X-ray microdiffraction images of antiferromagnetic domain evolution in chromium

Imaging mesoscopic antiferromagnetic spin textures in the dilute limit from single-geometry resonant coherent x-ray diffraction

The detection and manipulation of antiferromagnetic domains and topological antiferromagnetic textures are of central interest to solid-state physics. A fundamental step is identifying tools to probe the mesoscopic texture of an antiferromagnetic order parameter. In this work, we demonstrate that Bragg coherent diffractive imaging can be extended to study the mesoscopic texture of an antiferromagnetic order parameter using resonant magnetic x-ray scattering. We study the onset of the antiferromagnet transition in PrNiO₃, focusing on a temperature regime in which the antiferromagnetic domains are dilute in the beam spot and the coherent diffraction pattern modulating the antiferromagnetic peak is greatly simplified. We demonstrate that it is possible to extract the arrangements and sizes of these domains from single diffraction patterns and show that the approach could be extended to a time-structured light source to study the motion of dilute domains or the motion of topological defects in an antiferromagnetic spin texture.

Resonant nanodiffraction x-ray imaging reveals role of magnetic domains in complex oxide spin caloritronics

Spin electronic devices based on crystalline oxide layers with nanoscale thicknesses involve complex structural and magnetic phenomena, including magnetic domains and the coupling of the magnetism to elastic and plastic crystallographic distortion. The magnetism of buried nanoscale layers has a substantial impact on spincaloritronic devices incorporating garnets and other oxides exhibiting the spin Seebeck effect (SSE). Synchrotron hard x-ray nanobeam diffraction techniques combine structural, elemental, and magnetic sensitivity and allow the magnetic domain configuration and structural distortion to be probed in buried layers simultaneously. Resonant scattering at the Gd L₂ edge of Gd₃Fe₅O₁₂ layers yields magnetic contrast with both linear and circular incident x-ray polarization. Domain patterns facet to form low-energy domain wall orientations but also are coupled to elastic features linked to epitaxial growth. Nanobeam magnetic diffraction images reveal diverse magnetic microstructure within emerging SSE materials and a strong coupling of the magnetism to crystallographic distortion.

Simultaneous scanning near-field optical and X-ray diffraction microscopy for correlative nanoscale structure-property characterization

A multimodal imaging instrument has been developed that integrates scanning near-field optical microscopy with nanofocused synchrotron X-ray diffraction imaging. The instrument allows for the simultaneous nanoscale characterization of electronic/near-field optical properties of materials together with their crystallographic structure, facilitating the investigation of local structure-property relationships. The design, implementation and operating procedures of this instrument are reported. The scientific capabilities are demonstrated in a proof-of-principle study of the insulator-metal phase transition in samarium sulfide (SmS) single crystals induced by applying mechanical pressure via a scanning tip. The multimodal imaging of an in situ tip-written region shows that the near-field optical reflectivity can be correlated with the heterogeneously transformed structure of the near-surface region of the crystal.

Structures and magnetic properties of small [Formula: see text] and Co n-1Cr+ (n = 3-5) clusters

Small cobalt clusters [Formula: see text] and their single chromium atom doped counterparts Co _n-1Cr⁺ (n  =  3-5) were studied mass spectrometrically by measuring the infrared multiple photon dissociation (IRMPD) spectra of the corresponding argon tagged complexes. The geometric and electronic structures of the [Formula: see text] and Co _n-1Cr⁺ (n  =  3-5) clusters as well as their Ar complexes were optimized by density functional theory (DFT) calculations. The obtained lowest energy structures were confirmed by comparing the IRMPD spectra of [Formula: see text] and [Formula: see text] (n  =  3-5, m  =  3 and 4) with the corresponding calculated IR spectra. The calculations reveal that the doped Co _n-1Cr⁺ clusters retain the geometric structures of the most stable [Formula: see text] clusters. However, the coupling of the local magnetic moments within the clusters is altered in a size-dependent way: the Cr atom is ferromagnetically coupled in Co₂Cr⁺ and Co₃Cr⁺, while it is antiferromagnetically coupled in Co₄Cr⁺.

Dimensionality Effects in FeGe2 Nanowires: Enhanced Anisotropic Magnetization and Anomalous Electrical Transport

We report the synthesis of single-crystal iron germanium nanowires via chemical vapor deposition without the assistance of any catalysts. The assembly of single-crystal FeGe₂ nanowires with tetragonal C16 crystal structure shows anisotropic magnetic behavior along the radial direction or the growth axial direction, with both antiferromagnetic and ferromagnetic orders. Single FeGe₂ nanowire devices were fabricated using e-beam lithography. Electronic transport measurement in these devices show two resistivity anomalies near 250 K and 200 K which are likely signatures of the two spin density wave states in FeGe₂.

Dynamic X-ray diffraction imaging of the ferroelectric response in bismuth ferrite

X-ray diffraction imaging is rapidly emerging as a powerful technique by which one can capture the local structure of crystalline materials at the nano- and meso-scale. Here, we present investigations of the dynamic structure of epitaxial monodomain BiFeO₃ thin-films using a novel full-field Bragg diffraction imaging modality. By taking advantage of the depth penetration of hard X-rays and their exquisite sensitivity to the atomic structure, we imaged in situ and in operando, the electric field-driven structural responses of buried BiFeO₃ epitaxial thin-films in micro-capacitor devices, with sub-100 nm lateral resolution. These imaging investigations were carried out at acquisition frame rates that reached up to 20 Hz and data transfer rates of 40 MB/s, while accessing diffraction contrast that is sensitive to the entire three-dimensional unit cell configuration. We mined these large datasets for material responses by employing matrix decomposition techniques, such as independent component analysis. We found that this statistical approach allows the extraction of the salient physical properties of the ferroelectric response of the material, such as coercive fields and transient spatiotemporal modulations in their piezoelectric response, and also facilitates their decoupling from extrinsic sources that are instrument specific.

Laser-Induced Charge-Density-Wave Transient Depinning in Chromium

We report on time-resolved x-ray diffraction measurements following femtosecond laser excitation in pure bulk chromium. Comparing the evolution of incommensurate charge-density-wave (CDW) and atomic lattice reflections, we show that, a few nanoseconds after laser excitation, the CDW undergoes different structural changes than the atomic lattice. We give evidence for a transient CDW shear strain that breaks the lattice point symmetry. This strain is characteristic of sliding CDWs, as observed in other incommensurate CDW systems, suggesting the laser-induced CDW sliding capability in 3D systems. This first evidence opens perspectives for unconventional laser-assisted transport of correlated charges.

Spiral magnetic order and pressure-induced superconductivity in transition metal compounds

Magnetic and superconducting ground states can compete, cooperate and coexist. MnP provides a compelling and potentially generalizable example of a material where superconductivity and magnetism may be intertwined. Using a synchrotron-based non-resonant X-ray magnetic diffraction technique, we reveal a spiral spin order in MnP and trace its pressure evolution towards superconducting order via measurements in a diamond anvil cell. Judging from the magnetostriction, ordered moments vanish at the quantum phase transition as pressure increases the electron kinetic energy. Spins remain local in the disordered phase, and the promotion of superconductivity is likely to emerge from an enhanced coupling to residual spiral spin fluctuations and their concomitant suppression of phonon-mediated superconductivity. As the pitch of the spiral order varies across the 3d transition metal compounds in the MnP family, the magnetic ground state switches between antiferromagnet and ferromagnet, providing an additional tuning parameter in probing spin-fluctuation-induced superconductivity.

The relationship between magnetic order and superconductivity is one of the central issues in unconventional superconductors. Here, Wang et al. report a spiral spin order in MnP and trace its pressure evolution towards superconducting order, suggesting variable spiral pitch as a mechanism to tune spin-fluctuation-induced superconductivity.

Imaging nanoscale lattice variations by machine learning of x-ray diffraction microscopy data

We present a novel methodology based on machine learning to extract lattice variations in crystalline materials, at the nanoscale, from an x-ray Bragg diffraction-based imaging technique. By employing a full-field microscopy setup, we capture real space images of materials, with imaging contrast determined solely by the x-ray diffracted signal. The data sets that emanate from this imaging technique are a hybrid of real space information (image spatial support) and reciprocal lattice space information (image contrast), and are intrinsically multidimensional (5D). By a judicious application of established unsupervised machine learning techniques and multivariate analysis to this multidimensional data cube, we show how to extract features that can be ascribed physical interpretations in terms of common structural distortions, such as lattice tilts and dislocation arrays. We demonstrate this 'big data' approach to x-ray diffraction microscopy by identifying structural defects present in an epitaxial ferroelectric thin-film of lead zirconate titanate.

Hard X-ray polarizer to enable simultaneous three-dimensional nanoscale imaging of magnetic structure and lattice strain

Recent progress in the development of dichroic Bragg coherent diffractive imaging, a new technique for simultaneous three-dimensional imaging of strain and magnetization at the nanoscale, is reported. This progress includes the installation of a diamond X-ray phase retarder at beamline 34-ID-C of the Advanced Photon Source. The performance of the phase retarder for tuning X-ray polarization is demonstrated with temperature-dependent X-ray magnetic circular dichroism measurements on a gadolinium foil in transmission and on a Gd5Si2Ge2 crystal in diffraction geometry with a partially coherent, focused X-ray beam. Feasibility tests for dichroic Bragg coherent diffractive imaging are presented. These tests include (1) using conventional Bragg coherent diffractive imaging to determine whether the phase retarder introduces aberrations using a nonmagnetic gold nanocrystal as a control sample, and (2) collecting coherent diffraction patterns of a magnetic Gd5Si2Ge2 nanocrystal with left- and right-circularly polarized X-rays. Future applications of dichroic Bragg coherent diffractive imaging for the correlation of strain and lattice defects with magnetic ordering and inhomogeneities are considered.

Mesoscopic structural phase progression in photo-excited VO2 revealed by time-resolved x-ray diffraction microscopy

Dynamical phase separation during a solid-solid phase transition poses a challenge for understanding the fundamental processes in correlated materials. Critical information underlying a phase transition, such as localized phase competition, is difficult to reveal by measurements that are spatially averaged over many phase separated regions. The ability to simultaneously track the spatial and temporal evolution of such systems is essential to understanding mesoscopic processes during a phase transition. Using state-of-the-art time-resolved hard x-ray diffraction microscopy, we directly visualize the structural phase progression in a VO₂ film upon photoexcitation. Following a homogenous in-plane optical excitation, the phase transformation is initiated at discrete sites and completed by the growth of one lattice structure into the other, instead of a simultaneous isotropic lattice symmetry change. The time-dependent x-ray diffraction spatial maps show that the in-plane phase progression in laser-superheated VO₂ is via a displacive lattice transformation as a result of relaxation from an excited monoclinic phase into a rutile phase. The speed of the phase front progression is quantitatively measured, and is faster than the process driven by in-plane thermal diffusion but slower than the sound speed in VO₂. The direct visualization of localized structural changes in the time domain opens a new avenue to study mesoscopic processes in driven systems.

X-ray microdiffraction of biominerals

Biominerals have complex and heterogeneous architectures, hence diffraction experiments with spatial resolutions between 500 nm and 10 μm are extremely useful to characterize them. X-ray beams in this size range are now routinely produced at many synchrotrons. This chapter provides a review of the different hard X-ray diffraction and scattering techniques, used in conjunction with efficient, state-of-the-art X-ray focusing optics. These include monochromatic X-ray microdiffraction, polychromatic (Laue) X-ray microdiffraction, and microbeam small-angle X-ray scattering. We present some of the most relevant discoveries made in the field of biomineralization using these approaches.

Compact ultrahigh vacuum sample environments for x-ray nanobeam diffraction and imaging

X-ray nanobeams present the opportunity to obtain structural insight in materials with small volumes or nanoscale heterogeneity. The effective spatial resolution of the information derived from nanobeam techniques depends on the stability and precision with which the relative position of the x-ray optics and sample can be controlled. Nanobeam techniques include diffraction, imaging, and coherent scattering, with applications throughout materials science and condensed matter physics. Sample positioning is a significant mechanical challenge for x-ray instrumentation providing vacuum or controlled gas environments at elevated temperatures. Such environments often have masses that are too large for nanopositioners capable of the required positional accuracy of the order of a small fraction of the x-ray spot size. Similarly, the need to place x-ray optics as close as 1 cm to the sample places a constraint on the overall size of the sample environment. We illustrate a solution to the mechanical challenge in which compact ion-pumped ultrahigh vacuum chambers with masses of 1-2 kg are integrated with nanopositioners. The overall size of the environment is sufficiently small to allow their use with zone-plate focusing optics. We describe the design of sample environments for elevated-temperature nanobeam diffraction experiments demonstrate in situ diffraction, reflectivity, and scanning nanobeam imaging of the ripening of Au crystallites on Si substrates.

Spintronics in antiferromagnets

Magnetic domains and the walls between are the subject of great interest because of the role they play in determining the electrical properties of ferromagnetic materials and as a means of manipulating electron spin in spintronic devices. However, much less attention has been paid to these effects in antiferromagnets, primarily because there is less awareness of their existence in antiferromagnets, and in addition they are hard to probe since they exhibit no net magnetic moment. In this paper, we discuss the electrical properties of chromium, which is the only elemental antiferromagnet and how they depend on the subtle arrangement of the antiferromagnetically ordered spins. X-ray measurement of the modulation wavevector Q of the incommensurate antiferromagnetic spin-density wave shows thermal hysteresis, with the corresponding wavelength being larger during cooling than during warming. The thermal hysteresis in the Q vector is accompanied with a thermal hysteresis in both the longitudinal and Hall resistivity. During cooling, we measure a larger longitudinal and Hall resistivity compared with when warming, which indicates that a larger wavelength at a given temperature corresponds to a smaller carrier density or equivalently a larger antiferromagnetic ordering parameter compared to a smaller wavelength. This shows that the arrangement of the antiferromagnetic spins directly influences the transport properties. In thin films, the sign of the thermal hysteresis for Q is the same as in thick films, but a distinct aspect is that Q is quantized.

Scale-free structural organization of oxygen interstitials in La(2)CuO(4+y)

It is well known that the microstructures of the transition-metal oxides, including the high-transition-temperature (high-T(c)) copper oxide superconductors, are complex. This is particularly so when there are oxygen interstitials or vacancies, which influence the bulk properties. For example, the oxygen interstitials in the spacer layers separating the superconducting CuO(2) planes undergo ordering phenomena in Sr(2)O(1+y)CuO(2) (ref. 9), YBa(2)Cu(3)O(6+y) (ref. 10) and La(2)CuO(4+y) (refs 11-15) that induce enhancements in the transition temperatures with no changes in hole concentrations. It is also known that complex systems often have a scale-invariant structural organization, but hitherto none had been found in high-T(c) materials. Here we report that the ordering of oxygen interstitials in the La(2)O(2+y) spacer layers of La(2)CuO(4+y) high-T(c) superconductors is characterized by a fractal distribution up to a maximum limiting size of 400 mum. Intriguingly, these fractal distributions of dopants seem to enhance superconductivity at high temperature.

Observation and coupling of domains in a spin-spiral multiferroic

The coexistence, coupling, and manipulation of magnetic spiral domains and magnetically induced ferroelectric domains are spatially resolved by optical second harmonic generation in multiferroic MnWO4. Eight types of magnetic domains couple to two ferroelectric domains. An electric field uniquely creates a magnetic single-domain state. A magnetic field quenches the spontaneous polarization while retaining its magnetic origin so that the ferroelectric domains are concealed instead of destroyed.

Antiferromagnetic order with atomic layer resolution in EuTe(111) films

The temperature dependences of the magnetizations of individual atomic layers across an epitaxial antiferromagnetic EuTe film were derived from virtually background-free magnetic Bragg peaks with pronounced Laue oscillations recorded with soft x rays at the Eu-M5 resonance. The magnetizations of the outermost layers decrease significantly differently from those of bulk layers, in agreement with Heisenberg-Monte Carlo calculations. The results demonstrate the applicability of the method to complex ordering phenomena at surfaces and interfaces of thin films.

Direct measurement of antiferromagnetic domain fluctuations

Measurements of magnetic noise emanating from ferromagnets owing to domain motion were first carried out nearly 100 years ago, and have underpinned much science and technology. Antiferromagnets, which carry no net external magnetic dipole moment, yet have a periodic arrangement of the electron spins extending over macroscopic distances, should also display magnetic noise. However, this must be sampled at spatial wavelengths of the order of several interatomic spacings, rather than the macroscopic scales characteristic of ferromagnets. Here we present a direct measurement of the fluctuations in the nanometre-scale superstructure of spin- and charge-density waves associated with antiferromagnetism in elemental chromium. The technique used is X-ray photon correlation spectroscopy, where coherent X-ray diffraction produces a speckle pattern that serves as a 'fingerprint' of a particular magnetic domain configuration. The temporal evolution of the patterns corresponds to domain walls advancing and retreating over micrometre distances. This work demonstrates a useful measurement tool for antiferromagnetic domain wall engineering, but also reveals a fundamental finding about spin dynamics in the simplest antiferromagnet: although the domain wall motion is thermally activated at temperatures above 100 K, it is not so at lower temperatures, and indeed has a rate that saturates at a finite value-consistent with quantum fluctuations-on cooling below 40 K.

Microscopic and macroscopic signatures of antiferromagnetic domain walls

Magnetotransport measurements on small single crystals of Cr, the elemental antiferromagnet, reveal the hysteretic thermodynamics of the domain structure. The temperature dependence of the transport coefficients is directly correlated with the real-space evolution of the domain configuration as recorded by x-ray microprobe imaging, revealing the effect of antiferromagnetic domain walls on electron transport. A single antiferromagnetic domain wall interface resistance is deduced to be of order 5 x 10(-5) mu Omega cm(2) at a temperature of 100 K.

Imprinting vortices into antiferromagnets

The effect of imprinting symmetric and displaced vortex structures into an antiferromagnetic material is investigated in micron-sized disks consisting of exchange coupled ferromagnetic-antiferromagnetic bilayers. The imprint of displaced vortices manifests itself by the occurrence of a new type of asymmetric hysteresis loops characterized by curved, reversible, central sections with nonzero remanent magnetization. Such an imprint is achieved by cooling the disks through the blocking temperature of the system in small fields. Micromagnetic simulations reveal that asymmetric vortexlike loops naturally result from the competition between the different energies involved in the system.

Shear modulus and plasticity of a driven charge density wave

We have probed the effects of transverse variations in pinning strength on charge-density-wave (CDW) structure in NbSe3 by x-ray micro-beam diffraction. In ribbonlike crystals having a large longitudinal step in thickness, the CDW first depins on the thick side of the step, causing rotations of the CDW wave vector. By measuring these rotations as a function of position and electric field, the corresponding shear strains are determined, allowing the CDW's shear modulus to be estimated. These results demonstrate the usefulness of x-ray microdiffraction as a tool in studying collective dynamics in electronic crystals.

Domain walls in antiferromagnetically coupled multilayer films

We report experimentally observed magnetic domain-wall structures in antiferromagnetically coupled multilayer films with perpendicular anisotropy. Our studies reveal a first-order phase transition from domain walls with no net moment to domain walls with ferromagnetic cores. The transition originates from the competition between dipolar and exchange energies, which we tune by means of layer thickness. Although observed in a synthetic antiferromagnetic system, such domain-wall structures may be expected to occur in A-type antiferromagnets with anisotropic exchange coupling.

Oscillatory exchange bias due to an antiferromagnet with incommensurate spin-density waves

Oscillatory exchange bias in both magnitude and in sign has been observed in epitaxial (100)Cr/Ni(81)Fe19 bilayers due to the incommensurate spin-density waves in antiferromagnetic (100)Cr layers. Salient effects due to the spin-flip transition between longitudinal and transverse spin-density waves as well as that of expanding wavelength have been observed.

Not too big, not too small: the appropriate scale

The tools we use at the human scale, whether mechanical, medical or microelectronic, depend on materials for which some other scale of length or time is critical. Often this is the mesoscale, between the scales of engineering and of atomic science. Linking underlying processes to what we handle is sometimes called 'spanning' (or 'bridging') length scales, giving the impression that the mesoscale is a swamp to be crossed without getting mud on our boots. This is misleading: we do not wish to span the mesoscale, but to work at the appropriate scale, and to connect that to our human needs. The appropriate scale need not rule out multiscale computer modelling, in which some supercode integrates relevant scales in one pass, hoping to combine the best of methods for two or more levels. But the reality for such attempts, too often, is that the worst of both regimes are found. Happily, simpler strategies at a judicious scale will often suffice.