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Spontaneous magnon decays from nonrelativistic time-reversal symmetry breaking in altermagnets

Quasiparticles are central to condensed matter physics, but their stability can be undermined by quantum many-body interactions. Magnons, i.e., quasiparticles in quantum magnets, are particularly intriguing because their properties are governed by both real and spin space. While crystal symmetries may be low, spin interactions often remain approximately isotropic, limiting spontaneous magnon decay. Textbook wisdom holds that collinear Heisenberg magnets follow a dichotomy: ferromagnets host stable magnons, while antiferromagnetic magnons may decay depending on dispersion curvature. Up to now, relativistic spin-orbit coupling and noncollinear order that connect spin space to real space were shown to introduce more complex magnon instability mechanisms. Here, we show that even in nonrelativistic isotropic collinear systems, this conventional dichotomy is disrupted in altermagnets. Altermagnets, a newly identified class of collinear magnets, exhibit compensated spin order with nonrelativistic time-reversal symmetry breaking and even-parity band splitting. Using kinematic analysis, nonlinear spin-wave theory, and quantum simulations, we reveal that even weak band splitting opens a decay phase space, driving quasiparticle breakdown. Additionally, 𝑑-wave altermagnets form a rare “island of stability” at the Brillouin-zone center. Furthermore, our findings establish a quasiparticle stability trichotomy in collinear Heisenberg magnets and position altermagnets as a promising platform for unconventional spin dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Bosonization in three spatial dimensions and a 2-form gauge theory

We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form Z 2 gauge theory with an unusual Gauss law. An important property of this map is that it preserves the locality of the Hamiltonian. Here, the map depends explicitly on the choice of a spin structure of the spatial manifold. We give examples of 3d bosonic systems dual to free fermions. We also describe the corresponding Euclidean lattice models, which is analogous to the Steenrod square term in (3+1)D [compared to the Chern-Simon term in (2+1)D].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Solar System Escape Architecture for Revolutionary Science

Our most distance spacecraft, Voyager 1 and Voyager 2, recently reached the boundary of the solar system known as the Heliopause. Beyond this boundary lies interstellar space, and, at tremendous distance, the stars. The Voyager spacecraft have shown us that the Heliopause is a dynamic, rapidly changing environment, varying greatly as the fields and effects emanating from the sun are met by a host of forces pushing in from our nearby galactic neighborhood. This is the region we aim to explore. Specifically we aim to develop a mission architecture and spacecraft concept capable of reaching the Heliopause (approximately100 AU (Astronomical Units)) region in multiple directions of interest, with a variety of scientific instrument suites, within a reasonable timeframe (about 15 years.) This report details our Phase 1 work including science goal definition, trajectory planning, technology research, mission planning, instrument selection, spacecraft design, and more. We present an architecture employing a 250-meter by 250-meter solar sail with a 175 kilogram spacecraft. This spacecraft could carry a variety of instrument suites depending on the destination, time, and other factors. The spin-stabilized spacecraft would powered by a small radioisotope power system (about 20 watts), makes use of an optical communication system, and carries 3 extensible booms for instrument accommodation as visible in the sketch and rendering below. We conclude that it would be reasonable to implement the architecture described herein in the 2020-2030 timeframe based on likely near-term technological and material advances. We are confident that cruise times of around 15 years could be achieved to science-rich destinations. This report details the approach we used to come to these conclusions and identifies some of the steps along the way. We utilized a variety of methodologies involving our full capability at JPL (Jet Propulsion Laboratory) - from small point studies to large collaborative engineering processes. This paper also describes potential industry partnerships and costing information, and includes the methods used to account for our project’s significant deviation from any prior mission in the NASA costing tool database. Outreach and public engagement is an important part of NASA activities. We engaged in several different forms of this outreach and describe them in this report. We conclude with some open questions and a summary of activities we hope to engage in with Phase 2 funding. The entire team would like to thank the NIAC (NASA Innovative Advanced Concepts) program for the opportunity to investigate this fascinating and challenging concept. The Voyager program gives us tantalizing clues as to the nature and behavior of the Heliopause – the boundary between the sun’s influence and the interstellar medium. This information comes from forty-year old instruments designed to study the outer planets. A targeted Heliopause investigation would give insight into the formation of the solar system, the role of the sun in the local interstellar neighborhood, and contribute to human exploration planning by helping to predict periods of low galactic cosmic ray (GCR) penetration into the inner solar system.

Spacecraft↗

Precision X-ray Timing of RX J0806.3+1527 with CHANDRA: Evidence for Gravitational Radiation from an Ultracompact Binary

RX J0806.3+1527 is a candidate double degenerate binary with possibly the shortest known orbital period. The source shows an $\approx 100 \%$ X-ray intensity modulation at the putative orbital frequency of 3.11 mHz (321.5 s). If the system is a detached, ultracompact binary gravitational radiation should drive spin-up with a magnitude of $\dot\nu \sim 10(exp -16)$ Hi s$(exp -l}$. Efforts to constrain the X-ray frequency evolution to date have met with mixed success, principally due to the sparseness of earlier observations. Here we describe the results of the first phase coherent X-ray monitoring campaign on RX J0806.3+1527 with {\it Chandra) . We obtained a total of 70 ksec of exposure in 6 epochs logarithmically spaced over 320 days. With these data we conclusively show that the X-ray frequency is increasing at a rate of $3.77 \pm\ 0.8 \times l0(exp -16)$ Hz s$(exp -l)$. Using the ephemeris derived from the new data we are able to phase up all the earlier {\it Chandra) and ROSAT data and show they are consistent with a constant $\dot\nu = 3.63 \pm 0.06 \times 10(exp -16)$ Hz s$(exp -1)s over the past decade. This value appears consistent with that recently derived by Israel et al. largely from monitoring of the optical modulation, and is in rough agreement with the solutions reported initially by Hakala et al., based on ground-based optical observations. The large and stable $\dot\nu$ over a decade is consistent with gravitational radiation losses driving the evolution. An intermediate polar (IP) scenario where the observed X-ray period is the spin period of an accreting white dwarf appears less tenable because the observed $\dot\nu$ requires an $\dot m \approx 2 \times 10(exp -8)$ $M-{\odot)$ yr$(exp -l)$, that is much larger than that inferred from the observed X-ray luminosity (although this depends on the uncertain distance and bolometric corrections), and it is difficult to drive such a high $\dot m$ in a binary system with parameters consistent with all the multiwavelength data. If the ultracompact scenario is

Strohmayer, Tod↗

Electron Spin Polarization and Rectification Driven by Chiral Perylene Diimide-Based Nanodonuts

The chirality-induced spin selectivity (CISS) effect allows thin-film layers of chiral conjugated molecules to function as spin filters at ambient temperature. Through solvent-modulated dropcasting of chiral l- and d-perylene diimide (PDI) monomeric building blocks, two types of aggregate morphologies, nanofibers and nanodonuts, may be realized. Spin-diode behavior is evidenced in the nanodonut structures. Stacked PDI units, which form the conjugated core of these nanostructures, dominate the nanodonut–Au electrode contact; in contrast, the AFM tip contacts largely the high-resistance solubilizing alkyl chains of the chiral monomers that form these nanodonuts. Current–voltage responses of the nanodonuts, measured by magnetic conductive AFM (mC-AFM), demonstrate substantial spin polarizations as well as spin current rectification ratios (>10) that exceed the magnitudes of those determined to date for other chiral nanoscale systems. Furthermore, these results underscore the potential for chiral nanostructures, featuring asymmetric molecular junctions, to enable CISS-based nanoscale spin current rectifiers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Perspective: Magnon-magnon coupling in hybrid magnonics

The internal coupling of magnetic excitations (magnons) with themselves has created a new research sub-field in hybrid magnonics, i.e., magnon-magnon coupling, which focuses on materials discovery and engineering for probing and controlling magnons in a coherent manner. This is enabled by, one, the abundant mechanisms of introducing magnetic interactions, with examples of exchange coupling, dipolar coupling, Ruderman–Kittel–Kasuya–Yosida (RKKY) coupling, and Dzyaloshinskii–Moriya interaction (DMI) coupling, and two, the vast knowledge of how to control magnon band structure, including field and wavelength dependences of frequencies, for determining the degeneracy of magnon modes with different symmetries. In particular, we discuss how magnon-magnon coupling is implemented in various materials systems, with examples of magnetic bilayers, synthetic antiferromagnets, nanomagnetic arrays, layered van der Waals magnets, and (DMI spin-orbit torque materials) in magnetic multilayers. Here, we then introduce new concept of applications for these hybrid magnonic materials systems, with examples of frequency up/down conversion and magnon-exciton coupling, and discuss what properties are desired for achieving those applications.

Materials science↗

Microwave-Free Dynamic Nuclear Polarization via Sudden Thermal Jumps

Dynamic nuclear polarization (DNP) presently stands as the preferred strategy to enhance the sensitivity of nuclear magnetic resonance measurements, but its application relies on the use of high-frequency microwave to manipulate electron spins, an increasingly demanding task as the applied magnetic field grows. Here we investigate the dynamics of a system hosting a polarizing agent formed by two distinct paramagnetic centers near a level anticrossing. We theoretically show that nuclear spins polarize efficiently under a cyclic protocol that combines alternating thermal jumps and radio-frequency pulses connecting hybrid states with opposite nuclear and electronic spin alignment. Central to this process is the difference between the spin-lattice relaxation times of either electron spin species, transiently driving the electronic spin bath out of equilibrium after each thermal jump. Without the need for microwave excitation, this route to enhanced nuclear polarization may prove convenient, particularly if the polarizing agent is designed to feature electronic level anticrossings at high magnetic fields.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Rate of Para-Orthohydrogen Conversion in Cryogenic Vortex Tube

Raising efficiency of the cooling process for cryogenic hydrogen and minimizing hydrogen boil-off during storage and transportation of liquid hydrogen are critically important factors for widening implementation of hydrogen-based clean energy systems. One novel approach involves utilization of relatively simple catalyzed vortex tubes, where hydrogen in the primarily para- nuclear spin isomer form is converted into the ortho- form while consuming a significant amount of heat. To design such systems effectively, better understanding is required about catalyst-assisted para-orthohydrogen conversion rates in high-speed vortical flows. In this study, a computational fluid dynamics simulation has been set up to model an experimental system with cryogenic hydrogen vortex tubes. Mesh-verification and a validation study has been conducted first for a non-catalyzed tube. Then, the rate coefficient of the para-orthohydrogen conversion of cryogenic hydrogen has been determined by matching numerical results with experimental data available for a catalyzed vortex tube. Furthermore, the presented information can help design and optimize cryogenic hydrogen cooling within vortex tubes.

08 HYDROGEN↗

Proximity-induced magnetism and the enhancement of damping in ferromagnetic/heavy metal systems

The relationship between proximity-induced magnetism (PIM) at the heavy metal/ferromagnet interface and spin-transport across such interfaces has generated significant debate. To investigate the link between the two, element specific x-ray magnetic circular dichroism and ferromagnetic resonance measurements were made on the same CoFe/Au/Pt and NiFe/Au/Pt thin film samples with varying Au thickness, with complementary SIMS analysis, which shows evidence of Ni diffusion from NiFe into the Pt. An approximately linear relationship is observed between the magnitude of Pt PIM and magnitude of damping enhancement in both systems. The results demonstrate that electronic hybridization of the heavy metal and ferromagnet is required for a full understanding of damping enhancement and interfacial spintransport for spintronic devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Room-Temperature, Current-Induced Magnetization Self-Switching in A Van Der Waals Ferromagnet

2D layered materials with broken inversion symmetry are being extensively pursued as spin source layers to realize high-efficiency magnetic switching. Such low-symmetry layered systems are, however, scarce. In addition, most layered magnets with perpendicular magnetic anisotropy show a low Curie temperature. Here, in this study, the experimental observation of spin–orbit torque magnetization self-switching at room temperature in a layered polar ferromagnetic metal, Fe 2.5 Co 2.5 GeTe 2 is reported. The spin–orbit torque is generated from the broken inversion symmetry along the c-axis of the crystal. These results provide a direct pathway toward applicable 2D spintronic devices.

36 MATERIALS SCIENCE↗

UltraSail - Ultra-Lightweight Solar Sail Concept

UltraSail is a next-generation high-risk, high-payoff sail system for the launch, deployment, stabilization and control of very large (sq km class) solar sails enabling high payload mass fractions for high (Delta)V. Ultrasail is an innovative, non-traditional approach to propulsion technology achieved by combining propulsion and control systems developed for formation-flying micro-satellites with an innovative solar sail architecture to achieve controllable sail areas approaching 1 sq km, sail subsystem area densities approaching 1 g/sq m, and thrust levels many times those of ion thrusters used for comparable deep space missions. Ultrasail can achieve outer planetary rendezvous, a deep space capability now reserved for high-mass nuclear and chemical systems. One of the primary innovations is the near-elimination of sail supporting structures by attaching each blade tip to a formation-flying micro-satellite which deploys the sail, and then articulates the sail to provide attitude control, including spin stabilization and precession of the spin axis. These tip micro-satellites are controlled by 3-axis micro-thruster propulsion and an on-board metrology system. It is shown that an optimum spin rate exists which maximizes payload mass.

Burton, Rodney L.↗

Magnetization orientation-dependent Shubnikov-de Haas oscillations in ferromagnetic Weyl semimetal Co 3 Sn 2 S 2

We report a study of Shubnikov–de Haas oscillations in high-quality single crystals of ferromagnetic Weyl semimetal Co 3 Sn 2 S 2 . The Fermi surfaces resolved in our experiments are three-dimensional and reflect an underlying trigonal crystallographic symmetry. Combined with density functional calculations, we identify that multiple Fermi surfaces in the system—of both electron and hole nature—arise from the energy dispersion of the (spin-orbit gapped) mirror-protected nodal rings. We observe an evolution of the Fermi surfaces with in-plane magnetic fields, in contrast to field perpendicular to the kagome lattice planes, which has little effect. Viewed alongside the easy-axis anisotropy of the system, our observation reveals an evolution of the electronic structure of Co 3 Sn 2 S 2 —including the Weyl points—with the ferromagnetic moment orientation. Through the case study of Co 3 Sn 2 S 2 , our results provide concrete experimental evidence of an anisotropic interplay via spin-orbit coupling between the magnetic degrees of freedom and electronic band singularities, which has long been expected in semimetallic and metallic magnetic systems.

36 MATERIALS SCIENCE↗

Precision X-ray Timing of RX J0806.3+1527 with CHANDRA: Evidence for Gravitational Radiation from an Ultracompact Binary

RX J0806.3+1527 is a candidate double degenerate binary with possibly the shortest known orbital period. The source shows an approximately equal to 100% X-ray intensity modulation at the putative orbital frequency of 3.11 mHz (321.5 s). If the system is a detached, ultracompact binary gravitational radiation should drive spin-up with a magnitude of nu(sup dot) approximately 10(exp -16) Hz per second. Efforts to constrain the X-ray frequency evolution to date have met with mixed success, principally due to the sparseness of earlier observations. Here we describe the results of the first phase coherent X-ray monitoring campaign on RX J0806.3+1527 with Chandra. We obtained a total of 70 ksec of exposure in 6 epochs logarithmically spaced over 320 days. With these data we conclusively show that the X-ray frequency is increasing at a rate of 3.77 plus or minus 0.8 x 10(exp -16) Hz per second. Using the ephemeris derived from the new data we are able to phase up all the earlier Chandra and ROSAT data and show they are consistent with a constant nu(sup dot) = 3.63 plus or minus 0.06 x 10(exp -16) Hz per second over the past decade. This value appears consistent with that recently derived by Israel et al. largely from monitoring of the optical modulation, and is in rough agreement with the solutions reported initially by Hakala et al., based on ground-based optical observations. The large and stable nu(sup dot) over a decade is consistent with gravitational radiation losses driving the evolution. An intermediate polar (IP) scenario where the observed X-ray period is the spin period of an accreting white dwarf appears less tenable because the observed nu(sup dot) requires an m(sup dot) approximately equal to 4 x 10 (exp -8) solar mass yr(sup -l), that is much larger than that inferred from the observed X-ray luminosity (although this depends on the uncertain distance and bolometric corrections), and it is difficult to drive such a high m(sup dot) in a binary system with parameters consistent with all the multiwavelength data. If the ultracompact scenario is correct, then the X-ray flux cannot be powered by stable accretion which would drive the components apart, suggesting a new type of energy source (perhaps electromagnetic) may power the X-ray flux.

Strohymayer, Tod E.↗

Development and Demonstration of Active Noise Control Concepts

This report details design methods for and feasibility of an Active Noise Control (ANC) system using flush-wall-mounted sensors and actuators to reduce turbofan engine rotor-stator interaction noise. ANC concepts capable of suppressing discrete-tone spinning modes containing several cut-on radial mode were identified, developed analytically, and evaluated. Separate ANC systems that suppressed at least three radial modes in a cylindrical inlet duct and three radial modes in an exhaust annulus were developed. These designs resulted in inlet duct and exhaust duct tests that were performed at NASA on the 4-ft ANC Fan in the NASA Glenn AAPL facility. Effective suppression of 2-BPF spinning mode m = 2 tone noise was achieved over a range of fan speeds 1800 to 2450 rpm, where up to 4 radials were present. In the inlet duct, up to 12 dB reduction was obtained for 3 radial modes, and up to 4 dB was obtained with 4 radial modes. In the exhaust duct, up to 15 dB PWL reduction was obtained with either two or three radial modes present. Thus, the ability to suppress multiple radial modes for tones in both the inlet and exhaust ducts has been successfully demonstrated. Implications of ANC system design requirements on installation and system integration issues for ANC systems capable of suppressing higher order radial mode content when applied to a 767 using twin CF6 engines were evaluated analytically. The analytical results indicated an ANC system must be part of an integrated design to be effective.

Kraft, R.↗

Integrated Harsh Environment Gas / Temperature Wireless Microwave Acoustic Sensor System for Fossil Energy Applications

There is a significant need for sensors capable of detecting gases, such as H 2 , O 2 , NO x , SO x within harsh environments encountered in power plants, industrial manufacturing, oil and gas exploration, and aerospace applications. This project successfully demonstrated the use of wireless microwave acoustic sensor technology for the detection of gases (H 2 or O 2 ) from ambient temperatures up to 650°C. The work focused on langasite (LGS) based surface acoustic wave resonator (SAWR) sensors as the harsh-environment sensor platform and explored multiple combinations of high-temperature thin films and device structures which were used to increase the sensor platform stability and detection capability at temperatures in the operational range of 150°C to 700°C. Specific material configurations that were investigated include: yttria-stabilized-zirconia (YSZ) decorated with Pt nanoparticles, atomic layer deposited (ALD) Al 2 O 3 , palladium, and Pt/Al 2 O 3 co-deposited electrode alloys. Through the deposition of YSZ at temperatures as high as 850°C and the use of graded alloy concentrations of Pt in the fabrication of the Pt/Al 2 O 3 electrode structures, film stress problems were mitigated, and sensor operation and stability achieved. To test and evaluate SAWR sensor performance for the detection of H 2 and O 2 under the influence of temperature variations, a comprehensive gas sensor control system and test apparatus was created to operate within a laboratory box furnace-controlled environment. In addition to the advancement in thin film materials through the deposition and fabrication techniques mentioned above, the work characterized the performance of sensors containing these films in the presence of oxidizing and reducing gases between 25°C and 700°C. In particular, the work revealed that the exposure of the SAWR sensor surfaces to oxidizing environments significantly improve the sensor response to H 2 , whereas the exposure of the sensor to reducing environments at high temperatures (≈ 500°C) renders the sensor irresponsive to H 2 , requiring sensor surface treatment at high temperatures (above 500°C) to recover the responsiveness to H 2 . The SAWR sensors have been also tested for wireless operation and array operation using multiple orientations to resolve the detection of gases under temperature variations. The work developed at the University of Maine was aided by a collaboration with the NETL Research and Innovation Center, Pittsburgh, PA, where thin film materials and device structures fabricated at UMaine were tested and characterized using NETL gas reactors and surface analysis techniques. SAWR sensors fabricated at UMaine were exposed multiple times to temperatures up to 700°C and H 2 concentrations up to 100% in the NETL facilities to measure the sensor performance. Environetix Technologies Corporation, a UMaine harsh-environment sensor spin-off company, also provided support and assistance in sensor system testing and implementation. The sensor small size and configuration allows flexible sensor placement and embedding of multiple sensor arrays into a variety of components within power systems and other aerospace or industrial settings that need to be interrogated wirelessly. The SAW platform is an attractive option for high-temperature harsh-environment gas sensing applications due to its inherent features, namely small size, capability of battery-free and wireless operation, and cost effective scale production using well-established production techniques from the semiconductor industry. The research findings achieved in this work, particularly advances regarding the fabrication and performance of the SAWR gas sensor platform, can be adapted and transferred to industrial power plants and other harsh environments.

01 COAL, LIGNITE, AND PEAT↗

Fuel Distribution Estimate via Spin Period to Precession Period Ratio for the Advanced Composition Explorer

The spin period to precession period ratio of a non-axisymmetric spin-stabilized spacecraft, the Advanced Composition Explorer (ACE), was used to estimate the remaining mass and distribution of fuel within its propulsion system. This analysis was undertaken once telemetry suggested that two of the four fuel tanks had no propellant remaining, contrary to pre-launch expectations of the propulsion system performance. Numerical integration of possible fuel distributions was used to calculate moments of inertia for the spinning spacecraft. A Fast Fourier Transform (FFT) of output from a dynamics simulation was employed to relate calculated moments of inertia to spin and precession periods. The resulting modeled ratios were compared to the actual spin period to precession period ratio derived from the effect of post-maneuver nutation angle on sun sensor measurements. A Monte Carlo search was performed to tune free parameters using the observed spin period to precession period ratio over the life of the mission. This novel analysis of spin and precession periods indicates that at the time of launch, propellant was distributed unevenly between the two pairs of fuel tanks, with one pair having approximately 20% more propellant than the other pair. Furthermore, it indicates the pair of the tanks with less fuel expelled all of its propellant by 2014 and that approximately 46 kg of propellant remains in the other two tanks, an amount that closely matches the operational fuel accounting estimate. Keywords: Fuel Distribution, Moments of Inertia, Precession, Spin, Nutation

Moment of Inertia↗

MAP Attitude Control System Design and Analysis

The Microwave Anisotropy Probe (MAP) is a follow-on to the Differential Microwave Radiometer (DMR) instrument on the Cosmic Background Explorer (COBE) spacecraft. The MAP spacecraft will perform its mission in a Lissajous orbit around the Earth-Sun L(sub 2) Lagrange point to suppress potential instrument disturbances. To make a full-sky map of cosmic microwave background fluctuations, a combination fast spin and slow precession motion will be used. MAP requires a propulsion system to reach L(sub 2), to unload system momentum, and to perform stationkeeping maneuvers once at L(sub 2). A minimum hardware, power and thermal safe control mode must also be provided. Sufficient attitude knowledge must be provided to yield instrument pointing to a standard deviation of 1.8 arc-minutes. The short development time and tight budgets require a new way of designing, simulating, and analyzing the Attitude Control System (ACS). This paper presents the design and analysis of the control system to meet these requirements.

Andrews, S. F.↗

Altermagnetism, kagome flat band, and Weyl fermion states in magnetically intercalated transition metal dichalcogenides

Altermagnetic (AM) compounds have recently emerged as a promising platform for realizing unconventional quantum phases, enabled by their unique spin-split band structure at zero net magnetization. Here, we present a first-principles investigation of magnetically intercalated transition metal dichalcogenides (TMDs) of the form XY 4 Z 8 (X = Mn, Fe, Co, Ni, Cr, or V; Y = Nb or Ta; and Z = Se or S), identifying a subset of new versatile AM candidates. Our results establish a systematic correlation between interatomic geometry, quantified by the ratio of interlayer to intralayer spacing, and the magnetic ground states. Systems with A-type antiferromagnetic order exhibit momentum-dependent spin splitting consistent with AM behavior. The combination of the AM spin-splitting and the spin-orbit coupling leads to the emergence of Weyl nodes together with the corresponding topological Fermi arc surface states. Moreover, we identify flat bands near the Fermi level that originate from the intercalant-induced formation of an effective kagome-like sublattice in the TMD layer. These results collectively establish magnetically intercalated TMDs as a promising platform for engineering altermagnetism, flat bands, and Weyl fermions within a single material family, facilitating the development of topological and spintronic applications.

36 MATERIALS SCIENCE↗