In spite of the widespread use of rare-earth metals in magnetism, real space investigations of their magnetic domain structures remain scarce. Here we report on a systematic investigation on the structural and magnetic properties of Ho films by means of low-temperature spin-polarized scanning tunneling microscopy (SP-STM). The films are grown on W(110), resulting in well-ordered surfaces with stacking faults, glide dislocations, and double screw dislocations, all characteristic for epitaxial growth of hcp(0001) films on bcc(110) substrates. At low coverage up to $\approx 50$ atomic layers (AL), the surface magnetic structure of the Ho(0001) films is found to be dominated by ferromagnetic in-plane domains magnetized along six equivalent high-symmetry axes. Significant pinning of domain walls to crystalline defects is observed. For Ho coverages exceeding 50 AL, additional out-of-plane magnetized stripe domains superimposed to the in-plane magnetization are observed. We relate these stripe domains to the dipolar stray field associated with the known helical magnetic cone structure of Ho which leads to an uncompensated magnetization component along the $c$ axis, i.e., perpendicular to the surface. Domain wall analysis suggests Néel-capped Bloch-type walls with widths of $w_{60}\approx 1.2$ nm, $w_{120}\approx 3$ nm, and $w_{180}\approx 4$ nm for ${60}^{\circ }, {120}^{\circ }$, and ${180}^{\circ }$ walls, respectively. Magnetic field-dependent measurements reveal that the stripe domains are annihilated by an out-of-plane field of ${\mu }_{0}H=\pm 300$ mT.

We theoretically study nonperturbative strong-coupling phenomena in cavity magnonics systems in which the uniform magnetization dynamics (magnons) in a ferromagnet is coupled to the microwave magnetic field (photons) of a single $LC$ resonator. Starting from an effective circuit model that accounts for the magnetization dynamics described by the Landau-Lifshitz-Gilbert equation, we show that a nontrivial frequency shift emerges in the ultrastrong and deep-strong coupling regimes, whose microscopic origin remains elusive within a purely classical framework. The circuit model is further quantized to derive a minimal quantum-mechanical model for generic cavity magnonics, which corresponds to a two-mode version of the Hopfield Hamiltonian and explains the mechanism of the frequency shifts found in the classical circuit model. We also formulate the relation between the frequency shift and quantum quantities, such as the ground-state particle number, quantum fluctuations associated with the Heisenberg uncertainty principle, and entanglement entropy, providing a nondestructive means to experimentally access these quantum resources. By utilizing soft magnons in an anisotropic ferromagnet, we further demonstrate that these quantum quantities diverge at the zeros of the magnon band edges as a function of the external magnetic field. This work paves the way for cavity magnonics beyond the conventional strong-coupling regime.

The magnetic properties of two-dimensional altermagnets can be obtained from a square lattice Heisenberg model with antiferromagetic nearest-neighbor interaction and two types of next-nearest-neighbor interactions arranged in a checkerboard pattern. Using nonlinear spin-wave theory, we calculate for this model the corrections to the renormalized magnon spectrum and the staggered magnetization to first order in the inverse spin quantum number $1/S$. We also show that to order $1/S^2$ the ground state energy is not sensitive to the component of the interaction which is responsible for altermagnetism. At the $\mathrm{\Gamma }$ point, the $1/S$ correction to the magnon dispersion vanishes so that quantum fluctuations do not induce a gap in the magnon spectrum of altermagnets, as expected by Goldstone's theorem. We extract the leading $1/S$ corrections to the spin-wave velocity and the effective mass characterizing the curvature of the magnon dispersion in altermagnets.

The Yb-based triangular lattice delafossites $A\mathrm{Yb}{X}_2$ ($A=\text{alkali}$ metal, $X=\text{O}$, S, Se) have recently been studied as quantum spin liquid candidates. We report the synthesis of powders and single crystals of ${\mathrm{CuYbSe}}_2$ with a perfect triangular lattice of ${\mathrm{Yb}}^{3+}$ moments. Magnetic susceptibility and heat capacity measurements reveal no evidence of long-range magnetic ordering down to 1.8 K in spite of a significant antiferromagnetic exchange between ${\mathrm{Yb}}^{3+}$ moments, suggesting a frustrated magnetic system. Electrical resistivity measurements indicate insulating behavior, consistent with the localized nature of magnetic moments. Heat capacity reveals that ${\mathrm{CuYbSe}}_2$ can be treated as an effective spin $S=1/2$ triangular lattice antiferromagnet below $\sim 50$ K. Magnetic susceptibility measurements on single crystals reveal weak magnetic anisotropy. These properties position ${\mathrm{CuYbSe}}_2$ as another platform for exploring exotic magnetic ground states in triangular lattice systems.

Motivated by the sensitivity of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ to Fermi surface reconstructions under strain, we investigate how Fermi surface geometry and Van Hove singularities influence the optical Hall response and polar Kerr effect. Within a three-orbital model, we explore the impact of chemical potential and interlayer hopping on superconducting pairing and response functions. We find that $d_{x^2-y^2}$ and $d_{x^2-y^2}+ig$ symmetries are the leading candidates for the quasi-two-dimensional (quasi-2D) orbital, while a chiral $p$-wave state in quasi-1D orbitals is essential for generating an accessible Kerr angle. The Lifshitz transition is shown to affect coherence factors and density-of-states peaks, producing sharp signatures in $T_c$ and optical transport. Interorbital charge transfer further enhances these effects by modifying the balance between the contributions of the quasi-1D and quasi-2D orbitals. These results provide a framework for interpreting Kerr effect experiments in multiorbital superconductors.

Based on the two-band free-energy functional, we have investigated phase transitions of a three-dimensional granular superconductor through the Monte Carlo method and finite-size scaling analysis. In the ordered lattices for this superconductor consisting of Josephson-coupled grains, we obtain an intermediate phase above the critical intraband coupling strength while maintaining a constant interband coupling coefficient. This phase is distinct from both the low-temperature superconducting phase and the high-temperature normal phase, characterized by the absence of long-range phase coherence solely for the first band. This numerical prediction can be confirmed through magnetic susceptibility calculations, and the phase diagram is qualitatively consistent with the mean-field theoretical analysis. Additionally, we have considered the effects of interband interaction between the nearest-neighbor grains and random disorders in diluted lattices with three different site occupancies. When the occupation probability exceeds the percolation threshold, the results are qualitatively similar to those of ordered lattices, and the intermediate phase likewise appears by adjusting the intraband Josephson coupling coefficient. In contrast, below the percolation threshold, such a phase does not exist because the long-range phase coherence for both bands disappears.

We present models of topological insulating Hamiltonians exhibiting intrinsic altermagnetic features, protected by combined threefold or fourfold rotational symmetries with time-reversal. We demonstrate that the spin Chern number serves as a robust topological invariant in two-dimensional systems, while for three-dimensional structures, the topological nature is characterized by the spin Chern numbers computed on the $k_z=0$ and $k_z=\pi$ planes. The resulting phases support symmetry-protected boundary modes, including corner, hinges, and surface states, whose structure is determined by the magnetic symmetry and the local magnetic moments. Our findings bridge the fields of altermagnetism and topological quantum matter, and they establish a theoretical framework for engineering spintronic topological systems without net magnetization.

Single crystals of $(1\text{−}x){\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}{\mathrm{TiO}}_3\text{−}x{\mathrm{BaTiO}}_3$ $\left(\mathrm{NBT}\text{−}x\mathrm{BT}\right)$ with a composition below $(x=0.013)$ and above $(x=0.074)$ the morphotropic phase boundary (MPB) were studied by in situ high-pressure x-ray diffraction with synchrotron radiation and Raman spectroscopy. We show that both compounds undergo a reversible pressure-induced phase transition to structures with $Pnma$ symmetry, regardless of their symmetry at ambient conditions. The high-pressure phase resembles that recently reported for $x_{\mathrm{MPB}}=0.048$ [Sci. Rep. 14, 18799 (2024)], as the critical pressure $p_{\mathrm{c}}$ gradually increases with $x$. However, the pathway of developing the high-pressure phase varies with the composition, revealing distinct ways of Ba incorporation into the NBT matrix for the pseudorhombohedral $(x=0.013)$ and tetragonal $(x=0.074)$ phases. For $x<x_{\mathrm{MPB}}$ the ${\mathrm{Ba}}^{2+}$ cations are preferentially accommodated in the tetragonal-type nanodomains existing in the dominant pseudorhombohedral NBT matrix, whereas for $x>x_{\mathrm{MPB}}$, ${\mathrm{Ba}}^{2+}$ is dispersed in both the rhombohedral nanodomains and the dominant tetragonal matrix. Furthermore, for $x=0.074$ there are incommensurate structural modulations at ambient pressure, which up to $p_c$ remain unaffected by pressure, but vanish above $p_c$.

The stability of localization in the presence of interactions remains an open problem, with finite-size effects posing significant challenges to numerical studies. In this work, we investigate the perturbative stability of noninteracting localization under weak interactions, which allows us to analyze much larger system sizes. Focusing on disordered Anderson and quasiperiodic Aubry-André models in one dimension, and using the adiabatic gauge potential at first order in perturbation theory, we compute first-order corrections to noninteracting local integrals of motion (LIOMs). We find that for at least an $O\left(1\right)$ fraction of the LIOMs, the corrections are well-controlled and converge at large system sizes, while others suffer from resonances. Additionally, we introduce and study the charge-transport capacity of this weakly interacting model. To first order, we find that the charge transport capacity remains bounded in the presence of interactions. Taken together, these results demonstrate that localization is perturbatively stable to weak interactions at first order, implying that, at the very least, localization persists for parametrically long times in the inverse interaction strength. We expect this perturbative stability to extend to all orders at sufficiently strong disorder, where the localization length is short, representing the true localized phase. Conversely, our findings suggest that the previously proposed interaction-induced avalanche instability, namely, in the weakly localized regime of the Anderson and Aubry-André models, is a more subtle phenomenon arising only at higher orders in perturbation theory or through nonperturbative effects.

Nonequilibrium dynamics of unentangled and entangled pure states in interacting quantum systems is crucial for harnessing quantum information and to understand quantum thermalization. We develop a general Schwinger-Keldysh (SK) field theory for nonequilibrium dynamics of pure states of fermions. We apply our formalism to study the time evolution of initial density inhomogeneity and multipoint correlations of pure states in the complex Sachdev-Ye-Kitaev (SYK) models. We demonstrate a remarkable universality in the dynamics of pure states in the SYK model. We show that dynamics of almost all pure states in a fixed particle number sector is solely determined by a set of universal large-$N$ Kadanoff-Baym equations. Moreover, irrespective of the initial state the site- and disorder-averaged Green's function thermalizes instantaneously, whereas local and nonlocal Green's functions have finite thermalization rate. We provide understanding of our numerical and analytical large-$N$ results through random-matrix theory (RMT) analysis. Furthermore, we show that the thermalization of an initial pure product state in the noninteracting ${\mathrm{SYK}}_2$ model is independent of fermion filling and an initial density inhomogeneity decays with weak but long lived oscillations due to dephasing. In contrast, the interacting ${\mathrm{SYK}}_{q\ge 4}$ model thermalizes slower than the noninteracting model and exhibits filling-dependent monotonic relaxation of initial inhomogeneity. For evolution of entangled pure states, we show that the initial entanglement is encoded in the nonlocal and/or multipoint quantum correlations that relax as the system thermalizes.

We study the magnetic and electronic properties of Ni-intercalated ${\mathrm{NbSe}}_2$. We calculate the magnetic exchanges of ${\mathrm{Ni}}_x{\mathrm{NbSe}}_2$ ($x=1/3,1/4,$ and 1) and find that the out-of-plane magnetic coupling depends on the Ni connectivity: it is ferromagnetic when Ni atoms stack on top of each other and antiferromagnetic otherwise. Focusing on ${\mathrm{Ni}}_{0.25}{\mathrm{NbSe}}_2$, we identify a ground-state transition from a stripe antiferromagnetic phase with Kramers degeneracy to a ferromagnetic phase above a critical Coulomb interaction ${\mathrm{U}}_C$. Spin-orbit coupling lowers ${\mathrm{U}}_C$, aligns the easy axis along $z$, and stabilizes collinear antiferromagnetic and ferromagnetic states over the competing ${120}^{\circ }$ phase. Ni intercalation also strongly modifies the electronic structure, replacing the $\mathrm{\Gamma }$-point hole pocket of pristine ${\mathrm{NbSe}}_2$ with an electron pocket and shifting the Van Hove singularity away from the Fermi level, thereby suppressing potential instabilities. Finally, we investigate the altermagnetic phase in the broader class ${\mathrm{T}}_{0.25}{\mathrm{MX}}_2$, finding that spin-orbit effects induce orbital antiferromagnetism with weak ferromagnetism or ferrimagnetism depending on the Néel vector orientation. Our results demonstrate that Ni-intercalated ${\mathrm{NbSe}}_2$ provides a versatile platform to explore and tune multiple competing magnetic phases that lie close in energy.

The commonly believed absence of skyrmion Hall effect for topologically trivial magnetic skyrmions is reconsidered for bilayer skyrmions in synthetic antiferromagnets driven by spin-transfer and spin-orbit torques. Using a general Lagrangian formalism, we show that Bloch-type bilayer skyrmions acquire a finite Hall angle when driven by spin-orbit torque, while Néel-type skyrmions do not, in agreement with micromagnetic simulations. Both types of skyrmions exhibit current-induced elliptical deformation with minor and major axes aligned longitudinally and transversely to their velocity, respectively. A linear relation between velocity and longitudinal radius is derived with a coefficient proportional to the strength of spin-orbit torque. These effects are critical for antiferromagnetic skyrmion-based applications such as skyrmion racetrack memory. The Lagrange equations also reproduce the linear Hall-angle–helicity relation reported by Msiska et al. [Phys. Rev. Appl. 17, 064015 (2022)]. An intuitive explanation of the skyrmion Hall effect for arbitrary helicity based on the antiferromagnetic exchange torque is also provided.

Magnetotoroidal artificial spin ices (MT-ASIs) are arrangements of nanomagnets that exhibit spontaneous toroidization. A ferrotoroidic order could have implications on the propagation of spin waves through this artificial spin ice, including the development of topological edge modes. Here, we numerically investigate the magnetization dynamics of an MT-ASI with and without spatial symmetry breaking. Through micromagnetic simulations, we compute the energies and ferromagnetic resonance spectra of the four lowest-order states, which exhibit ferrotoroidicity, antiferrotoroidicity, and no toroidicity. As expected, we find that the resonant modes split when spatial symmetry is broken. To determine whether our system exhibits topologically protected edge modes, we perform semianalytical calculations to first estimate the ferromagnetic resonance and then compute the band structure. Our results show that symmetry-broken MT-ASIs are reconfigurable by magnetic field protocols, and that their band structures depend on magnetization state. Calculation of the Chern number indicates that the bands are topologically trivial in all cases, suggesting that the dynamic magnetic coupling is weak. The absence of a nonzero Chern number suggests that the dynamic coupling in ASIs is too weak to unlock their full potential in magnonics applications.

In altermagnets, time-reversal symmetry breaking spin polarizes electronic states, while total magnetization remains zero. In addition, at altermagnetic surfaces Rashba–spin orbit coupling is activated due to broken inversion symmetry, introducing a competing spin-momentum locking interaction. Here we show that their interplay leads to the formation of complex, chiral spin textures that offer nonlinear spin-to-charge conversion properties. Whereas altermagnetic order suppresses the canonical linear in-plane Rashba-Edelstein response, we establish the presence of an anomalous transversal Edelstein effect for planar applied electric and magnetic field or, alternatively, an in-plane magnetization. Additionally, we predict a purely electric-field-driven nonlinear out-of-plane magnetization. We compute the anomalous response within a general altermagnet $d$-wave model, with parameters extracted from the ab initio electronic structure of an altermagnetic bilayer. Our results suggest altermagnetic surfaces as a promising platform for unconventional spintronic functionalities.

We theoretically propose and analyze a Josephson-like magnetic tunnel junction (MTJ) structure that exhibits quantum spin dynamics analogous to those in superconducting Josephson junctions. By exploiting the isomorphism between the equations of motion for low-dissipation MTJs with easy-plane anisotropy and the Josephson phase dynamics, we construct a theoretical framework for realizing spintronic qubits. Within this framework, we identify the physical parameters, such as anisotropy constants, Gilbert damping, spin current amplitude, and geometric factors, that govern the transition from classical to quantum behavior. We show that different types of spintronic qubits, including analogs of charge, flux, and transmon superconducting qubits, can be implemented depending on the hierarchy of energy scales. A Hamiltonian formalism is developed for each regime, enabling an analytical treatment of the two-level quantum dynamics and estimation of coherence times. In particular, we demonstrate that the spin current can be used not only to excite but also to stabilize the qubit states through dissipation control. These findings provide a route toward integrating spintronic qubits into complementary metal-oxide-semiconductor compatible architectures and lay the groundwork for a fully spintronic platform for quantum computation.

${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$ has been proposed as a candidate for realizing the Kitaev quantum spin liquid (QSL). Its intriguing magnetic properties have motivated extensive investigations into its ground state and spin excitation spectrum. A central question concerns whether an in-plane magnetic field can stabilize a QSL state with fractionalized excitations prior to full spin polarization. Using time-domain terahertz spectroscopy, we systematically study the magnetic excitations in ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$ within the field-induced intermediate state regime (6 T $<B<$ 10 T). At 5 K, we observe a broad excitation feature superimposed on multiple sharp modes corresponding to magnons. Field-dependent measurements reveal that both the sharp modes and the continuum exhibit magnetic dipole activity. However, their temperature evolution is different. Temperature-dependent measurements at 10 T demonstrate that the sharp modes disappear abruptly near 15 K, consistent with the expected phase boundary. Conversely, the continuum intensity maximizes at this temperature and persists up to at least 40 K. The survival of the broad excitation continuum above the ordering temperature suggests strong spin correlations and quantum fluctuations in this regime.

We investigate the superconductivity of two-dimensional spin-1/2 Fermi systems with $d$-wave altermagnetism under external magnetic field near zero temperature. At large altermagnetic coupling, without magnetic field, we show that altermagnetism drives a second-order phase transition from the standard Bardeen-Cooper-Schrieffer (BCS) state to an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The inclusion of a magnetic field turns the BCS state into a long-sought polarized BCS superconductor with spin-population imbalance. It also shrinks the parameter window of the FFLO state and eventually leads to a nontrivial quantum tricritical Lifshitz point, where two second-order phase transition lines between the polarized BCS, FFLO, and normal states intersect. At small altermagnetic coupling, we find the usual route to the FFLO state driven by magnetic field. The presence of altermagnetic coupling narrows the phase window of the FFLO state and creates another quantum Lifshitz point, where a first-order transition curve meets a second-order transition line. Between the two Lifshitz points, the transition from the polarized BCS state to the normal state is smooth. Our predicted rich phase diagram is relevant to some recently discovered unconventional magnets, including ${\mathrm{RuO}}_2$ that exhibits a relatively high superconducting temperature in the thin film limit under applied strain. Our results of unconventional superfluidity are also testable in ultracold atom laboratories, where a spin-1/2 altermagnetic Fermi gas might be realizable upon loading into two-dimensional Hubbard lattices.

The recently discovered bilayer Ruddlesden-Popper nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ exhibits superconductivity with a remarkable transition temperature $T_c\approx 80$ K under applied pressures above 14.0 GPa. This discovery of a new family of high-temperature superconductors has garnered significant attention in the condensed matter physics community. In this work, we assume this high-temperature superconductor is mediated by phonons and investigate the pairing symmetry in two distinct models: (i) the full-coupling case, where the Ni-$d_{x^2-y^2}$ and Ni-$d_{3z^2-r^2}$ orbitals are treated equally in both interlayer and intralayer coupling interactions, and (ii) the half-coupling case, where the intralayer coupling involves only the $d_{x^2-y^2}$ orbital, while the interlayer coupling is restricted to the $d_{3z^2-r^2}$ orbital. Our calculations reveal that the interlayer coupling favors an $s\pm$-wave superconducting state, whereas the intralayer coupling promotes an $s++$-wave symmetry. Additionally, we discuss the implications of pair-hopping interactions on the superconducting properties. These findings provide valuable insights into the pairing mechanisms and symmetry of this newly discovered high-temperature superconductor.

Correlated electron physics is intrinsically a multiscale problem, since high-energy electronic states screen the interactions between the correlated electrons close to the Fermi level, thereby reducing the magnitude of the interaction strength and dramatically shortening its range. Thus the handling of screening is an essential ingredient in the first-principles modeling of correlated electron systems. Screening is an intrinsically dynamic process and the corresponding downfolding methods such as the constrained random phase approximation indeed produce a dynamic interaction. However, many low-energy methods require an instantaneous interaction as input, which makes it necessary to map the fully dynamic interaction to an effective instantaneous interaction strength. It is a priori not clear if and when such an effective model can capture the physics of the one with dynamic interaction and how to best perform the mapping. Here, we provide a systematic benchmark relevant to correlated materials, in the form of the Anderson impurity model. Overall, we find that a static approximation can be valid and that the moment-based approach recently proposed by Scott and Booth can be a good tool to find the value of the static interaction. We also identify physical regimes, especially under doping, where an instantaneous interaction cannot capture all of the relevant physics.

This paper investigates the energy and angular momentum radiation of altermagnets under Rashba spin-orbit coupling (RSOC) and external magnetic fields. Using an effective low-energy Hamiltonian, we derive electronic energy bands and calculate optical conductivity via the Kubo formula. Results show that RSOC strength, altermagnet interactions strength, and Néel vector direction notably affect the optical conductivity of altermagnet metals. Energy radiation is highly sensitive to Rashba spin-orbit coupling, with a saturation effect beyond a particular value, and its peak emission rate is lower than that of graphene due to reduced conductivity. Different from usual semiconductor, semimetal, or Dirac materials, e.g., graphene or silicene, altermagnets generate angular momentum radiation with specific Rashba spin-orbit coupling and altermagnet interaction strength. Angular momentum radiation is minimally reactive to Rashba spin-orbit coupling at low altermagnet interactions strength values but exhibits drastic oscillations between extreme values as altermagnet interactions strength reaches a critical point, showing high sensitivity. These findings suggest that adjusting these parameters can tailor altermagnet applications in spintronics and quantum technologies, potentially leading to innovative devices with customized radiation attributes.