Indicators of accuracy in structure factor measurement

Abrahams, S. C.

doi:10.1107/s0567739469000283

Cited by 44 publications

(8 citation statements)

References 2 publications

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“…Here, Te atoms are located at the Wyckoff site 2 d at ( x , y , z ) = (1/2, 2/3, z ) with z = 0.248 ± 0.001 and Cr atoms are located at the site 1 b (0 0 ½). We obtain a good unweighted residuum (Ru) 34 of 0.064 and a goodness of fit (GOF) 35 near 1.0 provided that a fraction of 0.40 ± 0.10 atoms per unit cell of intercalated Cr is located in the vdW gap at the Wyckoff site 1 a (0,0,0). On the basis of this structural model no significant improvement of the fit quality factors can be achieved by allowing for symmetry lowering such as e.g.…”

Section: Resultsmentioning

confidence: 94%

Observation of Néel-type skyrmions in acentric self-intercalated Cr1+δTe2

et al. 2022

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Transition-metal dichalcogenides intercalated with 3d-transition metals within the van der Waals (vdW) gaps have been the focus of intense investigations owing to their fascinating structural and magnetic properties. At certain concentrations the intercalated atoms form ordered superstructures that exhibit ferromagnetic or anti-ferromagnetic ordering. Here we show that the self-intercalated compound Cr1+δTe2 with δ ≈ 0.3 exhibits a new, so far unseen, three-dimensionally ordered (2×2×2) superstructure. Furthermore, high resolution X-ray diffraction reveals that there is an asymmetric occupation of the two inequivalent vdW gaps in the unit cell. The structure thus lacks inversion symmetry, which, thereby, allows for chiral non-collinear magnetic nanostructures. Indeed, Néel-type skyrmions are directly observed using Lorentz transmission electron microscopy. The skyrmions are stable within the accessible temperature range (100–200 K) as well as in zero magnetic field. The diameter of the Néel skyrmions increases with lamella thickness and varies with applied magnetic field, indicating the role of long-range dipole fields. Our studies show that self-intercalation in vdW materials is a novel route to the formation of synthetic non-collinear spin textures.

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Section: Resultsmentioning

confidence: 94%

Observation of Néel-type skyrmions in acentric self-intercalated Cr1+δTe2

et al. 2022

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“…Quantitative analysis of these data was carried out by a least‐squares refinement of the calculated intensities to those observed based on the SGR #156 ( P 3 m 1). An excellent fit could be achieved which is quantified by the goodness of fit (GOF) parameter of 1.06 [ 27 ] and the unweighted residuum (Ru) of 0.05 where Ru is defined as Ru = Σ||Fobs| – |Fcalc||/Σ|Fobs|, where the sum runs over all reflections. Ru represents the average relative deviation between the calculated (calc) and the experimental (obs) structure factor magnitudes.…”

Section: Resultsmentioning

confidence: 99%

Magnetic Skyrmions in a Thickness Tunable 2D Ferromagnet from a Defect Driven Dzyaloshinskii–Moriya Interaction

et al. 2022

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There is considerable interest in van der Waals (vdW) materials as potential hosts for chiral skyrmionic spin textures. Of particular interest is the ferromagnetic, metallic compound Fe3GeTe2 (FGT), which has a comparatively high Curie temperature (150–220 K). Several recent studies have reported the observation of chiral Néel skyrmions in this compound, which is inconsistent with its presumed centrosymmetric structure. Here the observation of Néel type skyrmions in single crystals of FGT via Lorentz transmission electron microscopy (LTEM) is reported. It is shown from detailed X‐ray diffraction structure analysis that FGT lacks an inversion symmetry as a result of an asymmetric distribution of Fe vacancies. This vacancy‐induced breaking of the inversion symmetry of this compound is a surprising and novel observation and is a prerequisite for a Dzyaloshinskii–Moriya vector exchange interaction which accounts for the chiral Néel skyrmion phase. This phenomenon is likely to be common to many 2D vdW materials and suggests a path to the preparation of many such acentric compounds. Furthermore, it is found that the skyrmion size in FGT is strongly dependent on its thickness: the skyrmion size increases from ≈100 to ≈750 nm as the thickness of the lamella is increased from ≈90 nm to ≈2 µm. This extreme size tunability is a feature common to many low symmetry ferro‐ and ferri‐magnetic compounds.

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“…In this context one might argue that the goodness-of-fit (GOF) parameter is the more suitable parameter for quantifying the fit quality. The GOF is given [46], where the difference between observed and calculated intensities is normalized to the uncertainties expressed by the standard deviation (σ ) and to (N − P ), i.e., the difference between the number of independent data points (N) and the number of parameters (P) which are varied. However, it should be noted that there are some issues, which are important and must critically be treated when the GOF is used in SXRD.…”

Section: A Data Analysismentioning

confidence: 99%

Atomic relaxations at the (0001) surface ofBi2Se3single crystals and ultrathin films

et al. 2014

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We present a surface x-ray analysis of the atomic structure of the (0001) surface of the topological insulator Bi 2 Se 3 , which was grown as a single crystal and as an ultrathin film on Si(111) using molecular beam epitaxy (MBE). In general we find that the top Se-Bi layer spacing is expanded between 2% and 17% relative to the bulk, while deeper layers and the first van der Waals gap are unrelaxed. The top layer expansion is directly related to the amount of surface contamination by carbon and oxygen. The near-surface structures of the single crystal and the MBE-grown thin film differ in the degree of (static) disorder: for the former an overall Debye parameter (B) per quintuple layer (QL) of 5Å 2 is found to decrease slowly with depth. MBE-grown Bi 2 Se 3 films exhibit the opposite scenario, characterized by an increase in B from about 10Å 2 for the topmost QL to values of B = 20-40Å 2 for the fourth QL. This is attributed to the lattice misfit to the Si(111) surface. Ab initio calculations reveal carbon to act as an n-dopant, while the first interlayer spacing expansion induces a shift of the Dirac point towards the Bi 2 Se 3 bulk conduction band minimum.

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Indicators of accuracy in structure factor measurement

Cited by 44 publications

References 2 publications

Observation of Néel-type skyrmions in acentric self-intercalated Cr1+δTe2

Observation of Néel-type skyrmions in acentric self-intercalated Cr1+δTe2

Magnetic Skyrmions in a Thickness Tunable 2D Ferromagnet from a Defect Driven Dzyaloshinskii–Moriya Interaction

Atomic relaxations at the (0001) surface ofBi2Se3single crystals and ultrathin films

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