion from $\ensuremath{\approx}41\text{ }\text{ }\mathrm{m}\mathrm{e}\mathrm{V}$ to the spin gap of $33\ifmmode\pm\else\textpm\fi{}1\text{ }\text{ }\mathrm{m}\mathrm{e}\mathrm{V}$. The other, of lower intensity, disperses from $\ensuremath{\approx}41\text{ }\text{ }\mathrm{m}\mathrm{e}\mathrm{V}$ to at least 55 meV. Our results exclude a quartet of vertical incommensurate rods in $\mathbf{q}$-$\ensuremath{\omega}$ space expected from spin waves produced by dynamical charge stripes as an origin of the observed incommensurate scattering in optimally doped YBCO.

A detailed inelastic neutron scattering study of the high temperature superconductor $\mathrm{Y}\mathrm{B}{\mathrm{a}}_{2}\mathrm{C}{\mathrm{u}}_{3}{\mathrm{O}}_{6.85}$ provides evidence of new resonant magnetic features, in addition to the well-known resonant mode at 41 meV: (i) a commensurate magnetic resonance peak at 53 meV with an even symmetry under exchange of two adjacent $\mathrm{C}\mathrm{u}{\mathrm{O}}_{2}$ layers, and (ii) high-energy incommensurate resonant spin excitations whose spectral weight is around 54 meV. The locus and the spectral weight of these modes provides unrevealed insight about the momentum shape of the electron-hole spin-flip continuum of $d$-wave superconductors.

The anisotropy of the magnetic incommensurate fluctuations in Sr2RuO4 has been studied by inelastic neutron scattering with polarized neutrons. We find a sizable enhancement of the out-of-plane component by a factor of 2 for intermediate energy transfer, which appears to decrease for higher energies. Our results qualitatively confirm calculations of the spin-orbit coupling, but the experimental anisotropy and its energy dependence are weaker than predicted.

Magnetic excitations in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ have been studied by inelastic neutron scattering. The magnetic fluctuations are dominated by incommensurate peaks related to the Fermi surface nesting of the quasi-one-dimensional ${d}_{\mathrm{xz}}$ and ${d}_{\mathrm{yz}}$ bands. The shape of the incommensurate signal agrees well with random phase approximation calculations. At the incommensurate Q positions the energy spectrum considerably softens upon cooling, pointing to a close magnetic instability: ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ does not exhibit quantum criticality but is very close to it. $\ensuremath{\omega}/T$ scaling may be fitted to the data for temperatures above 30 K. Below the superconducting transition, the magnetic response at the nesting signal is not found to change in the energy range down to 0.4 meV.