Bifurcation instructed design of multistate machines.

We propose a design paradigm for multistate machines where transitions from one state to another are organized by bifurcations of multiple equilibria of the energy landscape describing the collective interactions of the machine components. This design paradigm is attractive since, near bifurcations, small variations in a few control parameters can result in large changes to the system's state providing an emergent lever mechanism. Further, the topological configuration of transitions between states near such bifurcations ensures robust operation, making the machine less sensitive to fabrication errors and noise. To design such machines, we develop and implement a new efficient algorithm that searches for interactions between the machine components that give rise to energy landscapes with these bifurcation structures. We demonstrate a proof of concept for this approach by designing magnetoelastic machines whose motions are primarily guided by their magnetic energy landscapes and show that by operating near bifurcations we can achieve multiple transition pathways between states. This proof of concept demonstration illustrates the power of this approach, which could be especially useful for soft robotics and at the microscale where typical macroscale designs are difficult to implement.

Coherent detection of hidden spin-lattice coupling in a van der Waals antiferromagnet.

Strong interactions between different degrees of freedom lead to exotic phases of matter with complex order parameters and emergent collective excitations. Conventional techniques, such as scattering and transport, probe the amplitudes of these excitations, but they are typically insensitive to phase. Therefore, novel methods with phase sensitivity are required to understand ground states with phase modulations and interactions that couple to the phase of collective modes. Here, by performing phase-resolved coherent phonon spectroscopy (CPS), we reveal a hidden spin-lattice coupling in a vdW antiferromagnet FePS3 that eluded other phase-insensitive conventional probes, such as Raman and X-ray scattering. With comparative analysis and analytical calculations, we directly show that the magnetic order in FePS3 selectively couples to the trigonal distortions through partially filled t2g orbitals. This magnetoelastic coupling is linear in magnetic order and lattice parameters, rendering these distortions inaccessible to inelastic scattering techniques. Our results not only capture the elusive spin-lattice coupling in FePS3 but also establish phase-resolved CPS as a tool to investigate hidden interactions.

Anomalous magnetic noise in an imperfectly flat landscape in the topological magnet Dy2Ti2O7.

Noise generated by motion of charge and spin provides a unique window into materials at the atomic scale. From temperature of resistors to electrons breaking into fractional quasiparticles, "listening" to the noise spectrum is a powerful way to decode underlying dynamics. Here, we use ultrasensitive superconducting quantum interference device (SQUIDs) to probe the puzzling noise in a frustrated magnet, the spin-ice compound Dy2Ti2O7 (DTO), revealing cooperative and memory effects. DTO is a topological magnet in three dimensions-characterized by emergent magnetostatics and telltale fractionalized magnetic monopole quasiparticles-whose real-time dynamical properties have been an enigma from the very beginning. We show that DTO exhibits highly anomalous noise spectra, differing significantly from the expected Brownian noise of monopole random walks, in three qualitatively different regimes: equilibrium spin ice, a "frozen" regime extending to ultralow temperatures, and a high-temperature "anomalous" paramagnet. We present several distinct mechanisms that give rise to varied colored noise spectra. In addition, we identify the structure of the local spin-flip dynamics as a crucial ingredient for any modeling. Thus, the dynamics of spin ice reflects the interplay of local dynamics with emergent topological degrees of freedom and a frustration-generated imperfectly flat energy landscape, and as such, it points to intriguing cooperative and memory effects for a broad class of magnetic materials.

Emergence of Stable Meron Quartets in Twisted Magnets.

The investigation of twist engineering in easy-axis magnetic systems has revealed remarkable potential for generating topological spin textures. Implementing twist engineering in easy-plane magnets, we introduce a novel approach to achieving fractional topological spin textures, such as merons. Through atomistic spin simulations on twisted bilayer magnets, we demonstrate the formation of a stable double Meron pair, which we refer to as the "Meron Quartet" (MQ). Unlike a single pair, the merons within the MQ exhibit exceptional stability against pair annihilation due to the protective localization mechanism induced by the twist that prevents collision of the Meron cores. Furthermore, we showcase that the stability of the MQ can be enhanced by adjusting the twist angle, resulting in an increased resistance to external perturbations such as external magnetic fields. Our findings highlight the twisted magnet as a promising platform for achieving merons as stable magnetic quasiparticles in van der Waals magnets.

Theory of Moiré Magnetism and Multidomain Spin Textures in Twisted Mott Insulator-Semimetal Heterobilayers.

Motivated by the recent experimental developments in van der Waals heterostructures, we investigate the emergent magnetism in Mott insulator-semimetal moiré superlattices by deriving effective spin models and exploring their phase diagram by Monte Carlo simulations. Our analysis indicates that the stacking-dependent interlayer Kondo interaction can give rise to different types of magnetic order, forming domains within the moiré unit cell. In particular, we find that the AB (AA) stacking regions tend to order (anti)ferromagnetically for an extended range of parameters. The remaining parts of the moiré unit cell form ferromagnetic chains that are coupled antiferromagnetically. We show that the decay length of the Kondo interaction can control the extent of these phases. Our results highlight the importance of stacking-dependent interlayer exchange and the rich magnetic spin textures that can be obtained in van der Waals heterostructures.

Theory of Moiré Magnetism in Twisted Bilayer α-RuCl3.

Motivated by the recent developments in moiré superlattices of van der Waals magnets and the desire to control the magnetic interactions of α-RuCl3, here we present a comprehensive theory of the long-range ordered magnetic phases of twisted bilayer α-RuCl3. Using a combination of first-principles calculations and atomistic simulations, we show that the stacking-dependent interlayer exchange gives rise to an array of magnetic phases that can be realized by controlling the twist angle. In particular, we discover a complex hexagonal domain structure in which multiple zigzag orders coexist. This multidomain order minimizes the interlayer energy while enduring the energy cost due to domain wall formation. Further, we show that quantum fluctuations can be enhanced across the phase transitions. Our results indicate that magnetic frustration due to stacking-dependent interlayer exchange in moiré superlattices can be exploited to tune quantum fluctuations and the magnetic ground state of α-RuCl3.

Ultrafast Exciton Dynamics in the Atomically Thin van der Waals Magnet CrSBr.

Among atomically thin semiconductors, CrSBr stands out as both its bulk and monolayer forms host tightly bound, quasi-one-dimensional excitons in a magnetic environment. Despite its pivotal importance for solid-state research, the exciton lifetime has remained unknown. While terahertz polarization probing can directly trace all excitons, independently of interband selection rules, the corresponding large far-field foci substantially exceed the lateral sample dimensions. Here, we combine terahertz polarization spectroscopy with near-field microscopy to reveal a femtosecond decay of paramagnetic excitons in a monolayer of CrSBr, which is 30 times shorter than the bulk lifetime. We unveil low-energy fingerprints of bound and unbound electron-hole pairs in bulk CrSBr and extract the nonequilibrium dielectric function of the monolayer in a model-free manner. Our results demonstrate the first direct access to the ultrafast dielectric response of quasi-one-dimensional excitons in CrSBr, potentially advancing the development of quantum devices based on ultrathin van der Waals magnets.

Beyond Kitaev physics in strong spin-orbit coupled magnets.

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effectiveJeff=1/2magnetic moments. This includes, but not limited to,5d5iridates,4d5ruthenates and3d7cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.

Unraveling Exchange Coupling in Ferrites Nano-Heterostructures.

The magnetic coupling of a set of SrFe12 O19 /CoFe2 O4 nanocomposites is investigated. Advanced electron microscopy evidences the structural coherence and texture at the interfaces of the nanostructures. The fraction of the lower anisotropy phase (CoFe2 O4 ) is tuned to assess the limits that define magnetically exchange-coupled interfaces by performing magnetic remanence, first-order reversal curves (FORCs), and relaxation measurements. By combining these magnetometry techniques and the structural and morphological information from X-ray diffraction, electron microscopy, and Mössbauer spectrometry, the exchange intergranular interaction is evidenced, and the critical thickness within which coupled interfaces have a uniform reversal unraveled.

Enhancing Intrinsic Magnetic Hardness by Modulating Antagonistic Interactions in the Rare-Earth-Free Magnetic Solid Solution Hf2 Fe1-δ Ru5-x Irx+δ B2.

The quinary members in the solid solution Hf2 Fe1-δ Ru5-x Irx+δ B2 (x=1-4, VE=63-66) have been investigated experimentally and computationally. They were synthesized via arc-melting and analyzed by EDX and X-ray diffraction. Density functional theory (DFT) calculations predicted a preference for magnetic ordering in all members, but with a strong competition between ferro- and antiferromagnetism arising from interchain Fe-Fe interactions. The spin exchange and magnetic anisotropy energies predicted the lowest magnetic hardness for x=1 and 3 and the highest for x=2. Magnetization measurements confirm the DFT predictions and demonstrate that the antiferromagnetic ordering (TN =55-70 K) found at low magnetic fields changed to ferromagnetic (TC =150-750 K) at higher fields, suggesting metamagnetic behavior for all samples. As predicted, Hf2 FeRu3 Ir2 B2 has the highest intrinsic coercivity (Hc =74 kA/m) reported to date for Ti3 Co5 B2 -type phases. Furthermore, all coercivities outperform that of ferromagnetic Hf2 FeIr5 B2 , indicating the importance of AFM interactions in enhancing magnetic anisotropy in these materials. Importantly, two members (x=1 and 4) maintain intrinsic coercivities in the semi-hard range at room temperature. This study opens an avenue for controlling magnetic hardness by modulating antagonistic AFM and FM interactions in low-dimensional rare-earth-free magnetic materials.

Anilato-Based Coordination Polymers with Slow Relaxation of the Magnetization: Role of the Synthetic Method and Anilato Ligand.

We have prepared and characterized three coordination polymers formulated as [Dy2(C6O4Cl2)3(fma)6] ⋅ 4.5fma (1) and [Dy2(C6O4X2)3(fma)6] ⋅ 4fma ⋅ 2H2O with X=Br (2) and Cl (3), where fma=formamide and C6O4X2 2-=3,6-disubstituted-2,5-dihydroxy-1,4-benzoquinone dianion with X=Cl (chloranilato) and Br (bromanilato). Compounds 1 and 3 are solvates obtained with slow and fast precipitation methods, respectively. Compounds 2 and 3 are isostructural and only differ in the X group of the anilato ligand. The three compounds present (6,3)-gon two-dimensional hexagonal honey-comb structures. Magnetic measurements indicate that the three compounds show slow relaxation of the magnetization at low temperatures when a continuous magnetic field is applied, although with different relaxation times and energy barriers depending on X and the crystallisation molecules. Compounds 1-3 represent the first examples of anilato-based lattices with formamide and field-induced slow relaxation of the magnetization.

Gaining Insights into the Interplay between Optical and Magnetic Properties in Photoexcited Coordination Compounds.

We describe early and recent advances in the fascinating field of combined magnetic and optical properties of inorganic coordination compounds and in particular of 3d-4f single molecule magnets. We cover various applied techniques which allow for the correlation of results obtained in the frequency and time domain in order to highlight the specific properties of these compounds and the future challenges towards multidimensional spectroscopic tools. An important point is to understand the details of the interplay of magnetic and optical properties through performing time-resolved studies in the presence of external fields especially magnetic ones. This will enable further exploration of this fundamental interactions i. e. the two components of electromagnetic radiation influencing optical properties.

Fatal bowel perforation caused by ingestion of high-powered magnets in a 6-year-old boy.

Foreign body ingestion in children is a frequent cause for medical consultation. Although most foreign bodies are spontaneously eliminated from the gastrointestinal tract, life-threatening complications such as gastrointestinal obstruction or perforation can occur. We report the case of a 6-year-old boy who died 2 days after the onset of nausea and abdominal pain, with no foreign body ingestion witnessed or reported in the previous days. Autopsy showed a diffuse peritonitis and a perforation of the transverse colon caused by three high-powered magnets stacked together, and attached to the outer stomach wall via a fourth magnet located in the stomach. The cause of death was peritonitis due to bowel perforation by ingested magnets, which were shown to have come from a toy belonging to the child. Ingestion of multiple high-powered magnets carries a high risk of gastrointestinal complications and can exceptionally have a fatal outcome, especially as it often goes unreported and causes non-specific gastrointestinal symptoms that can delay diagnosis and management. This case highlights the need to raise public awareness of the potential risks of ingesting such magnets and to strengthen safety standards to protect children from this serious health hazard.

Tuning the magnetic properties of hard-soft Ba0.5Sr0.5Fe10Al2O19and Ni0.1Co0.9Fe2O4nanocomposites via one pot sol-gel auto combustion method for permanent magnet applications.

Permanent magnets generate magnetic fields that can be sustained when a reverse field is supplied. These permanent magnets are effective in a wide range of applications. However, strategic rare-earth element demand has increased interest in replacing them with huge energy product (BH)max. Exchange-coupled hard/soft ferrite nanocomposites have the potential to replace a portion of extravagant rare earth element-based magnets. In the present, we have reported the facile auto combustion synthesis of exchange-coupled Ba0.5Sr0.5Fe10Al2O19and Ni0.1Co0.9Fe2O4nanocomposites by increasing the content of soft ferrite over the hard fromx= 0.1 to 0.4 wt%. The XRD combined with Rietveld analysis reflected the presence of hexaferrite and spinel ferrite without the existence of secondary phases. The absorption bands from the Fourier transform infrared spectrum analysis proved the presence of M-O bonds in tetrahedral sites and octahedral sites. Rod and non-spherical images from TEM represent the hexaferrite and spinel ferrite. The smoothM-Hcurve and a single peak of the switching field distribution curve prove that the material has undergone a good exchange coupling. The nanopowders displayed an increase in saturation magnetization and a decrease in coercivity with the increases in the spinel content. The prepared nanocomposites were showing higher energy products. The composite with the ratiox= 0.2 displayed a higher value of (BH)maxof 13.16 kJ m-3.

Simulations of Transients in a Four-Pole Magnetic Bearing with Permanent Magnets.

This paper presents the design of and transient time simulations for a four-pole magnetic bearing with permanent magnets. The usage of permanent magnets reduces the consumption of electric energy in comparison to a traditional active magnetic bearing. Permanent magnets are installed in the yoke of the stator core to limit the cross-coupling of the magnetic flux generated by the windings. The first part of this paper presents the design of the magnetic bearing and its finite-element model, while the second part describes the field-circuit indirectly coupled finite-element model for the transient time simulation. The presented simulation model was used to calculate the transient response for the rotor lifting from the starting position, the step change in the rotor position and the change in the rotor position under an external impact force applied along the y-axis.

Strongly Coupled Magnon-Plasmon Polaritons in Graphene-Two-Dimensional Ferromagnet Heterostructures.

Magnons and plasmons are different collective modes, involving the spin and charge degrees of freedom, respectively. Formation of hybrid plasmon-magnon polaritons in heterostructures of plasmonic and magnetic systems faces two challenges, the small interaction of the electromagnetic field of the plasmon with the spins, and the energy mismatch, as in most systems plasmons have energies orders of magnitude larger than those of magnons. We show that graphene plasmons form polaritons with the magnons of two-dimensional ferromagnetic insulators, placed up to to half a micrometer apart, with Rabi splittings in the range of 100 GHz (dramatically larger than cavity magnonics). This is facilitated both by the small energy of graphene plasmons and the cooperative super-radiant nature of the plasmon-magnon coupling afforded by phase matching. We show that the coupling can be modulated both electrically and mechanically, and we propose a ferromagnetic resonance experiment implemented with a two-dimensional ferromagnet driven by graphene plasmons.

Topological Equivalence of Stripy States and Skyrmion Crystals.

Stripy states, consisting of a collection of stripy spin textures, are the precursors of skyrmion crystals (SkXs). The common belief is that stripy states and SkXs are topologically unconnected and that transitions between SkXs and stripy states are phase transitions. Here, we show that both stripy states and SkXs are skyrmion condensates and they are topologically equivalent. By gradually tuning the stripe whose width goes from smaller than to larger than skyrmion-skyrmion separation, the structure of a skyrmion condensate transforms smoothly and continuously from various stripy phases, including helical states and mazes, to crystals, showing that stripy states are topologically connected to SkXs.

Theoretical Study on the Raman Effect Due to Magnons in Two-Dimensional Magnets.

Raman spectroscopy is one of the most useful experimental tools for studying elementary excitations in two-dimensional (2D) materials. The Raman scattering due to phonons was widely employed for detecting structural evolutions, especially those caused by magnetic phase transitions in 2D magnets. A first-principles theory of the Raman scattering effect caused by magnons is still lacking. We theoretically study the magnon Raman effect in 2D magnet CrI3. We propose a first-principles method and have calculated the intensity of circularly polarized Raman signals due to different magnon modes in the CrI3 monolayer and bilayers. The calculated Raman intensities due to magnons in the CrI3 monolayer and the rhombohedral bilayer are consistent with the selection rule deduced from the magnon pseudoangular moment and the parity of magnon modes. We also find that the selection rule is violated in the symmetry-broken monoclinic bilayer due to interlayer coupling.

Ferromagnetic Interlayer Coupling in CrSBr Crystals Irradiated by Ions.

Layered magnetic materials are becoming a major platform for future spin-based applications. Particularly, the air-stable van der Waals compound CrSBr is attracting considerable interest due to its prominent magneto-transport and magneto-optical properties. In this work, we observe a transition from antiferromagnetic to ferromagnetic behavior in CrSBr crystals exposed to high-energy, non-magnetic ions. Already at moderate fluences, ion irradiation induces a remanent magnetization with hysteresis adapting to the easy-axis anisotropy of the pristine magnetic order up to a critical temperature of 110 K. Structure analysis of the irradiated crystals in conjunction with density functional theory calculations suggests that the displacement of constituent atoms due to collisions with ions and the formation of interstitials favors ferromagnetic order between the layers.

Ruderman-Kittel-Kasuya-Yosida-Type Interlayer Dzyaloshinskii-Moriya Interaction in Synthetic Magnets.

Conduction electron spins interacting with magnetic impurity spins can mediate an interlayer exchange interaction, namely, the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. This discovery opened the way to significant technological developments in the field of magnetic storage and spintronics. So far, the RKKY-type interlayer interaction has been found to construct symmetric coupling of magnetism; however, the asymmetric counterpart remains unexplored. Here we report unprecedented RKKY-type interlayer Dzyaloshinskii-Moriya interaction (DMI) in synthetic magnets, exhibiting a damped oscillatory feature. This asymmetric interlayer interaction is found to be dramatically dependent on the intermediate coupling layer. By introducing the Fert-Lévy model to the trilayer system, we reveal that the in-plane inversion symmetry breaking plays a pivotal role for generating interlayer DMI and the RKKY oscillation is an intrinsic behavior in metallic multilayers. Our finding fills up the empty block for RKKY-type asymmetric interlayer exchange coupling in comparison to the well-known (symmetric) RKKY-type interlayer exchange coupling.