We use spherical neutron polarimetry to determine the ground state magnetic structure of ${\mathrm{Mn}}_3\mathrm{Sn}$. We find that ${\mathrm{Mn}}_3\mathrm{Sn}$ adopts an inverse triangular structure with spins parallel to $\langle 100\rangle$ (type III) rather than spins parallel to $\langle 110\rangle$ (type IV). Density functional theory calculations reveal no energy difference between these two structures, suggesting that the selection is caused by subtle effects such as sixth-order anisotropy. Partial control of the magnetic domain population through a moderate magnetic field is key to distinguishing between the two models. We find that three of the six domains are approximately equally populated, while the others have negligible population. Upon entering the low temperature incommensurate phase, the domain structure is lost. The domains in this phase are decoupled from the magnetic field and can therefore not be controlled by any known method.

The mechanism of doping in the composite ${\mathrm{Pr}}_x{\mathrm{Y}}_{1-x}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ (Pr-YBCO) system is distinct from that of pure YBCO, offering a means to explore the requirements for the numerous electronic orders appearing in the phase diagram. One such example is the ubiquitous 2D charge order and concomitant Fermi surface reconstruction in underdoped YBCO. Here, using Hall effect measurements, we find signatures of a Fermi surface reconstruction similar to that in pure YBCO indicating the presence of 2D charge order in Pr-YBCO. Additionally, we find that the phase diagrams of Pr-YBCO and YBCO are symmetric despite the additional disorder in the former and the distinction between hole depletion through Pr substitution and through O reduction. This indicates that while the mechanism of doping differs, the amount of charge carriers in the planes is the most important factor governing the electronic orders in these systems.

${\mathrm{Ba}}_2{\mathrm{CuO}}_{3+\delta }$ $(\delta \sim 0.2)$ has recently attracted considerable interest as an unconventional cuprate superconductor, yet its precise crystal structure remains theoretically under debate, primarily because its primitive cell may contain hundreds of atoms, which exceeds the size limits of density functional theory (DFT). To address this issue, we combine DFT with Deep-Potential molecular dynamics (DPMD) to explore a wide range of oxygen-deficient configurations. First, we construct a comprehensive training set for $\delta =0.0-1.0$, to train the accurate interatomic potential, and perform large-scale DPMD simulations for ${\mathrm{Ba}}_2{\mathrm{CuO}}_{3+\delta }$. Both DFT and DPMD phonon calculations reveal that the previously reported high-symmetry phase of ${\mathrm{Ba}}_2{\mathrm{CuO}}_3$ hosts soft phonon induced by planar oxygen vibrations leads to a charge ordered phase with alternating long and short Cu-O bonds. This bond disproportionation corresponds to mixed Cu valence states of ${\mathrm{Cu}}^{+}$ $\left(3d^{10}\right)$ and ${\mathrm{Cu}}^{3+}$ $\left(3d^8\right)$. Moreover, for ${\mathrm{Ba}}_2{\mathrm{CuO}}_{3.2}$, DPMD calculations indicate that the ground state adopts a one-dimensional Cu-O chain structure, and total energy and phonon analyses identify several dynamically metastable structures, which complicates the experimental fabrication of superconducting samples. Finally, DPMD simulations demonstrate that external pressure does not alter the ground state of the one-dimensional chain even at 20 GPa. These results provide a robust theoretical foundation for determining the correct crystal structure of ${\mathrm{Ba}}_2{\mathrm{CuO}}_{3+\delta }$ and indicate that its electronic ground state fundamentally deviates from that of ${\mathrm{CuO}}_2$ planes in two-dimensional cuprates. The superconducting pairing mechanism in this system may lie beyond standard electron-phonon coupling or doped Hubbard model.

We propose a quantum theoretical model for magnon-phonon interaction in composite multiferroic systems (CMS) under external fields. The Hamiltonian of magnon-phonon interaction under external fields is expressed by considering the equivalent anisotropic field $H_K$ and coupling constant ${\sigma }_k$ that exhibit explicit functional dependence on external fields. Here, the coupling strength and frequency range of magnon-phonon interaction under different external fields are quantified by excitation spectrum. The results show that the external fields enable a giant enhancement of the strength of magnon-phonon interaction by about a factor of 334% in the case of CMS consisting of aluminum nitride and yttrium iron garnet. At the anticrossing regime (i.e., strong interaction regime) of the magnon-phonon interaction, we demonstrate the existence of two resonance peaks characterized (including S11, impedance and magnetic field) by the finite element analysis model. The simulation results showcase that the frequency interval has an obvious external field dependence, which agrees with our quantum theoretical model. Furthermore, we quantify the external field conditions of strong coupling, which demonstrated the tunability of the coupling strength by the external fields. Our work provides a universal method for revealing the evolution of magnon-phonon interaction under external fields, which also provides a fundamental theoretical tool for understanding and designing magnetoelastic coupling phenomena in multiferroic systems.

This work investigates the spin-wave dynamics in thick one-dimensional bicomponent magnonic crystals, focusing on the interplay between geometric confinement, material contrast, and dipolar exchange interactions. Using a combined plane-wave and dynamic-matrix formalism, the magnonic band structure and mode profiles are calculated for both Damon-Eshbach (DE) and backward-volume (BV) geometries, explicitly accounting for nonuniform dynamic magnetization across the film thickness. As a reference system, a uniform-thickness magnonic crystal is analyzed, revealing that the macrospin approximation fails beyond a critical thickness due to hybridization with higher-order perpendicular standing spin-wave modes, leading to nonmonotonic variations in the bandgap width and position. When vertical material contrast is introduced, pronounced localization phenomena emerge: in the DE configuration, low-frequency modes concentrate within the low-saturation-magnetization material through field-induced frequency detuning; in the BV geometry, the demagnetizing-field landscape generates flat, defect-like modes localized within the high-saturation-magnetization regions. These localization mechanisms remain robust over wide ranges of thickness and filling fraction and display a clear crossover from exchange-dominated uniform profiles in thin films to strongly confined modes in thicker structures. The results provide a comprehensive description of spin-wave behavior in three-dimensional periodic magnetic systems and offer design guidelines for magnonic architectures requiring tailored dispersion and controllable modal confinement.

We provide a theoretical description of diffusive charge and spin transport in hybrid devices containing altermagnets. Based on recently derived drift-diffusion equations for coupled charge and spin dynamics and general boundary conditions, our approach provides a unified description of the spin-splitter effect, i.e., the conversion of charge currents into spin currents, and its inverse in terms of experimentally accessible parameters. We analyze, analytically and numerically, the spin-splitter effect, demonstrating that an injected spin accumulation generates a measurable voltage difference across the transverse direction in the altermagnet. Motivated by a recent experiment, we also analyze a nonlocal spin-valve geometry in which an altermagnetic strip injects spin into a diffusive normal metal. We derive the resulting nonlocal voltage detected by a ferromagnetic electrode as a function of the relative orientation of the Néel vector and the ferromagnetic polarization, accounting for the main experimental findings. For this setup, we further address spin precession during diffusive transport by analyzing the spin Hanle effect. Our results provide theoretical explanations and predictions for several altermagnet hybrid structures.

Altermagnetism is a recently identified magnetic phase characterized by symmetry-enforced nonrelativistic spin splitting despite vanishing net magnetization. Here, using spin-space symmetry analysis and first-principles calculations, we show that inversion-symmetry-broken stackings of bilayer ${\mathrm{GdI}}_3$, a two-dimensional van der Waals antiferromagnet with localized Gd $4f$ moments, host stacking-tunable altermagnetism. While the magnetic order originates from localized $4f$ electrons, the altermagnetic spin splitting is carried by I $p$ states near the Fermi level, revealing a separation between the source of magnetism and the electronic states that encode the spin texture. Specific stackings, namely, ${\mathrm{AB}}^{*}/{\mathrm{BA}}^{*}$ and ${\mathrm{AC}}^{*}/{\mathrm{CA}}^{*}$, realize symmetry-protected altermagnetic phases, whereas the ${\mathrm{AA}}^{*}$ stacking remains spin degenerate. Moreover, the ${\mathrm{AB}}^{*}/{\mathrm{BA}}^{*}$ stackings simultaneously develop out-of-plane ferroelectric polarization, while the ${\mathrm{AC}}^{*}/{\mathrm{CA}}^{*}$ stackings remain nonferroelectric due to cancellation of local dipoles. Upon including spin-orbit coupling, the relevant antiunitary symmetries are lifted and the system transitions from an altermagnetic regime to a Rashba-type spin-split state with a rich momentum-space spin texture, while the total magnetization remains nearly zero. Our results establish bilayer ${\mathrm{GdI}}_3$ as a stacking-tunable platform for exploring the symmetry connection between altermagnetism, ferroelectricity, and relativistic spin textures.

Developing general design principles for two-dimensional (2D) high-$T_c$ superconductors remains a central challenge because reduced dimensionality fundamentally reshapes chemical bonding and electron-phonon interactions. Here, we identify a hybridization-based design principle for 2D hydrides, namely, strong $\sigma$-type hybridization between H $1s$ and transition-metal $e_g$ states that leaves the corresponding antibonding states partially occupied at the Fermi level. Guided by this principle, we show that monolayer ${\mathrm{NiH}}_3$, consisting of an edge-sharing ${\mathrm{NiH}}_6$ octahedral network, is a phonon-mediated superconductor with a predicted $T_c$ of 104 K. This high $T_c$ arises from strong coupling between the partially occupied Ni $e_g\text{−}\mathrm{H} 1s$ antibonding states near the Fermi level and Ni-dominated phonon modes. To demonstrate the generality of this principle, we further examine hole-doped ${\mathrm{CuH}}_3$ (0.1 hole/f.u.), which also exhibits superconductivity through the same hybridization mechanism, but with a reduced $T_c$ of 30 K because the Cu $e_g\text{−}\mathrm{H} 1s$ antibonding states are more fully occupied and thus contribute less to the density of states at the Fermi level and to the electron-phonon coupling. Our results provide a feasible route to enhancing electron-phonon coupling in 2D hydrides and highlight hybridization engineering as a promising strategy for designing high-$T_c$ superconductors.

We determine the exact asymptotic many-body wave function of a spin-$s$ Richardson-Gaudin model with a coupling inversely proportional to time, for time evolution starting from the ground state at $t=0^{+}$ and for arbitrary $s$. Contrary to common belief, the resulting wave function cannot be derived from the spin-$1/2$ case by merging spins, but instead requires independent treatment for each spin size. The steady state is nonthermal and, in contrast to the spin-$1/2$ case, does not conform to a natural Generalized Gibbs Ensemble. We show that mean-field theory is exact for any product of a finite number of spin operators on different sites. We discuss how these findings can be probed in cavity QED and trapped ion experiments.

We employ functional derivatives to calculate spectroscopy in nonequilibrium many-body systems. This allows for all vertex correction effects to be properly incorporated. We focus on electronic Raman scattering. As a concrete example, we present numerical results for the nonresonant contribution to the time-resolved electronic Raman scattering cross section in the $A_{1g}$ symmetry channel solved with dynamical mean-field theory. To do this, we add a small field to the Hamiltonian and take the functional derivative of the “Raman current” operator with respect to this field, which results in an exact expression for the greater Green's function that determines the Raman scattering cross section. This approach avoids the need to set up and solve Bethe-Salpeter equations, which are notoriously difficult to work with in nonequilibrium. We also work out formal expressions for the optical conductivity in the Appendix.

High thermoelectric efficiency has been reported in several antiperovskites, but strongly unbalanced n- and p-type thermoelectric performances still limit practical device integration. Here, we show that ${\mathrm{Ag}}_3\mathrm{SX}$ (X = Cl, Br, I) antiperovskites exhibit simultaneously favorable p- and n-type transport, and that halogen substitution further improves this ambipolar behavior through coupled lattice and electronic mechanisms. On the lattice side, heavier halogens soften the Ag-X framework and strengthen anharmonic phonon scattering, which markedly lowers the lattice thermal conductivity and helps drive the materials toward a glasslike transport regime. On the electronic side, halogen substitution modifies the relative contributions and hybridization of Ag-4d and chalcogen/halogen p states near the valence-band edge; together with the stronger spin–orbit coupling in the iodide, this leads to enhanced valence-band degeneracy while retaining sufficient band dispersion. As a result, ${\mathrm{Ag}}_3\mathrm{SI}$ exhibits ultralow lattice thermal conductivity (0.29 W/m K) and high carrier mobility (10–200 $\mathrm{c}{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$), achieving a maximum power factor of 2.5 $\mathrm{mW}/\mathrm{m}{\mathrm{K}}^2$. Under optimal doping, $\mathit{ZT}$ at 800 K reaches ≈2.42 for p-type and ≈1.87 for n-type carriers. These results identify ${\mathrm{Ag}}_3\mathrm{SX}$ compounds as promising ambipolar thermoelectric materials and highlight how lattice anharmonicity and band-edge reconstruction can be combined to optimize heat and charge transport.

The performance of traditional semiconductors as thermoelectric materials is often hindered by high lattice thermal conductivity, which counteracts otherwise favorable electronic properties. In this work, we identify ${\mathrm{LiTiTe}}_2$-type semiconducting compounds, a family of stable ternary derivatives of the nickel arsenide-structure of those traditional semiconductors, as a platform that effectively resolves this issue. These materials exhibit exceptionally low lattice thermal conductivities, competitive with state-of-the-art group IV-VI compounds. This strong phonon suppression arises from a complex bonding hierarchy that lowers the frequency of acoustic phonons and enhances anharmonic scattering. Crucially, the reduced crystal symmetry inherent to the ${\mathrm{LiTiTe}}_2$ structure-type induces an orbital energy splitting in the vicinity of the valence band maximum. We establish a direct correlation between this splitting and the peak power factor, validating it as an effective descriptor for screening high-performance thermoelectric materials. Orbital energy splitting tuned within the thermal activation window maximizes the power factor, suggesting that a finite splitting optimizes the balance between density-of-states enhancement and the mitigation of detrimental interband scattering. Guided by this principle, we identified ${\mathrm{NaBiS}}_2$ as a prime candidate that possesses both an intrinsically low thermal conductivity and natural band convergence. This synergy leads to an excellent figure of merit approaching 1.0 for $p$-type variant at high temperatures, based on a comprehensive scattering model that includes four-phonon processes and multiple electronic scattering mechanisms. Furthermore, we demonstrate that this splitting is tunable; applying hydrostatic pressure can effectively eliminate residual splitting, providing a direct pathway to engineer band convergence. This work introduces the engineering of orbital energy splitting as a new and powerful design strategy for discovering and optimizing advanced thermoelectric materials.

The magneto-optical properties of a ${\mathrm{Zn}}_{0.99}{\mathrm{Mn}}_{0.01}\mathrm{Se}/{\mathrm{Be}}_{0.93}{\mathrm{Mn}}_{0.07}\mathrm{Te}$ diluted magnetic semiconductor heterostructure with type-II band alignment are investigated at cryogenic temperatures down to 16 mK. The temperature of the Mn spin system, which at the lowest possible laser power reaches 270 mK, is evaluated from the giant Zeeman splitting of the direct exciton in the ${\mathrm{Zn}}_{0.99}{\mathrm{Mn}}_{0.01}\mathrm{Se}$ layers subject to an external magnetic field. The degree of circular polarization of the direct and indirect optical transitions, induced by the magnetic field, is a sensitive indicator for the laser heating of the Mn spin system. Evidence of spin-glass formation in the Mn spin system of the ${\mathrm{Be}}_{0.93}{\mathrm{Mn}}_{0.07}\mathrm{Te}$ layers with the critical temperature of $T_{\mathrm{SG}}=400\mathrm{mK}$ is found.

Breaking out-of-plane mirror symmetry of hexagonal $M\text{Se}$ ($M=\mathrm{Ga}$, In, Tl) induces a Janus monolayer enabling exceptionally low lattice thermal conductivity (${\kappa }_l$). At 300 K, lattice thermal conductivities of $\mathrm{GaS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}, \mathrm{InS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$, and $\mathrm{TlS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$ are 2.39, 0.59, and 0.77 $\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, respectively, raising the question of why the In-based system has lower ${\kappa }_l$ than the Tl-based one. Notably, the phonon softening across the entire frequency spectrum in $M\mathrm{S}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$ originates from mass anisotropy, which, together with pronounced anharmonic scattering strength (∼25) and strong rattling motions in $\mathrm{InS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$ and $\mathrm{TlS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$, fundamentally account for their minimal ${\kappa }_l$. Furthermore, Grüneisen parameters of $\mathrm{GaS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$ and $\mathrm{TlS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$ are positive, reflecting lattice expansion in the $ab$ plane, whereas the negative Grüneisen parameter in $\mathrm{InS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$ arises from lattice contraction, indicating pronounced anharmonicity within $\mathrm{InS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$. The “mushroom-shaped” electron localization function (ELF) around Te, mainly from nonbonding lone pairs, reveals localized charge distribution. Together with strong anharmonicity, phonon softening, and enhanced phonon scattering caused by structural asymmetry, these effects drive the ultralow ${\kappa }_l$ in $\mathrm{InS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$ and $\mathrm{TlS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$. Te substitution combined with spin–orbit coupling (SOC) suppresses the “sombrero-shaped” valence band maxima, producing a parabolic dispersion that lowers hole effective mass and improves charge transport. These results demonstrate that structural asymmetry induced by Te substitution, which breaks the out-of-plane mirror symmetry, plays a pivotal role in improving the thermoelectric performance, with a maximum ZT of 1.47 ($p$-type), 2.41 ($p$-type), and 2.01 ($n$-type) in $\mathrm{GaS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}, \mathrm{InS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$, and $\mathrm{TlS}{\mathrm{e}}_{0.5}\mathrm{T}{\mathrm{e}}_{0.5}$, respectively, at 800 K.

The use of macroscopic coherent quantum states at room temperature is crucial in modern quantum technologies. In light of recent experiments demonstrating high-temperature superfluorescence in hybrid perovskite thin films, in this work we investigate the stability of the superradiant state concerning exciton-phonon interactions, taking into account the specifics of perovskites. We focused on quasi-two-dimensional (quasi-2D) Wannier excitons interacting with longitudinal optical (LO) phonons in polar crystals, as well as with acoustic phonons. Our study leads to the derivation of nonlinear equations in the coordinate space that govern the exciton wave function's coefficient in the single-exciton basis for the lowest exciton state, which translates to the complex-valued polarization. The resulting equations take the form of a 2D nonlocal nonlinear Schrodinger (NLS) equation. We perform a linear stability analysis of the plane wave solutions for the equations in question, which allows us to establish stability criteria. This analysis is particularly important for evaluating the stability of the superradiant state in the considered quasi-2D structures, as the superradiant state represents a specific case of the plane wave solution. Our findings indicate that, when the exciton interacts with LO phonons, a plane wave solution is modulationally stable, provided that the square of its amplitude does not exceed a critical intensity value defined by the exciton-LO phonon interaction parameters. In scenarios involving the weakly nonlocal NLS equation, we find that it transitions into a purely nonlocal form. The linear stability analysis yields results that align with those derived from the equation that does not consider weak nonlocality in the long-wave limit. Furthermore, interactions between the exciton and acoustic phonons reduce the intensity of modulationally stable waves compared to the case without such interactions. Our analytical results are corroborated by numerical calculations. We also numerically solve the 2D nonlocal NLS equation in polar coordinates and obtain its fundamental soliton solution, which is stable.

Monolayer ${\mathrm{SnS}}_2$ has emerged as a promising visible-light photocatalyst for photoelectrochemical applications, owing to its strong optical absorption in the visible range and excellent chemical stability. Despite its reduced dimensionality—where excitonic effects are expected to be pronounced—comprehensive theoretical investigations of bound excitons in this material remain scarce. Notably, unlike most two-dimensional hexagonal crystals, monolayer ${\mathrm{SnS}}_2$ exhibits its lowest single-particle transition at the $M$ point of the Brillouin zone (BZ). Here, the electronic valence bands form a saddle point while conduction states display a minimum with pronounced anisotropy, creating a distinctive band topology whose impact on optical excitations we systematically explore. In this work, we present a first-principles study of bound excitons in monolayer ${\mathrm{SnS}}_2$ based on state-of-the-art many-body perturbation theory, employing the $\mathit{GW}$ approximation and the Bethe–Salpeter equation. We analyze how band symmetry and anisotropy shape the excitonic wave functions and transition dipole moments. By resolving the exciton dipoles in momentum space for different linear light polarizations, we demonstrate that linearly polarized light lifts the $C_3$ rotational symmetry relating the three inequivalent $M$ points, giving rise to three linearly independent excitonic states. This polarization-selective coupling, previously identified for saddle points in graphene, is achieved in ${\mathrm{SnS}}_2$ for bound excitons and provides a potential route toward state encoding schemes in valleytronics applications.

The average subsystem trace distance has been proposed as an indicator of quantum many-body chaos and integrability. However, evaluating it presents two main difficulties: high computational cost for large systems and ambiguities in defining and ordering eigenstates in integrable systems. In this work, we develop an efficient algorithm to compute the Bures distance between fermionic Gaussian states, enabling access to larger system sizes. Using this method, we calculate the average subsystem Bures distance for eigenstates in the spin-1/2 transverse-field Ising chain and the Dirac fermion formulation of the quadratic Sachdev–Ye–Kitaev (Dirac ${\mathrm{SYK}}_2$) model, as well as for random pure fermionic Gaussian states. To handle degeneracy in the Ising chain, we consider simultaneous eigenstates of all local conserved charges and employ these charges to systematically order degenerate states. Our results are consistent with the earlier conjecture of linear growth with subsystem size. We show that the distinct scaling of the average subsystem distances in chaotic versus integrable systems originates from discontinuities of local conserved charges across the spectrum in integrable models. For the Dirac ${\mathrm{SYK}}_2$ model and random pure Gaussian states, we obtain similar results for the average subsystem distances, which do not show a linear increase.

The prototypical Mott-Hubbard insulator ${\mathrm{LaVO}}_3$ undergoes a structural phase transition accompanied by the onset of spin and orbital ordering below 140 K. By combining ultrafast optical pump-probe spectroscopy and two-dimensional electronic spectroscopy, we investigate the interplay between fluctuations of the local spin and orbital order parameter and the lifetime of high-energy electron-hole excitations. Specifically, we demonstrate that the pump-induced perturbation of the order parameter leads to a change of the Hubbard exciton decoherence time and, consequently, of its homogeneous linewidth. Dynamical mean-field theory calculations confirm that the exciton scattering rate is crucially affected by the degree of order of the spin and orbital lattices in ${\mathrm{LaVO}}_3$. Our results demonstrate that multi-dimensional ultrafast optical spectroscopy can be used to track the dynamics of the order parameter, thus opening new routes in the study of correlated quantum materials characterized by intertwined orders.

We have investigated the orbital-dependent electronic states of ${\mathrm{Cd}}_6\mathrm{Ce}$, a prototype of strongly correlated rare-earth-based Tsai-type quasicrystals and approximants (ACs) by soft and hard x-ray photoemission spectroscopy. Our results reveal that the $4f$ orbitals are predominantly hybridized with the valence-band electrons far from the Fermi level ($E_F$), in sharp contrast to the hybridization with conduction electrons at $E_F$ seen for the intermetallic Ce-based compounds. This anomalous hybridization should be taken into account in discussing the unresolved magnetic ground state in ${\mathrm{Cd}}_6\mathrm{Ce}$. These findings suggest that Cd-based ACs, some of which show the multistep magnetic transitions, could provide a new platform for investigating novel magnetic properties that cannot be understood within the conventional framework of hybridization at $E_F$.