Inertial spin dynamics alters the resonant spin wave excitation resulting in the modification of the resonance field and relaxation in microwave spectroscopy of ferromagnets described by the conventional Landau-Lifshitz-Gilbert (LLG) equation. Here we present a complete theoretical framework which quantitatively predicts the dynamic response of the magnetization for ferromagnetic systems exhibiting inertia. We compute the tensor of the high-frequency magnetic susceptibility analytically using the linearization of the inertial LLG equation, with fewer approximations than in the inertial Smit-Beljers approach. Our solution yields the precession (ferromagnetic resonance) and nutation resonance frequency, relaxation and intensity for an arbitrary free energy density, allowing straightforward quantitative analysis of inertial effects in magnetic resonances. Using the typical parameters of permalloy as an example we calculate the impact of materials parameters including Gilbert damping and inertial relaxation time on the conventional magnetic resonant response as well as the amplitude, linewidth, and frequency of the typically subterahertz nutation resonance.

Two terbium tellurides, ${\mathrm{TbTe}}_3$ and ${\mathrm{Tb}}_2{\mathrm{Te}}_5$, were studied by means of thermodynamics, ultrafast pump-probe spectroscopy, and torque magnetometry. While the crystal structure and some physical properties of ${\mathrm{TbTe}}_3$ were established previously, the crystal structure of ${\mathrm{Tb}}_2{\mathrm{Te}}_5$ is reported based on the low-temperature (100 K) single crystal x-ray diffraction experiment. ${\mathrm{Tb}}_2{\mathrm{Te}}_5$ crystallizes in orthorhombic Cmcm space group with $a=4.3009\left(17\right)$, $b=43.107\left(18\right)$, $c=4.3016\left(17\right)\AA$, $V=797.5\left(6\right){\AA }^3$, and $Z=4$. In contrast to ${\mathrm{TbTe}}_3$, which experiences three successive magnetic phase transitions, ${\mathrm{Tb}}_2{\mathrm{Te}}_5$ orders antiferromagnetically in two steps at $T_{\mathrm{N}1}=9.0$ K and $T_{\mathrm{N}2}=6.8$ K, both readily suppressed by an external magnetic field. The third transition in ${\mathrm{TbTe}}_3$ is due to the interaction of the magnetic subsystem with the charge density waves. The interaction of magnetic and electronic subsystems in ${\mathrm{Tb}}_2{\mathrm{Te}}_5$ has been revealed by the pump probe. Torque measurements of ${\mathrm{TbTe}}_3$ show that the magnetic moments of Tb are oriented predominantly in the $ac$ plane at high temperatures and switch to the $b$ axis at low temperatures. In ${\mathrm{Tb}}_2{\mathrm{Te}}_5$, the magnetic moments of Tb are oriented predominantly in the $ac$ plane at low temperatures.

Spin-ice compounds enable the exploration of the dynamics of magnetic monopoles in condensed matter systems. In this study, we use AC calorimetry to probe the dynamic heat capacity response of the classical spin-ice compound ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at low temperatures (0.5–5 K). Using frequencies of 0.01–500 Hz, we observe a strong frequency dependence in the measured heat capacity, allowing us to study thermal-relaxation effects on the corresponding timescales. The relaxation time $\tau$ is determined from the frequency dependence of the heat capacity as the characteristic frequency below which the heat capacity saturates. Specific heat shows a maximum around 1 K. The extracted $\tau$ shows divergent behavior below this temperature, reaching $\sim 6\mathrm{s}$ at 0.65 K, similar to the relaxation time seen in previous studies. Performing dynamic Monte Carlo simulations, we verify that the specific heat frequency response has its origin in the slow magnetic monopole dynamics indigenous to spin ice. We find a timescale of $20\text{ms}$ per Monte Carlo step at $4\text{K,}$ in contrast to $2.5\text{ms}$ mentioned in previous studies by other techniques.

The recent experimental realization of emergent quasiparticles, such as spinons, doublons, and quartons, in a $\mathrm{spin}\text{−}1/2$ trimer chain has spurred new interest in low-dimensional magnetic systems. In this study, we investigate the dynamical properties of the isotropic $\mathrm{spin}\text{−}1$ trimer chain with antiferromagnetic intratrimer $(J>0)$ and intertrimer $(J^{\prime }>0)$ exchange couplings, unveiling various quasiparticles: magnons, singletons, triplons, pentons, and heptons. For weak intertrimer exchange coupling $J^{\prime }/J\ll 1$, it behaves as an effective $\mathrm{spin}\text{−}1$ chain with a valence bond solid ground state. Employing density-matrix renormalization group techniques, we compute the dynamical structure factor which reveals a gapped magnon band along with weakly dispersive singleton, excited triplon, and penton energy bands. The evolution of these excitations with intertrimer coupling $J^{\prime }$ is also examined, providing insight into the underlying excitation mechanisms. For a $\mathrm{spin}\text{−}1$ chain, these exotic quasiparticles eventually reduce to conventional magnon excitations as $J^{\prime }/J\to 1$. Our results also shed light on the rich and complex excitation spectrum of $\mathrm{spin}\text{−}1$ trimer chains and offer a unique perspective on the dynamics in quantum spin systems.

The ilmenite ${\mathrm{NiTiO}}_3$ consists of a buckled honeycomb lattice, with the Ni spins aligned ferromagnetically in-plane and antiferromagnetically out-of-plane. Using neutron spectroscopy, the magnetic structure and the dynamics were investigated as a function of temperature. Dispersive acoustic bands and nearly dispersionless optical bands at $\approx 3.7$ meV are described by a highly anisotropy Heisenberg model with stronger antiferromagnetic (AFM) out-of-plane, weaker ferromagnetic (FM) in-plane interactions and an anisotropy gap of 0.95 meV. The order parameter yields a critical exponent between the Heisenberg and two-dimensional Ising models, consistent with highly anisotropic Heisenberg systems. The frustration parameter $\approx 2$ supports a weakly frustrated system.

Recent experiments have realized large Chern number quantum anomalous Hall insulators in nonmoiré rhombohedral multilayer graphene proximitized by ${\mathrm{WS}}_2/{\mathrm{WSe}}_2$. We exploit a minimal model based on intravalley ($u_a$), intervalley ($u_t$), and valley-exchange ($u_e$) components of the interaction to capture the emergence and competition of layer-polarized and quantum anomalous Hall phases in rhombohedral multilayer graphene. Using renormalization group analysis, we show that the layer-antiferromagnetic phase emerges as the leading instability, in good agreement with experimental observations. When $u_t$ dominates, the layer-valley-polarized phase with Chern number $\mathcal{C}=2N$ may become the leading instability, which awaits confirmation in future experiments. We then elucidate how the interplay between proximity-induced spin-orbit field and interactions triggers quantum anomalous Hall insulator with $\mathcal{C}=N$ at the critical phases of the transition from layer-antiferromagnetic phase or layer-valley-polarized phase to the layer-polarized insulator and further prove that the quantum anomalous Hall insulators are stabilized by the dominance of $u_a$ and $u_t$ over $u_e$. Our theory provides a concise understanding of recent experiments and offers insights to the realization of dissipationless topotronics using nonmoiré graphene.

While transverse coupling (${\sigma }_x$) is commonly used in qubit-resonator systems, longitudinal coupling via ${\sigma }_z$ presents a tantalizing alternative: it does not hybridize the modes, eliminating Purcell decay, and it enables quantum-nondemolition qubit readout independent of the qubit-resonator frequency detuning. Here, we demonstrate longitudinal coupling between a $\left\{{\mathrm{Cr}}_7\mathrm{Ni}\right\}$ molecular spin qubit ensemble and the kinetic inductance of a granular aluminum superconducting microwave resonator. The inherent frequency independence of this coupling allows for the utilization of a 7.8-GHz readout resonator to measure the full $\left\{{\mathrm{Cr}}_7\mathrm{Ni}\right\}$ magnetization curve spanning 0–600 mT, corresponding to a spin frequency range of $f_{\text{spin}}=0$–15 GHz. For 2-GHz detuning from the readout resonator, we measure a $1/e$ spin relaxation time of $\tau =0.38$ s, limited by phonon decay to the substrate. Based on these results, we propose a path towards longitudinal coupling of single spins to a superconducting fluxonium qubit.

The antiferromagnetic parent phase of high-$T_c$ cuprates has been established as a Néel state of copper moments, but early work pointed out the important role of ligand oxygen orbitals. Using the three-orbital Emery model, we explore how, and under which conditions, doping-induced antiferromagnetic ordering of weak magnetic moments on the oxygen sites can lead to unconventional $d$-wave magnetism with spin-split electronic bands. The mechanism for forming such altermagnetic (AM) states in cuprates does not rely on a lowering of the crystal symmetry but rather on interaction-induced formation of magnetic moments on directional oxygen orbitals within the crystallographic unit cell. Therefore, we obtain two different types of AM, namely, a (0, 0)-AM and a ($\pi ,\pi$)-AM. We explore different regimes and challenges for realizing oxygen AM supported by Hartree-Fock calculations and complementary exact diagonalization of small clusters. While the region of interacting parameters needed to realize these states may be difficult to achieve in known high-$T_c$ cuprates, we propose a scenario to realize AM induced by oxygen magnetic moments in a cuprate-based candidate compound using density functional theory and discuss experimental implications.

Electrons in metals experience an effective vector potential when coupled to spin textures with nonzero scalar spin chirality, such as skyrmions. This coupling can generate a substantial field, leading to pronounced observable phenomena, including the topological Hall effect. Motivated by this, we consider a bilayer model in which the Majorana fermions in the Yao-Lee model on one layer interact with topological spin textures on the second layer via a spin-spin interaction. Unlike the Kitaev model, the Yao-Lee model remains exactly solvable, allowing us to perform Monte Carlo simulations to determine its ground state. Our analysis indicates that skyrmion crystals can give rise to a variety of flux patterns that are periodic arrangements of the ${\mathbb{Z}}_2$ fluxes with unusual patterns such as a kagome pattern. In addition, Majorana fermions acquire a substantial Berry phase from skyrmion crystals, resulting in phases with finite Chern numbers up to $\nu =5$. In the case of a single skyrmion defect in the magnetic layer, a corresponding defect in the vison configuration can be realized. These defects support localized states when the spin liquid is gapped. Similar to skyrmion crystals, spiral spin textures also give rise to a diverse range of flux crystals. However, in this case, most of these phases are gapless, with only a few being trivially gapped. Our results highlight the rich physics emerging from the interplay between topological spin textures and fractionalized quasiparticles in quantum spin liquids.

Altermagnetism has recently emerged as a distinct and fundamental class of magnetic order. Exploring its interplay with quantum phenomena such as unconventional superconductivity, density-wave instabilities, and many-body effects represents a compelling frontier. In this work, we theoretically confirm the presence of high-temperature metallic altermagnetism in ${\mathrm{KV}}_2{\mathrm{Se}}_2\mathrm{O}$. We demonstrate that the anomalous metal-insulator-metal transition arises from a Lifshitz transition associated with Fermi surface reconstruction. The previously reported spin-density wave gap is found to lie below the Fermi level in our study and is now recognized to be attributed to the V-shaped density of states, originating from orbital-selective and sublattice-resolved half-metal-like behavior on a specific vanadium atom. Furthermore, we identify the instability from the nesting of spin-momentum-locked one-dimensional Fermi surfaces, which induces the SDW state. These findings position ${\mathrm{KV}}_2{\mathrm{Se}}_2\mathrm{O}$ as a promising platform for investigating the interplay among altermagnetism, unconventional superconductivity, and density-wave order.

We investigate a quantum dot (QD) system coupled to a vibrational environment with a super-Ohmic spectral density and weakly coupled to a leaky cavity mode, a model relevant for semiconductor-based single-photon sources. The phonon coupling induces dephasing and broadens the absorption and emission line shapes, while the weakly coupled cavity mode leads to effective driving of the QD. To capture non-Markovian effects, we use non-Markovian quantum state diffusion and its extension the hierarchy of pure states to compute multitime correlation functions underlying absorption and resonance fluorescence spectra. We present numerical results for the absorption spectra at strong phonon coupling and finite temperature as well as for resonance fluorescence spectra at varying phonon coupling strengths and temperatures and analyze the visibility of the resonance fluorescence spectra to provide insights into how phonon coupling and thermal effects influence the spectral features.

This paper discusses a connection between two important classes of materials, namely quasicrystals and topological insulators as exemplified by the quantum Hall problem. It has been remarked that the quasicrystal “inherits” topological properties from the 2D quantum Hall model. The aim of this work is to show this explicitly by introducing the Fibonacci-Hall model as a link between a 1D quasicrystal and the magnetic problems. We show here how Chern numbers for bands in periodic approximants of quasicrystals can be computed, along with gap labels. The Chern numbers are thus seen as a consequence of a flux parameter ${\varphi }^S$ induced by the geometry of winding in 2D space of the quasicrystal. We show the existence of lines of Lifshitz transitions in the phase space of the model. These are marked by change of Chern number and in open systems by disappearance of edge states. Our extrapolation method can be generalized to higher dimensional 2D and 3D quasicrystals, where higher order Chern numbers could be computed, and importantly, related to experimentally measurable transport quantities.

Under high pressure, the group-VB transition metals vanadium (V) and niobium (Nb) exhibit simple crystal structures but complex physical behaviors, such as anomalous compression-induced softening and heating-induced hardening (HIH). Meanwhile, the impact of lattice thermal expansion-induced softening at elevated temperatures on HIH is yet to be investigated. Therefore, this study utilized ab initio (AIMD) and machine learning molecular dynamics (MLMD) to investigate the melting and abnormal mechanical softening-hardening behaviors of V and Nb under high pressure. Simulations reveal that the high-temperature Pnma phase of Nb reported in previous experimental studies is highly susceptible to mechanical instability and reverts to the body-centered cubic (bcc) phase. This discovery prompted a revised determination of the high-pressure melting line of Nb. The melting temperature of Nb significantly exceeds the existing theoretical and experimental estimate compared with that of V. AIMD simulations demonstrate that atomic thermal displacements have a greater influence on the HIH of V and Nb than pure electron temperature effects. In addition, the temperature-dependent anomalous elastic properties of V and Nb were investigated within a pressure range of 0–250 GPa using MLMD. The mechanical properties of V and Nb transitioned from HIH to heating-induced softening, elucidating the competition between thermal-expansion induced softening and HIH. This study advances fundamental understanding of V and Nb physics, providing crucial theoretical foundations for establishing accurate equations of state and constitutive models for these metals.

Dipolar-coupled single-domain nanomagnet lattices, known as artificial spin ice (ASI), exhibit geometric frustration, emergence, reconfigurability, and collective magnetization dynamics, making them a promising platform for magnetic logic devices, reconfigurable magnonics, and unconventional computing. One local feature that could serve as an information carrier in such systems is the emergent magnetic monopole. However, applied global magnetic fields often trigger uncontrolled avalanchelike switching of nanomagnets, leading to detrimental loss of encoded information. Microstate control and stepwise monopole motion remain a key challenge. In this work, we explore the nature of monopole motion in square ASI via so-called astroid clocking protocols and demonstrate controlled stepwise propagation. Using x-ray magnetic circular dichroism and magneto-optical Kerr microscopy imaging, we experimentally verify controlled single-step monopole motion in square ASI. We reveal a rich spectrum of emergent monopole pathways referred to as string, zigzag, and ferromagnetic domain regimes. Our finding shows that these pathways of monopole propagation are determined by the angle and strength of the clocking field. This approach offers a higher level of control of emergent magnetic monopole propagation in ASI, with potential applications in data storage and unconventional computing.

The development of a terahertz signal source operating at room temperature and having the ability to widely tune the frequency is an important scientific task. In this work, we theoretically justify the need for an experiment to observe an antiferromagnetic spin Hall oscillator (AFM SHO) with different easy plane orientations as an essential and integral step towards the creation of such terahertz signal sources. Here, we analyze both analytically and numerically the mathematical model for the canted AFM SHO with different positions of the easy plane and also verify the obtained results using micromagnetic simulations. We obtain analytical expressions for critical currents of the onset of self-oscillations and the end of damping oscillations and show that they both increase as the AFM easy plane approaches either of the two planes containing the spin current polarization vector.

Using first-principles calculations and an atomistic spin model, we predict the stabilization of a bilayer triple-Q state in an atomic Mn bilayer on Ir(111) due to interlayer higher-order exchange interactions. Based on density functional theory (DFT) we study the magnetic interactions and ground state in a Mn monolayer and bilayer on the Ir(111) surface. We calculate the energy dispersion of spin spirals (single-Q states) to scan a large part of the magnetic phase space and to obtain constants of pairwise exchange interactions. By including spin-orbit coupling, we determine the strength of the Dzyaloshinskii-Moriya interaction. To reveal the role of higher-order exchange interactions in these films, we consider multi-Q states obtained by a superposition of spin spirals. For the Mn monolayer in fcc stacking on Ir(111), the triple-Q state exhibits the lowest total energy in DFT, while the Néel state is most favorable for hcp stacking. For the Mn bilayer on Ir(111), two types of the triple-Q state are possible. In both magnetic configurations, a triple-Q state occurs within each of the Mn layers. However, only in one of them, the spin alignment between the layers is such that nearest neighbor spins of different layers also exhibit the tetrahedron angles that characterize the triple-Q state. We denote this state—which has the lowest total energy in our DFT calculations—as the ideal bilayer triple-Q state. This state exhibits significant topological orbital moments within each of the two Mn layers which are aligned in parallel resulting in a large topological orbital magnetization. We interpret the DFT results within an atomistic spin model, which includes pairwise Heisenberg exchange, the Dzyaloshinskii-Moriya interaction, as well as higher-order exchange interactions. We classify the different types of higher-order interactions into intralayer terms, i.e., acting only between spins within one of the layers, and interlayer interactions, in which spins in both layers are involved. We point out the role of an odd or even distribution of spins in the multispin interactions between the layers. Finally, we demonstrate that the stabilization of the ideal bilayer triple-Q state in a Mn bilayer on Ir(111) can only be explained upon taking the effect of interlayer higher-order exchange interactions into account.