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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Multiphase magnetism in Yb 2 Ti 2 O 7

We use neutron scattering to show that ferromagnetism and antiferromagnetism coexist in the low T state of the pyrochlore quantum magnet Yb 2 Ti 2 O 7 . While magnetic Bragg peaks evidence long-range static ferromagnetic order, inelastic scattering shows that short-range correlated antiferromagnetism is also present. Small-angle neutron scattering provides direct evidence for mesoscale magnetic structure that we associate with metastable antiferromagnetism. Classical Monte Carlo simulations based on exchange interactions inferred from ⟨ 111 ⟩ -oriented high-field spin wave measurements confirm that antiferromagnetism is metastable within the otherwise ferromagnetic ground state. The apparent lack of coherent spin wave excitations and strong sensitivity to quenched disorder characterizing Yb 2 Ti 2 O 7 is a consequence of this multiphase magnetism.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Flat-band tuning and emergent itinerant magnetism in Sr(Co 1− x Pd x ) 2 As 2

The interplay between magnetism and flat-band (FB) instability is a central theme in quantum materials research. A striking example is the emergence of magnetic order in a nominally nonmagnetic compound when a flat band is tuned near the Fermi energy (E F ). Here, in this study, we investigate this phenomenon in the Pauli paramagnet SrCo 2 As 2 , where an FB associated with Co e g orbitals lies close to E F . Remarkably, a minute substitution of the nonmagnetic element Pd onto the Co site (~2%) induces antiferromagnetic order with a transition temperature as high as T N = 25 K. Temperature- and magnetic-field-dependent magnetic and transport measurements, complemented by zero-field neutron diffraction, reveal a helical magnetic order for x ≤ 0.10 in Sr(Co 1−x Pd x ) 2 As 2 , transitioning to a complex ferromagnetic state at higher Pd concentrations. Spectroscopic evidence and theoretical band structure calculations demonstrate that electron doping shifts the flat band closer to E F , significantly enhancing the Stoner parameter. This enhancement drives a strong ferromagnetic instability, leading to helical magnetic ordering dominated by in-plane ferromagnetic interactions. The emergence of robust magnetic ordering through substitution with nonmagnetic elements is a unique phenomenon that underscores the pivotal role of flat-band instability in tuning magnetism in itinerant systems.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Computational discovery of two-dimensional rare-earth iodides: promising ferrovalley materials for valleytronics

Two-dimensional Ferrovalley materials with intrinsic valley polarization are rare but highly promising for valley-based nonvolatile random access memory and valley filter devices. These ferromagnetic materials exhibit valleys at or near the Fermi level with intrinsic magnetism. The strong coupling between magnetism and spin–orbit coupling induces intrinsic valley polarization. Using Kinetically Limited Minimization, an unconstrained crystal structure prediction algorithm, and prototype sampling based on first-principles calculations, we have discovered new Ferrovalley materials, rare-earth iodides RI 2 , where R is a rare-earth element belonging to Sc, Y, or La-Lu, and I is Iodine. The rare-earth iodides are layered and demonstrate either 2H, 1T, or 1T d phase as the ground state in bulk, analogous to transition metal dichalcogenides (TMDCs). The calculated exfoliation energy of monolayers (MLs) is comparable to that of graphene and TMDCs, suggesting possible experimental synthesis. The MLs in the 2H phase exhibit ferromagnetism due to unpaired electrons in d and f orbitals. Throughout the rare-earth series, d bands have valley polarization at K and $\overline{K}$ points in the Brillouin zone in the vicinity of the Fermi level. Large intrinsic valley polarization in the range of 15–143 meV without external stimuli is observed in these Ferrovalley materials, which can be enhanced further by applying an in-plane bi-axial strain. These valleys can selectively be probed and manipulated for information storage and processing, potentially offering superior performance beyond conventional electronics and spintronics. Here we further show that the 2H ferromagnetic phase of RI 2 MLs possesses non-zero Berry curvature and exhibits anomalous valley Hall effect with considerable anomalous Hall conductivity. Our work will incite exploratory synthesis of the predicted Ferrovalley materials and their application in valleytronics and beyond.

2D materials↗
DOE OSTI2026

Probing Quantum Anomalous Hall States in Twisted Bilayer WSe 2 via Attractive Polaron Spectroscopy

Moiré superlattices in semiconductors exhibit a rich variety of interaction-induced topological states, including quantum anomalous Hall (QAH) effects. A recent study hinted that twisted WSe 2 homobilayer (tWSe 2 ) could host a QAH state but lacked direct evidence of ferromagnetism, a key hallmark of this phase. Here, we report the first direct evidence of QAH states in tWSe 2 with spontaneous ferromagnetism. Specifically, we employ polarization-resolved attractive polaron spectroscopy on a dual-gated, 2° tWSe 2 and observe direct signatures of spontaneous time-reversal symmetry breaking at hole filling 𝜈 = 1. Together with a Chern number (𝐶) measurement via Streda formula analysis, we identify this magnetized state as a topological state, characterized by 𝐶 = 1. Furthermore, we demonstrate that these topological and magnetic properties are tunable via a finite displacement field, between a QAH ferromagnetic state and an antiferromagnetic state. Our findings position tWSe 2 as a highly versatile, stable, and optically addressable platform for investigating topological order and strong correlations in two-dimensional landscapes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2026

Spin reorientations in structurally metastable, disordered, and hexagonal Cr 7 ⁢Te 8

Vapor deposited two-dimensional Cr 7 ⁢Te 8 displays unusual temperature dependent Hall effect properties, including a room-temperature anomalous Hall effect, sign reversals of the Hall resistivity on cooling, and a peak in the Hall resistivity at low temperatures. The two-dimensional Cr 7⁢ Te 8 heterostructures that form the basis of these measurements are hexagonal in structure. We study the magnetic and structural properties of bulk Cr 7 ⁢Te 8 synthesized by quenching from 1000⁢°C with the goal of relating the magnetic, structural, and electronic properties. This quenched phase is metastable, hexagonal, and displays different magnetic properties from the slow-cooled and more thermodynamically stable monoclinic phase. High-resolution x-ray diffraction of the quenched hexagonal phase finds a first-order transition to a lower symmetry monoclinic phase on heating above ∼550 K. Magnetic susceptibility measurements of the quenched hexagonal phase reveal ferromagnetic ordering above room temperature, along with the two distinct transitions at ∼220 K and ∼70 K. Through neutron diffraction studies, we find the ∼220 K anomaly is a spin reorientation transition of the ferromagnetically aligned magnetic moments and the ∼70K feature represents a transition from a high-temperature ferromagnet to a low-temperature antiferromagnet. We suggest that these magnetic transitions are related to changes in the unit-cell dimensions and are connected to the temperature-dependent Hall resisitivity studied in two-dimensional heterostructures. This implies a link between structural, magnetic, and electronic properties in the “pseudo” two-dimensional chromium tellurides.

Chemical synthesis↗
DOE OSTI2020

Carrier- and strain-tunable intrinsic magnetism in two-dimensional $MAX_3$ transition metal chalcogenides

Here, we present a density functional theory study of the carrier-density and strain dependence of magnetic order in two-dimensional (2D) $MAX_3$ ($\textit{M}$ = V, Cr, Mn, Fe, Co, Ni; $\textit{A}$ = Si, Ge, Sn; and $\textit{X}$ = S, Se, Te) transition metal trichalcogenides. Our ab initio calculations show that this class of compounds includes wide and narrow gap semiconductors, metals, and half-metals, and that most of these compounds are magnetic. Although antiferromagnetic order is most common, ferromagnetism is predicted in $\textit{M}$SiSe 3 for $\textit{M}$ = Mn and Ni; in $\textit{M}$SiTe 3 for $\textit{M}$ = V and Ni; in MnGeSe 3 ; $\textit{M}$GeTe 3 for $\textit{M}$ = Cr, Mn, and Ni; in FeSnS 3 ; and in MSnTe 3 for $\textit{M}$ = V, Mn, and Fe. Among these compounds CrGeTe 3 , VSnTe 3 , and CrSnTe 3 are ferromagnetic semiconductors. Our calculations suggest that the competition between antiferromagnetic and ferromagnetic order can be substantially altered by strain engineering, and in the semiconductor case also by gating. The associated critical temperatures can be enhanced by means of carrier doping and strains.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Properties of La 0.7 Ca 0.3 MnO 3 under extreme tensile strain

The complex phase diagram of manganites with simultaneously active spin, charge, orbital, and lattice degrees of freedom continues providing surprises. In a recent groundbreaking experiment, membranes of the perovskite manganite La 0.7 Ca 0.3 MnO 3 (LCMO) deposited on a flexible polymer layer were strained up to 8% [S. S. Hong et al., Science 368, 71 (2020)], much more than achieved by regular strain induced by a rigid substrate. By increasing this strain, a metal-insulator transition was reported. Here we reproduce the results of the experiments using Monte Carlo simulations of the two-orbital double-exchange model including Jahn-Teller distortions at hole density x=1/3. The full phase diagram with varying temperature and Jahn-Teller coupling λ is presented. When the bandwidth W of mobile electrons is reduced, thus when the effective Jahn-Teller coupling λ/W is increased, a metal-insulator transition is found in our simulations, between a ferromagnetic metallic state with uniform charge distribution and an insulator with diagonal charge stripes that retains its ferromagnetic character. In between the hole-rich diagonals, staggered orbital order occurs. We also report resistivity and magnetization measurements alongside with spin correlations and charge structure factors. Our overall conclusions are in agreement with the recent experimental and density functional theory results by Hong et al., and we confirm much earlier ground state predictions of striped ferromagnetic order using energy optimization techniques by T. Hotta et al. [Phys. Rev. Lett. 86, 4922 (2001)]. The experimental observation of one of the states predicted by theory suggests that diagonal stripes could be achieved at other hole densities as well, such as x=1/4, if LCMO membranes with that hole doping were subject to similar strains.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Dimensional crossover in spin Hall oscillators

Auto-oscillations of magnetization driven by direct spin current have been previously observed in multiple quasi-zero-dimensional (0D) ferromagnetic systems such as nanomagnets and nanocontacts. Recently, it was shown that pure spin Hall current can excite coherent auto-oscillatory dynamics in quasi-one-dimensional (1D) ferromagnetic nanowires but not in quasi-two-dimensional (2D) ferromagnetic films. Here we study the 1D to 2D dimensional crossover of current-driven magnetization dynamics in wire-based Pt/Ni 80 Fe 20 bilayer spin Hall oscillators via varying the wire width. We find that increasing the wire width results in an increase of the number of excited auto-oscillatory modes accompanied by a decrease of the amplitude and coherence of each mode. We also observe a crossover from a hard to a soft onset of the auto-oscillations with increasing wire width. The amplitude of auto-oscillations rapidly decreases with increasing temperature suggesting that interactions of the phase-coherent auto-oscillatory modes with incoherent thermal magnons play an important role in suppression of the auto-oscillatory dynamics. Our measurements in this work set the upper limit on the dimensions of an individual spin Hall oscillator and elucidate the mechanisms leading to suppression of coherent auto-oscillations with increasing oscillator size.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Magnetoresistance effects in a spin-fermion model for multilayers

Here, we consider a spin-fermion model consisting of free electrons coupled to classical spins where the latter are embedded in a quasi-one-dimensional superlattice structure consisting of spin blocks separated by spinless buffers. Using a spiral ansatz for the spins, we study the effect of the electron mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction on the $\textit{T}$ = 0 ground state of the system. We find that the RKKY interaction can lead to ferromagnetic, antiferromagnetic, or intermediate spiral phases for different system parameters. When the width is much larger than the length of the individual blocks, the spiral phases are suppressed, and the ground state oscillates between ferromagnetic and antiferromagnetic orders as the size of the buffer regions is varied. This is accompanied by a corresponding oscillation in the Drude weight reflecting an increased conductivity in the ferromagnetic state compared to the antiferromagnetic one. These results are reminiscent of classic giant magnetoresistance phenomena observed in a similar geometry of thin sandwiched magnetic and nonmagnetic layers. Our analysis provides a robust framework for understanding the role of the RKKY interaction on the ground-state order and corresponding transport properties of such systems, extending beyond the conventional perturbative regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Electronic structure and topology across T c in the magnetic Weyl semimetal Co 3 Sn 2 S 2

Co 3 Sn 2 S 2 is a magnetic Weyl semimetal, in which ferromagnetic ordering at 177 K is predicted to stabilize Weyl points. We perform temperature and spatial dependent angle--resolved photoemission spectroscopy measurements through the Curie temperature (T c ), which show large band shifts and renormalization concomitant with the onset of magnetism. We argue that Co 3 Sn 2 S 2 evolves from a Mott ferromagnet below T c to a correlated metallic state above T c . To understand the magnetism, we derive a tight-binding model of Co-3d x 2 -y 2 orbitals on the kagome lattice. At the filling obtained by first-principles calculations, this model reproduces the ferromagnetic ground state, and results in the reduction of Coulomb interactions due to cluster effects. Using a disordered local moment simulation, we show how this reduced Hubbard U leads to a collapse of the bands across the magnetic transition, resulting in a correlated state which carries associated characteristic photoemission signatures that are distinct from those of a simple lifting of exchange splitting. Finally, the behavior of topology across T c is discussed in the context of this description of the magnetism.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Evidence for electronic signature of a magnetic transition in the topological magnet HoSbTe

Topological insulators with intrinsic magnetic order are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. To study these systems and their physics, people have proposed a variety of magnetic topological insulator systems, including HoSbTe, an antiferromagnetic weak topological insulator candidate. Here, in this work, we use scanning tunneling microscopy to probe the electronic structure of HoSbTe with antiferromagnetic and ferromagnetic orders that are tuned by applying an external magnetic field. Although around the Fermi energy we find minor differences between the quasiparticle interferences under the ferromagnetic and antiferromagnetic orders, deep inside the valance region, a quasiparticle interference signal emerges with ferromagnetism. This observation is consistent with our first-principles calculations indicating the magnetism-driven transition of the electronic states in this spin-orbit coupled topological magnet.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Coexisting structural disorder and robust spin-polarization in half-metallic FeMnVAl

We report half-metallic ferromagnets (HMFs) are one of the most promising materials in the field of spintronics due to their unique band structure, consisting of one spin subband having metallic characteristics along with another subband with semiconductor-like behavior. In this work, we report the synthesis of a novel quaternary Heusler alloy—FeMnVAl—and we have studied the structural, magnetic, transport, and electronic properties complemented with first-principles calculations. Among different possible structurally ordered arrangements, the optimal structure is identified by theoretical energy minimization. The corresponding spin-polarized band-structure calculations indicate the presence of a half-metallic ferromagnetic ground state. A detailed and careful investigation of the x-ray diffraction data, Mössbauer spectra, and nuclear magnetic resonance spectra suggests the presence of site disorder between the Fe and Mn atoms in the stable ordered structure of the system. The magnetic susceptibility measurement clearly establishes a ferromagnetic-like transition below ~213 K. The Fe Mössbauer spectrometry measurements suggest that only the Mn spins could be responsible for the magnetic order, which is consistent with our theoretical calculation. Surprisingly, the density-functional-theory calculations reveal that the spin-polarization value is almost immunized (92.4% → 90.4%) from the Mn-Fe structural disorder, even when nonmagnetic Fe and moment-carrying Mn sites are entangled inseparably. The robustness of spin polarization and half-metallicity in the studied FeMnVAl compound comprising structural disorder is thus quite interesting and could provide a new direction to investigate and understand the exact role of disorders on spin polarization in this class of materials, beyond the available knowledge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Spin-orbital liquids and insulator-metal transitions on the pyrochlore lattice

The two orbital Hubbard model, with the electrons additionally coupled to a complex magnetic background, arises in the pyrochlore molybdates. The background involves local moments Hund's coupled to the electrons, driving double exchange ferromagnetism, and antiferromagnetic (AF) tendency arising from competing superexchange. The key scales include the Hubbard repulsion and the superexchange, both of which can be tuned in these materials. They control the phase transition from a ferromagnetic metal to a spin glass metal and then to a spin glass (Mott) insulator. We provide a comprehensive description of the ground state of this model using an unrestricted Hartree-Fock scheme implemented via a simulated annealing procedure and establish the metal-insulator transition line for varying Hubbard interaction and superexchange. The electrons see an effective disorder, due to orbital frustration, already in the ferromagnetic phase. The disorder is further enhanced by antiferromagnetic coupling and the resulting magnetic disorder. As a result, increasing AF coupling shifts the metal-insulator transition to lower Hubbard interaction and gives it an additional "Anderson" character. In conclusion, we provide detailed results on the magnetic and orbital correlations, the density of states, and the optical conductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Triangular lattice Hubbard model physics at intermediate temperatures

Moiré systems offer an exciting playground to study the many-body effects of strongly correlated electrons in regimes that are not easily accessible in conventional material settings. Motivated by a recent experiment on WSe 2 /WS 2 moiré bilayers [Y. Tang et al., Nature (London) 579, 353 (2020)], which realized a triangular superlattice with a small hopping (of approximately 10 Kelvin), with tunable density of holes, we explore the Hubbard model on the triangular lattice for intermediate temperatures t ≲ T < U. Employing finite-temperature Lanczos calculations and closely following the fitting protocols used in the experiment, we recover the observed trends in the reported Curie-Weiss temperature Θ with filling, using the reported interaction strength U/t=20. Here, we focus on the large increase of |Θ| on decreasing the density below half filling and the sign change of Θ at higher fillings, which signals the onset of ferromagnetism. The increase in |Θ| is also seen in the t–J model (the low-energy limit of the Hubbard model) in the intermediate temperature range, which we clarify is opposite to the trend in its high temperature limit. Differences between the low, intermediate, and high temperature regimes are discussed. Our numerical calculations also capture the crossover between short-range antiferromagnetic to ferromagnetic order in the intermediate temperature regime, a result broadly consistent with the experimental findings. We find that this behavior is a finite-temperature remnant of the underlying zero-temperature phase transition, which we explore with ground-state density matrix renormalization group calculations. We provide evidence of ferromagnetism characterized by weak (but robust) correlations that explain the small Θ seen in the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

High spin polarization in the disordered quaternary Heusler alloy FeMnVGa

Here in this paper, we report the successful synthesis of a Fe-based highly spin-polarized quaternary Heusler alloy FeMnVGa and its structural, magnetic, and transport properties probed through different experimental methods and theoretical techniques. Density functional theory (DFT) calculations performed on different types of structures reveal that the structure with Ga at 4a, V at 4b, Mn at 4c, and Fe at 4d (space group F$\bar{4}$3m) possess minimum energy among all the ordered variants. Ab initio simulations in the most stable ordered structure show that the compound is a ferromagnet having a large spin-polarization (89.9%). Neutron diffraction reveals that the compound crystallizes in disordered type-2 structure (space group Fm$\bar{3}$m) in which Ga occupies at 4a, V 4b and Fe/Mn occupy 4c/4d sites with 50:50 proportions. The structural disorder is further confirmed by x-ray diffraction, extended x-ray absorption fine structure, 57 Fe Mössbauer spectrometry results, and DFT calculations. Magnetization studies suggest that the compound orders ferromagnetically below T C ~ 293 K and the saturation magnetization follows the Slater-Pauling rule. Mössbauer spectrometry, along with neutron diffraction, suggest that Mn is the major contributor to the total magnetism in the compound, consistent with the theoretical calculations, which also indicates that spin polarization remains high (81.3%), even in the presence of such large atomic disorder. The robustness of the half-metallic ferromagnetic (HMF) property in the presence of disorder is a quite unique characteristic over other reported HMF in literature and makes this compound quite promising for spintronics applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Magnetoresistance anomaly during the electrical triggering of a metal-insulator transition

Phase separation naturally occurs in a variety of magnetic materials and it often has a major impact on both electric and magnetotransport properties. In resistive switching systems, phase separation can be created on demand by inducing local switching, which provides an opportunity to tune the electronic and magnetic state of the device by applying voltage. Here we explore the magnetotransport properties in the ferromagnetic oxide La 0.7 ⁢Sr 0.3 ⁢MnO 3 (LSMO) during the electrical triggering of an intrinsic metal-insulator transition (MIT), which produces volatile resistive switching. This switching occurs in a characteristic spatial pattern, i.e., the formation of a high-resistance barrier perpendicular to the current flow, enabling an electrically actuated ferromagnetic-paramagnetic-ferromagnetic phase separation. At the threshold voltage of the MIT triggering, both anisotropic and colossal magnetoresistances exhibit anomalies including a large increase in magnitude and a sign flip. Computational analysis revealed that these anomalies originate from the coupling between the switching-induced phase separation state and the intrinsic magnetoresistance of LSMO. Furthermore, this work demonstrates that driving the MIT material into an out-of-equilibrium resistive switching state provides the means for electrical control of the magnetotransport phenomena.

Complex oxides↗
DOE OSTI2024

Direct and indirect spin current generation and spin-orbit torques in ferromagnet/nonmagnet/ferromagnet trilayers

Spin-orbit torques in ferromagnet/nonmagnet/ferromagnet trilayers are studied using a combination of symmetry analysis, circuit theory, semiclassical simulations, and first-principles calculations using the nonequilibrium Green's function method with supercell disorder averaging. Here, we focus on unconventional processes involving the interplay between the two ferromagnetic layers, which are classified into direct and indirect mechanisms. The direct mechanism involves spin current generation by one ferromagnetic layer and its subsequent absorption by the other. In the indirect mechanism, the in-plane spin-polarized current from one ferromagnetic layer “leaks” into the other layer, where it is converted into an out-of-plane spin current and reabsorbed by the original layer. The direct mechanism results in a predominantly dampinglike torque, which damps the magnetization towards a certain direction 𝐬 𝑑 . The indirect mechanism results in a predominantly fieldlike torque with respect to a generally different direction 𝐬 𝑓 . Similarly to the current-in-plane giant magnetoresistance, the indirect mechanism is only active if the thickness of the nonmagnetic spacer is smaller than or comparable to the mean free path. Numerical calculations for a semiclassical model based on the Boltzmann equation confirm the presence of both direct and indirect mechanisms of spin current generation. First-principles calculations reveal sizable unconventional spin-orbit torques in Co/Cu/Co, Py/Cu/Py, and Co/Pt/Co trilayers and provide strong evidence of indirect spin current generation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Mapping the three-dimensional fermiology of the triangular lattice magnet EuAg 4 Sb 2

In this paper, we report the temperature-field phase diagram as well as present a comprehensive study of the electronic structure and three-dimensional fermiology of the triangular-lattice magnet EuAg 4 ⁢Sb 2 , utilizing quantum oscillation measurements, angle-resolved photoemission spectroscopy, and first-principles calculations. The complex magnetic phase diagram of EuAg 4 ⁢Sb 2 highlights many transitions through nontrivial AFM states. Shubnikov-de Haas and de Haas-van Alphen oscillations were observed in the polarized ferromagnetic state of EuAg 4 ⁢Sb 2 , revealing three pairs of distinct spin-split frequency branches with small effective masses. A comparison of the angle-dependent oscillation data with first-principles calculations in the ferromagnetic state and angle-resolved photoemission spectra shows good agreement, identifying tubular hole pockets and hourglass-shaped hole pockets at the Brillouin zone center, as well as diamond-shaped electron pockets at the zone boundary. As the temperature increases, the frequency branches of the tiny hourglass pockets evolve into a more cylindrical shape, while the larger pockets remain unchanged. This highlights that variations in exchange splitting, driven by changes in the magnetic moment, primarily impact the small Fermi pockets without significantly altering the overall band structure. As a result, this is consistent with first-principles calculations, which show minimal changes near the Fermi level across ferromagnetic and simple antiferromagnetic states or under varying on-site Coulomb repulsion.

36 MATERIALS SCIENCE↗