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Probing topological phases in a perturbed Kane-Mele model via RKKY interaction: Application to monolayer jacutingaite Pt 2 ⁢HgSe 3

Quantum spin Hall insulators (QSHIs) leverage strong spin-orbit coupling (SOC) for efficient spin manipulation, making them promising for spintronics. Here, in this study, we investigate the noncollinear Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities in a perturbed Kane-Mele model with strong SOC, relevant to monolayer jacutingaite Pt 2 ⁢HgSe 3 as a prominent QSHI. Following the previous studies that mainly focused on the model and its general applications, we provide a systematic examination of the effects of various perturbations and strong spin-orbit hybridizations, which drive phase transitions that have not been extensively explored before. By incorporating these perturbations into the model and accurately accounting for spin-orbit hybridizations through spin-space Green's functions and the RKKY interactions, we uncover distinct, relative (rather than absolute) signatures of different phase transitions. These phase transitions are induced by both static and dynamic perturbations on the magnetic impurities. Notably, we identify additional phases emerging from the interplay with the magnetic substrate. All these influence the switching between ferromagnetic and antiferromagnetic, as well as clockwise and counterclockwise magnetic interactions. Our results provide a practical way to track topological phases through magnetic properties, offering new insights into phase control and spin manipulation in QSHIs.

Kane-Mele model

Anisotropic light-tailored RKKY interaction in two-dimensional 𝑑-wave altermagnets

Altermagnets are known in spintronics for their intrinsic spin-splitting and unconventional magnetic responses, particularly to magnetic impurities. However, effectively controlling the magnetic exchange interactions in altermagnets is challenging for practical applications. Here, in this work, we propose using circularly polarized light to tune the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in two-dimensional 𝑑-wave altermagnets. Using the real-space retarded Green's functions approach, our results show that while the Heisenberg and Ising exchanges dominate, a notable Dzyaloshinskii–Moriya (DM) interaction also plays a key role. Furthermore, the inherent strength of altermagnetism imprints chirp-like signatures into the magnetic responses, which can be dynamically tuned via light. We mainly demonstrate that gate-induced Rashba spin-orbit coupling is essential in response to light—light selectively and anisotropically adjusts the DM interaction without affecting the other exchanges. Our findings further indicate that rotating the altermagnet by 45° relative to the light's polarization direction generates a Dirac-like dispersion and different DM interactions. We finally extract critical thresholds where light reverses DM interactions along one axis or balances both in-plane components. The anisotropic light-driven control of RKKY interactions in altermagnets not only highlights their unique properties but also opens new avenues for engineering tailored magnetic characteristics in spintronic applications.

altermagnetism

Nuclear spin coherence and RKKY interaction in superconducting Nb 3 Sn

We have investigated the normal and superconducting states of the technologically important compound Nb$_3$Sn using $^{93}$Nb nuclear magnetic resonance. From spin-lattice relaxation we find strong suppression of the zero-temperature superconducting order parameter by magnetic field. Additionally we have identified an anomalously large electron-nuclear exchange interaction from spin-spin relaxation measurements, an order of magnitude beyond that of the nuclear dipolar coupling. This RKKY interaction evolves from normal to superconducting states, becoming essentially Lorentzian in the low temperature limit.

Zhai, Gan [Northwestern U.] (ORCID:000000016623956

Intricacies of frustrated magnetism in the Kondo metal YbAgGe

The combination of localized magnetic moments, their frustration and interaction with itinerant electrons is a key challenge of condensed matter physics. Frustrated magnetic interactions promote degenerate ground states with enhanced fluctuations, a topic that is predominantly studied in magnetic insulators. The coupling between itinerant and localized electrons in metals add complexity to the problem, and is presently formulated only for extreme cases in which the itinerant electrons mediate exchange between localized spins (RKKY interaction) or suppress the formation of magnetic moments (Kondo screening). Here, we report an in-depth experimental study of the distorted Kagome metal YbAgGe, unravelling the open questions of how frustration, localized magnetism and itinerant electrons are intertwined in frustrated Kondo metals. We find that coupled itinerant and localized electrons give rise to dynamic magnetic correlations below T* ≈ 20 K. At lower temperature, frustrated magnetic interactions establish anisotropic magnetic short-range correlations that culminate into antiferromagnetic long-range order below T N = 0.68 K with a significantly reduced modulated magnetic moment. We show that local moment Hamiltonians can yield limited understanding of the microscopic behaviour in frustrated metals, and prompt the extension of more sophisticated model Hamiltonians incorporating itinerant effects.

Mazzone, Daniel G. [PSI Center for Neutron and Muo

Pseudogap and Fermi arc induced by Fermi surface nesting in a centrosymmetric skyrmion magnet

Skyrmions in noncentrosymmetric materials are believed to occur due to the Dzyaloshinskii-Moriya interaction. By contrast, the skyrmion formation mechanism in centrosymmetric materials remains elusive. Here, in this work, we reveal the intrinsic electronic structure of the centrosymmetric GdRu 2 Si 2 by selectively measuring magnetic domains using angle-resolved photoemission spectroscopy (ARPES). We found robust Fermi surface (FS) nesting, consistent with the magnetic modulation q -vector detected by the previous resonant x-ray scattering measurements. The pseudogap opens at the nested FS portions, which vary for different magnetic domains. The anomalous pseudogap disconnects the FS to generate Fermi arcs with twofold symmetry. These results indicate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction plays a decisive role in generating the screw spin modulation responsible for the skyrmion formation in GdRu 2 Si 2 . Furthermore, we demonstrate the flexible nature of magnetism in GdRu 2 Si 2 by manipulating magnetic domains with magnetic field and temperature cyclings, providing potential future applications for data storage and processing devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Collinear antiferromagnetic order in a quasi-two-dimensional triangular lattice compound DyNiAl 4 Ge 2

The two-dimensional magnetic triangular lattice, with rare-earth local moments coupled through long-range interactions and hosting strong spin-orbit coupling, serves as an ideal platform for exploring novel quantum phenomena. Here, we report the physical properties of DyNiAl 4 Ge 2 single crystals through comprehensive structural, magnetic, heat capacity, electrical transport, and neutron powder diffraction measurements. DyNiAl 4 Ge 2 crystallizes in a trigonal lattice with the space group $R\bar{3}m$, where Dy atoms form two-dimensional triangular lattice layers within the 𝑎𝑏 plane and stack along the 𝑐 axis. Magnetic susceptibility measurement reveals a magnetic phase transition at 𝑇 𝑁 = 9.0 K, further confirmed by the 𝜆-shaped peak in the heat capacity curve. The obtained temperature-magnetic field phase diagram is relatively simple compared to other isostructural compounds, suggesting the absence of magnetic frustration. This is further evidenced by neutron powder diffraction, which shows a collinear antiferromagnetic ground state with a propagation vector 𝒌 = (0, 0, 1.5), implying the absence of magnetic frustration in DyNiAl 4 Ge 2 . In this magnetic structure, Dy moments are aligned ferromagnetically within each triangular layer and arranged antiferromagnetically between adjacent layers along the 𝑐 axis. In conclusion, our results establish DyNiAl 4 Ge 2 as a model system for understanding the interplay between RKKY interaction and geometrical frustration in this family of compounds.

Wu, HengHeng [Chinese Academy of Sciences (CAS), S

Magnetic order and excitations in Ce 3 TiBi 5 and Ce 3 ZrBi 5

The R 3 MBi 5 rare-earth intermetallics (R = rare earth, M = Ti, Zr, Sc) provide a versatile platform to explore how Kondo hybridization, Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange, magnetic frustration, and broken inversion symmetry may cooperate to generate unusual magnetic behavior. We present a comprehensive neutron scattering investigation of the magnetic structure, crystal electric field (CEF), and low-energy excitations in the locally noncentrosymmetric Kondo-lattice compounds Ce 3 TiBi 5 and Ce 3 ZrBi 5 . Powder and single-crystal neutron diffraction reveals incommensurate cycloidal antiferromagnetic order in Ce 3 TiBi 5 with propagation vector k = (0, 0, 0.388) and a reduced ordered moment of m = 0.53(3)μ B . Ce 3 ZrBi 5 exhibits a qualitatively similar magnetic diffraction profile, with k ≃ (0, 0, 0.37). Inelastic neutron scattering measurements resolve two clear, well-separated CEF excitations in both compounds with nearly the same profile, confirming a well-isolated Kramers doublet ground state. At low energies, a broad, quasi-elastic magnetic response is observed at T ≃ T N , whose momentum-dependence is inconsistent with that expected from conventional collective excitations of localized moments. This discrepancy, along with a Kondo temperature estimate T K ~ 6 - 7 K—comparable to T N —indicates sizable Kondo hybridization, which accounts for the moment reduction and the spiral magnetic order that appears to involve the magnetic hard direction. Our results place these compounds in a regime where local inversion symmetry breaking, anisotropic CEF effects, and competing Kondo and RKKY interactions collectively give rise to unconventional magnetic order.

Kondo interaction

Toward understanding the dimensional crossover of canonical spin-glass thin films

Spin-glass thin films exhibit many features different from the bulk. The freezing temperatures of spin-glass films are suppressed for reduced thickness and follow the Kenning relation. The dynamics are altered near the vacuum interface. These phenomena are closely related to the lower critical dimension of spin glasses, the spin-glass correlation length, and the dimensional crossover from d = 3 to d = 2. In this article, we review the experimental facts and theoretical perspectives for spin-glass thin films. We focus on canonical spin-glass systems with the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between magnetic impurities in a nonmagnetic host. Open questions to be addressed are emphasized.

interfacial effects

Robust qubit interactions mediated by photonic topological edge states

Here, we investigate the coupling of two spatially separated qubits via topologically protected edge states in a two-dimensional Hofstadter lattice. In this hybrid platform, the qubits are coupled to distinct edge sites of the lattice, enabling long-range interactions mediated by topological edge modes. We solve the full system Hamiltonian and analyze the resulting eigenstate structure to uncover the conditions under which coherent qubit interactions emerge. Our analysis reveals that the effective coupling is highly sensitive to the qubit placement, energy detuning, and the topological character of the edge spectrum. We obtain an analytical solution that goes beyond the perturbative regime, capturing the full interplay between the qubits and edge modes. These results provide a foundation for exploring information transport and many-body effects in engineered quantum systems where interactions are mediated by topological edge modes.

Chern insulators

Coexistence of commensurate and incommensurate antiferromagnetic ground states in Co 𝑥 ⁢NbSe 2 single crystal

In Co 𝑥 ⁢NbSe 2 , crystal symmetry and cobalt site occupation drive the formation of two distinct magnetic phases. At 𝑥=1/4, the centrosymmetric structure (𝑃⁢6 3 /𝑚⁢𝑚⁢𝑐) promotes Co-Co interactions leading to the formation of an 𝐴-type antiferromagnetic structure phase with a transition temperature of 𝑇$^𝐴_𝑁$=169K. At 𝑥=1/3, the noncentrosymmetric structure (𝑃⁢6 3 ⁢22) induces a lower-temperature magnetic phase with 𝑇$^S_𝑁$=28K. We report the coexistence of both substructures within a superlattice, with a nuclear propagation vector of (1/3, 1/3, 0) relative to the host lattice. Single crystals of Co 0.28 ⁢NbSe 2 exhibit both magnetic transitions, with 𝑇$^𝐴_𝑁$ corresponding to the 𝑥∼1/4 phase and 𝑇$^S_𝑁$ corresponding to the 𝑥∼1/3 phase. Magnetic susceptibility and specific heat measurements confirm these transitions, although only the high-temperature 𝑇$^𝐴_𝑁$ phase significantly affects resistivity. We successfully isolate each phase in powder samples, while single crystals with an intercalation ratio of 𝑥=0.28 display the coexistence of both phases in a single sample. Using single-crystal neutron diffraction, we solved the magnetic structure of the high-temperature centrosymmetric phase (𝑇$^𝐴_𝑁$), and neutron powder diffraction revealed the double-𝑞 magnetic structure of the low-temperature noncentrosymmetric phase (𝑇$^S_𝑁$).

RKKY interaction

Collinear ferromagnetism with reduced moment length in kagome magnet Nd 3 ⁢Ru 4 ⁢Al 12

Here, we determine the magnetic ground state of the kagome lattice magnet Nd 3 ⁢Ru 4⁢ Al 12 by single-crystal neutron diffraction, supported by experiments with polarized neutrons. We identify this material as a collinear ferromagnet (“hex-FM”) with uniform moment length and ordering vector 𝑸 = 0, in contrast to a previous, seminal report that proposed unequal moment lengths on two Nd sites, here called the “ortho-FM” state. Our analysis of the flipping ratio in polarized neutron scattering is consistent with the hex-FM state. The results provide a microscopic basis for understanding the large fluctuation-induced Hall and Nernst responses near 𝑇 C ≈ 41K, as previously reported for Nd 3 ⁢Ru 4 ⁢Al 12 .

RKKY interaction

Perspective: Magnon-magnon coupling in hybrid magnonics

The internal coupling of magnetic excitations (magnons) with themselves has created a new research sub-field in hybrid magnonics, i.e., magnon-magnon coupling, which focuses on materials discovery and engineering for probing and controlling magnons in a coherent manner. This is enabled by, one, the abundant mechanisms of introducing magnetic interactions, with examples of exchange coupling, dipolar coupling, Ruderman–Kittel–Kasuya–Yosida (RKKY) coupling, and Dzyaloshinskii–Moriya interaction (DMI) coupling, and two, the vast knowledge of how to control magnon band structure, including field and wavelength dependences of frequencies, for determining the degeneracy of magnon modes with different symmetries. In particular, we discuss how magnon-magnon coupling is implemented in various materials systems, with examples of magnetic bilayers, synthetic antiferromagnets, nanomagnetic arrays, layered van der Waals magnets, and (DMI spin-orbit torque materials) in magnetic multilayers. Here, we then introduce new concept of applications for these hybrid magnonic materials systems, with examples of frequency up/down conversion and magnon-exciton coupling, and discuss what properties are desired for achieving those applications.

Materials science

A magnon band analysis of GdRu 2 Si 2 in the field-polarized state

Understanding the formation of skyrmions in centrosymmetric materials is a problem of fundamental and technological interest. GdRu 2 Si 2 is a candidate material that hosts a variety of multi-Q magnetic phases, including in zero-field. Here, inelastic neutron scattering is used to measure the spin excitations in the field-polarized phase of GdRu 2 Si 2 . Linear spin wave theory and a method of interaction invariant path analysis are used to derive a Hamiltonian accounting for the spectra. The Hamiltonian, dominated by bilinear (Ruderman-Kittel-Kasuya-Yosida) Heisenberg exchange, compares favorably to ab initio calculations. Dipolar interactions are a secondary energy scale to consider, with J D.D ~ 0.05 J RKKY . However, it is shown that in the field-polarized phase the dipolar interactions ‘self screen’ so that their effect is largely suppressed. No specific evidence for higher-order exchange is found. These aspects are discussed in the context of the lower field multi-Q states and the anisotropy of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Two-channel multi-impurity Kondo model: RKKY-induced criticality

We show that the Ruderman-Kittel-Kasua-Yoisida interaction between overscreened spins in two-channel Kondo impurity systems is a relevant perturbation when the number of impurities N is greater than 3 driving the system to a new quantum critical point with anomalous dimensions $\frac{1}{(𝑁+1)}$ for the spin operator and the Sommerfeld coefficient of the specific heat scales as 𝛾 ∼ 𝑇 −$\frac{3}{𝑁+1}$ . The critical point universal properties are relevant to many strong correlation problems, such as impurity placed in a Majorana metal and the multichannel Kondo lattice model of heavy fermion materials. In conclusion, we discuss relevance of our results for cluster DMFT studies of quantum criticality.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Competing magnetic phases in Li-Fe-Ge kagome systems

Competing interlayer magnetic interactions in kagome magnets can lead to diverse magnetic phases, which enable promising topological or quantum material properties. In this work, the electronic structure and magnetic properties are studied using first-principles calculations for the Li⁢Fe6⁢G⁡e6, Li⁢Fe6⁢G⁡e4, and Li⁢Fe6⁢G⁡e5 compounds sharing the kagome F⁡e3⁢Ge layer motif but with different interlayer arrangements. For Li⁢Fe6⁢G⁡e4 and Li⁢Fe6⁢G⁡e5, the predicted magnetic ground states are collinear antiferromagnetic (AFM) states involving a mix of ferromagnetic (FM) and AFM interlayer orientations. In contrast, for Li⁢Fe6⁢G⁡e6, an incommensurate cycloidal spin spiral ground state is stabilized, although its energy is close to a collinear A-type AFM state. The analysis of magnetic RKKY exchange coupling confirms the results of calculations. The values of atomic magnetic moments are in good agreement with existing experimental estimations. Our experiments on Li⁢Fe6⁢G⁡e6 single crystals reveals AFM ordering at ∼540 K and transition to another magnetic phase with a small FM component, possibly with spin canting, below ∼270 K.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND