TbV_6Sn_6 is a topological metal where ferromagnetic Tb ions with strong uniaxial magnetic anisotropy interact with V kagome layers. Inelastic neutron scattering (INS) measurements show that the Tb ions adopt an Ising doublet ground state. Here, we consider whether a transverse magnetic field can drive TbV_6Sn_6 toward a quantum critical point, providing a rare example of transverse-field Ising criticality in a metallic compound. High-field magnetization measurements reveal a first-order-like spin-reorientation transition at 25.6 T. Our INS-based magnetic model finds that this is caused by an avoided crossing of an excited-state singlet with the ground-state doublet. Surprisingly, our model predicts that quantum critical and tricritical points are accessible within the range of experimentally determined model parameters and may be reached by varying the direction of an applied magnetic field.

CaMn_2P_2 exemplifies the realization of a frustrated J_1-J_2-J_3 Heisenberg model of a corrugated honeycomb magnetic lattice. Previous studies show that below the Néel temperature (T_ N), the system forms a cycloidal 6× 6 ab-plane magnetic unit cell that conforms with various magnetic space groups. Here, we present single-crystal neutron-diffraction studies across expansive reciprocal-space volumes, confirming the cycloidal magnetic structure while uncovering further distinctive features. We find evidence for three magnetic domains, the analysis of which narrows the possible magnetic model structures. At T_ N, the insulator exhibits a sharp phase transition, above which the spin structure transforms into a spiral spin liquid state, evident via a continuous ring of scattering with degenerate wavevectors corresponding to a collection of short-range spiral spin configurations. These degenerate states emerge as thermal fluctuations effectively reduce the J_3 interaction. The integration of experimental, theoretical, and real-space simulation results reveals the intricate balance of exchange interactions (J_1-J_2-J_3) that stabilizes the ground-state magnetic structure and drives the emergence of a sought-after U(1)-symmetric spiral spin-liquid state with easy-plane anisotropy above the transition temperature.

Kagome metals can host unconventional electronic phenomena that emerge from their frustrated lattice geometry and associated band topology. Correlated electronic orders, such as charge-density waves and superconductivity, are observed to intertwine with subtle time-reversal symmetry breaking whose microscopic origin is not currently understood. Here, we provide evidence for such time-reversal symmetry breaking in the kagome metal TbV$_6$Sn$_6$ arising from staggered magnetic moments within the kagome layers. TbV$_6$Sn$_6$ consists of metallic V kagome layers separated by Tb triangular layers that host Ising ferromagnetic order. Deep in the ferromagnetic state, the Tb Ising doublet ground state should display a single, dispersionless spin-flip excitation. Instead, inelastic neutron scattering reveals two sharp excitations associated with inequivalent Tb sites, demonstrating that a symmetry-broken phase coexists with Ising ferromagnetism. No additional structural or magnetic phase transitions are detected, and first-principles calculations rule out lattice distortions as the origin of the splitting. We attribute this effect to time-reversal symmetry breaking encoded by small V moments that couple to the Tb sublattice and leave a measurable spectral fingerprint. Our results establish rare-earth local moment spectroscopy as a sensitive probe of subtle broken symmetries and highlight an unexpected interplay between kagome magnetism and rare-earth local moment magnetism.

The axion is a hypothetical fundamental particle that is conjectured to correspond to the coherent oscillation of the θ field in quantum chromodynamics1,2. Its existence would solve multiple fundamental questions, including the strong CP problem of quantum chromodynamics and dark matter, but the axion has never been detected. Electrodynamics of condensed-matter systems can also give rise to a similar θ, so far studied as a static, quantized value to characterize the topology of materials3-5. Coherent oscillation of θ in condensed matter has been proposed to lead to physics directly analogous to the high-energy axion particle-the dynamical axion quasiparticle (DAQ)6-23. Here we report the observation of the DAQ in MnBi2Te4. By combining a two-dimensional electronic device with ultrafast pump-probe optics, we observe a coherent oscillation of θ at about 44 gigahertz, which is uniquely induced by its out-of-phase antiferromagnetic magnon. This represents direct evidence for the presence of the DAQ, which in two-dimensional MnBi2Te4 is found to arise from the magnon-induced coherent modulation of the Berry curvature. The DAQ also has implications in light-matter interaction and coherent antiferromagnetic spintronics24, as it might lead to axion polaritons and electric control of ultrafast spin polarization6,15-20. Finally, the DAQ could be used to detect axion particles21-23. We estimate the detection frequency range and sensitivity in the millielectronvolt regime, which has so far been poorly explored.

SrCr2As2 is an itinerant antiferromagnet in the same structural family as the SrCr2As2 high-temperature superconductors. We report our calculations of exchange-coupling parameters J(ij) for SrCr2As2 using a static linear-response method based on first-principles electronic-structure calculations. We find that the dominant nearest-neighbor exchange coupling J(1) > 0 is antiferromagnetic whereas the next-nearest-neighbor exchange coupling J(2) < 0 is ferromagnetic with J(2)/J(1) = -0.68, reinforcing the checkerboard in-plane magnetic structure. Thus, unlike other transition-metal arsenides based on Mn, Fe, or Co, we find no competing magnetic interactions in SrCr2As2 , which aligns with experimental findings. Moreover, the orbital resolution of exchange interactions shows that J(1 )and J(2) are dominated by direct exchange mediated by the Cr d orbitals. To validate the calculations we conduct inelastic neutron-scattering measurements on powder samples that show steeply dispersive magnetic excitations arising from the magnetic P points and persisting up to energies of at least 175 meV. The spin-wave spectra are then modeled using the Heisenberg Hamiltonian with the theoretically calculated exchange couplings. The calculated neutron-scattering spectra are in good agreement with the experimental data.

Quantum materials with stacked van der Waals (vdW) layers hosting non-trivial band structure topology and magnetism have shown many interesting properties. Using high throughput density functional theory calculations, we design and predict tetragonal vdW-layered quantum materials in the MPd5I2 structure (M=Ga, In and 3d transition metals). We show that besides the known AlPd5I2, the -MPd5- structural motif of three-atomic-layer slabs separated by two I layers can accommodate a variety of metal atoms giving arise to topologically non-trivial features and highly tunable magnetic properties in both bulk and single layer 2D structures. Among them, TiPd5I2 and InPd5I2 host a pair of Dirac points and likely an additional strong topological insulator state for the band manifolds just above and below the top valence band, respectively, with their single layers hosting or near quantum spin Hall states. CrPd5I2 is a ferromagnet with a large out-of-plane magneto-anisotropy energy, desirable for rare-earth-free permanent magnets.

The addition of magnetic impurities in topological insulators can drive ferromagnetic order that leads to novel quantum anomalous Hall transport well below the Curie temperature. The fragility of the quantized regime has been ascribed to the random nature of the magnetic moment distribution. Here, we refine this hypothesis by using inelastic neutron scattering and density-functional theory calculations to show that two antagonistic components define the magnetism in Mn-substituted SnTe, thereby limiting the effectiveness of dilute magnetic TIs. One component is strongly bound antiferromagnetic dimers that compete with ferromagnetic order. The other component consists of undimerized moments where ferromagnetic order develops via long-range interactions.

Magnetic dopants in three-dimensional topological insulators (TIs) offer a promising avenue for realizing the quantum anomalous Hall effect (QAHE) without the necessity for an external magnetic field. Understanding the relationship between site occupancy of magnetic dopant elements and their effect on macroscopic property is crucial for controlling the QAHE. By combining atomic-scale energy-dispersive X-ray spectroscopy (EDS) maps obtained by aberration-corrected scanning transmission electron microscopy (AC-STEM) and novel data processing methodologies, including semi-automatic lattice averaging and frame registration, we have determined the substitutional sites of Mn atoms within the 1.2% Mn-doped Sb2Te3 crystal. More importantly, the methodology developed in this study extends beyond Mn-doped Sb2Te3 to other quantum materials, traditional semiconductors, and even electron irradiation sensitive materials.

We report neutron-diffraction results for the body-centered-tetragonal series Eu(Co_1-xNi_x)_2-yAs_2, x=0.10, 0.20, 0.42, and 0.82, y≤0.08, that detail changes to the magnetic ordering with nominal hole doping. We report the antiferromagnetic (AFM) propagation vectors, magnetic transition temperatures, and values for the ordered magnetic moments. We find a nonmonotonic change of the AFM propagation vector with x, with a minimum occurring at the tetragonal to collapsed-tetragonal phase crossover. For x=0.10 and 0.82 we find c-axis-helix ordering of the Eu magnetic moments (spins) similar to x=0 and 1, with the spins oriented within the 𝐚𝐛-plane. For x=0.20 and 0.42 we find higher-temperature c-axis-FM order and lower-temperature c-axis-cone order. Using the extinction conditions for the space group, we discovered that the Eu spins are ordered in the higher-temperature c-axis-FM phase for intermediate values of x, contrary to a previous report suggesting only Co/Ni spin ordering. Although we cannot directly confirm that the Co/Ni spins are also ordered, we suggest that c-axis itinerant FM ordering of the Co/Ni spins could provide a molecular field that drives parasitic FM ordering of the Eu spins, which in turn provides the anisotropy for the lower-temperature c-axis-cone order.

Density functional theory (DFT), including its extensions designed to treat strongly correlated localized electron systems such as DFT+U and DFT+dynamical mean field theory, has proven exceedingly useful in studying the magnetic properties of solids. However, materials with rare earths (R) have remained a notable exception. The most vital rare-earth magnetic properties, such as magnetocrystalline anisotropy (MA), have been notoriously elusive due to the ubiquitous self-interaction error present in nearly all available DFT flavors. In this work, we show explicitly how the orbital dependence of self-interaction error may contradict Hund's rules and plague MA calculations, and how analyzing DFT metastable states that respect Hund's rules can alleviate the problem. We systematically investigate and discuss several rare-earth-containing families, RCo_5, R_2Fe_14B, RFe_12, and RMn_6Sn_6, to benchmark the MA calculations in DFT+U. For all compounds we investigated, we found that our methodology reproduces the magnetic easy-axis, easy-plane, and non-trivial easy-cone anisotropies in full agreement with low-temperature experimental measurements. Besides the fully-numerical ab initio approach, we further illustrate an efficient semi-analytical perturbation method that treats the crystal field as a perturbation in the limit of large spin-orbit coupling. This approach evaluates the rare-earth anisotropy by assessing the dependence of crystal-field energy on spin-quantization axis rotation using 4f crystal-field levels obtained from non-spin-orbit calculations. Our analytical method provides a quantitative microscopic understanding of the factors that control MA and can be used for predicting new high-MA materials.

The magnetic interactions in the antiferromagnetic (AFM) Dirac semimetal candidate SrMnSb_2 are investigated using ab initio linear response theory and inelastic neutron scattering (INS). Our calculations reveal that the first two nearest in-plane couplings (J_1 and J_2) are both AFM in nature, indicating a significant degree of spin frustration, which aligns with experimental observations. The orbital resolution of exchange interactions shows that J_1 and J_2 are dominated by direct and superexchange, respectively. In a broader context, a rigid-band model suggests that electron doping fills the minority spin channel and results in a decrease in the AFM coupling strength for both J_1 and J_2. To better compare with INS measurements, we calculate the spin wave spectra within a linear spin wave theory, utilizing the computed exchange parameters. Although the calculated spin wave spectra somewhat overestimate the magnon bandwidth, they exhibit overall good agreement with measurements from INS experiments.

We report neutron diffraction results for the body-centered-tetragonal series Eu(Co1-xNix)2-yAs2, x = 0.10, 0.20, 0.42, and 0.82, y 0.10, that detail changes to the magnetic ordering with nominal hole doping. We report the antiferromagnetic (AFM) propagation vectors, magnetic transition temperatures, and the ordered magnetic moments. We find a nonmonotonic change of the AFM propagation vector with x, with a minimum occurring at the tetragonal to collapsed-tetragonal phase crossover. For x = 0.10 and 0.82 we find c-axis helix ordering of the Eu magnetic moments (spins) similar to x = 0 and 1, with the spins oriented within the ab-plane. For x = 0.20 and 0.42 we find higher-temperature c-axis ferromagnetic (FM) order and lower-temperature c-axis cone order. Using the extinction conditions for the space group, we discovered that the Eu spins are ordered in the higher-temperature c-axis FM phase for intermediate values of x, contrary to a previous report suggesting only Co/Ni spin ordering. Although we cannot directly confirm that the Co/Ni spins are also ordered, we suggest that c-axis itinerant-FM ordering of the Co/Ni spins could provide a molecular field that drives FM ordering of the Eu spins, which in turn provides the anisotropy for the lower-temperature c-axis cone order.

Magnetic kagome metals are a promising platform to develop unique quantum transport and optical phenomena caused by the interplay between topological electronic bands, strong correlations, and magnetic order. This interplay may result in exotic quasiparticles that describe the coupled electronic and spin excitations on the frustrated kagome lattice. Here, we observe novel elementary magnetic excitations within the ferromagnetic Mn kagome layers in TbMn 6 Sn 6 using inelastic neutron scattering. We observe sharp, collective acoustic magnons and identify flat-band magnons that are localized to a hexagonal plaquette due to the special geometry of the kagome layer. Surprisingly, we observe another type of elementary magnetic excitation; a chiral magnetic quasiparticle that is also localized on a hexagonal plaquette. The short lifetime of localized flat-band and chiral quasiparticles suggest that they are hybrid excitations that decay into electronic states.

We report the single crystal growth and characterization of EuIn$_2$, a magnetic topological semimetal candidate according to our density functional theory (DFT) calculations. We present results from electrical resistance, magnetization, M\"ossbauer spectroscopy, and X-ray resonant magnetic scattering (XRMS) measurements. We observe three magnetic transitions at $T_{\text{N}1}\sim 14.2~$K, $T_{\text{N}2}\sim12.8~$K and $T_{\text{N}3}\sim 11~$K, signatures of which are consistently seen in anisotropic temperature dependent magnetic susceptibility and electrical resistance data. M\"ossbauer spectroscopy measurements on ground crystals suggest an incommensurate sinusoidally modulated magnetic structure below the transition at $T_{\text{N}1}\sim 14~$K, followed by the appearance of higher harmonics in the modulation on further cooling roughly below $T_{\text{N}2}\sim13~$K, before the moment distribution squaring up below the lowest transition around $T_{\text{N}3}\sim 11~$K. XRMS measurements showed the appearance of magnetic Bragg peaks below $T_{\text{N}1}\sim14~$K, with a propagation vector of $\bm{\tau}$ $=(\tau_h,\bar{\tau}_h,0)$, with $\tau_h$varying with temperature, and showing a jump at $T_{\text{N}3}\sim11$~K. The temperature dependence of $\tau_h$ between $\sim11$~K and $14$~K shows incommensurate values consistent with the Mössbauer data. XRMS data indicate that $\tau_h$ remains incommensurate at low temperatures and locks into $\tau_h=0.3443(1)$.

We revisit the intriguing magnetic behavior of the paradigmatic itinerant frustrated magnet SrCo2As2, which shows strong and competing magnetic fluctuations yet does not develop long-range magnetic order. By cal-culating the static spin susceptibility x (q) within a realistic 16-orbital Hubbard-Hund model, we determine the leading instability to be ferromagnetic (FM). We then explore the effect of doping and calculate the critical Hubbard interaction strength Uc that is required for the development of magnetic order. We find that Uc decreases under electron doping and with increasing Hund's coupling J, but increases rapidly under hole doping. This suggests that magnetic order could possibly emerge under electron doping but not under hole doping, which agrees with experimental findings. We map out the leading magnetic instability as a function of doping and Hund's coupling and find several antiferromagnetic phases in addition to FM. We also quantify the degree of itinerant frustration in the model and resolve the contributions of different orbitals to the magnetic susceptibility. Finally, we discuss the dynamic spin susceptibility x (q, w) at finite frequencies, where we recover the anisotropy of the peaks at Qn = (n, 0) and (0, n) observed by inelastic neutron scattering that is associated with the phenomenon of itinerant magnetic frustration. By comparing results between theory and experiment, we conclude that the essential experimental features of doped SrCo2As2 are well captured by an itinerant Hubbard-Hund multiorbital model if one considers a small shift of the chemical potential towards hole doping.

TbMn6Sn6 is a metallic ferrimagnet that displays signatures of band topology arising from a combination of uniaxial ferromagnetism and spin-orbit coupling within its Mn kagome layers. Whereas the low energy magnetic excitations can be described as collective spin waves using a local moment Heisenberg model, sharply defined optical and flat-band collective magnon modes are not observed. In their place, we find overdamped chiral and flat-band spin correlations that are localized to hexagonal plaquettes within the kagome layer.

Predicting magnetic ordering in kagome compounds offers the possibility of harnessing topological or flat-band physical properties through tuning of the magnetism. Here, we examine the magnetic interactions and phases of ErMn_6Sn_6 which belongs to a family of RMn_6Sn_6, R= Sc, Y, Gd–Lu, compounds with magnetic kagome Mn layers, triangular R layers, and signatures of topological properties. Using results from single-crystal neutron diffraction and mean-field analysis, we find that ErMn_6Sn_6 sits close to the critical boundary separating the spiral-magnetic and ferrimagnetic ordered states typical for nonmagnetic versus magnetic R layers, respectively. Finding interlayer magnetic interactions and easy-plane Mn magnetic anisotropy consistent with other members of the family, we predict the existence of a number of temperature and field dependent collinear, noncollinear, and noncoplanar magnetic phases. We show that thermal fluctuations of the Er magnetic moment, which act to weaken the Mn-Er interlayer magnetic interaction and quench the Er magnetic anisotropy, dictate magnetic phase stability. Our results provide a starting point and outline a multitude of possibilities for studying the behavior of Dirac fermions in RMn_6Sn_6 compounds with control of the Mn spin orientation and real-space spin chirality.

Magnetic defects play an important, but poorly understood, role in magnetic topological insulators (TIs). For example, topological surface transport and bulk magnetic properties are controlled by magnetic defects in Bi_2Se_3-based dilute ferromagnetic (FM) TIs and MnBi_2Te_4 (MBT)-based antiferromagnetic (AFM) TIs. Despite its nascent ferromagnetism, our inelastic neutron scattering data show that a fraction of the Mn defects in Sb_2Te_3 form strong AFM dimer singlets within a quintuple block. The AFM superexchange coupling occurs via Mn-Te-Mn linear bonds and is identical to the AFM coupling between antisite defects and the FM Mn layer in MBT, establishing common interactions in the two materials classes. We also find that the FM correlations in (Sb_1-xMn_x)_2Te_3 are likely driven by magnetic defects in adjacent quintuple blocks across the van der Waals gap. In addition to providing answers to long-standing questions about the evolution of FM order in dilute TI, these results also show that the evolution of global magnetic order from AFM to FM in Sb-substituted MBT is controlled by defect engineering of the intrablock and interblock coupling.

We report on elastic and inelastic neutron scattering from single-grain isotopically-enriched samples to elucidate the local magnetic correlations between Tb^3+ moments in quasicrystalline i-Tb-Cd. The inelastic neutron scattering measurements of the CEF excitations demonstrated that the Tb^3+ moments are directed primarily along the local five-fold axes of the Tsai-type cluster as was found for the TbCd6 approximant phase. Based on the inelastic measurements, we consider of a simple Ising-type model for the moment configurations on a single Tb^3+ icosahedron and enumerate the lowest energy moment configurations. We then calculate the diffuse scattering from these configurations and compare with the experimental magnetic diffuse scattering measurements to identify the most likely single cluster moment configurations and find reasonable agreement between the broad features observed in our scattering simulations. We further consider the role of higher-order (longer range) intercluster correlations for the magnetic scattering.