Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “2D magnet”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Low-Temperature 2D/2D Ohmic Contacts in WSe 2 Field-Effect Transistors as a Platform for the 2D Metal–Insulator Transition

in this work, we report the fabrication of hexagonal-boron-nitride (hBN) encapsulated multiterminal WSe 2 Hall bars with 2D/2D low-temperature Ohmic contacts as a platform for investigating the two-dimensional (2D) metal-insulator transition. We demonstrate that the WSe 2 devices exhibit Ohmic behavior down to 0.25 K and at low enough excitation voltages to avoid current-heating effects. Additionally, the high-quality hBN-encapsulated WSe 2 devices in ideal Hall-bar geometry enable us to accurately determine the carrier density. Measurements of the temperature (T) and density (n s ) dependence of the conductivity σ(T, n s ) demonstrate scaling behavior consistent with a metalinsulator quantum phase transition driven by electron-electron interactions, but where disorder-induced local magnetic moments are also present. Our findings pave the way for further studies of the fundamental quantum mechanical properties of 2D transition metal dichalcogenides using the same contact engineering.

2D materials↗
DOE OSTI2020

Strong surface magnetic field generation in relativistic short pulse laser–plasma interaction with an applied seed magnetic field

Abstract While plasma often behaves diamagnetically, we demonstrate that the laser irradiation of a thin opaque target with an embedded target-transverse seed magnetic field B seed can trigger the generation of an order-of-magnitude stronger magnetic field with opposite sign at the target surface. Strong surface field generation occurs when the laser pulse is relativistically intense and results from the currents associated with the cyclotron rotation of laser-heated electrons transiting through the target and the compensating current of cold electrons. We derive a predictive scaling for this surface field generation, B gen ∼ −2 πB seed Δ x / λ 0 (in the large spot size limit), where Δ x is the target thickness and λ 0 is the laser wavelength, and conduct 1D and 2D particle-in-cell simulations to confirm its applicability over a wide range of conditions. We additionally demonstrate that both the seed and surface-generated magnetic fields can have a strong impact on application-relevant plasma dynamics, for example substantially altering the overall expansion and ion acceleration from a μ m-thick laser-irradiated target with a kilotesla-level seed magnetic field.

Weichman, K. (ORCID:0000000234877922)↗
DOE OSTI2023

Edge Channel Transmission through a Quantum Point Contact in the Two-Dimensional Topological Insulator Cadmium Arsenide

Cadmium arsenide (Cd 3 As 2 ) thin films feature a two-dimensional topological insulator (2D TI) phase for certain thicknesses, which theoretically hosts a set of counterpropagating helical edge states that are characteristic of a quantum spin Hall (QSH) insulator. In devices containing electrostatically defined junctions and for magnetic fields below a critical value, chiral edge modes of the quantum Hall effect can coexist with QSH-like edge modes. In this work, we use a quantum point contact (QPC) device to characterize edge modes in the 2D TI phase of Cd 3 As 2 and to understand how they can be controllably transmitted, which is important for use in future quantum interference devices. We investigate equilibration among both types of modes and find non-spin-selective equilibration. We also demonstrate the effect of the magnetic field on suppressing equilibration. We discuss the potential role of QSH-like modes in a transmission pathway that precludes full pinch-off.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1993

The thermal structure of the magnetized solar transition region

The detailed thermal structure of the magnetized solar transition region, as measured by its differential emission measure DEM(T), is unknown. Proposals have been made that envision a significant lower-temperature contribution to the energy balance from cross-field (ion) heat flux. In this paper, we describe a self-consistent 2D MHD simulation (including the full effects of anisotropic thermal conduction) of a conceptual model due to Athay (1990). We display the detailed irregular thermal and magnetic structure of the transition region and demonstrate that the predicted DEM agrees with observations, particularly in the T less than 10 exp 5 K regime where previous theories had difficulty.

Mok, Y.↗
DOE OSTI2020

Topological materials by molecular beam epitaxy

Topology appears across condensed matter physics to describe a wide array of phenomena which could alter, augment, or fundamentally change the functionality of many technologies. Linking the basic science of topological materials to applications requires producing high-quality thin films. This will enable combining dissimilar materials while utilizing dimensionality, symmetry, and strain to create or control the electronic phase, as well as platforms to fabricate novel devices. Yet, one of the longstanding challenges in the field remains understanding and controlling the basic material properties of epitaxial thin films. Here, we discuss how understanding the fundamental properties of topological materials grown by molecular beam epitaxy (MBE) is key to deepening the knowledge of the basic physics, while developing a new generation of topological devices. A focus will be on the MBE growth of intrinsic materials, creation, and control of superconducting and magnetic topological phases. Addressing these questions in the coming decade will undoubtedly uncover many surprises as new materials are discovered and their growth as high-quality thin films is refined.

2d quantum materials↗
NASA NTRS2004

High Power Density Motors

With the growing concerns of global warming, the need for pollution-free vehicles is ever increasing. Pollution-free flight is one of NASA's goals for the 21" Century. , One method of approaching that goal is hydrogen-fueled aircraft that use fuel cells or turbo- generators to develop electric power that can drive electric motors that turn the aircraft's propulsive fans or propellers. Hydrogen fuel would likely be carried as a liquid, stored in tanks at its boiling point of 20.5 K (-422.5 F). Conventional electric motors, however, are far too heavy (for a given horsepower) to use on aircraft. Fortunately the liquid hydrogen fuel can provide essentially free refrigeration that can be used to cool the windings of motors before the hydrogen is used for fuel. Either High Temperature Superconductors (HTS) or high purity metals such as copper or aluminum may be used in the motor windings. Superconductors have essentially zero electrical resistance to steady current. The electrical resistance of high purity aluminum or copper near liquid hydrogen temperature can be l/lOO* or less of the room temperature resistance. These conductors could provide higher motor efficiency than normal room-temperature motors achieve. But much more importantly, these conductors can carry ten to a hundred times more current than copper conductors do in normal motors operating at room temperature. This is a consequence of the low electrical resistance and of good heat transfer coefficients in boiling LH2. Thus the conductors can produce higher magnetic field strengths and consequently higher motor torque and power. Designs, analysis and actual cryogenic motor tests show that such cryogenic motors could produce three or more times as much power per unit weight as turbine engines can, whereas conventional motors produce only 1/5 as much power per weight as turbine engines. This summer work has been done with Litz wire to maximize the current density. The current is limited by the amount of heat it generates. By increasing the heat transfer out of the wire, the wires can carry a larger current and therefore produce more force. This was done by increasing the surface area of the wire to allow more coolant to flow over it. Litz wire was used because it can carry high frequency current. It also can be deformed into configurations that would increase the surface area. The best configuration was determined by heat transfer and force plots that were generated using Maxwell 2D. Future work will be done by testing and measuring the thrust force produced by the wires in a magnetic field.

Kascak, Daniel J.↗
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↗
DOE OSTI2024

Theory for Cd 3 As 2 thin films in the presence of magnetic fields

Here we present a theory for thin films of the Dirac semimetal Cd 3 ⁢As 2 in the presence of magnetic fields. We show that, above a critical thickness, specific subbands n of thin film Cd 3 ⁢As 2 are in a quantum spin Hall insulator regime and study their response to in- and out-of-plane magnetic fields. We find that sufficiently large in-plane Zeeman fields drive the system toward a 2D Dirac semimetal regime, provided the field is directed perpendicular to a high-symmetry mirror plane. For other directions, we find the Dirac points to be weakly gapped. We further investigate how the system responds to finite out-of-plane field components, both starting from the quantum spin Hall regime at small in-plane fields and from the 2D Dirac semimetal regimes at larger in-plane fields, addressing recent experimental observations in A. C. Lygo et al. [Phys. Rev. Lett. 130, 046201 (2023)] and B. Guo et al. [Phys. Rev. Lett. 131, 046601 (2023)].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

New Quantum Phenomena by Combining 2D Materials with Complex Oxides

This project focused on forming clean interfaces between exfoliated 2D materials and epitaxial oxides with the goal of determining the extent to which the electronic and magnetic properties of the former are influenced by the latter. Clear effects were observed in both device structures for which electronic transport properties were measured and unpatterned interfaces interrogated by polarized light to determine magnetic dichroic response. This work resulted in one paper already published and two others to be written, pending the outcome of ongoing experiments and theoretical calculations

36 MATERIALS SCIENCE↗
NASA NTRS1992

Alfvenic drift Kelvin-Helmholtz instability in the presence of an equilibrium electric field

The Alfvenic drift Kelvin-Helmholtz instability of a high-beta plasma in the presence of equilibrium magnetic and electric fields perpendicular to each other are studied. The plasma components are assumed to have 2D sheared velocity in y and z directions. The dispersion relation is derived, and the instability criterion is determined. It is shown that the equilibrium electric field has either stabilizing or destabilizing effect depending on certain conditions discussed in the paper.

Sharma, Avadhesh C.↗
DOE OSTI2021

Magnetotransport in semiconductors and two-dimensional materials from first principles

Here we demonstrate a first-principles method to study magnetotransport in materials by solving the Boltzmann transport equation (BTE) in the presence of an external magnetic field. Our approach employs ab initio electron-phonon interactions and takes spin-orbit coupling into account. We apply our method to various semiconductors (Si and GaAs) and two-dimensional (2D) materials (graphene) as representative case studies. The magnetoresistance, Hall mobility, and Hall factor in Si and GaAs are in very good agreement with experiments. In graphene, our method predicts a large magnetoresistance, consistent with experiments. Analysis of the steady-state electron occupations in graphene shows the dominant role of optical phonon scattering and the breaking of the relaxation time approximation. Our paper provides a detailed understanding of the microscopic mechanisms governing magnetotransport coefficients, establishing the BTE in a magnetic field as a broadly applicable first-principles tool to investigate transport in semiconductors and 2D materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Haldane topological spin-1 chains in a planar metal-organic framework

Haldane topological materials contain unique antiferromagnetic chains with symmetry-protected energy gaps. Such materials have potential applications in spintronics and future quantum computers. Haldane topological solids typically consist of spin-1 chains embedded in extended three-dimensional (3D) crystal structures. Here, we demonstrate that [Ni(μ-4,4'-bipyridine)(μ-oxalate)] n (NiBO) instead adopts a two-dimensional (2D) metal-organic framework (MOF) structure of Ni 2+ spin-1 chains weakly linked by 4,4'-bipyridine. NiBO exhibits Haldane topological properties with a gap between the singlet ground state and the triplet excited state. The latter is split by weak axial and rhombic anisotropies. Several experimental probes, including single-crystal X-ray diffraction, variable-temperature powder neutron diffraction (VT-PND), VT inelastic neutron scattering (VT-INS), DC susceptibility and specific heat measurements, high-field electron spin resonance, and unbiased quantum Monte Carlo simulations, provide a detailed, comprehensive characterization of NiBO. Vibrational (also known as phonon) properties of NiBO have been probed by INS and density-functional theory (DFT) calculations, indicating the absence of phonons near magnetic excitations in NiBO, suppressing spin-phonon coupling. The work here demonstrates that NiBO is indeed a rare 2D-MOF Haldane topological material.

36 MATERIALS SCIENCE↗
DOE OSTI2026

The Role of Magnetic Reconnection in Energizing Protons and Heavier Ions at the Heliospheric Current Sheet

During near-Sun crossings of the heliospheric current sheet (HCS), Parker Solar Probe (PSP) observed populations of high-energy protons and heavier ions, indicating possible energization by magnetic reconnection up to 10 s–100 s keV nucleon −1 . Here we study ion acceleration by magnetic reconnection at the HCS. To estimate ion energization, we solve the Parker transport equation coupled to a large-scale 2D MHD reconnection simulation. We find that multiple ion species develop power-law distributions with both spectral index and high-energy cutoff E max consistent with in situ data. By accounting for the injection physics determined by kinetic simulations, we confirm that the charge-to-mass ratio scales as E max ∝ (Q/M) α with α ∼ 0.8–1.1, approximately consistent with PSP measurements in the broader range α ∼ 0.6–1.7. In the limit where ions are injected at the same energy per nucleon, α can be as low as ∼0.3. These findings further support the role of magnetic reconnection in producing high-energy heavy ions at the HCS.

Murtas, Giulia [West Virginia Univ., Morgantown, W↗
DOE OSTI2022

Polaronic Conductivity in Cr 2 Ge 2 Te 6 Single Crystals

We report that intrinsic 2D ferromagnetic semiconductors are an important class of materials for spin-charge conversion applications. Cr 2 Ge 2 Te 6 retains long-range magnetic order in the bilayer at cryogenic temperatures and shows complex magnetic interactions with considerable magnetic anisotropy. Here, a series of structural, magnetic, X-ray scattering, electronic, thermal transport and first-principles calculation studies are performed, which reveal that localized electronic charge carriers in Cr 2 Ge 2 Te 6 are dressed by the surrounding lattice and are involved in polaronic transport via hopping that is observed via magnetocrystalline anisotropy. This opens the possibility for manipulation of charge transport in Cr 2 Ge 2 Te 6 —based devices by electron–phonon- and spin–orbit coupling-based tailoring of polaron properties.

2D materials↗
DOE OSTI2023

Interplay between magnetism and band topology in the kagome magnets R Mn 6 Sn 6

Kagome-lattice magnets R Mn 6 Sn 6 recently emerged as a new platform to exploit the interplay between magnetism and topological electronic states. Some of the most exciting features of this family are the dramatic dependence of the easy magnetization direction on the rare-earth specie, despite other magnetic and electronic properties being essentially unchanged, and the kagome geometry of the Mn planes that in principle can generate flat bands and Dirac points; gapping of the Dirac points by spin-orbit coupling has been suggested recently to be responsible for the observed anomalous Hall response in the member TbMn 6 Sn 6 . In this paper, we address both issues with ab initio calculations. We have discovered the significant role played by higher-order crystal-field parameters and rare-earth magnetic anisotropy constants in these systems. Further, we demonstrate that the microscopic origin of rare-earth magnetic anisotropy can also be quantified and understood at various levels: ab initio, phenomenological, and analytical. In particular, using a simple and physically transparent analytical model based on perturbation theory, we are able to explain, with full quantitative agreement, the evolution of rare-earth magnetic anisotropy across the series. We analyze in detail the topological properties of Mn-dominated bands and demonstrate how they emerge from the multiorbital planar kagome model. We further show that, despite this fact, most of the topological features at the Brillouin zone corner K are strongly 3D and therefore cannot explain the observed quasi-2D anomalous Hall effect, while the most pronounced quasi-2D dispersion are too far removed from the Fermi level. By employing self-consistent calculations with ab initio many-body approaches, we demonstrate that the exchange-correlation effects beyond the density functional theory for itinerant Mn- d electrons do not significantly alter the obtained electronic and magnetic structure. Therefore, we conclude that, contrary to previous claims, the most pronounced 2D kagome-derived topological band features bear little relevance to transport in RMn 6 Sn 6 , albeit they may possibly be brought to focus by electron or hole doping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

One Structure, Two Elements—LuGe 2 Superconductor vs Ordinary Metallic Conductor LuSn 2 . A Case Study on How Site-Selective Germanium for Tin Atom Substitution Leads to Modulating of the Charge Distribution

The substitution of chemically similar elements in a given crystal structure is an effective way to enhance physical properties, but the understanding on such improvements is usually impeded because the substitutions are random, and the roles of the different atoms cannot be distinguished by crystallographic symmetry. Herein, we provide a detailed crystallographic analysis and property measurements for the continuous solid solutions LuGe x Sn 2–x (0 < x < 2). The results show that there is no apparent change of the global symmetry, with the end-members LuGe 2 and LuSn 2 , as well as the intermediate LuGe x Sn 2–x compositions adopting the ZrSi 2 type structure (space group Cmcm, Pearson index oC12). Yet, the refinements of the crystal structures from single-crystal X-ray diffraction data show that Ge–Sn atom substitutions are not random, but occur preferentially at the zig-zag chain. The patterned distribution of two group 14 elements leads to a significant variation in chemical bonding and charge ordering within the other structural fragment, the 2D square nets, thereby resulting in tuned electron transport. The enhancement is greater than the typical Bloch-Gruneisen model, and more akin to the parallel-resistor model. Magnetization measurements on single crystals show bulk superconductivity in all LuGe x Sn 2–x samples with shielding fractions as high as 90%. Specific heat data confirm the effect to originate from residual metallic tin in the material, indicating that Sn atom substitutions in the 2D square nets cause disruptions of the hypervalent bonding and local anisotropy, which ultimately leads to vanishing of the superconducting state in the end-member LuGe 2 . This work sheds light on how the complexity in chemical interactions by two different carbon congeners leads to changes in the physical properties and how they can be correlated with the induced charge distribution. Furthermore, these studies also provide a general approach to modulation of charge density, and thus, of emerging physical properties in other classes of intermetallic systems based on the main-group elements of groups 13 to 15.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1999

Dynamics of Single Chains of Suspended Ferrofluid Particles

We present an experimental study of the dynamics of isolated chains made of super-paramagnetic particles under the influence of a magnetic field. The motivation of this work is to understand if the chain fluctuations exist and, if it does, how does the fluctuation affect chain aggregation. We find that single chains strongly fluctuate and that the characteristic frequency of their fluctuations is inversely proportional to the magnetic field strength. The higher the field the lower the characteristic frequency of the chain fluctuations. In the high magnetic field limit, chains behave like rigid rods without any internal motions. In this work, we used ferrofluid particles suspended in water. These particles do not have any intrinsic magnetization. Once a magnetic field is applied, a dipole moment is induced in each particle, proportional to the magnetic field. A dipolar magnetic interaction then occurs between particles. If dipole-dipole magnetic energy is higher than the thermal energy, the result is a structure change inside the dipolar fluid. The ratio of these two energies is expressed by a coupling constant lambda as: lambda = (pi(a(exp 3))(chi(exp 2))(mu(sub 0))(H(sub 0))(exp 2))/18kT Where a is the particle radius, mu(sub 0) is the vacuum magnetic permeability, H(sub 0) the applied magnetic field, k the Boltzmann constant and T the absolute temperature. If lambda > 1, magnetic particles form chains along the field direction. The lateral coalescence of several chains may form bigger aggregates especially if the particle volume fraction is high. While many studies and applications deal with the rheological properties and the structural changes of these dipolar fluids, this work focuses on the understanding of the chain dynamics. In order to probe the chain dynamics, we used dynamic light scattering (DLS) in self-beating mode as our experimental technique. The experimental geometry is such that the scattering plane is perpendicular to the magnetic field. Therefore, only motions in this plane are probed. A very dilute sample of a ferrofluid emulsion with a particle volume fraction of 10(exp -5) is used in this experiment. We chose such a low volume fraction to avoid multiple light scattering as well as lateral chain-chain aggregation. DLS measures the dynamic structure factor S(q,t) of the sample (q is the scattering wave vector, t is the time). In the absence of the magnetic field, identical particles of ferrofluid droplets are randomly distributed and S(q,t) reduces to exp(-q(exp 2)2D(sub 0)t). D(sub 0)=(kT/(6(pi)(eta)(a)) is the diffusion coefficient of Brownian particles (where Xi = (6(pi)(eta)(a)) is the Stokes frictional coefficient of a spherical particle in a fluid of viscosity eta). If interactions or polydispersity can not be ignored, an effective diffusion coefficient is introduced. Formally, D(sub eff) is defined as: D(sub eff) = - q(exp -2) partial derivative of (ln(S(q,t)) with respect to time, as t goes to 0. D(sub eff) reduces to D(sub 0) if no interactions and only a few particles size are present. Therefore, we can use DLS to measure particle size. The particle radius was found to be a=0.23 mu m with 7% of polydispersity. In this case, if we vary the scattering angle theta (and so q) we do not have any change in the measured diffusion coefficient: it is q-independent. When a magnetic field is applied, particles aggregate into chains if lambda > 1. We first studied the kinetics of the chain formation when lambda = 406. At a fixed scattering angle, we measured diffusion coefficient D(sub eff) as a function of time. Experimentally, we find that D(sub eff) decreases monotonously with time. Physically, this means that chains are becoming longer and longer. Since we are only sensitive to motions in the scattering plane and since chains have their main axis perpendicular to this plane, the measured diffusion coefficient is the trans-verse diffusion coefficient. We can relate D(sub eff) to the mean number of particles per chain N(t) at a given time and to the diffusion coefficient of an isolated particle D(sub 0) as D(sub eff)=f(N(t))D(sub 0). Since f(N) is known from other recent work, N can be expressed as a function of the time. We found a square root dependency: N(t) proportional to the square root of t. As expected for very low volume fraction, this behavior is characteristic of a diffusion-limited aggregation as suggested by several authors and by our previous work. In this study, we focus on the dependence of the effective diffusion coefficient on the scattering angle and the magnetic field strength. After the magnetic field is applied (lambda = 406) for a long time, typically 6 hours, kinetics of chain formation becomes very slow. Chain size does not vary much over the next hour period. Thus, we can perform different interesting experiments. First, at a fixed magnetic field, we measure the effective diffusion coefficient as a function of the scattering angle (from 5 to 130 deg). Our results show that the measured diffusion coefficient increases linearly with the scattering angle: D(sub eff) proportional to q. If we do the same experiment for different lambda values, D(sub eff) depends on lambda as D(sub eff) proportional to lambda(exp -1/2). We also find for different lambda values that the same asymptotic D(sub eff) value is obtained when q approaches zero. The angle dependency of D(sub eff) suggests that an additional motion exists besides chain drifting. Chain size is constant during experiment, which was verified by measuring the same diffusion coefficient at the beginning and at the end of the angle switching. If chains are rigid, D(sub eff) is independent of q. Therefore, we found that D(sub eff) not only measures the motion of the entire chain but also its internal fluctuations. These internal motions are the fluctuations of the particles in the chain. To understand the q dependency of D(sub eff), let us look at the probing length used. In our study, the characteristic length scale probed is l=2pi/q which is in the range of 0.9<l/a<20. When l is much larger than the particle radius (l/a going to infinity) we are mainly sensitive to the center of mass diffusion of the chain. D(sub eff) is then the diffusion of the entire chain and depends only on N but not on q and lambda. The value D(sub eff) allows us to obtain the number of particles per chain N. In the opposite limit (i.e. l/a < 1), we are sensitive to motions on the size of individual particles. The main contributions to the measured diffusion coefficient come from internal motions of the chains (i.e. particles' fluctuations inside the chain). We investigated also the effect of the chain size on D(sub eff). For the same value of the magnetic interaction lambda and different chain sizes, we found that the slope of D(sub eff) versus q decreases when N increases as a power law D(sub eff) proportional to N(exp -0.7). This is an important behavior because this means that the longer the chain the slower its internal fluctuations besides the whole chain motion.

Cutillas, S.↗