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NASA NTRS1990

XES studies of density of states of high temperature superconductors

X-ray emission spectroscopic studies concerning the superconducting crystals, thin films and ceramics of the Y-Ba-Cu-O, Tm-Ba-Cu-O, Bi-Sr-Ca-Cu-O, Bi-Pb-Sr-Ca-Cu-O and T1-Ba-Ca-Cu-O types are presented. The contributions of the 13d(9)L, 13d(10)L, 13d(10)LL and 13d(10)L(2) configurations, where L denotes a ligand hole at the oxygen orbitals in the spectroscopic pattern of these superconductors are discussed. An attempt to connect the x-ray 'as registered' Cu L emission spectra with the density of states close to the Fermi level, considering an influence of the CuL3 absorption edge, is presented. The corrected intensity distributions below the Fermi level are found to correspond to the theoretical density of states. Furthermore, an approach to the average valence of copper based on the account of the self-absorption and fluorescence effects and on the configurations listed above is shown. The average valence of copper in the materials investigated is estimated to lie in the range of +2.10 to 2.32 when the formal trivalent copper is considered as that characterized by the 13d(9)L configuration. The density of states at the Fermi level was estimated to be 2.4 states/eV-cell for a Bi-Sr-Ca-Cu-O crystal and 3.6 states/eV-cell for a Tl-Ba-Ca-Cu-O ceramic.

Jasiolek, Gabriel↗

NASA NTRS1991

XES studies of density of states of high temperature superconductors

X-ray emission spectroscopic studies concerning the superconducting crystals, thin films, and ceramics of the Y-Ba-Cu-O, Tm-Ba-Cu-O, Bi-Sr-Ca-Cu-O, Bi-Pb-Sr-Ca-Cu-O, and Tl-Ba-Ca-Cu-O types are presented. The contributions of the 13d(9)L, 13d(10)L, 13d(10)LL, and 13d(10)L(2) configurations, where L denotes a ligand hole at the oxygen orbitals in the spectroscopic pattern of these superconductors are discussed. An attempt to connect the x-ray 'as registered' Cu L(alpha) emission spectra with the density of states close to the Fermi level, considering an influence of the CuL3 absorption edge, is presented. The corrected intensity distributions below the Fermi level are found to correspond to the theoretical density of states. Furthermore, an approach to the average valence of copper basing on the account of the self-absorption and fluorescence effects and on the configurations listed above is shown. The average valence of copper in the materials investigated is estimated to lie in the range of +2.10 to 2.32 when the formal trivalent copper is considered as that characterized by the 13d(9)L configuration. The density of states at the Fermi level was estimated to be 2.4 states/eV-cell for a Bi-Sr-Ca-Cu-O crystal and 3.6 states/eV-cell for a Tl-Ba-Ca-CU-O ceramic.

Jasiolek, Gabriel↗

NASA NTRS1990

Resonant tunneling IR detectors

Researchers propose a novel semiconductor heterojunction photodetector which would have a very low dark current and would be voltage tunable. A schematic diagram of the device and its band structure are shown. The two crucial components of the device are a cathode (InGaAs) whose condition band edge is below the conduction band edge of the quantum wells and a resonant tunneling filter (GaAs-AlGaAs). In a standard resonant tunneling device the electrodes are made of the same material as the quantum wells, and this device becomes highly conducting when the quantum levels in the wells are aligned with the Fermi level in the negatively biased electrode. In contrast, the researchers device is essentially non-conducting under the same bias conditions. This is because the Fermi Level of the cathode (InGaAs) is still well below the quantum levels so that no resonant transport occurs and the barriers (AlGaAs) effectively block current flow through the device. However, if light with the same photon energy as the conduction-band discontinuity between the cathode and the quantum wells, E sub c3-E sub c1, is shone on the sample, free carriers will be excited to an energy corresponding to the lowest quantum level in the well closest to the cathode (hv plue E sub c1 = E sub o). These electrons will resonantly tunnel through the quantum wells and be collected as a photocurrent in the anode (GaAs). To improve the quantum efficiency, the cathode (InGaAs) should be very heavily doped and capped with a highly reflective metal ohmic contact. The thickness of the device should be tailored to optimize thin film interference effects and afford the maximum absorption of light. Because the device relies on resonant tunneling, its response should be very fast, and the small voltages needed to change the responsivity should allow for very high frequency modulation of the photocurrent. In addition, the device is tuned to a specific photon energy so that it can be designed to detect a fairly narrow range of wavelengths. This selectivity is important for reducing the photocurrent due to spurious light sources.

Woodall, Jerry M.↗

DOE OSTI2025

Electron correlation and incipient flat bands in the Kagome superconductor CsCr 3 Sb 5

Correlated kagome materials exhibit a compelling interplay between lattice geometry, electron correlation, and topology. In particular, the flat bands near the Fermi level provide a fertile playground for novel many-body states. Here we investigate the electronic structure of CsCr 3 Sb 5 using high-resolution angle-resolved photoemission spectroscopy and ab-initio calculations. Our results suggest that Cr 3d electrons are intrinsically incoherent, showing strong electron correlation amplified by Hund’s coupling. Notably, we identify incipient flat bands close to the Fermi level, which are expected to significantly influence the electronic properties of the system. Across the density-wave-like transition at 55 K, we observe a drastic enhancement of the electron scattering rate, which aligns with the semiconducting-like property at high temperatures. These findings establish CsCr 3 Sb 5 as a strongly correlated Hund’s metal with incipient flat bands near the Fermi level, which provides an electronic basis for understanding its novel properties compared to the weakly correlated AV 3 Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1972

Electron spin resonance of ultraviolet radiation induced defects in ZnO thermal control coating pigment.

Electron spin resonance measurements on variously treated zinc oxide powders reveal that the resonance signal at g = 1.956 is due to one electron trapped oxygen ion vacancy level, at a depth of (0.31 plus or minus 0.02) eV below the conduction band. The electrons at this level are delocalized. Schottky barrier influences nearly the entire bulk of the powder sample, and the bending of the bands caused by chemisorbed oxygen puts the vacancy level above the Fermi level almost through the entire bulk.

Mookherji, T.↗

DOE OSTI2025

The Electron Thermal Conductivity of Pu and Zr Substituted $\mathcal{γ}$-U

Uranium alloys are attractive recycled nuclear fuels because of their high thermal conductivity (𝑘) and fissile density. Limited experimental studies of the 𝑘 of U-Pu-Zr alloys in the range of 15 to 20 wt% Pu and 6 to 15 wt% Zr indicate that increasing the content of either Zr or Pu tends to lower 𝑘. However, which element has the greater effect on 𝑘, and the associated mechanisms, remains unclear. Here, in this study, the electron thermal conductivity (𝑘 𝑒 ) of U-Pu-Zr compositions are calculated using density functional theory. The electronic structure is evaluated to understand the effects of plutonium (Pu) and zirconium (Zr) substitution on the 𝑘 𝑒 of 𝛾-U. Alloys of up to 37.5 at. % Pu and 37.5 at. % Zr are examined. Two methods are applied to calculate 𝑘 𝑒 ; we find that the accuracy of each method depends on the electronic and mass similarities between the solute and solvent atoms. Specifically, when the solute atom is similar in electronic structure and mass, the more accurate method is that which employs the electron relaxation time of 𝛾-U, while if the elements are dissimilar, a mixed method that mixes several parameters associated with JNW_S⁢3033426825100132 from each element in the alloy is best. The introduction of all alloying elements decreases 𝑘 𝑒 ; however, in binary compounds, Pu and Zr have different effects. Pu flattens the electronic bands but compensates for this deleterious effect by increasing electron density near the Fermi level. Zr flattens the electronic bands more severely without adding electron density near the Fermi level. Therefore, Zr decreases 𝑘 𝑒 more than Pu in binary compounds. In ternary compounds, the difference between Pu and Zr is minimal due to the phononic change from the large mass change of Zr substitution, even at 12.5 at. %. Thus, we predict that higher loadings of Pu, and potentially other actinides, can be added to U-Pu-Zr compositions for faster recycling of spent fuel without sacrificing 𝑘. We also note that these 𝑘 𝑒 calculation methods can be applied to non-fuel alloys that require 𝑘 𝑒 predictions, such as cladding, heat exchanger, and structural materials.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Electrical transport and torque magnetometry studies of the kagome compound LuV 6 ⁢Sn 6 under high magnetic fields

We present a comprehensive investigation of the kagome metal LuV 6 ⁢Sn 6 through magnetotransport and torque magnetometry studies in magnetic fields up to 41 T and temperatures as low as 0.3 K. Magnetoresistance measurements up to 31 T reveal clear Shubnikov–de Haas (SdH) oscillations with two dominant frequency peaks: 𝐹 𝛼 =12 T and 𝐹 𝛽 =155 T. The Berry phase Φ 𝐁 , calculated from Landau level fan diagrams, indicates a nontrivial topology for both the 𝛼- and 𝛽-orbits. To explore the possibility of higher-frequency signals in LuV 6 ⁢Sn 6 , we employed another technique: torque magnetometry. Torque measured with applied fields up to 41 T reveals clear de Haas–van Alphen (dHvA) oscillations, with frequency signals as high as 10 kT. Angular and temperature-dependent quantum oscillation measurements allowed us to extract the effective mass of charge carriers and map the Fermi surface of LuV 6 ⁢Sn 6 . To complement the experimental findings, we performed electronic band structure and Fermi surface calculations. The electronic bands of LuV 6 ⁢Sn 6 reveal intriguing features, including flat bands, van Hove singularities, and Dirac points near the Fermi level. Two bands cross the Fermi level, contributing a deformed cylindrical shape at the Γ-point and small chainlike Fermi surfaces near the Brillouin zone boundaries. Theoretical quantum oscillation frequencies derived from Fermi surface cross-sectional areas align well with experimental SdH and dHvA results. These combined experimental and theoretical insights provide a deeper understanding of the electronic structure of LuV 6 ⁢Sn 6 and establish the foundation for exploring electronic properties in other vanadium- and titanium-based kagome systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Electronic Structure of Compressively Strained Bilayer Nickelate Thin Film

The discovery of superconductivity in bulk bilayer nickelates under high pressure, and its subsequent stabilization in compressively strained thin films at ambient pressure, has established a new platform for exploring high-𝑇 c superconductivity beyond the cuprates. Central to this development is the prominent role of the 3⁢𝑑$^2_𝑧$ orbital in shaping the low-energy electronic structure, imposing constraints on microscopic theories and fueling debate over the superconducting mechanism. Here we report a systematic in situ angle-resolved photoemission spectroscopy study of compressively strained bilayer nickelate thin films spanning Ca doping, oxygen stoichiometry and film thickness. Despite variations in oxygen-vacancy disorder and surface termination, the electronic structure remains robust and exhibits a systematic strain-driven evolution consistent with an intermediate-correlation regime. In particular, we demonstrate a Ca-doping-induced electronic structure evolution that is consistent with Fermi-level crossing of the 𝛾 band and is decoupled from the presence of superconductivity, suggesting that, while important for the 𝛾 band to be near the Fermi level, the debated 𝛾 crossing and the resulting Fermi pocket may not be a prerequisite for superconductivity. Together, our results establish key spectroscopic constraints on the minimal fermiology and correlation strength relevant to superconductivity in bilayer nickelates, providing an experimental foundation for microscopic theories of their pairing mechanism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1995

Structural, dynamical and electronic properties of CaCuO2

The scalar relativistic version of an accurate first principles full potential self-consistent linearized muffin tin orbital (LMTO) method has been employed for describing the physical properties of the parent system of the high-T(sub c) oxide superconductors, i.e., CaCuO2. The presently employed modified version of the LMTO method is quite fast and goes beyond the usual LMTO ASA method in the sense that it permits a completely general shape of the potential and the charge density. Also, in contrast to LMTO ASA, the present method is also capable of treating distorted lattice structures accurately. The calculated values of the lattice parameters of pure CaCuO2 lie within 3% of the experimentally measured values for the Sr-doped system Ca(0.86)Sr(0.14)CuO(2). The computed electronic structures and the density of states is quite similar to those of the other oxide superconductors, except of their three- dimensional character because of the presence of strong coupling between the closely spaced CuO2 layers. The van Hove singularity peak appears slightly below the Fermi level and a small concentration of oxygenation /or/ substitutional doping may pin it at the Fermi level. The calculated frequencies for some symmetric frozen phonons for undoped CaCuO2 are quite near to the measured data for the Sr-doped CaCuO2.

Agrawal, Bal K.↗

DOE OSTI2026

Chemical bonding, phase stability and magnetic property in Sm 2 Fe 17 X 3 (X=H, C, N): A first-principles perspective

As a promising alternative to Nd–Fe–B magnets, the critical rare earth free Sm 2 Fe 17 X 3 (X = C, N) exhibits potential for high-performance magnets. However, their poor phase stability remains a major obstacle to developing bulk magnets. We investigated the phase stability and intrinsic magnetic properties of Sm 2 Fe 17 X 3 (X = H, C, N) using first-principles calculations and chemical bond analysis. The formation energies are negative, while the decomposition energies are −1.53, 0.348, and −0.74 eV per formula unit for X = H, C, and N, respectively, which is responsible for the weak thermal stability. Our chemical bond analysis reveals that the bonding asymmetry between Sm–X and Fe–X interactions creates local structural distortions and degrades the phase stability of Sm 2 Fe 17 X 3 . The project Crystal Orbital Hamilton Population (-pCOHP) analysis indicates that the Sm–X bonding remains positive up to the Fermi level, indicating stable bonding interactions. Here, in contrast, the Fe–X bonding becomes negative near the Fermi level, signifying anti-bonding contributions that reduce structural stability. Interstitial atoms X expand the lattice and enhance Fe magnetic moments, but Fe–X bonding suppresses neighboring Fe moments. Electron transfer from Sm to X modifies the valence state of Sm and the crystal field at the site, contributing to enhanced magnetocrystalline anisotropy in Sm 2 Fe 17 X 3 . Among the interstitial elements, carbon and nitrogen—with their larger atomic radius and higher electronegativity—induce greater lattice expansion and form stronger bonds with neighboring Sm and Fe atoms compared to hydrogen. Consequently, Sm 2 Fe 17 X 3 (X = C and N) exhibits better phase stability and significant improvement in magnetic properties.

Chemical bonding↗

DOE OSTI2025

Electronic structure of compressively strained thin film La$_2$PrNi$_2$O$_7$

The discovery of superconductivity in the bulk nickelates under high pressure is a major advance in physics. The recent observation of superconductivity at ambient pressure in compressively strained bilayer nickelate thin films has now enabled direct characterization of the superconducting phase through angle resolved photoemission spectroscopy (ARPES). Here we present an in-situ ARPES study of compressively strained La$_2$PrNi$_2$O$_7$ films grown by oxide molecular beam epitaxy, and the ozone treated counterparts with an onset T$_c$ of 40 K, supplemented with results from pulsed laser deposition films with similar T$_c$. We resolve a systematic strain-driven electronic band shift with respect to that of bulk crystals, in qualitative agreement with density functional theory (DFT) calculations. However, the strongly renormalized flat 3$d_{z2}$ band shifts a factor of 5-10 smaller than anticipated by DFT. Furthermore, it stays ~70 meV below the Fermi level, contradicting the expectation that superconductivity results from the high density of states of this band at the Fermi level. We also observed a non-trivial k$_z$ dispersion of the cuprate-like 3$d_{x2-y2}$ band. Combined with results from both X-ray diffraction and DFT, we suggest that the strained films are under ~5 GPa effective pressure, considerably larger than the naïve expectation from the DFT relaxed structure. Finally, the ~70 meV energy position is intriguingly close to the collective mode coupling more prominently seen in thin films, in the energy range of both oxygen related phonons and the maximum of the spin excitation spectrum.

FOS: Physical sciences↗

DOE OSTI2026

Operando Spectroscopic Analysis of Photovoltage Generation in Hematite Photoanodes

Solar-driven water splitting requires sufficient photovoltage to drive both water oxidation and proton reduction. Understanding the factors driving and limiting photovoltage generation is therefore crucial to optimizing photoelectrode design but has proven challenging to determine under operando conditions for photoanodes driving slow multiredox reactions such as water oxidation. In this work, operando optical spectroscopy is employed to measure the hole quasi-Fermi level (E F,p ) position in model hematite photoanodes as a function of applied bias and light intensity. The quasi-Fermi level splitting determined from these data are shown be in excellent agreement with the directly measured photovoltages, demonstrating the primarily electrochemical rather than primarily electrostatic origin of photovoltage in these photoelectrodes. E F,p pinning is observed at low light intensities and biases, indicative of hole trap states lying ∼0.2 eV above the valence band edge with a density of ∼1 nm −2 . Hole accumulation in these trap states is correlated with first order water oxidation. At higher light intensities and/or more anodic bias, E F,p becomes unpinned, assigned to saturation of these trap states, and correlated with the onset of third order water oxidation to molecular oxygen. Comparison with rate law analyses for other photoanodes indicates that such hole trap states may be a ubiquitous feature of metal oxides and suggests that materials processing strategies to suppress the density of such states would be a promising strategy to enhance photoanode performance.

Hematite↗

DOE OSTI2024

Band structure and Fermi surface nesting in LaSb 2

Here we use high-resolution angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) to investigate the electronic structure of the charge density wave (CDW) system LaSb 2 . This compound is among an interesting group of materials that manifests both a CDW transition and lower temperature superconductivity. We find the DFT calculations to be in good agreement with our ARPES data. The Fermi surface of LaSb 2 consists of two small hole pockets close to Γ and four larger pockets near the Brillouin zone boundary. The key features of the Fermi surface do not vary significantly with temperature. A saddle point is present at -0.19 eV below the Fermi level at Γ. Saddle points in the band structure have more pronounced effects on materials properties when they are located closer to the Fermi level, making doped LaSb 2 compounds a potential interesting subject of future research. Multiple peaks are present in the generalized, electronic susceptibility calculations, indicating the presence of three possible nesting vectors. We were not able to detect any signatures of the CDW transition at 355 K down to the lowest temperature of 7 K, pointing to the subtle nature of this transition. This is unusual, given that such a high transition temperature is expected to be associated with the presence of a large CDW gap. This is confirmed through investigation of the Fermi surface and through analysis of momentum distribution curves. It is possible that changes are subtle and occur below current sensitivity of our measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1996

X-Ray Photoemission Measurements of La(1-x)Ca(x)CoO3(x = 0, 0.5)

X-ray photoemission measurements of the core levels and valence electronic structure of LaCoO3 and La(0.5)Ca(0.5)CoO3 high quality epitaxial films are presented. Shifts of the core levels and main valence band features are consistent with a doping-induced change in the chemical potential. Oxygen states are found to significantly contribute to a peak in the valence band at 1 eV binding energy, verifying earlier results of cluster calculations. A Fermi level crossing of this same band upon doping is observed, yielding a high Fermi level density of states.

Vasquez, R. P.↗

DOE OSTI2025

Correlating Nb-SRF Surface Processing with Evolution of Surface Electronic States

The few nanometers of the surface exposed to RF field plays a major role in defining the RF performance of superconducting cavities. Over the past two decades, several pioneering surface treatment and processing methods have emerged, enabling remarkable improvements in cavity performance by simultaneously achieving high Q with increasing Eacc. These processing methods include: thermal treatment under ultra-high vacuum (UHV) conditions across lo¬¬¬¬¬¬¬w-, mid-, and high-temperature ranges and high temperature treatments under controlled N2 atmosphere. These processes also produce distinct surface oxide configurations with different valence states, thicknesses, and uniformity, as well as different oxygen concentration profiles in bulk Nb. In this work, we are trying to understand how do surface-processing methods and the resulting oxide/oxygen profiles affect the electronic structure of surface and the mechanism of superconductivity? With the help of Fermilab’s in-house X-ray photoemission facility and, in collaboration with the synchrotron-based angle-resolved photoemission (ARPES) facility at Argonne National Laboratory, we are investigating how the valence band structure and density of states (DoS) near the Fermi level modify with different surface treatments. Our observations show that different surface-processing methods lead to distinct evolutions of the valence-band states near the Fermi level during the superconducting transition. This behavior suggests variations in Nb-O orbital hybridizations and points towards the possibility of different underlying mechanisms of superconductivity governed by the surface chemistry and oxide configuration. We also correlate these distinct superconducting mechanisms with RF cavity performance, specifically focusing on measured surface resistance, the nature of the Q-slope, and quench fields observed in SRF measurements. These results will enable us to identify the potential limiting factors and relevant controllable parameters that can be further optimized to improve the performance of SRF cavities.

Tripathi, Malvika [Fermilab]↗

DOE OSTI2025

Overcoming the challenges of accessing topological hallmarks in Sb(112)

Sb is topologically non-trivial and semi-metallic, but differs from many topological semi-metals because of its continuous band gap. By measuring its (112) surface using angle- and spin-resolved photoemission spectroscopy, Sb(112) was shown to have 1D spin-polarised surface states resembling those on vicinal Bi surfaces and many topological insulators and topological semi-metals. The shape and spin-polarisation of the measured features and the calculated bands agreed. However, the measured features had a slightly steeper energy dispersion and different Fermi-momenta than the calculated bands. Both theoretical and experimental methods were necessary when determining the topology of Sb(112). The presence of projected bulk states near the Fermi-level and varying surface localisation of the electronic states meant it was challenging to deduce the topology of Sb(112) from the number of bands crossing the Fermi-level or a continuous contour in the bulk band gap. Ultimately, the calculations and measurements suggest that there are topological surface states on the Sb(112) surface.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Pressure-induced 𝐵⁢1 to 𝐵⁢2 phase transition in CeN studied by 𝑎⁢𝑏 𝑖⁢𝑛⁢𝑖⁢𝑡⁢𝑖⁢𝑜 correlation matrix renormalization theory calculations

We apply correlation matrix renormalization theory (CMRT) to cerium nitride (CeN) under pressure. For 𝐵⁢1 (NaCl-type) phase, CMRT gives an equation of state consistent with ambient pressure experiments. It produces electronic density-of-state (DOS) characterized by a sharp 4⁢𝑓 quasiparticle resonance peak pinned at the Fermi level and two subbands formed by strong hybridization between the localized Ce-4⁢𝑓 electrons and the itinerant Ce-5⁢𝑑 and N-2⁢𝑝 electrons below the Fermi level, consistent with x-ray photoemission spectroscopy experiments. Upon compression, CMRT predicts a first-order 𝐵⁢1 → 𝐵⁢2 (CsCl-type) transition with ∼11% volume collapse in agreement with experiments. Across the transition, the 4⁢𝑓 spectrum broadens, the 4⁢𝑓 orbital occupancy increases, and the hybridization with conduction states enhances, signaling a crossover from partially localized to more itinerant 4⁢𝑓 behavior. Furthermore, these features are in excellent agreement with experimental observations, demonstrating that CMRT provides a parameter-free description and prediction of correlation-driven structural and electronic transitions in rare-earth compounds.

Ab initio calculations↗

DOE OSTI2024

UOTe: Kondo‐Interacting Topological Antiferromagnet in a Van der Waals Lattice

Since the initial discovery of 2D van der Waals (vdW) materials, significant effort has been made to incorporate the three properties of magnetism, band structure topology, and strong electron correlations—to leverage emergent quantum phenomena and expand their potential applications. However, the discovery of a single vdW material that intrinsically hosts all three ingredients has remained an outstanding challenge. Here, in this work, the discovery of a Kondo-interacting topological antiferromagnet is reported in the vdW 5f electron system UOTe. It has a high antiferromagnetic (AFM) transition temperature of 150 K, with a unique AFM configuration that breaks the combined parity and time reversal (PT) symmetry in an even number of layers while maintaining zero net magnetic moment. This angle-resolved photoemission spectroscopy (ARPES) measurements reveal Dirac bands near the Fermi level, which combined with the theoretical calculations demonstrate UOTe as an AFM Dirac semimetal. Within the AFM order, the presence of the Kondo interaction is observed, as evidenced by the emergence of a 5ƒ flat band near the Fermi level below 100 K and hybridization between the Kondo band and the Dirac band. The density functional theory calculations in its bilayer form predict UOTe as a rare example of a fully-compensated AFM Chern insulator.

36 MATERIALS SCIENCE↗