${\mathrm{EuAl}}_4$, a centrosymmetric magnetic rare-earth transition-metal intermetallic compound, exhibits intriguing properties, such as topological states and topological magnetic textures (skyrmions). The surface termination and morphology of the cleaved surface are still not fully explored, leading to a challenging understanding of surface sensitive measurements. Here, the cleaved ${\mathrm{EuAl}}_4\left(001\right)$ surface is studied via scanning tunneling microscopy and spectroscopy (STM/S) and low-energy electron diffraction (LEED). Topographic images reveal a step-and-terrace morphology with terrace sizes ranging from a few nanometers to a few microns. The step heights are determined to be predominately one-half unit cell ($\sim 5.58\AA$). The terraces exhibit a surface morphology with a roughness of $\sim 1.50\AA$. This is believed to be caused by equivalent Eu-Al and Al-Eu cleavage planes due to the centrosymmetric crystal structure together with the energetic cleaving process that disrupts the surface topography. Spectroscopic measurements on the surface yielded three distinct types of spectra, primarily contributed by Al adatoms (type 1), Eu adatoms (type 2), and a combination of both (type 3), as elucidated with the help of density functional theory calculations. Our results show that the cleaved ${\mathrm{EuAl}}_4$ (${\mathrm{BaAl}}_4$ family) surface exhibits a higher level of disorder than ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type compounds.

Altermagnets are a novel platform to realize exotic electromagnetic properties distinct from those of conventional ferromagnets and antiferromagnets. We report results of microfocused angle-resolved photoemission spectroscopy (ARPES) on ${\mathrm{RuO}}_2$, in which its altermagnetic nature has been under fierce debate in connection with crystal-orientation-dependent spintronic functionalities. By elucidating the band structure of the (100), (110), and (101) surfaces of a bulk single crystal using micro-ARPES, we found that, irrespective of the surface orientation, the experimental band structures show a good agreement with the bulk-band calculations for the nonmagnetic phase, but display a severe disagreement with those for the antiferromagnetic phase. Moreover, spin-resolved ARPES signifies a negligible spin polarization in the bulk bands, suggesting the absence of antiferromagnetism and altermagnetic spin splitting. In addition, we identified a nearly flat surface band and a dispersive one near the Fermi level at the (100)/(110) and (101) surfaces, respectively. Our first-principles calculations and analysis of Berry phase attribute these states to the topological surface bands emerging from the bulk Dirac nodal lines around the Fermi level. Our results indicate that such topological surface/interface states must be considered to understand the spintronic functionalities of ${\mathrm{RuO}}_2$ and may provide new insights into its catalytic characteristics.

Materials tunable between heavy-fermion metals and antiferromagnetic insulators near quantum criticality are promising candidates for exploring unconventional superconductivity, yet such a behavior is rare in transition metal oxides. Here, we report the high-pressure synthesis and characterization of two Pb-based $A$-site ordered perovskites, ${\mathrm{PbCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ and ${\mathrm{PbCu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$, which are characterized as a heavy-fermion metal and an antiferromagnetic insulator, respectively. Systematic $B$-site substitution in ${\mathrm{PbCu}}_3{\mathrm{Ru}}_{4-x}{\mathrm{Ti}}_x{\mathrm{O}}_{12}$ ($x=0-4$) reveals a continuous evolution of electronic and magnetic properties, with intermediate compositions exhibiting divergent low-temperature specific heat, indicative of proximity to a quantum critical point. The experimental observation supported by density functional theory calculations reveal that ${\mathrm{PbCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$ exhibits more enhanced effective mass than ${\mathrm{CaCu}}_3{\mathrm{Ru}}_4{\mathrm{O}}_{12}$, attributed to its enhanced Fermi-level density of states and narrower bandwidth, driven by the elongated Ru-O bonds and the covalent character of ${\mathrm{Pb}}^{2+}$. These results establish ${\mathrm{PbCu}}_3{\mathrm{Ru}}_{4-x}{\mathrm{Ti}}_x{\mathrm{O}}_{12}$ as a rare platform to study quantum criticality and strong correlations in transition-metal oxides and demonstrate that combine $A$-site and $B$-site tuning provides an effective route to tailor electronic and magnetic properties.

We present a first-principles study of a carbon-nitrogen (CN) impurity complex in silicon as an isoelectronic alternative to the $T$ center [(CCH)${}_{\mathrm{Si}}$]. The latter has been pursued for applications in quantum information science, yet its sensitivity to the presence of hydrogen is still problematic. Our proposed complex has no hydrogen, thereby eliminating this issue. First, we show that the CN complex is stable against decomposition into substitutional and interstitial defects. Next, we show that due to being isoelectronic to the $T$ center, the CN complex has a similar electronic structure, and therefore could be used in similar applications. We assess several low-energy configurations of the CN complex, finding (CN)${}_{\mathrm{Si}}$ to be stable and have the largest Debye-Waller factor. We predict a zero-phonon line (ZPL) of 828 meV (in the telecom $S$ band) and a radiative lifetime of 4.2 $\mu \mathrm{s}$, comparable to the $T$ center. Due to the presence of a bound exciton, choice of the exchange-correlation functional and also supercell-size scaling of the ZPL and transition dipole moment require special scrutiny; we rigorously justify our extrapolation schemes that allow computing values in the dilute limit.

Caustics are intricate and challenging to control near-field interference patterns that exist in a wide range of physical systems, and which usually exhibit a reciprocal wave propagation. Here, we utilize the highly anisotropic dispersion and inherent nonreciprocity of a magnonic system to shape nonreciprocal emission of causticlike spin wave beams in an extended yttrium iron garnet (YIG) film from a nanoconstricted waveguide. We introduce a near-field diffraction model to study spin-wave beam forming in homogeneous in-plane magnetized thin films, and reveal the propagation of nonreciprocal spin-wave beams directly emitted from the nanoconstriction by spatially resolved microfocused Brillouin light spectroscopy. The experimental results agree well with both micromagnetic simulation, and the near-field diffraction model. The proposed method can be readily implemented to study spin-wave interference at the sub-µm scale, which is central to the development of wave-based computing applications and magnonic devices.

For one-dimensional noninteracting complex fermions we compute numerically the probability distribution of the change in the entanglement entropy (EE) after saturation resulting from a single measurement of the occupation number by using different measurement protocols. In the thermodynamic limit, the system is in the area-law phase for any monitoring strength, however we can also study the distribution in the critical phase characterized by a logarithmic scaling of the EE with system size by considering a sufficiently weak monitoring strength. For a quantum state diffusion protocol, where the change in EE is defined between two consecutive time steps, the distribution, Gaussian for weak monitoring, gradually develops symmetric exponential tails. For strong monitoring, the core turns from Gaussian to strongly peaked at zero suggesting the dominance of quantum Zeno effect. For the quantum jump and the projective measurement protocols, we observe clear deviations from Gaussianity characterized by broader and asymmetric tails, exponential for positive values of the change, and a peak at zero, likely a precursor of Zeno effect, that increases with the system size and the monitoring strength. Intriguingly, the distribution is spatially inhomogeneous. For sites around the boundary separating the subsystems defining the EE, the distribution is close to Gaussian with a broad support while for the rest of the sites it has asymmetric exponential tails and a much narrower support. As the monitoring strength increases, the full distribution is controlled by the boundary sites.

We consider learnability transitions in monitored quantum systems that undergo noisy evolution, subject to a global strong symmetry—i.e., in addition to the measuring apparatus, the system can interact with an unobserved environment, but does not exchange charge with it. As in the pure-state setting, we find two information-theoretic phases—a sharp (fuzzy) phase in which an eavesdropper can rapidly (slowly) learn the symmetry charge. However, because the dynamics is noisy, both phases can be simulated efficiently using tensor networks. Indeed, even when the true dynamics is unitary, introducing noise by hand allows an eavesdropper to efficiently learn the symmetry charge from local measurements, as we demonstrate. We identify the fuzzy phase in this setting as a mixed-state phase that exhibits spontaneous strong-to-weak symmetry breaking.

We explore the nonreciprocity of spin-wave excitations in the Rashba-Hubbard ferromagnet on a square lattice. Our study reveals that the propagation of spin-wave excitations exhibit nonreciprocal behavior, i.e., spin waves traveling in opposite directions display asymmetry in energy dispersion $\omega \left(\mathbf{q}\right)\ne \omega (-\mathbf{q})$, which also results in an asymmetric behavior of group velocity, spin stiffness, etc. We find that this asymmetric behavior arises only when the magnetic moments are aligned inside the atomic plane, while the excitations remain symmetric for out-of-plane magnetization. The first dominating term in the low-energy dispersion is linear. However, if the magnetic moments are out-of-plane, then the first dominant term is quadratic instead. The low-energy nonquadratic behavior is examined in the intermediate-to-strong coupling regime for various strengths of Rashba spin-orbit coupling.

$\alpha \text{-MnTe}$ is a $p$-type semiconducting altermagnet with a Néel temperature near $300\text{K}$. Due to the altermagnetic nature, $\mathcal{PT}$ symmetry is broken and Kramers degeneracy is lifted in the valence band maxima along the $\mathrm{\Gamma }\text{−}K$ line and the $A$ point. However, the energy difference is found to be small, and any small shift in the spectrum can dramatically change the linear-response transport properties. Here we show that a strain modulating the [0001] axis of the unit cell by $\sim \pm 0.5\%$ can significantly change the transport signature by switching the thermal window between the two regions of the valence band. When the $\mathrm{\Gamma }\text{−}K$ line is dominating, the planar Hall effect and the anisotropic magnetoresistance can be enhanced by an order of magnitude, with the maximum up to $\sim 70\%$.

A microscopic understanding of magnetic exchange parameters beyond the conventional Heisenberg and Dzyaloshinskii-Moriya interaction (DMI) is crucial for $3d$ difluorides, particularly for ${\mathrm{NiF}}_2$, where spins are tilting about $0.{43}^{\circ }$ along the $z$ axis, which cannot be explained by DMI. It was proposed by Moriya Phys. Rev. 117, 635 (1960) that this canting is related to single-site anisotropy, but the anisotropic contribution to magnetic exchange remains insufficiently addressed. It is unclear what role anisotropic exchange plays in comparison with single-site anisotropy, which can also induce a spin canting. Motivated by Moriya’s work, we have calculated from first principles the full anisotropic exchange matrix for $3d$ rutile difluorides and performed a systematic comparison of ${\mathrm{MnF}}_2, {\mathrm{FeF}}_2, {\mathrm{CoF}}_2$, and ${\mathrm{NiF}}_2$. Our approach integrates symmetry-based spin-Hamiltonian construction and first-principles calculations, enabling the determination of the minimal form of the magnetic exchange matrix in the presence of spin-orbit coupling.

Non-Fermi liquid behavior occurs in systems with enhanced electron correlation, violating the conventional Landau's Fermi liquid theory. Understanding the nature of this behavior remains an essential aspect of studying unconventional superconducting and quantum phase transitions. In this paper we report the potential presence of non-Fermi liquid behavior in single crystals of ${\mathrm{TbAl}}_2{\mathrm{Si}}_2$ with ${\mathrm{CaAl}}_2{\mathrm{Si}}_2$-type structure. The magnetic susceptibility and heat capacity reveal two magnetic phase transitions at $T{}_{N1}$ = 15.5 K and $T{}_{N2}$ = 12.5 K. Multiple field-induced magnetic phase transitions are observed in field-dependent magnetization. Neutron powder diffraction reveals an incommensurate spin density wave order for ${\mathrm{TbAl}}_2{\mathrm{Si}}_2$ with a propagation vector $k$ = (0, 0.283, 0.0262) below $T_{N1}$ and a spin reorientation transition at $T_{N2}$. Moreover, the electrical resistivity of ${\mathrm{TbAl}}_2{\mathrm{Si}}_2$ exhibits a nearly linear temperature dependence at 2–5 K reminiscent of non-Fermi liquid behavior, which is also confirmed by the logarithmic increase of magnetic susceptibility $\chi$ in the same temperature range. Upon ramping up the magnetic field, the non-Fermi-liquid-like behavior remains robust until it evolves into a Fermi liquid state at 40 kOe. As a result, this possible coexistence of non-Fermi liquid behavior and an incommensurate spin density wave in a Tb-based compound provides opportunities for investigating non-Fermi liquid behavior and its correlation with magnetism.

Electrical manipulation of chiral noncollinear antiferromagnetic (AFM) order via spin-orbit torque (SOT) has attracted significant attention in terms of both fundamental insights and applications in information technology. Here we investigate the alternating chirped current pulse (ACCP) driven resonant excitation of noncollinear AFM order of pristine ${\mathrm{Mn}}_3\text{Sn}$, and thus achieves efficient reversal of octupole moment, defined as a cluster magnetic order parameter, without an external field. The reversal proceeds via out-of-plane rotation of the octupole moment, whose precessional dynamics exhibit a counter-rotation relative to the atomic moments. The enhanced efficiency of field-free deterministic switching arises from resonant energy exchange between the octupole moment and the SOT fields in ACCP: the octupole moment resonantly absorbs (emits) energy from (to) the SOT fields before (after) crossing the energy barrier. Therefore, these findings deepen the understanding of field-free SOT-driven octupole moment dynamics and propose a pathway toward ultrafast, low-power spintronic devices.

Scanning tunneling microscopy (STM) measurements have been extensively performed on the easily cleavable (011) surface of ${\mathrm{UTe}}_2$, using both normal-metal and superconducting tips. Motivated by these experiments, we theoretically investigate the topological surface states on the (011) surface of ${\mathrm{UTe}}_2$. We find that a two-dimensional nearly flat band emerges in the $B_{3u}$ state, giving rise to a pronounced zero-energy peak in the surface density of states. This flat band is supported by two key mechanisms: (i) nontrivial Berry phases defined at multiple momenta give rise to low-energy in-gap states, and (ii) weak spin conservation allows the gap function to acquire phase winding. Furthermore, to investigate the relation between the zero-bias peak observed in recent STM experiments with a superconducting tip and the topological surface states, we calculate the nonequilibrium dc tunneling current in a junction between an $s$-wave superconductor and the (011) surface of ${\mathrm{UTe}}_2$. Our results provide crucial insights into the superconducting pairing symmetry realized in ${\mathrm{UTe}}_2$.

Strong disorder drives conventional Hermitian systems into Anderson insulating states, suppressing all topological phases. Here, we unveil symmetry-protected, anomalous topological phases in the strong disorder limit of a non-Hermitian system, characterized by a scale-invariant merging of zero-energy modes. Using the maximally symmetric $J_x$ lattice as an ideal platform and introducing specifically engineered (ABBA-type) symmetry-preserving non-Hermitian disorder, we observe a sequence of disorder-induced phase transitions: from a trivial insulator into and through a non-Hermitian topological Anderson insulator (TAI) phase, culminating in a stable anomalous non-Hermitian TAI phase characterized by a quantized polarization $P_x\approx 0.25$. Within this anomalous phase protected by the mobility gap, the zero-energy modes exhibit a distinct ($N$/2)-mode coalescence that scales with system size. Our findings demonstrate that non-Hermitian disorder engineered to preserve symmetry can induce and protect novel topological order inaccessible to conventional Hermitian disorder, thereby advancing the fundamental understanding of topological phenomena mediated by the interplay of disorder and non-Hermiticity.

The stable and metastable magnetic orders in one-dimensional PtFePt and PtMnPt stripes, as well as the collective spin reorientations connecting them, are investigated by combining first-principles electronic theory with a detailed characterization of the associated energy landscapes. The relative stability of collinear and noncollinear magnetic orders is determined within density-functional theory by computing the frozen-magnon dispersion relations ${\varepsilon }_{\delta \gamma }^{\alpha }\left(q\right)$ as functions of wave number $q$, spin-polarization plane $\delta \gamma$, and chirality $\alpha =\pm 1$. The effective interactions between the local magnetic moments ${\mathit{\mu }}_i$ at the $3d$ transition metal atoms are derived, including the local magnetic anisotropy energies $K_i^{\delta }$, the symmetric exchange couplings $J_{ij}^{\delta }$, and the Dzyaloshinskii-Moriya (DM) vectors ${\mathit{D}}_{ij}$, where $\delta =x,y,z$ denotes the direction relative to the stripe geometry. The consequences of applying an external electric field (EF) on the magnetic couplings are quantified. Significant DM interactions are triggered by the EF, which breaks the inversion symmetry of the stripes. First-nearest-neighbor DM coupling dominates in ferromagnetic PtFePt, whereas second-nearest-neighbor DM coupling dominates in antiferromagnetic PtMnPt. The magnetic energy landscapes of the corresponding classical spin Hamiltonians $H\left[{\mathit{\mu }}_i\right]$ are systematically explored without imposing any constraints on the orientations of ${\mathit{\mu }}_i$. The metastable magnetic configurations involve domain walls (DWs) superimposed on the ferromagnetic (PtFePt) or antiferromagnetic (PtMnPt) backgrounds, whose width can be tuned by the applied EF. The morphology of the transition states and the minimum-energy paths connecting the local minima reveal the mechanisms for the creation, annihilation, and translation of magnetic domains (MDs). One observes that MDs with walls of opposite chirality, yielding a total winding number ${\eta }_z=0$, identical to that of the ground state, are unstable, whereas domains with walls of the same chirality and ${\eta }_z=\pm 1$ are stabilized by significant energy barriers. Extremely small upper bounds for the energy barriers associated with domain-wall translations along the stripes are found, implying remarkably high mobility. The roles of the microscopic interactions $K_i^{\delta }, J_{ij}^{\delta }$, and ${\mathit{D}}_{ij}$ in the topological protection, energy barriers, and relative stability of magnetic configurations are disclosed. The present investigations may serve as a methodological blueprint for advancing our understanding of the local-environment dependence of interactions between magnetic moments, their role in collective responses and relaxation processes, and the energy landscapes that underlie the physics of magnetic low-dimensional systems and nanostructures.

Chains of triangular nanographene (triangulene), recently identified as realizing the valence-bond solid phase of a spin-1 chain, offer a promising platform for quantum information processing. We propose a spin-singlet qubit based on these chains grown on a superconducting substrate. Using the numerical renormalization group (NRG), we identify a manifold consisting of the two lowest-lying, spin-singlet states isolated from doublet states of opposite fermion parity, which undergo an avoided crossing. A qubit utilizing these states is thus protected from random Zeeman and/or spin-orbit coupling. Despite the unavoidable effect of quasiparticle poisoning on qubit performance, the isolation of the singlet states offers additional protection. In addition, we introduce a mesoscopic device architecture, based on a triple quantum dot coupled to a superconducting junction, that quantum simulates the spin chain and enables control and readout of the qubit. An effective two-level description of the device is validated using time-dependent NRG.

We consider superconductivity in two-dimensional delicate topological bands, where the total Chern number vanishes but the Brillouin zone can be divided into subregions with a quantized nontrivial Chern number. We formulate a lower bound on the geometric contribution to the superfluid weight in terms of the sum of the absolute values of these sub-Brillouin zone Chern numbers. We verify this bound in Chern dartboard insulators, where the delicate topology is protected by mirror symmetry. In iso-orbital models, where the mirror representation is the same along all high-symmetry lines, the lower bound increases linearly with the number of mirror planes. This work points to delicate bands as promising candidates for particularly stable superconductivity, especially in narrow bands where the kinetic energy is suppressed due to lattice effects.