Magnetic-crystallographic phase diagram of superconducting parent compound Fe1+x_{1+x}Te

hrough neutron diffraction experiments, including spin-polarized measurements, we find a collinear incommensurate spin-density wave with propagation vector $\mathbf k =$ ($0.4481(4) \, \,0 \, \, \frac1 2$) at base temperature in the superconducting parent compound Fe$_{1+x}$Te. This critical concentration of interstitial iron corresponds to $x \approx 12$ and leads crystallographic phase separation at base temperature. The spin-density wave is short-range ordered with a correlation length of 22(3) \AA, and as the ordering temperature is approached its propagation vector decreases linearly in the H-direction and becomes long-range ordered. Upon further populating the interstitial iron site, the spin-density wave gives way to an incommensurate helical ordering with propagation vector $\mathbf k =$ ($0.3855(2) \, \,0 \, \, \frac1 2$) at base temperature. For a sample with $x \approx 9(1)$, we also find an incommensurate spin-density wave that competes with the bicollinear commensurate ordering close to the N\'eel point. The shifting of spectral weight between competing magnetic orderings observed in several samples is supporting evidence for the phase separation being electronic in nature, and hence leads to crystallographic phase separation around the critical interstitial iron concentration of 12%. With results from both powder and single crystal samples, we construct a magnetic-crystallographic phase diagram of Fe$_{1+x}$Te for $ 5% < x <17%

Polarization-analyzed small-angle neutron scattering. II. Mathematical angular analysis

Polarization-analyzed small-angle neutron scattering (SANS) is a powerful tool for the study of magnetic morphology with directional sensitivity. Building upon polarized scattering theory, this article presents simplified procedures for the reduction of longitudinally polarized SANS into terms of the three mutually orthogonal magnetic scattering contributions plus a structural contribution. Special emphasis is given to the treatment of anisotropic systems. The meaning and significance of scattering interferences between nuclear and magnetic scattering and between the scattering from magnetic moments projected onto distinct orthogonal axes are discussed in detail. Concise tables summarize the algorithms derived for the most commonly encountered conditions. These tables are designed to be used as a reference in the challenging task of extracting the full wealth of information available from polarization-analyzed SANS

Particle Moment Canting in CoFe2O4 Nanoparticles

Polarization-analyzed small-angle neutron scattering methods are used to determine the spin morphology in high crystalline anisotropy, 11 nm diameter CoFe2O4 nanoparticle assemblies with randomly oriented easy axes. In moderate to high magnetic fields, the nanoparticles adopt a uniformly canted structure, rather than forming domains, shells, or other arrangements. The observed canting angles agree quantitatively with those predicted from an energy model dominated by Zeeman and anisotropy competition, with implications for the technological use of such nanoparticles

Resolving material-specific structures within Fe₃O₄|γ-Mn₂O₃ core|shell nanoparticles using anomalous small-angle X-ray scattering

Here it is demonstrated that multiple-energy, anomalous small-angle X-ray scattering (ASAXS) provides significant enhancement in sensitivity to internal material boundaries of layered nanoparticles compared with the traditional modeling of a single scattering energy, even for cases in which high scattering contrast naturally exists. Specifically, the material-specific structure of monodispersed Fe₃O₄|γ-Mn₂O₃ core|shell nanoparticles is determined, and the contribution of each component to the total scattering profile is identified with unprecedented clarity. We show that Fe₃O₄|γ-Mn₂O₃ core|shell nanoparticles with a diameter of 8.2 ± 0.2 nm consist of a core with a composition near Fe₃O₄ surrounded by a (Mn(x)Fe(1-x))₃O₄ shell with a graded composition, ranging from x ≈ 0.40 at the inner shell toward x ≈ 0.46 at the surface. Evaluation of the scattering contribution arising from the interference between material-specific layers additionally reveals the presence of Fe₃O₄ cores without a coating shell. Finally, it is found that the material-specific scattering profile shapes and chemical compositions extracted by this method are independent of the original input chemical compositions used in the analysis, revealing multiple-energy ASAXS as a powerful tool for determining internal nanostructured morphology even if the exact composition of the individual layers is not known a priori

Core-shell magnetic morphology of structurally uniform magnetite nanoparticles

A new development in small-angle neutron scattering with polarization analysis allows us to directly extract the average spatial distributions of magnetic moments and their correlations with three-dimensional directional sensitivity in any magnetic field. Applied to a collection of spherical magnetite nanoparticles 9.0 nm in diameter, this enhanced method reveals uniformly canted, magnetically active shells in a nominally saturating field of 1.2 T. The shell thickness depends on temperature, and it disappears altogether when the external field is removed, confirming that these canted nanoparticle shells are magnetic, rather than structural, in origin

Internal magnetic structure of magnetite nanoparticles at low temperature

Small-angle neutron scattering with polarization analysis reveals that Fe3O4 nanoparticles with 90 Å diameters have ferrimagnetic moments significantly reduced from that of bulk Fe3O4 at 10 K, nominal saturation. Combined with previous results for an equivalent applied field at 200 K, a core-disordered shell picture of a spatially reduced ferrimagnetic core emerges, even well below the bulk blocking temperature. Zero-field cooling suggests that this magnetic morphology may be intrinsic to the nanoparticle, rather than field induced, at 10 K

Magnetic Particle Self-Assembly at Functionalized Interfaces

We study the assembly of magnetite nanoparticles in water-based ferrofluids in wetting layers close to silicon substrates with different functionalization without and with an out-of-plane magnetic field. For particles of nominal sizes 5, 15, and 25 nm, we extract density profiles from neutron reflectivity measurements. We show that self-assembly is only promoted by a magnetic field if a seed layer is formed at the silicon substrate. Such a layer can be formed by chemisorption of activated N-hydroxysuccinimide ester-coated nanoparticles at a (3-aminopropyl)triethoxysilane functionalized surface. Less dense packing is reported for physisorption of the same particles at a piranha-treated (strongly hydrophilic) silicon wafer, and no wetting layer is found for a self-assembled monolayer of octadecyltrichlorosilane (strongly hydrophobic) at the interface. We show that once the seed layer is formed and under an out-of-plane magnetic field further wetting layers assemble. These layers become denser with time, larger magnetic fields, higher particle concentrations, and larger moment of the nanoparticles

Nanoconfinement-Induced Phase Segregation of Binary Benzene–Cyclohexane Solutions within a Chemically Inert Matrix

Binary solutions provide a fertile arena to probe intermolecular and molecular/surface interactions under nanoconfinement. Here, the phase segregation of a solution comprising 0.80 mol fraction benzene and 0.20 mol fraction cyclohexane confined within SiO₂ nanopores was evaluated using small-angle neutron scattering with hydrogen–deuterium contrast matching. It is demonstrated that benzene and cyclohexane are fully miscible at 303 K (30 °C), yet they unambiguously phase segregate by 153 K (−120 °C), which is below their respective freezing points and below the cubic-to-monoclinic phase transition of cyclohexane. Specifically, the cyclohexane and benzene separate into a core|shell morphology with cyclohexane concentrated toward the nanopore centers. Additionally, pure benzene is shown to form a frozen core of bulk density with a thin shell of slightly reduced density immediately adjacent to the SiO₂ nanopore wall at 153 K. Because the SiO₂ matrix is chemically inert to cyclohexane and benzene, the observed radially dependent phase segregation is strong evidence for the effects of confinement alone, with minimal host–wall attraction