Papers

We investigated the electronic structure of a delafossite oxide CuAlO$_2$ in comparison with CuCrO$_2$, using vacuum ultraviolet (VUV) and hard x-ray (HX) photoemission spectroscopy (PES) and band structure calculations within the local-density approximation +$U$ scheme. Cu 3$p\! -\! 3d$ resonant PES and Cu $2p$ core-level HX-PES give concrete evidence that the Cu valence in CuAlO$_2$ is monovalent, which makes a sharp contrast to CuCrO$_2$ that showed contradictory results depending upon probing methods [Yokobori et al., Phys. Rev. B 87, 195124 (2013)]. We further noticed weak but detectable satellite structures due to Cu$^{2+}$ state in the Cu $2p$ HX-PES spectrum of CuCrO$_2$, surprisingly, without an observable main peak due to the Cu$^{2+}$ state. Comparisons between the valence-band HX-PES spectra and the band structure calculations revealed a significant amount of the Cu $4s$ and Al $3s$/Cr $4s$ states in the valence band. The above results can reasonably be explained by the Cu $3d, 4s-$Cr $3d$ charge transfer model that we previously proposed in the above paper, thereby demonstrating the critical role of empty $3d$ orbitals in the electronic structure of the copper delafossite oxides.

Manipulating spin using contactless and non-invasive optical approaches is one of the forefront topic in the modern spintronic science and technology. Prior studies on optically-induced spin reorientation usually scales with spin-orbit coupling strength, setting a limitation on composing heavy elements. In this work, we extend such a limit into nonrelativistic regime by exploring noncollinear magnetic configuration. Using a general spin group-theoretical investigation, we show how the symmetric operators in both spin and lattice spaces control the spin torque and quantum geometry of Bloch wavefunction–including both quantum metric and Berry curvature. We describe their site-resolved spin symmetries and unravel their selection rules. Furthermore, we adopt a Kagomé lattice model and a realistic material family to showcase the local spin torque under light irradiation. Since the nonrelativistic spin splitting usually spans on the order of electron-volt, significantly larger than typical spin-orbit induced splitting, the nonrelativistic light-induced spin torque is concomitantly much stronger. This work extends the previous opto-spintronics from relativistic to nonrelativistic limit, significantly broadening its realization platform.

Topological insulators lie outside the standard Landau paradigm: Instead of being characterized by local order parameters and spontaneous symmetry breaking, their defining properties are encoded in the global structure of their quantum states and manifested as robust boundary states. Crystalline higher-order topological insulators can extend this principle by hosting localized corner modes in two and higher dimensions. Although these boundary modes can be detected spectroscopically through the local density of states, determining the underlying bulk topology, for example through nested Wilson loops, remains an outstanding experimental challenge. Here we use up to 728 qubits in a superconducting analogue-digital quantum simulator to realize and probe a hierarchy of one-, two-, and three-dimensional topological insulators governed by effective tight-binding Hamiltonians. By reconstructing complex propagators from real-space measurements, we obtain complementary boundary and bulk characterizations: local densities of states reveal localized boundary modes, whereas experimentally reconstructed band projectors yield bulk topological invariants, culminating in a three-dimensional octupole moment extracted through third nested Wilson loops. These results establish a route to realizing, characterizing, and manipulating topologically protected states in programmable three-dimensional quantum matter.

Models of curvature-driven membrane sorting couple composition directly to membrane bending elasticity. Here we show that shape deformations can destabilize a homogeneous state without this composition-dependent mechanical coupling. We analyze the eigenspectrum of the Laplace-Beltrami operator on deformed spheres analytically, and verify it numerically. As the deformation amplitude increases, the spectral degeneracy breaks, and the lowest nonzero eigenvalue decreases substantially. Using Cahn-Hilliard dynamics, we show that this eigenvalue softening provides a purely geometric route to phase separation.

We present an empirical model that analytically relates the parameters of the extended Kubo-Toyabe (KT) function $G_z^{\rm EA}(t;\Delta,\nu_{\rm i},Q)$, which describes muon spin relaxation ($\mu$SR) induced by jump diffusion of ions using the Edwards-Anderson parameter $Q$, to those of the conventional KT function $G_z^{\rm KT}(t;\Delta_{\rm KT},\nu_{\rm KT})$ that serves as an approximation of $G_z^{\rm EA}(t)$. The proposed formulae successfully reproduce the anomalous temperature dependences of the linewidth $\Delta_{\rm KT}(T)$ and the fluctuation rate $\nu_{\rm KT}(T)$ which are artifacts observed upon analyzing $\mu$SR data on ion diffusion using $G_z^{\rm KT}(t)$. Applying this model to $\Delta_{\rm KT}$ and $\nu_{\rm KT}$ published in the literature of battery materials yields activation energy $E_{\rm i}$ and pre-exponential factor $\nu_{\rm i0}$ in the Arrhenius equation for ion diffusion, $\nu_{\rm i}(T)=\nu_{\rm i0} e^{-E_{\rm i}/kT}$, that are in excellent agreement with those deduced using other techniques, transforming peculiar artifacts into a powerful diagnostic tool.

Superionic conductors are promising electrolyte candidates for all-solid-state batteries, thanks to their liquid-like ionic mobility. In the prototypical lithium-ion oxide superionic conductor with antifluorite structure, the high-temperature transition to the fast-ion regime has long been attributed to volume-driven harmonic phonon softening. However, this quasi-harmonic picture neglects the strong lattice anharmonicity inherent to the fast-ion regime, leaving the microscopic origin of the transition unresolved. Here, we apply non-perturbative lattice dynamics combined with a first-principles-accurate machine-learning interatomic potential to study the phase transition in Li$_2$O. We demonstrate that anharmonicity, rather than volume expansion alone as commonly assumed, plays the decisive role in determining the transition temperature and the underlying mechanism. Finally, we analyze the spectral properties using the time-dependent self-consistent harmonic approximation, revealing the breakdown of the quasi-particle picture in this material. The spectral function and the infrared response provide signtures of the phase transition that can be investigated experimentally using inelastic neutron or X-ray scattering and infrared spectroscopy. All these results establish the extreme anharmonicity of Li$_2$O near the superionic regime and provide a lattice-dynamic framework for understanding and engineering the fast-ion transition in this type of materials.

The accurate estimation of the ionic activity coefficients is paramount for the characterization of the electrochemical reactions driving energy storage processes as well as the biological mechanisms involving ATP hydrolysis. The numerical evaluation of the ionic activity coefficients by computational methods is rendered difficult by the infinite dilution limit involved in the integral identity between the Helmholtz free energy and the equation of state of the electrolyte. By combining a recently introduced self-consistent Debye-Huckel formalism and its analytically tractable low density limit, we develop a computationally efficient approach enabling the accurate calculation of the free energy and the related thermodynamic functions of aqueous electrolytes over a broad range of ionic concentration and electrostatic coupling strength. Via comparison with numerical simulations and experimental data, it is shown that our approach can predict the salt dependence of the Helmholtz free energy, the entropy, and the ionic activity coefficients from the electrostatically driven submolar ion concentrations to the hard-core dominated molar density regime.

Fracture in polymer networks is strongly influenced by how network architecture and topology organize damage in space. Although these materials can sustain large deformations under homogeneous loading, they often fail in a brittle and flaw-sensitive manner once defects are present. Here we show that network heterogeneity is one key architectural parameter controlling this transition. Using a discrete mesoscale network model that explicitly resolves strand-level prestretch, force transmission, and irreversible bond scission, we demonstrate that heterogeneity in prestretch and strand lengths broadens crack-induced deformation, delocalizes bond rupture, and enlarges the fracture process zone. In polydisperse networks, increasing contour-length disorder broadens the prestretch distribution and systematically increases both toughness and the intrinsic length scale governing flaw sensitivity. Bimodal networks amplify this mechanism further through combined contrasts in prestretch and strand lengths, producing the largest damage zones and the highest toughness among the architectures studied. Inspired by the results, we derive a scaling estimate relating the emergent fracture-active length to the spatial range of crack-induced deformation and the logarithmic spread of strands' remaining stretch to rupture.

Short-wavelength spin waves are central to miniaturizing magnonic devices and to studying exchange-dominated magnetization dynamics. Yet the wave-vector range between roughly 30 and 300 radians per micrometre has remained difficult to access experimentally, posing challenges for both excitation and detection. This Perspective reviews recent advances in emerging measurement techniques and discusses prospects for their future development. Optical and microwave techniques are restricted to the vicinity of the Brillouin-zone centre. Inelastic neutron, electron and resonant hard x-ray scattering cover the full Brillouin zone but lack the energy resolution needed for low-frequency magnons at intermediate wave vectors. This Perspective examines five emerging approaches that are beginning to close this gap: Mie-enhanced Brillouin light scattering, colour-centre magnetometry, magnon momentum microscopy, extreme-ultraviolet transient-grating spectroscopy, and time-resolved scanning transmission x-ray microscopy. For each, we discuss the physical principle, demonstrated capabilities, current limitations and prospects for development. Compared side by side, the techniques give complementary access to magnon frequencies, local stray fields, real-space dynamics and momentum-space distributions, and they differ in their sensitivity to coherent and incoherent excitations. We therefore discuss the main advantages and use cases of each technique and consider the practical requirements for addressing different scientific questions. We highlight opportunities for further development, including higher sensitivity, improved spatial and temporal resolution, and broader frequency and wave-vector coverage. Together, these advances could enable, for example, systematic studies of nonlinear magnon interactions at nanoscale wavelengths and investigations of emerging magnetic materials such as altermagnets.

In Fermi's 1926 note, the expression assigned to the probability that all partial sums remain below a threshold is the complementary crossing probability. We obtain the correct probability from the same diffusion equation and locate the inconsistency in the final integration. We then state the limit for independent increments under the Lindeberg condition. A counterexample with smooth densities shows that small individual variances do not suffice to justify this limit. The probabilistic results are classical; the purpose of this note is to reconcile the stated event with the printed calculation and to make the sufficient hypotheses for the discrete limit explicit.

In this study, an artificial intelligence-assisted evaluation of the refractive indices of different materials is performed. The evaluation of the refractive index is necessary to design photonic devices for various classical and quantum photonic applications, and to theoretically analyse experimental results. The refractive index is one of the crucial parameters that affect the interaction of light with matter. Although the refractive index can be measured experimentally, its estimation via computational means provide the advantage of not requiring costly instrumentation, trained researchers and could avoid potential laboratory-based uncertainties. Therefore, in this study, artificial intelligence is implemented to estimate the optical constants of two types of materials, i.e., noble metals, and semiconductors. To this end, an artificial neural network is used to estimate the real and the imaginary parts of the refractive index of a specific material for various wavelengths of light. Then, the knowledge of the trained neural network is employed to initiate and train new neural networks to estimate the refractive indices of other materials. For the training of a neural network, various methods can be deployed. However, the application of the training can be a time-consuming process. A transfer learning approach is here implemented to provide a faster training solution for the problem under study. The implementation of transfer learning allows training the neural networks for a new material with higher speed or accuracy when compared to non-knowledge transfer-based training. Our results show the efficiency of the proposed technique in accurately evaluating the real and imaginary parts of the refractive index of different materials.

Local out-of-time-order correlators (OTOCs) measure the growth of initially small commutators. For bounded local operators, this growth ends when the local commutator becomes of order one, but in an extended system the region over which it is large can continue to expand. We study this spatial proliferation using three related observables: the local squared commutator $C_r(t)$, its spatial sum $\bar C(t) = \sum_r C_r(t)$, and the symmetrically regularised connected dOTOC $D(t)$ of two extensive observables. We show that Lieb–Robinson locality gives $\bar C(t) \lesssim t^d$. We then prove that, in a Gibbs state with uniform exponential clustering, the full dOTOC obeys the same bound, $D(t) \lesssim t^d$, improving our earlier suboptimal $t^{3d}$ bound. We illustrate these results in two quantum many-body systems: a Brownian coupled-cluster model and a finite-temperature SYK chain. In both cases, an exact disorder symmetry relates $D(t)$ to $\bar C(t)$ and allows us to follow the same extensive observable from the pre-scrambling Lyapunov regime into the post-scrambling growth associated with an expanding saturated region. This late-time power-law growth is the concrete realisation of the weak quantum chaos introduced in our earlier work.

Quantum localization, the phenomenon by which wave diffusion is halted, here understood as the superposition of propagating waves, can have many different origins, such as onsite random potentials in Anderson localization. However, some systems exhibit complex geometries and could potentially reproduce similar results without external potentials. In this work, we study how localization of single particle states is affected by the underlying topology of a simple but highly predictive complex network model: the geometric soft configuration model $\mathbb S^1$. By tuning the model's temperature and heterogeneity parameters, we are able to generate different structural patterns and focus on the transition from a small-world to a non-small-world regime. Our study suggests that small-world networks tend to have extended states, which spread the whole system's size, in contrast to non-small-world networks which tend to localize, showing how complex connectivity can play the role assigned to random energetic disorder.

Pulsed laser deposition (PLD) expands the compositional and structural possibilities of high-entropy oxide (HEO) thin films through far-from-equilibrium growth and kinetic arrest of metastable configurations. This review connects growth kinetics and epitaxial constraints to the roles of individual cations in shaping the resulting films. We focus primarily on rock salt MgCoNiCuZnO and its derivatives, with selected fluorite, spinel, and perovskite examples illustrating broader applicability. In MgCoNiCuZnO, Co valence and Cu coordination illustrate how chemistry and growth conditions jointly enable lattice tuning and coherent nanostructure formation, while aliovalent and size-misfit additions expand the accessible defect and compositional landscapes. These coupled degrees of freedom underpin anomalous crystallinity, the coexistence of extensive chemical disorder with exceptional crystalline quality and epitaxial order, including full coherence in selected systems, particularly rock salts grown on MgO. This combination opens opportunities to discover and engineer functional configurations in high-quality single-layer films and heterostructures.

We numerically study spectral and wave-function properties, as well as time evolution, in finite-size commensurate approximations of the 3D Aubry-André model. We explicitly show, through scaling analysis, the existence of two critical points. One of the critical points is a localization-delocalization transition in real-space, similar to the critical point in the 3D Anderson model. The other is a localization-delocalization transition in a dual momentum space, which does not have any analog in the 3D Anderson model. We estimate their values from spectral measures, such as the gap ratio and the spectral form factor, as well as from wave-function measures, such as the inverse participation ratio and the participation entropy. Additionally, we demonstrate that both critical points exhibit hallmarks of critical points between quantum ergodicity and localization. First, the eigenstates and the eigenspectrum at the critical point fulfill the mutual universal relation between the eigenspectrum compressibility $\chi$ and the eigenstate fractal dimension $d^{(1)}$ [S. Jiricek et al., Proc. Nat. Acad. Sci. 123, e2518027123 (2026)]. Second, the dynamics of the wave packet at the critical point is governed by the critical dynamical exponent $z$, characterized by the spectral fractal dimension and the dimensionality of the lattice [M. Hopjan and L. Vidmar, Phys. Rev. Lett. 135, 060401 (2025)]. Thus, similarly to the 3D Anderson model, the critical dynamical exponent is sub-diffusive with the value of $z=3$.

We investigate a minimal visual perception-driven model of self-propelled particles that interact through purely position-based cohesive steering within a finite vision cone, in the absence of velocity alignment and physical volume exclusion. Building on a previously proposed minimal cognitive model, we extend the interaction range from the previously studied short-range and distance-independent limits to an intermediate regime, enabling a systematic investigation of how a finite vision range influences collective behavior. We find that this regime exhibits a rich state diagram that combines characteristics of both limiting cases while giving rise to qualitatively new collective states. Besides the gas, nematic-band, and polar file states, we uncover the emergence of active foams – system-spanning fractal-like networks sustained by dynamically evolving particle streams. These structures arise solely from non-reciprocal vision-based interactions and are absent in both the short and long vision-range limits. For larger vision angles, the system self-organizes into a variety of aggregate morphologies, including condensates, rings, and multi-twist filaments, revealing a strong interplay between interaction range and anisotropic perception in shaping collective organization.

Proton exchange membrane water electrolysis (PEMWE) is among the most promising techniques to provide hydrogen as both energy carrier and feedstock for the chemical industry, due to its compatibility with intermittent renewable electricity sources. However, a major bottleneck in scaling up PEMWE is the limited supply of the anode catalyst Ir. This work shows a novel approach to tailoring ionomer-free catalyst layers based on custom-made microporous substrates and two different atomic layer deposition (ALD) processes, both using Ir(EtCp)(CHD) precursor. Thermal ALD using O3 as counter-reactant yields mostly metallic Ir/IrOx and an electrode Ir loading of 0.21 mg/cm2. The PEMWE cell-level performance is comparable to a commercial catalyst-coated membrane anode despite 7x lower loading, and is maintained over an accelerated durability test equivalent to 600 h of intermittent operation. Moreover, using a low-loading ALD-made cathode, the total platinum group metal loading is only 0.24 mg/cm2. Plasma-enhanced ALD reduces the Ir loading to 0.04 mg/cm2 by tailoring the catalyst distribution, however, yields lower-activity IrO2. Finally, direct ALD catalyst deposition needs no ionomer-bearing ink. The anodes are therefore compatible with various membrane materials, as demonstrated in a CO2 electrolysis experiment with an anion exchange membrane.

Magpie is a fully graphical linear spin-wave software which has its main focus on 3-d visualisation of magnetic models and magnon dispersion relations. The software is distributed under an open-source license and is written in high-performance, portable C++. Its modular architecture allows for a rapid development of new calculation modules and permits the inclusion into external applications. Included code generators ensure seamless interoperability with other linear spin-wave libraries.

The integer and fractional quantum Hall effects reveal that quantized physical responses can take integer and fractional values, respectively. This naturally raises the question of whether quantization can extend beyond rational numbers to an irrational value. Here we show that such a quantized response can emerge from the limiting behavior of a finite, experimentally realizable geometric network. We develop a method based on infinite geometric structures, in which a sequence of finite networks rapidly converges toward an infinite limit. Following this approach, we identify a planar network whose normalized resistance converges to the irrational value $\sqrt{3}$, and realize a finite approximation with high-precision geometric control. The measured normalized resistance is $1.735 \pm 0.001\, h/e^2$ for a fully occupied Landau level in the designed pattern. Our experimental results extend the concept of quantization beyond rational values and demonstrate that an irrational quantized response can be approached through a finite physical system.

Levitated dielectric sensors are often treated as perturbative probes of a pre-existing optical field. We show that this picture fails for a novel sensor geometry: a dielectric plate whose transverse extent captures the full optical mode. Even an optically thin sensor with modest refractive index can heavily restructure the intracavity fields, effectively partitioning a cavity into two subcavities with substantial cross-coupling and producing new optical resonances and trapping sites with properties which deviate from the standard intuition. Conventional perturbative expressions for the cavity frequency shift and optomechanical coupling depart from the exact solution at thicknesses as small as $\sim\lambda/(10n)$. Furthermore, cavity locking decreases the coupling and increases the trap stiffness by orders of magnitude, and the coupled subcavity structure permits appreciable optical cooling at zero detuning, a distinct behavior unique to this nonperturbative regime. These effects, sharing a common origin, establish a distinct regime of cavity optomechanics in which the sensor is no longer merely a probe of the cavity field, but an element that helps define it.

Strongly interacting fermionic chains obeying a $Z_n$ symmetry can host topological phases with highly degenerate ground-state manifolds. The different ground states are connected by strongly bound fractionalized edge modes called parafermionic zero modes. While exactly preserved under time evolution at zero temperature, interactions lead to a destabilization of these modes at finite energy densities, and, given a generic Hamiltonian, obtaining the lifetime of these modes is often impossible as it requires knowledge of the full spectrum of the Hamiltonian or long time evolutions. Here, we propose a novel quantum-inspired algorithm that can be used to variationally search for these almost strong zero modes in generic parafermionic chain models. We demonstrate analytically and numerically that our ansatz faithfully reproduces the exact results and finds strongly bound parafermionic operators in the non-integrable Kitaev-Hubbard chain and chiral Potts model. Our results further allow us to verify the existence of a true strong zero mode in the symmetrical limit of the chiral Potts model for $Z_3$-parafermions.

Spatial interference can break the inversion symmetry of an effective Josephson potential even in a laterally homogeneous junction with inversion-symmetric local energy. We derive a general criterion based on harmonic-dependent complex spatial form factors: a single local harmonic remains a shifted cosine, whereas multiple harmonics can acquire phases incompatible with any common inversion center, permitting cubic interactions and three-wave mixing. Phase reflection reverses all odd-order expansion coefficients about corresponding minima while preserving the even-order ones. For a capacitively shunted junction at fixed charging energy and arbitrary offset charge, it also preserves the complete quantum spectrum, enabling reversal of the odd nonlinear sector without spectral retuning. A centered cross junction with multiple local harmonics is one concrete example. Within the imposed-field model, a three-component magnetic field can generate an inversion-asymmetric effective potential, and reversing an odd number of field components exactly reflects it without changing the quantum spectrum of the capacitively shunted junction.

The coexistence of multiple classes of localized states, including different types of topological corner states, is highly desired; yet its realization typically requires sufficiently strong long-range couplings, bringing challenges to experimental realizations across a wide range of systems. Here, we demonstrate the emergence of multiple localized corner modes evolution under purely nearest-neighbor coupling conditions without long-range couplings, not even next-nearest-neighbour couplings, and experimentally confirm their coexistence in a single lattice. Our platform simultaneously hosts type-I and type-II corner states, corner localized bound states in the continuum, flat-band states, and edge states. We experimentally realize such lattice using topolectrical circuits, a system that can strictly exclude long-range coupling by design, enabling direct characterizations of both the energy-band spectrum and the spatial profiles of the localized eigenmode. This work demonstrates that solely modifying nearest-neighbor couplings can replace the role of long-range interactions in realizing multiple types of corner states, providing a deterministic and widely accessible route to multiple corner-state classes and rich localized states, with immediate potential for mode-division multiplexing and multimode topological devices.

The anomalous Hall effect (AHE) in magnetic Weyl semimetals arises from distinct microscopic origins-intrinsic Berry curvature and extrinsic scattering mechanisms-yet reversible switching between these regimes within a single material platform remains elusive. Here, we demonstrate that off-stoichiometric tuning of the Al/Si ratio (from ~1.05 to ~0.75) reversibly drives an intrinsic-extrinsic-intrinsic crossover of the AHE in PrAlSi single crystals. Across four compositions spanning a narrow Si variation (PrAl0.93Si0.89 to PrAl0.79Si1.06), the anomalous Hall conductivity (AHC) exhibits a non monotonic arch (170-1413- 507-164 {\Omega}-1cm-1). The intermediate composition PrAl0.90Si0.94 (Al/Si ~0.96) exhibits high carrier mobility, multi carrier transport, yielding a giant AHC of 1413 {\Omega}-1cm-1 dominated by extrinsic skew-scattering. The Si-poor and Si-rich compositions exhibit lower AHC values and intrinsic Berry-curvature-dominated AHE, establishing a composition-driven intrinsic-extrinsic-intrinsic crossover. Deviating from the intermediate composition suppresses mobility and reverses carrier type from hole-like to electron-like. The Al/Si ratio thus serves as a chemical knob that primarily modulates the Fermi level via compositional band filling, while off-stoichiometry-induced chemical disorder plays a subordinate role in determining the AHE mechanism. These results position off-stoichiometric PrAlSi as a tunable platform where subtle compositional variation reversibly switches the AHE mechanism.

A gap exists in connecting biological evolution within the framework of statistical mechanics. It has been hoped that statistical mechanics would provide us with a general predictive principle for the emergence of novelty and complexity. However, the emergence of novel functional features initiated by stochastic processes remains difficult to describe, because these processes commonly arise outside near-equilibrium or linear-response regimes. To understand how environmental influences generate diverse, open-ended, complex objects by driving physical systems to specific regions of phase space over long spatial and temporal scales, a new approach to non-equilibrium thermodynamics is necessary. Here, we present the coupling of assembly theory (AT) with statistical mechanics as a framework that works within the laws of thermodynamics, but can contextualise the processes of novelty, complexity, and evolution within these laws. We map construction processes from physical space to assembly space (AS) and introduce the concept of an assembler, a machine that constructs objects contingent on previous states and is represented by bitwise operations. Using this approach, we apply principles from stochastic thermodynamics with AT to define selection within large combinatorial spaces1 and estimate the work required to create novel and complex objects. This approach allows us to represent complex processes, such as selection, within large combinatorial spaces as a set of rules for a memory-feedback loop followed by the assembler. This framework concretely defines the relationships between thermodynamics and information theory by introducing a novel aspect of physics that uses history and causal contingency to influence the probabilistic time evolution of complex systems.

Magnetic circular dichroism (MCD) is an optical probe of orbital time reversal symmetry breaking. Although frequency integrated MCD is related to the self-rotation contribution to orbital magnetization at zero field, its magnetic response generally differs from the thermodynamic orbital susceptibility. Here, we define the MCD susceptibility and derive general expressions for multiband systems using an electromagnetic $U(1)$ gauge invariant approach. For insulators, the response contains contributions from the non-Abelian quantum metric, Berry curvature, and field induced interband mixing. For metals, a finite temperature Green function formulation separates the smooth response into Fermi sea and Fermi surface contributions. An independent Landau level calculation confirms the expressions for the zero-field MCD moment and its linear magnetic response. In a continuum model for twisted bilayer graphene, the MCD susceptibility vanishes within the charge neutrality gap, while the thermodynamic orbital susceptibility remains markedly diamagnetic. Near the gap edges, the orbital moment term dominates the response. Features near the van Hove energies are associated with density of states enhancement. These results clarify how the two susceptibilities reflect different orbital processes even for the same electronic structure and thus establish the MCD susceptibility as a distinct probe of orbital magnetic response.

Magnetic frustration is commonly quantified by the frustration index, calculated from the Curie-Weiss and Neel temperatures. Because both quantities are not simultaneously available for most materials, direct prediction of the magnetic frustration index remains challenging. Here, we propose a machine learning workflow for indirect prediction of the frustration index and consequent screening of potential frustrated magnetic compounds through independent prediction of Curie-Weiss and Neel temperatures. In our work, composition-based models implemented via the CatBoost algorithm, trained on experimental data were optimized using chemically informed dataset subdivision. The highest predictive accuracy was achieved for the rare earth-oxide model in predicting Neel and for the rare earth model in predicting Curie-Weiss. Ensemble uncertainty was incorporated through a conservative frustration index to improve the reliability of candidate selection. Screening of approximately 67000 Materials Project compounds identified 20 high-confidence frustrated magnetic candidates, including several experimentally known frustrated magnets and previously unexplored oxide systems potential for further investigation.

Hidden beneath the vanishing charge Hall response of altermagnets are spin-up and spin-down Hall currents of opposite sign—concealed, not absent—whose cancellation is enforced by symmetry. When these spin states are locked to distinct valleys, the hidden currents constitute a spin-valley Hall effect. Here we show that in 2D altermagnets with spin-valley-layer coupling (SVLC), a gate field unveils this hidden spin-valley Hall response.~By lifting the symmetry-enforced compensation between valleys with opposite layer polarizations, the field converts the hidden response into a net charge Hall signal, yielding a gate-switchable electric Hall effect (EHE) enabled by SVLC. Using collinear spin layer group (cSLG) theory, we classify all 158 altermagnetic cSLGs, identify 32 that support SVLC, and predict monolayer Mg$_2$Os$_2$(SO$_5$)$_2$ and the Ca(CoN)$_2$-family as candidate materials. First-principles calculations for Mg$_2$Os$_2$(SO$_5$)$_2$ reveal reversible valley splitting, a gate-switchable Hall response, and a Kerr rotation exceeding 1 mrad whose sign reverses together with the EHE signal. These results establish a symmetry-based route to all-electrical valley-spin control and identify altermagnets as promising platforms for high-performance valley transport and electrically switchable magneto-optics.

Structural disorder is generally regarded as detrimental to magnetism. Since magnetic properties are governed by both the arrangement of magnetic atoms and the crystal environment, including non-magnetic atoms that mediate exchange interactions, the distinct role of magnetic and non-magnetic disorder remains less understood. The recently reported anti-Heusler alloy, Al$_2$MnCu, forming with $\sim$50% intra-symmetry site disorder (B2) involving the magnetic Mn atom and $\sim$5% inter-symmetry site disorder associated with non-magnetic Al and Cu atoms, offers a good platform to disentangle the individual roles of magnetic and non-magnetic atomic disorder. Our magnetic critical analysis, in the vicinity of the Curie temperature ($T_{\rm C}$), does not lead to any conventional single universality class expected for a standard ferromagnet; instead, the non-monotonic temperature dependence of effective critical exponents points towards more complex magnetic interactions, akin to inhomogeneous ferromagnets. Dc magnetometry complemented by higher-harmonic ac magnetic susceptibility data, further confirms the persistence of locally ordered magnetic clusters above $T_{\rm C}$. Theoretical analysis establishes that the enhancement of the local magnetic ordering temperature arises directly from the strengthening of exchange interactions due to the small degree of non-magnetic disorder, whereas $T_{\rm C}$ is hardly influenced by the much larger level of magnetic-atom disorder. The combined experimental and theoretical investigations on the anti-Heusler alloy Al$_2$MnCu reveal and explain the unusual observation of nonmagnetic disorder-induced elevation of $T_{\rm C}$, providing a paradigm for the counterintuitive role of disorder in magnetic materials.

We predict an intrinsic orbital Nernst effect in reciprocal photonic lattices with real Bloch modes. In the collisionless regime, a thermal gradient generates a transverse angular-displacement response although band angular moments and ordinary Berry curvatures vanish. The response is carried by angular-density dipoles formed through virtual mixing of distinct spatial modes. Their correlation with band velocity survives thermal averaging and is independently recovered from the angular-density readout of unitarily evolved wave packets. Two controls expose the mechanism: a fixed-generator two-level system has zero antisymmetric intrinsic response, and flattening the dispersion suppresses transport without changing the eigenstates. A canonical scalar Maxwell calculation realizes the effect through symmetry-selected virtual channels, even when one band dominates the thermal population. These findings establish an orbital-dipole mechanism for intrinsic thermal angular transport in real photonic bands.