Larmor Diffraction Research Articles

Cryogenic Digital Image Correlation as a Probe of Strain in Iron-Based Superconductors

Abstract Uniaxial strain is a powerful tuning parameter that can control symmetry and anisotropic electronic properties in iron-based superconductors. However, accurately characterizing anisotropic strain can be challenging and complex. Here, we utilize a cryogenic optical system equipped with a high-spatial-resolution microscope to characterize surface strains in iron-based superconductors using the digital image correlation method. Compared with other methods such as high-resolution X-ray diffraction, strain gauge, and capacitive sensor, digital image correlation offers a non-contact, full-field measurement approach, acting as an optical virtual strain gauge that provides high spatial resolution. The results measured on detwinned BaFe2As2 are quantitatively consistent with the distortion measured by X-ray diffraction and neutron Larmor diffraction. These findings highlight the potential of cryogenic digital image correlation as an effective and accessible tool for probing the isotropic and anisotropic strains, facilitating the application of uniaxial strain tuning in the study of quantum materials.

Symmetry Breaking and Ascending in the Magnetic Kagome Metal FeGe

Spontaneous symmetry breaking—the phenomenon in which an infinitesimal perturbation can cause the system to break the underlying symmetry—is a cornerstone concept in the understanding of interacting solid-state systems. In a typical series of temperature-driven phase transitions, higher-temperature phases are more symmetric due to the stabilizing effect of entropy that becomes dominant as the temperature is increased. However, the opposite is rare but possible when there are multiple degrees of freedom in the system. Here, we present such an example of a symmetry-ascending phenomenon upon cooling in a magnetic kagome metal FeGe by utilizing neutron Larmor diffraction and Raman spectroscopy. FeGe has a kagome lattice structure with simple A-type antiferromagnetic order below Néel temperature TN≈400 K and a charge density wave (CDW) transition at TCDW≈110 K, followed by a spin-canting transition at around 60 K. In the paramagnetic state at 460 K, we confirm that the crystal structure is indeed a hexagonal kagome lattice. On cooling to around TN, the crystal structure changes from hexagonal to monoclinic with in-plane lattice distortions on the order of 10−4 and the associated splitting of the double-degenerate phonon mode of the pristine kagome lattice. Upon further cooling to TCDW, the kagome lattice shows a small negative thermal expansion, and the crystal structure gradually becomes more symmetric upon further cooling. A tendency of increasing the crystalline symmetry upon cooling is unusual; it originates from an extremely weak structural instability that coexists and competes with the CDW and magnetic orders. These observations are against the expectations for a simple model with a single order parameter and hence can only be explained by a Landau free energy expansion that takes into account multiple lattice, charge, and spin degrees of freedom. Thus, the determination of the crystalline lattice symmetry as well as the unusual spin-lattice coupling is a first step towards understanding the rich electronic and magnetic properties of the system, and it sheds new light on intertwined orders where the lattice degree of freedom is no longer dominant. Published by the American Physical Society 2024

Studies on the structure and the magnetic properties of high-entropy spinel oxide (MgMnFeCoNi)Al2O4

The study of high-entropy materials has attracted enormous interest since they could show new functional properties that are not observed in their related parent phases. Here, we report single crystal growth, structure, thermal transport, and magnetic property studies on a novel high-entropy oxide with the spinel structure (MgMnFeCoNi)Al2O4. We have successfully grown high-quality single crystals of this high-entropy oxide using the optical floating zone growth technique for the first time. The sample was confirmed to be a phase pure high-entropy oxide using x-ray diffraction and energy-dispersive spectroscopy. Through magnetization measurements, we found (MgMnFeCoNi)Al2O4 exhibits a cluster spin glass state, though the parent phases show either antiferromagnetic ordering or spin glass states. Furthermore, we also found that (MgMnFeCoNi)Al2O4 has much greater thermal expansion than its CoAl2O4 parent compound using high resolution neutron Larmor diffraction. We further investigated the structure of this high-entropy material via Raman spectroscopy and extended x-ray absorption fine structure spectroscopy (EXAFS) measurements. From Raman spectroscopy measurements, we observed (MgMnFeCoNi)Al2O4 to display a combination of the active Raman modes in its parent compounds with the modes shifted and significantly broadened. This result, together with the varying bond lengths probed by EXAFS, reveals severe local lattice distortions in this high-entropy phase. Additionally, we found a substantial decrease in thermal conductivity and suppression of the low temperature thermal conductivity peak in (MgMnFeCoNi)Al2O4, consistent with the increased lattice defects and strain. These findings advance the understanding of the dependence of thermal expansion and transport on the lattice distortions in high-entropy materials.

Hidden Charge Order in an Iron Oxide Square-Lattice Compound.

Since the discovery of charge disproportionation in the FeO_{2} square-lattice compound Sr_{3}Fe_{2}O_{7} by Mössbauer spectroscopy more than fifty years ago, the spatial ordering pattern of the disproportionated charges has remained "hidden" to conventional diffraction probes, despite numerous x-ray and neutron scattering studies. We have used neutron Larmor diffraction and Fe K-edge resonant x-ray scattering to demonstrate checkerboard charge order in the FeO_{2} planes that vanishes at a sharp second-order phase transition upon heating above 332K. Stacking disorder of the checkerboard pattern due to frustrated interlayer interactions broadens the corresponding superstructure reflections and greatly reduces their amplitude, thus explaining the difficulty of detecting them by conventional probes. We discuss the implications of these findings for research on "hidden order" in other materials.

Neutron Spin‐Echo Instrumentation for Magnetic Scattering

Neutron spin‐echo (NSE) spectroscopy is a powerful tool for the study of magnon lifetimes and magnetic critical dynamics. The unique property of NSE is the energy resolution in the range. The first NSE spectrometers were optimized for quasielastic scattering at small momentum transfers and delivered substantial contributions to the understanding of critical dynamics in ferromagnets and dynamic correlations in spin glasses. The subsequent resonant NSE (NRSE) technique extends the parameter range toward large momentum and energy transfers and permits to measure magnon lifetimes across the Brillouin zone. NRSE also comprises the Larmor diffraction (LD) mode with a resolution for lattice spacings and their variance of order . LD proves useful to determine magnetostriction effects, small lattice distortions related to magnetic ordering, mosaic spread in crystals, and the size distribution of antiferromagnetic domains. Both typical experiments and the related technical innovation are reviewed and an outlook on future developments is given.

Neutron Larmor diffraction on powder samples.

A hitherto unrecognized resolution effect in neutron Larmor diffraction (LD) is reported, resulting from small-angle neutron scattering (SANS) in the sample. Small distortions of the neutron trajectories by SANS give rise to a blurring of the Bragg angles of the order of a few hundredths of a degree, leading to a degradation of the momentum resolution. This effect is negligible for single crystals but may be significant for polycrystalline or powder samples. A procedure is presented to correct the LD data for the parasitic SANS. The latter is accurately determined by the SESANS technique (spin-echo small-angle neutron scattering), which is readily available on Larmor diffractometers. The analysis technique is demonstrated on LD and SESANS data from α-Fe2O3 powder samples. The resulting d-spacing range agrees with experimental data from high-resolution synchrotron radiation powder diffraction on the same sample.

New capabilities in high-resolution neutron Larmor diffraction at ORNL

Using superconducting magnetic Wollaston prisms, high-resolution neutron Larmor diffraction has been implemented at the High-Flux Isotope Reactor of Oak Ridge National Laboratory (ORNL), Tennesse, USA. This technique allows the inverse relationship between the achievable diffraction resolution and the usable neutron flux to be overcome. Instead of employing physically tilted radio-frequency spin flippers, the method uses magnetic Wollaston prisms which are electromagnetically tuned by changing the field configurations in the device. As implemented, this method can be used to measure lattice-spacing changes induced, for example, by thermal expansion or strain with a resolution of Δd/d ≃ 10−6, and the splitting of sharp Bragg peaks with a resolution of Δd/d = 3 × 10−4. The resolution for discerning a change in the profile of a Bragg peak is Δd/d < 10−5. This is a remarkable degree of precision for a neutron diffractometer as compact as the one used in this implementation. Higher precision could be obtained by implementing this technique in an instrument with a larger footprint. The availability of this technique will provide an alternative when standard neutron diffraction methods fail and will greatly benefit the scientific communities that require high-resolution diffraction measurements.

Neutron Larmor diffraction with double and single precession arm

A review is given of double and single arm Larmor diffraction. With the former a lattice-spacing resolution down to 10-6 can be obtained. The latter is a good high-resolution alternative if the sample or sample environment disturbs the magnetic field, e.g. ferromagnetic samples or applied magnetic fields. By choosing the tilt angle of the precession fields the optimum resolution can be set at a scattering angle at choice. The resolution for both single-crystal and polycrystalline samples is discussed in depth and is compared with conventional neutron-diffraction techniques.

High resolution neutron Larmor diffraction using superconducting magnetic Wollaston prisms

The neutron Larmor diffraction technique has been implemented using superconducting magnetic Wollaston prisms in both single-arm and double-arm configurations. Successful measurements of the coefficient of thermal expansion of a single-crystal copper sample demonstrates that the method works as expected. The experiment involves a new method of tuning by varying the magnetic field configurations in the device and the tuning results agree well with previous measurements. The difference between single-arm and double-arm configurations has been investigated experimentally. We conclude that this measurement benchmarks the applications of magnetic Wollaston prisms in Larmor diffraction and shows in principle that the setup can be used for inelastic phonon line-width measurements. The achievable resolution for Larmor diffraction is comparable to that using Neutron Resonance Spin Echo (NRSE) coils. The use of superconducting materials in the prisms allows high neutron polarization and transmission efficiency to be achieved.

Neutron Larmor diffraction investigation of the rare-earth pyrochlores R2Ti2O7 ( R=Tb , Dy, Ho)

In this work we present a neutron Larmor diffraction study of the rare earth pyrochlores $R_2$Ti$_2$O$_7$, with $R$ = Tb, Dy, Ho. We measured the temperature dependence of the lattice parameter with precision $10^{-5}$, between 0.5 K and 300 K in each of the three compounds. The lattice parameter of the spin ices Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ enters into the derivation of the charge of the emergent magnetic monopole excitations suggested to exist in these materials. We found that throughout the range of applicability of the theory of emergent monopoles in the spin ices there will be no renormalization of the monopole charge due to lattice contraction. In Tb$_2$Ti$_2$O$_7$ strong magnetoelastic interactions have been reported. We found no sign of the previously reported negative thermal expansion, but did observe anomalies in the thermal expansion that can be correlated with previously observed interactions between phonon and crystal field excitations. Other features in the thermal expansion of all three compounds can be related to previously observed anomalies the elastic constants, and explained by the phonon band structure of the rare earth titanates. The temperature dependence of the lattice strain in all three compounds can be correlated with the thermal population of excited crystal field levels.

Impact of uniaxial pressure on structural and magnetic phase transitions in electron-doped iron pnictides

We use neutron resonance spin echo and Larmor diffraction to study the effect of uniaxial pressure on the tetragonal-to-orthorhombic structural ($T_s$) and antiferromagnetic (AF) phase transitions in iron pnictides BaFe$_{2-x}$Ni$_{x}$As$_{2}$ ($x=0,0.03,0.12$), SrFe$_{1.97}$Ni$_{0.03}$As$_2$, and BaFe$_2$(As$_{0.7}$P$_{0.3}$)$_2$. In antiferromagnetically ordered BaFe$_{2-x}$Ni$_{x}$As$_{2}$ and SrFe$_{1.97}$Ni$_{0.03}$As$_2$ with $T_N$ and $T_s$ ($T_N\leq T_s$), a uniaxial pressure necessary to detwin the sample also increases $T_N$, smears out the structural transition, and induces an orthorhombic lattice distortion at all temperatures. By comparing temperature and doping dependence of the pressure induced lattice parameter changes with the elastoresistance and nematic susceptibility obtained from transport and ultrasonic measurements, we conclude that the in-plane resistivity anisotropy found in the paramagnetic state of electron underdoped iron pnictides depends sensitively on the nature of the magnetic phase transition and a strong coupling between the uniaxial pressure induced lattice distortion and electronic nematic susceptibility.

Magnetostriction and Magnetostructural Domains in Antiferromagnetic YBa2Cu3O6.

We use high-resolution neutron Larmor diffraction and capacitative dilatometry to investigate spontaneous and forced magnetostriction in undoped, antiferromagnetic YBa_{2}Cu_{3}O_{6.0}, the parent compound of a prominent family of high-temperature superconductors. Upon cooling below the Néel temperature T_{N}=420 K, Larmor diffraction reveals the formation of magnetostructural domains of characteristic size ∼240 nm. In the antiferromagnetic state, dilatometry reveals a minute (4×10^{-6}) orthorhombic distortion of the crystal lattice in external magnetic fields. We attribute these observations to exchange striction and spin-orbit coupling induced magnetostriction, respectively, and show that they have an important influence on the thermal and charge transport properties of undoped and lightly doped cuprates.

Magnetised foils as white beam π/2 flippers for polarised neutrons

Magnetic foils as white beam π/2 flippers for polarised neutrons will be discussed. Their main advantage is the application for Larmor precession in strongly inclined precession regions as used in Larmor diffraction and especial in Spin Echo Small Angle Neutron Scattering (SESANS). Inclination angles of a few degrees in fields from mT up to hundreds of mT are achievable that are not possible with present conventional coils. The application in Larmor diffraction will be discussed and the application in SESANS will be explained in detail and supported by a simulated experiment.

Neutron resonance spin-echo upgrade at the three-axis spectrometer FLEXX.

We describe the upgrade of the neutron resonance spin-echo setup at the cold neutron triple-axis spectrometer FLEXX at the BER II neutron source at the Helmholtz-Zentrum Berlin. The parameters of redesigned key components are discussed, including the radio frequency (RF) spin-flip coils, the magnetic shield, and the zero field coupling coils. The RF-flippers with larger beam windows allow for an improved neutron flux transfer from the source to the sample and further to the analyzer. The larger beam cross sections permit higher coil inclination angles and enable measurements on dispersive excitations with a larger slope of the dispersion. Due to the compact design of the spin-echo units in combination with the increased coil tilt angles, the accessible momentum-range in the Larmor diffraction mode is substantially enlarged. In combination with the redesigned components of the FLEXX spectrometer, including the guide, the S-bender polarizer, the double focusing monochromator, and a Heusler crystal analyzer, the count rate increased by a factor of 15.5, and the neutron beam polarization is enhanced. The improved performance extends the range of feasible experiments, both for inelastic scattering on excitation lifetimes in single crystals, and for high-resolution Larmor diffraction. The experimental characterization of the instrument components demonstrates the reliable performance of the new neutron resonance spin-echo option, now available for the scientific community at FLEXX.

Neutron resonance spin flippers: static coils manufactured by electrical discharge machining.

Radiofrequency spin flippers (RFSF) are key elements of Neutron Resonance Spin Echo (NRSE) spectrometers, which allow performing controlled manipulations of the beam polarization. We report on the design and test of a new type of RFSF which originality lies in the new manufacturing technique for the static coil. The largely automated procedure ensures reproducible construction as well as an excellent homogeneity of the neutron magnetic resonance condition over the coil volume. Two salient features of this concept are the large neutron window and the closure of the coil by a μ-metal yoke which prevents field leakage outside of the coil volume. These properties are essential for working with large beams and enable new applications with coils tilted with respect to the beam axis such as neutron Larmor diffraction or the study of dispersive excitations by inelastic NRSE.

Possible realization of an antiferromagnetic Griffiths phase in Ba(Fe1−xMnx)2As2

We investigate magnetic ordering in metallic Ba[Fe(1-x)Mn(x)](2)As(2) and discuss the unusual magnetic phase, which was recently discovered for Mn concentrations x > 10%. We argue that it can be understood as a Griffiths-type phase that forms above the quantum critical point associated with the suppression of the stripe-antiferromagnetic spin-density-wave (SDW) order in BaFe2As2 by the randomly introduced localized Mn moments acting as strong magnetic impurities. While the SDW transition at x = 0, 2.5% and 5% remains equally sharp, in the x = 12% sample we observe an abrupt smearing of the antiferromagnetic transition in temperature and a considerable suppression of the spin gap in the magnetic excitation spectrum. According to our muon-spin-relaxation, nuclear magnetic resonance and neutron-scattering data, antiferromagnetically ordered rare regions start forming in the x = 12% sample significantly above the N\'eel temperature of the parent compound. Upon cooling, their volume grows continuously, leading to an increase in the magnetic Bragg intensity and to the gradual opening of a partial spin gap in the magnetic excitation spectrum. Using neutron Larmor diffraction, we also demonstrate that the magnetically ordered volume is characterized by a finite orthorhombic distortion, which could not be resolved in previous diffraction studies most probably due to its coexistence with the tetragonal phase and a microstrain-induced broadening of the Bragg reflections. We argue that Ba[Fe(1-x)Mn(x)](2)As(2) could represent an interesting model spin-glass system, in which localized magnetic moments are randomly embedded into a SDW metal with Fermi surface nesting.

Polarized Neutron on URu2Si2

Abstract Polarized neutron scattering has shed a new light on URu 2 Si 2 . This compound studied for almost thirty years presents two tran- sitions: a superconducting state below 1.2K (T sc ) and a well-defined bulk transition at 17.8K (T 0 ). In spite of intensive research, no local probe has defined the order parameter associated with this transition (the famous Hidden Order (HO)). Neutron Larmor diffraction measurements combined with uniaxial stress experiments have shown that the relevant parameter that governs the magnetic properties is the a -lattice parameter. Induced magnetization distribution measured by elastic polarized neutron scattering shows a subtle change when entering the HO state that suggests a freezing of rank 5 multipoles (i.e. dotriacontapole). Polarized inelastic neutron measurements have shown the existence of two well defined excitations on the top of a broad continuum. How- ever only the AF excitation vanishes at T 0 and as well as when URu 2 Si 2 switches between HO to AF state under pressure. These excitations seem to correspond also to transitions between singlet levels.

Neutron Larmor Diffraction study of the BaM2(XO4)2 (M = Co, Ni; X = As, P) compounds

Neutron Larmor Diffraction is a relatively new concept in neutron scattering which allows high resolution studies of subtle structural features in condensed matter. Several setups exist in various neutron facilities around the world. One of them is the Zero-field spin-Echo for Triple-Axis option (ZETA), available on the thermal triple-axis spectrometer IN22 (CEA-CRG beamline at Institut Laue Langevin). We have used ZETA to study thermal evolution of lattice constants in serveral systems of physical interest. Among them, the BaM2(XO4)2 family is a serie of compounds which have been intensively studied for three decades, mainly because of their fundamental though puzzling magnetic properties. In this paper, we aim to shed a new light on the physical understanding of those systems by investigating the link between structural and magnetic ordering. The magnetoelastic effect is found to be weak but can be resolved thanks to the high resolution provided by NLD.

Spin flippers for Larmor labeling methods in monochromatic and white neutron beams

Spin flippers are considered and distinguished in low and high field flippers. The first ones are used in normal polarized neutron beam applications and also in normal spin-echo set-ups. The last ones are essential in their application for labeling the direction of a neutron beam as occurs in spin-echo small angle scattering and high resolution Larmor diffraction. The advantages and disadvantages of the various flippers are discussed.

A resolution model for mode multiplets probed with neutron resonance spin-echo spectroscopy

A resolution model, which takes into account a violation of the spin-echo conditions for inelastic scattering as it is appropriate for high resolution spin-echo measurements of mode multiplets, is experimentally tested. Phase-sensitive measurements were performed while a dispersion surface is moved through the resolution ellipsoid of a triple-axis background spectrometer. The results are found to be in agreement with the model predictions. A tunable, artificially split dispersion was realized with a double crystal setup mounted on a piezoelectric device allowing for rotation and tilt of the first crystal, while the second one was rigidly fixed. Elastic measurements with the instrument configured in Larmor diffraction geometry were used to probe the crystal orientation with high sensitivity. First inelastic measurements are in agreement with a simplified model indicating persistence of the echo modulation over the entire spin-echo time range probed by the experiment.