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At least 163 records · Page 9

Lattice distortions and the metal–insulator transition in pure and Ti-substituted Ca 3 Ru 2 O 7

Here, we report pair distribution function studies on the relationship between the metal–insulator transition (MIT) and lattice distortions in pure and Ti-substituted bilayer Ca 3 Ru 2 O 7 . Structural refinements performed as a function of temperature, magnetic field and length scale reveal the presence of lattice distortions not only within but also orthogonal to the bilayers. Because of the distortions, the local and average crystal structure differ across a broad temperature region extending from room temperature to temperatures below the MIT. The coexistence of distinct lattice distortions is likely to be behind the marked structural flexibility of Ca 3 Ru 2 O 7 under external stimuli. This observation highlights the ubiquity of lattice distortions in an archetypal Mott system and calls for similar studies on other families of strongly correlated materials.

36 MATERIALS SCIENCE↗

Ultrafast One-Dimensional Peierls-Distortion Dynamics in 1⁢T′−Re⁢S 2 Revealed by 4D Electron Microscopy

Rhenium disulfide (ReS 2 ), a prototypical 2D semiconductor with an anisotropic 1⁢T′ structure due to the pronounced Peierls distortion, has demonstrated great potential for polarization-dependent optoelectronics and photonics. Here, we report an ultrafast phase transition occurring within 1 ps, accompanied by a one-dimensional Peierls-distortion relaxation in 1⁢T′−ReS 2 revealed with combined 4D electron microscopy and time-dependent density functional theory calculations. Upon femtosecond laser pulse excitation, the Re-Re dimerization morphology rapidly transforms from a diamond cluster to zigzag chains and persists for several nanoseconds. Here, this ultrafast Peierls-distortion relaxation is further verified by transient changes in optical anisotropy via polarization-dependent transient absorption spectroscopy. Time-dependent density functional theory calculations attribute this novel phase transition to strong correlation between Peierls distortion and impulsive photoexcited carrier doping, predicting a transient band-gap collapse. This Letter opens up an exciting avenue for ultrafast control of Peierls-distortion-induced anisotropy and the metal-insulator transition in 1⁢T′−ReS 2 .

1T’-ReS2↗

Circular Trajectory Approach for Online Sinusoidal Signal Distortion Monitoring and Visualization

The increasing complexity and uncertainties of modern power systems are placing significant demands on signal monitoring techniques. This work proposes the Circular Trajectory Approach (CTA) for online sinusoidal signal distortion monitoring and visualization. CTA can detect distortions of a sinusoidal signal. Compared with existing waveform anomaly detection techniques, CTA is faster in detection and less computation intensive. It thus supports edge devices and online applications. CTA also offers a new means of sinusoidal signal distortion visualization. It can reveal the distorted sections in a sinusoidal cycle and clearly display the distortions. The proposed approach is tested on real data from an open source EPRI dataset.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Lattice Distortion and Phase Stability of Pd-Doped NiCoFeCr Solid-Solution Alloys

In the present study, we have revealed that (NiCoFeCr)100−xPdx (x= 1, 3, 5, 20 atom%) high-entropy alloys (HEAs) have both local- and long-range lattice distortions by utilizing X-ray total scattering, X-ray diffraction, and extended X-ray absorption fine structure methods. The local lattice distortion determined by the lattice constant difference between the local and average structures was found to be proportional to the Pd content. A small amount of Pd-doping (1 atom%) yields long-range lattice distortion, which is demonstrated by a larger (200) lattice plane spacing than the expected value from an average structure, however, the degree of long-range lattice distortion is not sensitive to the Pd concentration. The structural stability of these distorted HEAs under high-pressure was also examined. The experimental results indicate that doping with a small amount of Pd significantly enhances the stability of the fcc phase by increasing the fcc-to-hcp transformation pressure from ~13.0 GPa in NiCoFeCr to 20–26 GPa in the Pd-doped HEAs and NiCoFeCrPd maintains its fcc lattice up to 74 GPa, the maximum pressure that the current experiments have reached.

36 MATERIALS SCIENCE↗

Modeling fuel assembly distortion in light water reactors using BISON

Individual fuel rods in a light water reactor fuel assembly (FA) often have different power profiles that result in a spatial temperature gradient in the FA. This temperature gradient causes some rods to elongate more than others which could in turn distort the entire FA. Such FA distortion has been known to cause operational difficulties with refueling and with the insertion of control rods [1]. Numerical modeling of FA distortion due to differential elongation of fuel rods requires: (i) modeling the thermal elongation as well as the creep and irradiation induced elongation of the fuel rods, and (ii) modeling the bending response of the FA due to the differential elongation of the fuel rods. Past studies on this topic have been focused on the mechanical deformation of the FA with simplistic modeling of fuel rod elongation. In this paper, a simulation approach is presented that directly couples 2D axisymmetric fuel performance models of the individual fuel rods in a FA with structural beam models of the fuel rods in a FA using the Bison code [2]. This allows all of the mechanisms internal to the fuel rod leading to cladding elongation to be accounted for in the FA distortion model. To demonstrate this capability, the bowing of a simplified and idealized 6x6 FA (Fig. 1a), modeled using beam elements, is analyzed under different spatially varying power profiles. For this study, the guide tubes are rigidly connected to the spacer grid. Also, the fuel rods are rigidly connected to the spacer grid in all directions except the vertical direction (Y) along which slipping can occur between the fuel rods and spacer grids, depending on the friction coefficient between them. Coupling the thermo-mechanical response of individual fuel rods to the global mechanical behavior of the FA can shed light on the mechanisms that cause distortion of the FA and potential solutions to address this issue.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Perovskite LaPbMSbO{sub 6} (M=Co, Ni): Structural distortion, magnetic and dielectric properties

The B-site ordered double perovskite oxides LaPbMSbO{sub 6} (M=Co, Ni) have been synthesized via the modified Sol–Gel precursor two-step route. Rietveld refinements reveal strong abnormal structural distortion and BO{sub 6} octahedral deformation appearing along the ab plane. Owing to the cooperative Jahn–Teller effect of Co{sup 2+} and Pb{sup 2+} ions, the Co-related compound exhibits almost complete Co{sup 2+}–Sb{sup 5+} order. For magnetic properties, spin-canted antiferromagnetic state with high extent of magnetic frustration is confirmed. The Ni-related compound presents heavier magnetic frustration for introducing tiny disorder on site occupation accompanied with valence state and further enhancing the complexity of magnetic competition. Dielectric measurements present a considerable temperature dependent dielectric relaxation with great dc-like loss feature in the LaPbCoSbO{sub 6}. For LaPbNiSbO{sub 6}, however, the permittivity with low dielectric loss is shown to be insensitive to either temperature or frequency. The corresponding electronic active energy manifests that the weakly bounded 3d-electron is prone to hop in a more distorted Co–Sb sublattice. - Graphical abstract: XRD Rietveld refinement result of LaPbCoSbO{sub 6} presented a large BO{sub 6} octahedral distortion along the ab plane. Based upon the variations from Co–O–Sb bond angles, a fierce competition from many extended magnetic coupling routes (M–O–O–M) would induce a considerably large magnetic frustration and electron hopping restriction. - Highlights: • Highly ordered LaPbMSbO{sub 6} (M=Co, Ni) were synthesized. • Abnormal structural distortion appeared in the ab plane. • Strong magnetic frustration was confirmed via M{sup 2+}–O–O–M{sup 2+} route. • Dielectric measurements presented a large difference between Co and Ni samples. • 3d-electronic structure determines lattice distortion and physical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Polyhedral Distortions and Unusual Magnetic Order in Spinel FeMn 2 O 4

Spinel compounds AB 2 X 4 consist of both tetrahedral (AX 4 ) and octahedral (BX 6) environments with the former forming a diamond lattice and the latter a geometrically frustrated pyrochlore lattice. Exploring the fascinating physical properties and their correlations with structural features is critical in understanding these materials. FeMn 2 O 4 has been reported to exhibit one structural transition and two successive magnetic transitions. In this work, we report the polyhedral distortions and their correlations to the structural and two magnetic transitions in FeMn 2 O 4 by employing the high-resolution neutron powder diffraction. The cation distribution is found to be ($Mn_{0.9}^{2+}Fe_{0.1}^{3+}$)$_{A}$($Mn^{3+}Fe_{0.9}^{3+}Mn_{0.1}^{2+}$)$_{B}$O 4 . While large trigonal distortion is found even in the high-temperature cubic phase, the first-order cubic-tetragonal structural transition associated with the elongation of both tetrahedra and octahedra with shared oxygen atoms along the c axis occurs at T S ≈ 750 K, driven by the Jahn–Teller effect of the orbital active B-site Mn 3+ cation. Strong magnetoelastic coupling is unveiled at T N1 ≈ 400 K as manifested by the appearance of Néel-type collinear ferrimagnetic order, an anomaly in both tetrahedral and octahedral distortions, as well as an anomalous decrease of the lattice constants c and a weak anomaly of a. Upon cooling to T N2 ≈ 65 K, it evolves to a noncollinear ferrimagnetic order accompanied by the different moments at the split magnetic sites B1 and B2. Only one-half of the B-site Mn 3+ /Fe 3+ spins, i.e., the B2-site spins in the pyrochlore lattice, are canted, which is a unique magnetic order among spinels. The canting angle between A-site and B2-site moments is ~25°, but the B1-site moment stays antiparallel to the A-site moment even at 10 K. This noncollinear order is accompanied by a modification of the O–B–O bond angles in the octahedra without significant change in lattice constants or tetrahedral/octahedral distortion parameters, indicating a distinct magnetoelastic coupling. We demonstrate distinct roles of the A-site and B-site magnetic cations in the structural and magnetic properties of FeMn 2 O 4 . Our study indicates that FeMn 2 O 4 is a wonderful platform to unveil interesting magnetic order and to investigate their correlations with polyhedral distortions and lattice.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Node Distortion as a Tunable Mechanism for Negative Thermal Expansion in Metal–Organic Frameworks

Chemically functionalized series of metal–organic frameworks (MOFs), with subtle differences in local structure but divergent properties, provide a valuable opportunity to explore how local chemistry can be coupled to long-range structure and functionality. Using in situ synchrotron X-ray total scattering, with powder diffraction and pair distribution function (PDF) analysis, we investigate the temperature dependence of the local- and long-range structure of MOFs based on NU-1000, in which Zr 6 O 8 nodes are coordinated by different capping ligands (H 2 O/OH, Cl – ions, formate, acetylacetonate, and hexafluoroacetylacetonate). We show that the local distortion of the Zr 6 nodes depends on the lability of the ligand and contributes to a negative thermal expansion (NTE) of the extended framework. Using multivariate data analyses, involving non-negative matrix factorization (NMF), we demonstrate a new mechanism for NTE: progressive increase in the population of a smaller, distorted node state with increasing temperature leads to global contraction of the framework. The transformation between discrete node states is noncooperative and not ordered within the lattice, i.e., a solid solution of regular and distorted nodes. Density functional theory calculations show that removal of ligands from the node can lead to distortions consistent with the Zr···Zr distances observed in the experiment PDF data. Control of the node distortion imparted by the nonlinker ligand in turn controls the NTE behavior. Furthermore, these results reveal a mechanism to control the dynamic structure of MOFs based on local chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Overcoming potential energy distortions in constrained internal coordinate molecular dynamics simulations

The Internal Coordinate Molecular Dynamics (ICMD) method is an attractive molecular dynamics (MD) method for studying the dynamics of bonded systems such as proteins and polymers. It offers a simple venue for coarsening the dynamics model of a system at multiple hierarchical levels. For example, large scale protein dynamics can be studied using torsional dynamics, where large domains or helical structures can be treated as rigid bodies and the loops connecting them as flexible torsions. ICMD with such a dynamic model of the protein, combined with enhanced conformational sampling method such as temperature replica exchange, allows the sampling of large scale domain motion involving high energy barrier transitions. Once these large scale conformational transitions are sampled, all-torsion, or even all-atom, MD simulations can be carried out for the low energy conformations sampled via coarse grained ICMD to calculate the energetics of distinct conformations. Such hierarchical MD simulations can be carried out with standard all-atom forcefields without the need for compromising on the accuracy of the forces. Using constraints to treat bond lengths and bond angles as rigid can, however, distort the potential energy landscape of the system and reduce the number of dihedral transitions as well as conformational sampling. We present here a two-part solution to overcome such distortions of the potential energy landscape with ICMD models. To alleviate the intrinsic distortion that stems from the reduced phase space in torsional MD, we use the Fixman compensating potential. To additionally alleviate the extrinsic distortion that arises from the coupling between the dihedral angles and bond angles within a force field, we propose a hybrid ICMD method that allows the selective relaxing of bond angles. This hybrid ICMD method bridges the gap between all-atom MD and torsional MD. We demonstrate with examples that these methods together offer a solution to eliminate the potential energy distortions encountered in constrained ICMD simulations of peptide molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Wavefront distortion correction in scanning tunneling microscope image

Here, we report an algorithm to identify and correct distorted wavefronts in atomic resolution scanning tunneling microscope images. This algorithm can be used to correct nonlinear in-plane distortions without prior knowledge of the physical scanning parameters, the characteristics of the piezoelectric actuator, or individual atom positions. The 2D image is first defined as a sum of sinusoidal plane waves, where a nonlinear distortion renders a curve for an otherwise ideal linear wavefront. Using the Fourier transforms of local areas of the image, the algorithm generates a wavefront vector field. The identified wavefronts are subsequently linearized for each plane wave without changing lattice orders, giving rise to distortion corrections. Our algorithm is complementary to conventional post-processing algorithms that require prior detection of real space features, which can also be used to correct nonlinear distortions in 2D images acquired by other microscopy techniques.

47 OTHER INSTRUMENTATION↗

Distortions in charged-particle images of laser direct-drive inertial confinement fusion implosions

Energetic charged particles generated by inertial confinement fusion (ICF) implosions encode information about the spatial morphology of the hotspot and dense fuel during the time of peak fusion reactions. The knock-on deuteron imager (KoDI) was developed at the Omega Laser Facility to image these particles in order to diagnose low-mode asymmetries in the hotspot and dense fuel layer of cryogenic deuterium–tritium ICF implosions. However, the images collected are distorted in several ways that prevent reconstruction of the deuteron source. In this paper, we describe these distortions and a series of attempts to mitigate or compensate for them. We present several potential mechanisms for the distortions, including a new model for scattering of charged particles in filamentary electric or magnetic fields surrounding the implosion. Particle-tracing is used to create synthetic KoDI data based on the filamentary field model that reproduces the main experimentally observed image distortions. We conclude that the filamentary scattering model best matches the observed image distortions. Finally, we discuss potential impacts of filamentary fields on other charged-particle diagnostics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Spatial and spectral image distortions caused by diffraction of an ordinary polarised light beam by an ultrasonic wave

We consider the problem of determining the spatial and spectral image distortions arising from anisotropic diffraction by ultrasonic waves in crystals with ordinary polarised light (o → e). By neglecting the small-birefringence approximation, we obtain analytical solutions that describe the dependence of the diffraction angles and wave mismatch on the acousto-optic (AO) interaction geometry and crystal parameters. The formulas derived allow one to calculate and analyse the magnitude of diffraction-induced spatial and spectral image distortions and to identify the main types of distortions: chromatic compression and trapezoidal deformation. A comparison of the values of these distortions in the diffraction of ordinary and extraordinary polarised light shows that they are almost equal in magnitude and opposite in signs, so that consistent diffraction (o → e → o or e → o → e) in two identical AO cells rotated through 180° in the plane of diffraction can compensate for these distortions. (diffraction of radiation)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Limits on the fluctuating part of y-type distortion monopole from Planck and SPT results

We use the published Planck and SPT cluster catalogs [1,2] and recently published y-distortion maps [3] to put strong observational limits on the contribution of the fluctuating part of the y-type distortions to the y-distortion monopole. Our bounds are 5.4× 10{sup −8} < ( y) < 2.2× 10{sup −6}. Our upper bound is a factor of 6.8 stronger than the currently best upper 95% confidence limit from COBE-FIRAS of ( y) <15× 10{sup −6}. In the standard cosmology, large scale structure is the only source of such distortions and our limits therefore constrain the baryonic physics involved in the formation of the large scale structure. Our lower limit, from the detected clusters in the Planck and SPT catalogs, also implies that a Pixie-like experiment should detect the y-distortion monopole at >27-σ. The biggest sources of uncertainty in our upper limit are the monopole offsets between different HFI channel maps that we estimate to be <10{sup −6}.

79 ASTRONOMY AND ASTROPHYSICS↗

Another look at distortions of the Cosmic Microwave Background spectrum

We review aspects of Cosmic Microwave Background (CMB) spectral distortions which do not appear to have been fully explored in the literature. In particular, implications of recent evidences of heating of the intergalactic medium (IGM) by feedback from active galactic nuclei are investigated. Taking also into account the IGM heating associated to structure formation, we argue that values of the y parameter of several × 10{sup −6}, i.e. a factor of a few below the COBE/FIRAS upper limit, are to be expected. The Compton scattering by the re-ionized plasma also re-processes primordial distortions, adding a y-type contribution. Hence no pure Bose-Einstein-like distortions are to be expected. An assessment of Galactic and extragalactic foregrounds, taking into account the latest results from the Planck satellite as well as the contributions from the strong CII and CO lines from star-forming galaxies, demonstrates that a foreground subtraction accurate enough to fully exploit the PIXIE sensitivity will be extremely challenging. Motivated by this fact we also discuss methods to detect spectral distortions not requiring absolute measurements and show that accurate determinations of the frequency spectrum of the CMB dipole amplitude may substantially improve over COBE/FIRAS limits on distortion parameters. Such improvements may be at reach of next generation CMB anisotropy experiments. The estimated amplitude of the Cosmic Infrared Background (CIB) dipole might be detectable by careful analyses of Planck maps at the highest frequencies. Thus Planck might provide interesting constraints on the CIB intensity, currently known with a ≅ 30% uncertainty.

79 ASTRONOMY AND ASTROPHYSICS↗

The effects of the small-scale behaviour of dark matter power spectrum on CMB spectral distortion

After numerous astronomical and experimental searches, the precise particle nature of dark matter is still unknown. The standard Weakly Interacting Massive Particle(WIMP) dark matter, despite successfully explaining the large-scale features of the universe, has long-standing small-scale issues. The spectral distortion in the Cosmic Microwave Background(CMB) caused by Silk damping in the pre-recombination era allows one to access information on a range of small scales 0.3 Mpc < k < 10{sup 4} Mpc{sup −1}, whose dynamics can be precisely described using linear theory. In this paper, we investigate the possibility of using the Silk damping induced CMB spectral distortion as a probe of the small-scale power. We consider four suggested alternative dark matter candidates—Warm Dark Matter (WDM), Late Forming Dark Matter (LFDM), Ultra Light Axion (ULA) dark matter and Charged Decaying Dark Matter (CHDM); the matter power in all these models deviate significantly from the ΛCDM model at small scales. We compute the spectral distortion of CMB for these alternative models and compare our results with the ΛCDM model. We show that the main impact of alternative models is to alter the sub-horizon evolution of the Newtonian potential which affects the late-time behaviour of spectral distortion of CMB. The y -parameter diminishes by a few percent as compared to the ΛCDM model for a range of parameters of these models: LFDM for formation redshift z {sub f} = 10{sup 5} (7%); WDM for mass m {sub wdm} = 1 keV (2%); CHDM for decay redshift z {sub decay} = 10{sup 5} (5%); ULA for mass m {sub a} = 10{sup −24} eV (3%). This effect from the pre-recombination era can be masked by orders of magnitude higher y -distortions generated by late-time sources, e.g. the Epoch of Reionization and tSZ from the cluster of galaxies. We also briefly discuss the detectability of this deviation in light of the upcoming CMB experiment PIXIE, which might have the sensitivity to detect this signal from the pre-recombination phase.

79 ASTRONOMY AND ASTROPHYSICS↗

Using CMB spectral distortions to distinguish between dark matter solutions to the small-scale crisis

The dissipation of small-scale perturbations in the early universe produces a distortion in the blackbody spectrum of cosmic microwave background photons. In this work, we propose to use these distortions as a probe of the microphysics of dark matter on scales 1 Mpc{sup -1}∼< k ∼< 10{sup 4} Mpc{sup -1}. We consider in particular models in which the dark matter is kinetically coupled to either neutrinos or photons until shortly before recombination, and compute the photon heating rate and the resultant μ-distortion in both cases. We show that the μ-parameter is generally enhanced relative to ΛCDM for interactions with neutrinos, and may be either enhanced or suppressed in the case of interactions with photons. The deviations from the ΛCDM signal are potentially within the sensitivity reach of a PRISM-like experiment if σ{sub DM-γ} ∼> 1.1 × 10{sup -30} (m{sub DM}/GeV) cm{sup 2} and σ{sub DM-ν} ∼> 4.8 × 10{sup -32} (m{sub DM}/GeV) cm{sup 2} for time-independent cross sections, and σ{sup 0}{sub DM-γ} ∼> 1.8 × 10{sup -40} (m{sub DM}/GeV) cm{sup 2} and σ{sup 0}{sub DM-ν} ∼> 2.5 × 10{sup -47} (m{sub DM}/GeV) cm{sup 2} for cross sections scaling as temperature squared, coinciding with the parameter regions in which late kinetic decoupling may serve as a solution to the small-scale crisis. Furthermore, these μ-distortion signals differ from those of warm dark matter (no deviation from ΛCDM) and a suppressed primordial power spectrum (a strongly suppressed or negative μ-parameter), demonstrating that CMB spectral distortion can potentially be used to distinguish between solutions to the small-scale crisis.

79 ASTRONOMY AND ASTROPHYSICS↗

Non percolative nature of the metal-insulator transition and persistence of local Jahn-Teller distortions in the rhombohedral regime of La 1-x Ca x MnO 3

Evolution of the average and local crystal structure of Ca-doped LaMnO 3 has been studied across the metal to insulator (MI) and the orthorhombic to rhombohedral (OR) structural phase transitions over a broad temperature range for two Ca concentrations (x = 0.18,0.22). Combined Rietveld and high real space resolution atomic pair distribution function (PDF) analysis of neutron total scattering data was carried out with aims of exploring the possibility of nanoscale phase separation (PS) in relation to MI transition, and charting the evolution of local Jahn-Teller (JT) distortion of MnO 6 octahedra across the OR transition at T S ~720 K. The study utilized explicit two-phase PDF structural modeling, revealing that away from T MI there is no evidence for nanoscale phase coexistence. The local JT distortions disappear abruptly upon crossing into the metallic regime both with doping and temperature, with only a small temperature-independent signature of quenched disorder being observable at low temperature as compared to CaMnO 3 . The results hence do not support the percolative scenario for the MI transition in La 1–x Ca x MnO 3 based on PS, and question its ubiquity in the manganites. In contrast to LaMnO 3 that exhibits long-range orbital correlations and sizable octahedral distortions at low temperature, the doped samples with compositions straddling the MI boundary exhibit correlations (in the insulating regime) limited to only ~1 nm with observably smaller distortions. In the x = 0.22 sample local JT distortions are found to persist across the OR transition and deep into the R phase (up to ~1050 K), where they are crystallographically prohibited. As a result, their magnitude and subnanometer spatial extent remain unchanged.

36 MATERIALS SCIENCE↗

Exotic energy injection in the early Universe. II. CMB spectral distortions and constraints on light dark matter

Here, we calculate the post-recombination contribution to the cosmic microwave background (CMB) spectral distortion due to general exotic energy injections, including dark matter (DM) decaying or annihilating to Standard Model particles. Upon subtracting the background distortion that would be present even without such energy injections, we find residual distortions that are still potentially large enough to be detectable by future experiments such as PIXIE. The distortions also have a high-energy spectral feature that is a unique signature of the injection of high-energy particles. We present a calculation of the global ionization history in the presence of decaying dark matter with sub-keV masses, and also show that previous calculations of the global ionization history in the presence of energy injection are not significantly modified by these additional spectral distortions. Our improved treatment of low-energy electrons allows us to extend calculations of the CMB anisotropy constraints for decaying DM down to arbitrarily low masses. We also recast these bounds as constraints on the coupling of axionlike particles to photons.

79 ASTRONOMY AND ASTROPHYSICS↗