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We report the results of an unpolarized small-angle neutron-scattering (SANS) study on Mn-Zn ferrite (MZFO) magnetic nanoparticles with the aim to elucidate the interplay between their particle size and the magnetization configuration. We study different samples of single-crystalline MZFO nanoparticles with average diameters ranging between 8 to 80 nm, and demonstrate that the smallest particles are homogeneously magnetized. However, with increasing nanoparticle size, we observe the transition from a uniform to a nonuniform magnetization state. Field-dependent results for the correlation function confirm that the internal spin disorder is suppressed with increasing field strength. The experimental SANS data are supported by the results of micromagnetic simulations, which confirm an increasing inhomogeneity of the magnetization profile of the nanoparticle with increasing size. The results presented demonstrate the unique ability of SANS to detect even very small deviations of the magnetization state from the homogeneous one.

Tuning the interactions in magnetic materials by pressure or chemical substitution is a much visited route to discover new and exotic phases of condensed matter. A well known example is doping the archetype chiral magnet MnSi with Fe. Here, the authors use small-angle neutron scattering to track the evolution of the helimagnetic order in Mn${}_{1\ensuremath{-}x}$Fe${}_{x}$Si with Fe doping. They discover that the long-range helimagnetic order found in MnSi is suppressed already at ${x}^{*}$ $\ensuremath{\approx}$ 0.11, well before the critical concentration of $x$ $\ensuremath{\approx}$ 0.17. Finite isotropic helimagnetic correlations persist for $x$ $g$ ${x}^{*}$ that can only be partly aligned by magnetic fields through a complex magnetization process.

We investigated the phase-transition kinetics of magnetic skyrmion lattice (SkL) in MnSi by means of stroboscopic small-angle neutron scattering (SANS). Temporal evolutions of SANS patterns were measured with time resolution of 13 ms while sweeping temperature as fast as $50{\mathrm{Ks}}^{\ensuremath{-}1}$. It turned out that the paramagnetic-to-SkL transition immediately occurs upon traversing the equilibrium phase boundary on the rapid cooling, whereas the SkL-to-conical transition can be kinetically avoided to realize the low-temperature metastable SkL with a long-range magnetic order. The formation of the metastable SkL was found to be strongly dependent not only on cooling rate, but also on magnetic field and trajectory in the $H\text{\ensuremath{-}}T$ phase diagram.

Neutron and x-ray scattering measurements were performed on $(\mathrm{N}{\mathrm{a}}_{1/2}\mathrm{B}{\mathrm{i}}_{1/2})\mathrm{Ti}{\mathrm{O}}_{3}\text{\ensuremath{-}}x\phantom{\rule{0.28em}{0ex}}\mathrm{at}%\mathrm{BaTi}{\mathrm{O}}_{3}$ (NBT-$x\mathrm{BT}$) single crystals ($x=4$, 5, 6.5, and 7.5) across the morphotropic phase boundary (MPB), as a function of both composition and temperature, and probing both structural and dynamical aspects. In addition to the known diffuse scattering pattern near the $\mathrm{\ensuremath{\Gamma}}$ points, our measurements revealed new, faint superlattice peaks, as well as an extensive diffuse scattering network, revealing a short-range ordering of polar nanoregions (PNR) with a static stacking morphology. In samples with compositions closest to the MPB, our inelastic neutron scattering investigations of the phonon dynamics showed two unusual features in the acoustic phonon branches, between the superlattice points, and between the superlattice points and $\mathrm{\ensuremath{\Gamma}}$ points, respectively. These critical elements are not present in the other compositions away from the MPB, which suggests that these features may be related to the tilt modes coupling behavior near the MPB.

Chiral magnetism plays an increasingly important role in condensed matter investigations driven by the discovery of exotic spin textures, such as the topologically protected chiral skyrmions that can form a lattice under magnetic fields. The nature and universality of the phase diagram in cubic chiral magnets has been the subject of numerous experimental and theoretical investigations, including the transition to the helimagnetic state. In MnSi, the archetypal system in this family, this transition is of first order and involves a precursor phase, where strong chiral fluctuating correlations build up. This work presents an experimental investigation of the structural and dynamical aspects of the phase transition in Fe${}_{1-x}$Co${}_{x}$Si, a system that belongs to the same family as MnSi but with the additional possibility to tune important physical interactions and parameters through variation of the Fe and Co concentration. In this system, the combination of small-angle neutron scattering and neutron spin echo spectroscopy uncovers that the scenario of the transition is qualitatively very different from that in MnSi. This goes beyond what can be expected from a comparison of the relevant length scales and thus challenges the validity of a universal approach to the helimagnetic transition in cubic chiral magnets.

Small angle neutron scattering measurements have been performed to study the thermodynamic stability of skyrmion-lattice phases in Cu$_2$OSeO$_3$. We found that the two distinct skyrmion-lattice phases [SkX(1) and SkX(2) phases] can be stabilized through different thermal histories; by cooling from the paramagnetic phase under finite magnetic field, the SkX(2) phase is selected. On the other hand, the 30$^{\circ}$-rotated SkX(1) phase becomes dominant by heating the sample from the ordered conical phase under finite field. This difference in stabilization is surprisingly similar to the irreversibility observed in spin glasses. The zero-field cooling results in the co-existence of the two phases. It is further found that once one of the skyrmion-lattice phases is formed, it is hardly destabilized. This indicates unusual thermal stability of the two skyrmion-lattice phases originating from an unexpectedly large energy barrier between them., 9 pages, 10 figures

Small angle neutron scattering measurements on a bulk single crystal of the doped chiral magnet ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}\mathrm{Si}$ with $x=0.3$ reveal a pronounced effect of the magnetic history and cooling rates on the magnetic phase diagram. The extracted phase diagrams are qualitatively different for zero and field cooling and reveal a metastable skyrmion lattice phase outside the $A$ phase for the latter case. These thermodynamically metastable skyrmion lattice correlations coexist with the conical phase and can be enhanced by increasing the cooling rate. They appear in a wide region of the phase diagram at temperatures below the $A$ phase but also at fields considerably smaller or higher than the fields required to stabilize the $A$ phase.

The Dzyaloshinski-Moriya interaction (DMI) originates from the relativistic spin-orbit coupling, and in low-symmetry crystal structures without inversion centers it gives rise to antisymmetric magnetic exchange. DMI plays an important role in the formation of inhomogeneous spin structures such as long-wavelength spirals, vortex states, and skyrmion textures. Even in high-symmetry lattices, where the antisymmetric DM term would normally vanish, DMI is present in the vicinity of any lattice defect and can influence the magnetic microstructure of polycrystalline materials with a large defect density. In this work the authors have studied the impact of the DMI on the magnetic small-angle neutron scattering (SANS) cross section, which is able to probe long-wavelength magnetization fluctuations in the bulk and on the nanometer length scale. The analysis of the authors provides a promising way to characterize the DMI in defect-rich materials.

We study magnetic domains in ${\text{Nd}}_{2}{\text{Fe}}_{14}\text{B}$ single crystals using high resolution magnetic force microscopy (MFM). Previous MFM studies and small angle neutron scattering experiments suggested the presence of nanoscale domains in addition to optically detected micrometer-scale ones. We find, in addition to the elongated, wavy nanodomains reported by a previous MFM study, that the micrometer-sized, star-shaped fractal pattern is constructed of an elongated network of nanodomains $\ensuremath{\sim}20$ nm in width, with resolution-limited domain walls thinner than 2 nm. While the microscopic domains exhibit significant resilience to an external magnetic field, some of the nanodomains are sensitive to the magnetic field of the MFM tip.

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.

Liquid hydrogen is a dense Bose fluid whose equilibrium properties are both calculable from first principles using various theoretical approaches and of interest for the understanding of a wide range of questions in many body physics. Unfortunately, the pair correlation function $g(r)$ inferred from neutron scattering measurements of the differential cross section $d\sigma \over d\Omega$ from different measurements reported in the literature are inconsistent. We have measured the energy dependence of the total cross section and the scattering cross section for slow neutrons with energies between 0.43~meV and 16.1~meV on liquid hydrogen at 15.6~K (which is dominated by the parahydrogen component) using neutron transmission measurements on the hydrogen target of the NPDGamma collaboration at the Spallation Neutron Source at Oak Ridge National Laboratory. The relationship between the neutron transmission measurement we perform and the total cross section is unambiguous, and the energy range accesses length scales where the pair correlation function is rapidly varying. At 1~meV our measurement is a factor of 3 below the data from previous work. We present evidence that these previous measurements of the hydrogen cross section, which assumed that the equilibrium value for the ratio of orthohydrogen and parahydrogen has been reached in the target liquid, were in fact contaminated with an extra non-equilibrium component of orthohydrogen. Liquid parahydrogen is also a widely-used neutron moderator medium, and an accurate knowledge of its slow neutron cross section is essential for the design and optimization of intense slow neutron sources. We describe our measurements and compare them with previous work., Comment: Edited for submission to Physical Review B

To extract a pure atomic-resolution hologram around hydrogen from a two-dimensional (2D) neutron intensity distribution around a single crystal, enhancement of the holographic signal and suppression of the diffuse scattering are important; sample cooling can achieve both. To estimate the performance of sample cooling in achieving these requirements, the angular anisotropy of the neutron intensities around a ${\mathrm{PdH}}_{0.78}$ single crystal was measured at 300 K and 100 K. In addition to the reduction in the diffuse scattering intensity, the pattern itself changed markedly upon sample cooling, thus indicating a significant modification of the hydrogen lattice dynamics. The reconstruction from a hologram, which was obtained by subtracting the diffuse scattering pattern, shows images of H and Pd nuclei as negative and positive peaks, respectively. In particular, such reconstruction at 100 K exhibits distinct H images at distant positions owing to the suppression of hydrogen motion. These features are important for the determination of hydrogen sites in various materials.

We present a study of the model spin-glass LiHo0.5Er0.5F4 using simultaneous ac susceptibility, magnetization, and magnetocaloric effect measurements along with small angle neutron scattering (SANS) at sub-Kelvin temperatures. All measured bulk quantities reveal hysteretic behavior when the field is applied along the crystallographic c axis. Furthermore, avalanchelike relaxation is observed in a static field after ramping from the zero-field-cooled state up to 200–300 Oe. SANS measurements are employed to track the microscopic spin reconfiguration throughout both the hysteresis loop and the related relaxation. Comparing the SANS data to inhomogeneous mean-field calculations performed on a box of one million unit cells provides a real-space picture of the spin configuration. We discover that the avalanche is being driven by released Zeeman energy, which heats the sample and creates positive feedback, continuing the avalanche. The combination of SANS and mean-field simulations reveal that the conventional distribution of cluster sizes is replaced by one with a depletion of intermediate cluster sizes for much of the hysteresis loop.

We have observed a magnetic vortex lattice (VL) in BaFe2(As0.67P0.33)(2) (BFAP) single crystals by small-angle neutron scattering. With the field along the c axis, a nearly isotropic hexagonal VL was formed in the field range from 1 to 16 T, and no symmetry changes in the VL were observed. The temperature dependence of the VL signal was measured and confirms the presence of (non-d-wave) nodes in the superconducting gap structure for measurements at 5 T and below. The nodal effects were suppressed at high fields. At low fields, a VL reorientation transition was observed between 1 and 3 T, with the VL orientation changing by 45 degrees. Below 1 T, the VL structure was strongly affected by pinning and the diffraction pattern had a fourfold symmetry. We suggest that this (and possibly also the VL reorientation) is due to pinning to defects aligned with the crystal structure, rather than being intrinsic. The temperature dependence of the scaled intensity suggests that BFAP possesses at least one full gap and one nodal gap with circular symmetry. Judging from the symmetry, the node structure should take the form of an "accidental" circular line node, which is consistent with recent angle-resolved photoemission spectroscopy results.

We report on small angle neutron scattering measurements of the vortex lattice in twin-free YBa2Cu3O7, extending the previously investigated maximum field of 11~T up to 16.7~T with the field applied parallel to the c axis. This is the first microscopic study of vortex matter in this region of the superconducting phase. We find the high field VL displays a rhombic structure, with a field-dependent coordination that passes through a square configuration, and which does not lock-in to a field-independent structure. The VL pinning reduces with increasing temperature, but is seen to affect the VL correlation length even above the irreversibility temperature of the lattice structure. At high field and temperature we observe a melting transition, which appears to be first order, with no detectable signal from a vortex liquid above the transition.

Using the small angle neutron scattering (SANS) technique we investigated the vortex lattice (VL) in the mixed state of the stannide superconductor Yb$_{3}$Rh$_{4}$Sn$_{13}$. We find a single domain VL of slightly distorted hexagonal geometry for field strengths between 350 and 18500 G and temperatures between T = 0.05 and T = 6.5 K. We observe a clear in-plane rotation of the VL for different magnetic field directions relative to the crystallographic axes. We also find that the hexagonal symmetry of the VL is energetically favorable in Yb$_{3}$Rh$_{4}$Sn$_{13}$ for external fields oriented along axes of different symmetries: twofold [110], threefold [111] and fourfold [100]. The observed behavior is different from other conventional and unconventional superconductors. The superconducting state is characterized by an isotropic gapped order parameter with an amplitude of $\Delta(0)$ = 1.57 $\pm$ 0.05 meV. At the lowest temperatures the field dependence of the magnetic form factor in our material reveals a London penetration depth of $\lambda_{L}$ = 2508 $\pm$ 17 $\AA$ and a Ginzburg coherence length of $\xi$ = 100 $\pm$ 1.3 $\AA$, i.e., it is a strongly type-II superconductor, $\kappa$ = $\lambda_{L}/\xi$ = 25.

The author describes a new algorithm, based on Bayesian principles, for the analysis of small angle neutron scattering (SANS) data. This work represents a significant improvement over existing methods, and it is expected to have a broad range of applicability going beyond the SANS community.

We report a study of the basal-plane anisotropy of the superfluid density in underdoped YBa2Cu4O8 (Y124), showing the effects of both the CuO2 planes and the fully occupied CuO chains. From small-angle neutron scattering measurements of the vortex lattice, we can infer the superconducting (SC) properties for a temperature (T) range T = 1.5 K to T-c and magnetic induction B from 0.1 to 6 T. We find that the superfluid density along a has a simple d-wave T dependence. However, along b (the chain direction) the superfluid density falls much more rapidly with T and also with increasing field. This strongly suggests the suppression of proximity-effect-induced superconductivity in the CuO chains. In addition, our results do not support a common framework for the low-field in-plane SC response in Y124 and related YBa2Cu3O7, and also indicate that any magnetic field induced charge-density-wave order in Y124 exists only for fields above 6 T.

A calculation is performed of the imaginary part of the electron magnetic susceptibility, as function of energy and momentum in the vicinity of the maximum of the inelastic neutron scattering. Compared to the previous calculation a slight bending of the energy bands in the vicinity of extended saddle point singularities is taken into account. It is shown that this simple picture fits qualitatively the recently observed experimental data on the fine structure in momentum space of the inelastic neutron scattering cross section in the vicinity of the maximum at different energies.

Several previous studies of ${\mathrm{K}}_{1\ensuremath{-}x}{\mathrm{Li}}_{x}{\mathrm{TaO}}_{3}$ (KLT) have revealed the presence, above the structural transition, of polar nanoregions. Recently, these have been shown to play an essential role in the relaxor behavior of KLT. In order to characterize these regions, we have performed a neutron-scattering study of KLT crystals with different lithium concentrations, both above and below the critical concentration. This study reveals the existence of diffuse scattering that appears upon formation of these regions. The rodlike distribution of the diffuse scattering along cubic directions indicates that the regions form in the shape of discs in the various cubic planes. From the width of the diffuse scattering we extract values for a correlation length or size of the regions as a function of temperature. Finally, on the basis of the reciprocal lattice points around which the diffuse scattering is most intense, we conclude that the regions have tetragonal symmetry. The large increase in Bragg intensities at the first-order transition suggests that the polar regions freeze to form large structural domains and the transition is triggered by the percolation of strain fields through the crystals.

Theoretical and experimental studies have been made on crystal-truncation-rod (CTR) scattering when x rays satisfy the Bragg condition. Calculations were made on the basis of a dynamical theory in Darwin's approach extended to a multibeam case. Calculated results indicated that the profile of intensity changes of CTR scattering as a function of incident angle under the Bragg condition is sensitive to surface structures. It was made clear by kinematical treatment that the profile reflects x-ray intensity changes of the standing-wave field at an atomic layer on a substrate crystal when x-ray scattering amplitude by the surface layer is larger than CTR scattering amplitude by the substrate, particularly in the case of intensity measurements on fractional-order rods of superstructures formed on the substrate crystal. The experimental result obtained for a Si (001) crystal was in good agreement with the theoretical calculation. Detailed analysis suggested that a strain field caused by the native oxide layer spreads from the surface of the substrate crystal to a depth of hundreds of \AA{}.

The current densities in partially filled electron shells of free atoms or ions, when analyzed in terms of multipole expansions, do not carry signatures that would distinguish orbital and spin currents. The same holds for the orbital and spin contributions to elastic neutron scattering amplitude, which are related to Fourier transforms of the respective current densities. The pitfalls of the so-called dipole approximation, which appears to enable a distinction, are pointed out and errors involved are calculated for some free-ion and crystal-field states.

Resonant scattering by cavity polaritons in a semiconductor microcavity is investigated. The bidimensional photonic behavior is well shown by the angular spread of the Rayleigh scattered light on the elastic cone. Moreover, the strong coupling between the excitonic oscillator and the cavity mode enables the simultaneous observation of both (i) universal properties of disordered systems such as coherent backscattering over a large angular width, and (ii) scattering anisotropy due to the microscopic nature of the scatterer.

In this work, the many-spin interactions taking place in ${\mathrm{Mn}}_{12}$ large-spin clusters are extensively studied using the 8-spin model Hamiltonian, for which we determine the possible parameters based on experimental data. Account of the many-spin excitations satisfactorily explains positions of the neutron scattering peaks, results of EPR measurements, and the temperature dependence of magnetic susceptibility. In particular, strong Dzyaloshinsky-Morya interactions are found to be important for description of neutron scattering data.

Pulsed neutron-diffraction measurements were carried out on powder samples of ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{MnO}}_{3}$ $(0l~xl~0.5)$ in order to study the local atomic structure of this system known for its colossal magnetoresistance phenomenon. The results are analyzed in terms of the atomic pair-density function to elucidate the role of local lattice distortion in the magnetic and charge transport properties. It is shown that the Jahn-Teller (JT) distortions are locally present even when the crystallographic structure suggests otherwise, and indicate the formation of small lattice polarons in the insulating phase. Local JT distortions are observed even in the metallic phase up to $x=0.35,$ suggesting that the charge distribution in the metallic phase just above the metal-insulator transition may not be spatially uniform. It is possible that charges are partially confined by spin and lattice resulting in microscopic separation of the charge-rich and charge-poor regions.

The dynamic structure factor $S(Q,\ensuremath{\omega})$ for lead fluoride ${\mathrm{PbF}}_{2}$ in the normal and the superionic states at $T=293$ and 823 K has been investigated by cold neutron scattering. In the superionic state on a constant Q scale, two symmetrical peaks at low energies over a limited range of wave-vector transfers are observed. This structure is similar to the long-wavelength collective excitations (Brillouin doublet) specific to some liquid metals. Such an observation could support the idea of liquidlike behavior at the level of the anion sublattice in the superionic state. However, the energies of these excitations are about one order of magnitude smaller and the corresponding Q values are rather high compared to those of the collective modes observed in the simple classical liquids. Therefore these excitations are of different nature from those characteristic for a classical liquid.

We report coherent inelastic neutron-scattering spectra for the network glass former ${\mathrm{B}}_{2}{\mathrm{O}}_{3}$ measured at temperatures from 100 to 1300 K ${(T}_{g}\ensuremath{\sim}525 \mathrm{K}).$ At the first sharp diffraction peak, which stems from the van der Waals packing of layerlike units, one finds a correlated in-phase motion of these units at low frequency, and in addition a quasi-incoherent contribution for all temperatures. The contribution of the in-phase motion in the frequency range of the boson peak and the fast relaxations is significantly higher than the one expected for the sound waves.

Determinations of the generalized neutron vibrational density of states (GVDOS) made on samples of Se-As-Ge glass alloys by neutron inelastic scattering at the NIST Center for Neutron Research are presented. It is observed that up to a certain characteristic vibrational energy the GVDOS are nearly identical for alloys over a broad range of compositions as long as they have the same average coordination number $〈r〉.$ In the present work this feature, referred to as the vibrational isocoordinate rule (VIR), is established for samples of Se-As-Ge alloys over the entire glass-forming region with $〈r〉$ ranging from 2.16 through the theoretical rigidity percolation threshold 2.4 up to 3.2. Compositional exceptions to the VIR have been found along and near the Se-As binary alloy line above $〈r〉=2.4.$

Specific heat, elastic neutron scattering, and torque measurements have been performed on the two quasi-one-dimensional cuprates ${\mathrm{Ca}}_{0.83}{\mathrm{CuO}}_{2}$ and ${\mathrm{Sr}}_{0.73}{\mathrm{CuO}}_{2}.$ These compounds consist of infinite ${\mathrm{CuO}}_{2}$ chains, which are highly hole doped. In both compounds a peak in the specific heat, attributed to a static magnetic transition, has been observed at $T\ensuremath{\sim}10 \mathrm{K}.$ Magnetic Bragg peaks were identified in the neutron diffraction patterns, giving evidence of a three-dimensional long-range ordered ground state.

The inelastic-neutron-scattering spectrum of totally hydrogenated 4-methyl-pyridine (4MP-h7) at 0.5 K reveals three bands whose widths are limited to the resolution function of the spectrometer: 9 meV. Within the quantum sine-Gordon theory, these bands are assigned to in-phase ~537 meV! and out-of-phase ~470 meV! tunneling transitions and to the traveling transition of the breather mode ~516 meV!. The spectra of isotopic mixtures with the totally deuterated analogue (4MP-d7), containing 85%, 65%, and 50% of 4MP-h7 , respectively, were obtained at 1.8 K with the same resolution. The frequency of the breather traveling state is progressively shifted downwards to 506 meV. The frequency shift is represented with the breather mode in clusters of hydrogenated molecules. Simultaneously, an additional band is observed between 490 and 497 meV whose intensity is proportional to the amount of deuterated molecules. This band is attributed to the breathermode interaction with isolated deuterated molecules. The breather wave form and the effective potential for the impurity are calculated. For the sample containing 50% of each isotopomer, new bands at 478 and 464 meV are attributed to the breather mode in rather small hydrogenated clusters with deuterated clusters as reflective boundaries. @S0163-1829~98!09441-7#