Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings.

Magnetic skyrmions are topological solitons with a nanoscale winding spin texture that hold promise for spintronics applications1-4. Skyrmions have so far been observed in a variety of magnets that exhibit nearly parallel alignment for neighbouring spins, but theoretically skyrmions with anti-parallel neighbouring spins are also possible. Such antiferromagnetic skyrmions may allow more flexible control than conventional ferromagnetic skyrmions5-10. Here, by combining neutron scattering measurements and Monte Carlo simulations, we show that a fractional antiferromagnetic skyrmion lattice is stabilized in MnSc2S4 through anisotropic couplings. The observed lattice is composed of three antiferromagnetically coupled sublattices, and each sublattice is a triangular skyrmion lattice that is fractionalized into two parts with an incipient meron (half-skyrmion) character11,12. Our work demonstrates that the theoretically proposed antiferromagnetic skyrmions can be stabilized in real materials and represents an important step towards their implementation in spintronic devices.

Nonequilibrium dynamics of α-RuCl3 - a time-resolved magneto-optical spectroscopy study.

We present time-resolved magneto-optical spectroscopy on the magnetic Mott-Hubbard-insulating Kitaev spin liquid candidate α-RuCl3 to investigate the nonequilibrium dynamics of its antiferromagnetically ordered zigzag groundstate after photoexcitation. A systematic study of the transient magnetic linear dichroism under different experimental conditions (temperature, external magnetic field, photoexcitation density) gives direct access to the dynamical interplay of charge excitations with the zigzag ordered state on ultrashort time scales. We observe a rather slow initial demagnetization (few to 10s of ps) followed by a long-lived non-thermal antiferromagnetic spin-disordered state (100-1000s of ps), which can be understood in terms of holons and doublons disordering the antiferromagnetic background after photoexcitation. Varying temperature and fluence in the presence of an external magnetic field reveals two distinct photoinduced dynamics associated with the zigzag and quantum paramagnetic disordered phases. The photo-induced non-thermal spin-disordered state shows universal compressed-exponential recovery dynamics related to the growth and propagation of zigzag domains on nanosecond time scales, which is interpreted within the framework of the Fatuzzo-Labrune model for magnetization reversal. The study of nonequilibrium states in strongly correlated materials is a relatively unexplored topic, but our results are expected to be extendable to a large class of Mott-Hubbard insulator materials with strong spin-orbit coupling.

Strain-Stabilized (π, π) Order at the Surface of Fe1+xTe.

A key property of many quantum materials is that their ground state depends sensitively on small changes of an external tuning parameter, e.g., doping, magnetic field, or pressure, creating opportunities for potential technological applications. Here, we explore tuning of the ground state of the nonsuperconducting parent compound, Fe1+xTe, of the iron chalcogenides by uniaxial strain. Iron telluride exhibits a peculiar (π, 0) antiferromagnetic order unlike the (π, π) order observed in the Fe-pnictide superconductors. The (π, 0) order is accompanied by a significant monoclinic distortion. We explore tuning of the ground state by uniaxial strain combined with low-temperature scanning tunneling microscopy. We demonstrate that, indeed under strain, the surface of Fe1.1Te undergoes a transition to a (π, π)-charge-ordered state. Comparison with transport experiments on uniaxially strained samples shows that this is a surface phase, demonstrating the opportunities afforded by 2D correlated phases stabilized near surfaces and interfaces.

Density Functional Theory Approach to the Vibrational Properties and Magnetic Specific Heat of the Covalent Chain Antiferromagnet KFeS2.

Ternary potassium-iron sulfide, KFeS2, belongs to the family of highly anisotropic quasi-one-dimensional antiferromagnets with unusual "anti-Curie-Weiss" susceptibility, quasi-linearly growing with a rising temperature up to 700 K, an almost vanishing magnetic contribution to the specific heat, drastically reduced magnetic moment, etc. While some of the measurements can be satisfactorily described, the deficiency of the entropy changes upon the magnetic transition and the spin state of the iron ion remains a challenge for the further understanding of magnetism. In this work, high-quality single-crystalline samples of KFeS2 were grown by the Bridgman method, and their stoichiometry, crystal structure, and absence of alien magnetic phases were checked, utilizing wave-length dispersive X-ray electron-probe microanalysis, powder X-ray diffraction, and 57Fe Mössbauer spectroscopy, respectively. An ab initio approach was developed to calculate the thermodynamic properties of KFeS2. The element-specific phonon modes and their density of states (PDOS) were calculated applying the density functional theory in the DFT + U version, which explicitly takes into account the on-site Coulomb repulsion U of electrons and their exchange interaction J. The necessary calibration of the frequency scale was carried out by comparison with the experimental iron PDOS derived from the inelastic nuclear scattering experiment. The infrared absorption measurements confirmed the presence of two high-frequency peaks consistent with the calculated PDOS. The calibrated PDOS allowed the calculation of the lattice contribution to the specific heat of KFeS2 by direct summation over the phonon modes without approximations and adjustable parameters. The temperature-dependent magnetic specific heat evaluated by subtraction of the calculated phonon contribution from the experimental specific heat provides a lower boundary for estimating the reduced spin state of the iron ion.

High-resolution neutron depolarization microscopy of the ferromagnetic transitions in Ni3Al and HgCr2Se4 under pressure.

We performed neutron imaging of ferromagnetic transitions in Ni3Al and HgCr2Se4 crystals. These neutron depolarization measurements revealed bulk magnetic inhomogeneities in the ferromagnetic transition temperature with spatial resolution of about 100 µm. To obtain such spatial resolution, we employed a novel neutron microscope equipped with Wolter mirrors as a neutron image-forming lens and a focusing neutron guide as a neutron condenser lens. The images of Ni3Al show that the sample does not homogeneously go through the ferromagnetic transition; the improved resolution allowed us to identify a distribution of small grains with slightly off-stoichiometric composition. Additionally, neutron depolarization imaging experiments on the chrome spinel, HgCr2Se4, under pressures up to 15 kbar highlight the advantages of the new technique especially for small samples or sample environments with restricted sample space. The improved spatial resolution enables one to observe domain formation in the sample while decreasing the acquisition time despite having a bulky pressure cell in the beam.

Pressure-Induced Changes in the Crystal Structure and Electrical Conductivity of GeV4S8.

Lacunar spinels, represented by AM4X8 compounds (A = Ga or Ge; M = V, Mo, Nb, or Ta; X = S or Se), form a unique group of ternary chalcogenide compounds. Among them, GeV4S8 has garnered significant attention due to its distinctive electrical and magnetic properties. While previous research efforts have primarily focused on studying how this material behaves under cooling conditions, pressure is another factor that determines the state and characteristics of solid matter. In this study, we employed a diamond anvil cell in conjunction with high-energy synchrotron X-ray diffraction, Raman spectroscopy, four-point probes, and theoretical computation to thoroughly investigate this material. We found that the structural transformation from cubic to orthorhombic was initiated at 34 GPa and completed at 54 GPa. Through data fitting of volume vs pressure, we determined the bulk moduli to be 105 ± 4 GPa for the cubic phase and 111 ± 12 GPa for the orthorhombic phase. Concurrently, electrical resistance measurements indicated a semiconductor-to-nonmetallic conductor transition at ∼15 GPa. Moreover, we experimentally assessed the band gaps at different pressures to validate the occurrence of the electrical phase transition. We infer that the electrical phase transition correlates with the valence electrons in the V4 cluster rather than the crystal structure transformation. Furthermore, the computational results, electronic density of states, and band structure verified the experimental observation and facilitated the understanding of the mechanism governing the electrical phase transition in GeV4S8.

Magnetization reversal through an antiferromagnetic state.

Magnetization reversal in ferro- and ferrimagnets is a well-known archetype of non-equilibrium processes, where the volume fractions of the oppositely magnetized domains vary and perfectly compensate each other at the coercive magnetic field. Here, we report on a fundamentally new pathway for magnetization reversal that is mediated by an antiferromagnetic state. Consequently, an atomic-scale compensation of the magnetization is realized at the coercive field, instead of the mesoscopic or macroscopic domain cancellation in canonical reversal processes. We demonstrate this unusual magnetization reversal on the Zn-doped polar magnet Fe2Mo3O8. Hidden behind the conventional ferrimagnetic hysteresis loop, the surprising emergence of the antiferromagnetic phase at the coercive fields is disclosed by a sharp peak in the field-dependence of the electric polarization. In addition, at the magnetization reversal our THz spectroscopy studies reveal the reappearance of the magnon mode that is only present in the pristine antiferromagnetic state. According to our microscopic calculations, this unusual process is governed by the dominant intralayer coupling, strong easy-axis anisotropy and spin fluctuations, which result in a complex interplay between the ferrimagnetic and antiferromagnetic phases. Such antiferro-state-mediated reversal processes offer novel concepts for magnetization control, and may also emerge for other ferroic orders.

Broadband magnetic resonance spectroscopy in MnSc[Formula: see text]S[Formula: see text].

Recent neutron scattering experiments suggested that frustrated magnetic interactions give rise to antiferromagnetic spiral and fractional skyrmion lattice phases in MnSc[Formula: see text]S[Formula: see text] . Here, to trace the signatures of these modulated phases, we studied the spin excitations of MnSc[Formula: see text]S[Formula: see text] by THz spectroscopy at 300 mK and in magnetic fields up to 12 T and by broadband microwave spectroscopy at various temperatures up to 50 GHz. We found a single magnetic resonance with frequency linearly increasing in field. The small deviation of the Mn[Formula: see text] ion g-factor from 2, g = 1.96, and the absence of other resonances imply very weak anisotropies and negligible contribution of higher harmonics to the spiral state. The significant difference between the dc magnetic susceptibility and the lowest-frequency ac susceptibility in our experiment implies the existence of mode(s) outside of the measured frequency windows. The combination of THz and microwave experiments suggests a spin gap opening below the ordering temperature between 50 GHz and 100 GHz.

Slowdown of photoexcited spin dynamics in the non-collinear spin-ordered phases in skyrmion host GaV4S8.

Formation of magnetic order alters the character of spin excitations, which then affects transport properties. We investigate the photoexcited ultrafast spin dynamics in different magnetic phases in Néel-type skyrmion host GaV4S8 with time-resolved magneto-optical Kerr effect experiments. The coherent spin precession, whose amplitude is enhanced in the skyrmion-lattice phase, shows a signature of phase coexistence across the magnetic phase transitions. The incoherent spin relaxation dynamics slows down by a factor of two in the skyrmion-lattice/cycloid phases, indicating significant decrease in thermal conductivity triggered by a small change of magnetic field. The slow heat diffusion in the skyrmion-lattice/cycloid phases is attributed to the stronger magnon scattering off the domain walls formed in abundance in the skyrmion-lattice/cycloid phase. These results highlight the impact of spatial spin structure on the ultrafast heat transport in spin systems, providing a useful insight for the step toward ultrafast photocontrol of the magnets with novel spin orders.

How Correlations and Spin-Orbit Coupling Work within Extended Orbitals of Transition-Metal Tetrahedra of 4d/5d Lacunar Spinels.

Spin-orbit quartet ground states are associated with rich phenomenology, ranging from multipolar phases in f1 rare-earth borides to magnetism emerging through covalency and vibronic couplings in d1 transition-metal compounds. The latter effect has been studied since the 1960s on t2g1 octahedral ML6 units in both molecular complexes and extended solid-state lattices. Here we analyze the Jeff = 3/2 quartet ground state of larger cubane-like M4L4 entities in lacunar spinels, composed of transition-metal (M) tetrahedra caged by chalcogenide ligands (L). These represent a unique platform where spin-orbit coupling acts on molecular-like, delocalized t2 orbitals. Using quantum chemical methods, we pin down the interplay of spin-orbit couplings in such a setting and many-body physics related to other molecular-like single-electron levels, both below and above the reference t21. We provide a different interpretation of resonant inelastic X-ray scattering data on GaTa4Se8 and, by comparing magnetic susceptibility data with calculated g factors, valuable insights into the important role of vibronic couplings.

Manipulating surface magnetic order in iron telluride.

Control of emergent magnetic orders in correlated electron materials promises new opportunities for applications in spintronics. For their technological exploitation, it is important to understand the role of surfaces and interfaces to other materials and their impact on the emergent magnetic orders. Here, we demonstrate for iron telluride, the nonsuperconducting parent compound of the iron chalcogenide superconductors, determination and manipulation of the surface magnetic structure by low-temperature spin-polarized scanning tunneling microscopy. Iron telluride exhibits a complex structural and magnetic phase diagram as a function of interstitial iron concentration. Several theories have been put forward to explain the different magnetic orders observed in the phase diagram, which ascribe a dominant role either to interactions mediated by itinerant electrons or to local moment interactions. Through the controlled removal of surface excess iron, we can separate the influence of the excess iron from that of the change in the lattice structure.

Sub-gap optical response in the Kitaev spin-liquid candidate α-RuCl3.

We report detailed optical experiments on the layered compound α-RuCl3 focusing on the THz and sub-gap optical response across the structural phase transition from the monoclinic high-temperature to the rhombohedral low-temperature structure, where the stacking sequence of the molecular layers is changed. This type of phase transition is characteristic for a variety of tri-halides crystallizing in a layered honeycomb-type structure and so far is unique, as the low-temperature phase exhibits the higher symmetry. One motivation is to unravel the microscopic nature of THz and spin-orbital excitations via a study of temperature and symmetry-induced changes. The optical studies are complemented by thermal expansion experiments. We document a number of highly unusual findings: A characteristic two-step hysteresis of the structural phase transition, accompanied by a dramatic change of the reflectivity. A complex dielectric loss spectrum in the THz regime, which could indicate remnants of Kitaev physics. Orbital excitations, which cannot be explained based on recent models, and an electronic excitation, which appears in a narrow temperature range just across the structural phase transition. Despite significant symmetry changes across the monoclinic to rhombohedral phase transition and a change of the stacking sequence, phonon eigenfrequencies and the majority of spin-orbital excitations are not strongly influenced. Obviously, the symmetry of a single molecular layer determines the eigenfrequencies of most of these excitations. Only one mode at THz frequencies, which becomes suppressed in the high-temperature monoclinic phase and one phonon mode experience changes in symmetry and stacking. Finally, from this combined terahertz, far- and mid-infrared study we try to shed some light on the so far unsolved low energy (<1 eV) electronic structure of the ruthenium 4d 5 electrons in α-RuCl3.

Ultra-robust high-field magnetization plateau and supersolidity in bond-frustrated MnCr2S4.

Frustrated magnets provide a promising avenue for realizing exotic quantum states of matter, such as spin liquids and spin ice or complex spin molecules. Under an external magnetic field, frustrated magnets can exhibit fractional magnetization plateaus related to definite spin patterns stabilized by field-induced lattice distortions. Magnetization and ultrasound experiments in MnCr2S4 up to 60 T reveal two fascinating features: (i) an extremely robust magnetization plateau with an unusual spin structure and (ii) two intermediate phases, indicating possible realizations of supersolid phases. The magnetization plateau characterizes fully polarized chromium moments, without any contributions from manganese spins. At 40 T, the middle of the plateau, a regime evolves, where sound waves propagate almost without dissipation. The external magnetic field exactly compensates the Cr-Mn exchange field and decouples Mn and Cr sublattices. In analogy to predictions of quantum lattice-gas models, the changes of the spin order of the manganese ions at the phase boundaries of the magnetization plateau are interpreted as transitions to supersolid phases.

Characteristics of ferroelectric-ferroelastic domains in Néel-type skyrmion host GaV4S8.

GaV4S8 is a multiferroic semiconductor hosting Néel-type magnetic skyrmions dressed with electric polarization. At Ts = 42 K, the compound undergoes a structural phase transition of weakly first-order, from a non-centrosymmetric cubic phase at high temperatures to a polar rhombohedral structure at low temperatures. Below Ts, ferroelectric domains are formed with the electric polarization pointing along any of the four 〈111〉 axes. Although in this material the size and the shape of the ferroelectric-ferroelastic domains may act as important limiting factors in the formation of the Néel-type skyrmion lattice emerging below TC = 13 K, the characteristics of polar domains in GaV4S8 have not been studied yet. Here, we report on the inspection of the local-scale ferroelectric domain distribution in rhombohedral GaV4S8 using low-temperature piezoresponse force microscopy. We observed mechanically and electrically compatible lamellar domain patterns, where the lamellae are aligned parallel to the (100)-type planes with a typical spacing between 100 nm-1.2 µm. Since the magnetic pattern, imaged by atomic force microscopy using a magnetically coated tip, abruptly changes at the domain boundaries, we expect that the control of ferroelectric domain size in polar skyrmion hosts can be exploited for the spatial confinement and manipulation of Néel-type skyrmions.

Evidence for orbital order and its relation to superconductivity in FeSe0.4Te0.6.

The emergence of nematic electronic states accompanied by a structural phase transition is a recurring theme in many correlated electron materials, including the high-temperature copper oxide- and iron-based superconductors. We provide evidence for nematic electronic states in the iron-chalcogenide superconductor FeSe0.4Te0.6 from quasi-particle scattering detected in spectroscopic maps. The symmetry-breaking states persist above T c into the normal state. We interpret the scattering patterns by comparison with quasi-particle interference patterns obtained from a tight-binding model, accounting for orbital ordering. The relation to superconductivity and the influence on the coherence length are discussed.

Multiferroicity and skyrmions carrying electric polarization in GaV4S8.

Skyrmions are whirl-like topological spin objects with high potential for future magnetic data storage. A fundamental question that is relevant to both basic research and application is whether ferroelectric (FE) polarization can be associated with skyrmions' magnetic texture and whether these objects can be manipulated by electric fields. We study the interplay between magnetism and electric polarization in the lacunar spinel GaV4S8, which undergoes a structural transition associated with orbital ordering at 44 K and reveals a complex magnetic phase diagram below 13 K, including ferromagnetic, cycloidal, and Néel-type skyrmion lattice (SkL) phases. We found that the orbitally ordered phase of GaV4S8 is FE with a sizable polarization of ~1 µC/cm(2). Moreover, we observed spin-driven excess polarizations in all magnetic phases; hence, GaV4S8 hosts three different multiferroic phases with coexisting polar and magnetic order. These include the SkL phase, where we predict a strong spatial modulation of FE polarization close to the skyrmion cores. By taking into account the crystal symmetry and spin patterns of the magnetically ordered phases, we identify exchange striction as the main microscopic mechanism behind the spin-driven FE polarization in each multiferroic phase. Because GaV4S8 is unique among known SkL host materials owing to its polar crystal structure and the observed strong magnetoelectric effect, this study is an important step toward the nondissipative electric field control of skyrmions.

Magnetic microscopy. Real-space imaging of the atomic-scale magnetic structure of Fe(1+y)Te.

Spin-polarized scanning tunneling microscopy (SP-STM) has been used extensively to study magnetic properties of nanostructures. Using SP-STM to visualize magnetic order in strongly correlated materials on an atomic scale is highly desirable, but challenging. We achieved this goal in iron tellurium (Fe(1+ y)Te), the nonsuperconducting parent compound of the iron chalcogenides, by using a STM tip with a magnetic cluster at its apex. Our images of the magnetic structure reveal that the magnetic order in the monoclinic phase is a unidirectional stripe order; in the orthorhombic phase at higher excess iron concentration (y > 0.12), a transition to a phase with coexisting magnetic orders in both directions is observed. It may be possible to generalize the technique to other high-temperature superconductor families, such as the cuprates.