We investigated temperature-driven spin reorientation (SR) in the itinerant kagome magnet Fe3Sn2 using high-resolution synchrotron x-ray diffraction, neutron diffraction, magnetometry, and magnetic force microscopy (MFM), further supported by phenomenological analysis. Our study reveals a crossover from the state with easy-plane anisotropy to the high-temperature state with uniaxial easy-axis anisotropy taking place between similar to 40 and 130 K through an intermediate easy-cone (or tilted spin) state. This state, induced by the interplay between the anisotropy constants K1 and K2, is clearly manifested in the thermal evolution of the magnetic structure factor, which reveals a gradual change of the SR angle theta between 40 and 130 K. We also found that the SR is accompanied by a magnetoelastic effect. Zero-field MFM images across the SR range show a transformation in surface magnetic patterns from a dendritic structure at 120 K to domain-wall-dominated MFM contrast at 40 K. Our analysis suggests that the SR and associated microstructural transformations are the results of competing first-and second-order anisotropy constants.

Ferro-/ferri- and antiferromagnetically ordered phases are typically exclusive in nature, thus, their coexistence in atomic-scale proximity is expected only in heterostructures. Breaking this paradigm and broadening the range of unconventional magnetic states, we report here on the observation of a new, atomic-scale hybrid spin state. This ordering is stabilized in three-dimensional crystals of the polar antiferromagnet Co2Mo3O8 by magnetic fields applied perpendicular to the Co honeycomb layers and possesses a spontaneous in-plane ferromagnetic moment. Our microscopic spin model, capturing the observed field dependence of the longitudinal and transverse magnetization as well as the magnetoelectric/elastic properties, reveals that this novel spin state is composed of an alternating stacking of antiferromagnetic and ferrimagnetic honeycomb layers. The strong intralayer and the weak interlayer exchange couplings together with competing anisotropies at octahedral and tetrahedral Co sites are identified as the key ingredients to stabilize antiferromagnetic and ferrimagnetic layers in such close proximity. We show that the proper balance of magnetic interactions can extend the stability range of this hybrid phase down to zero magnetic field. The possibility to realize a layer-by-layer stacking of such distinct spin orders via suitable combinations of microscopic interactions opens a new dimension toward the nanoscale engineering of magnetic states.

Quasimolecular orbitals in cluster Mott insulators provide a route to tailor exchange interactions, which may yield novel quantum phases of matter. We demonstrate the cluster Mott character of the lacunar spinel GaTa4Se8 using resonant inelastic x-ray scattering (RIXS) at the Ta L3 edge. Electrons are fully delocalized over Ta4 tetrahedra, forming quasimolecular Jtet = 3/2 moments. The modulation of the RIXS intensity as function of the transferred momentum q allows us to determine the cluster wave function, which depends on competing intracluster hopping terms that mix states with different character. This mixed wave function is decisive for the macroscopic properties since it affects intercluster hopping and exchange interactions and furthermore renormalizes the effective spin-orbit coupling constant. The versatile wave function, tunable via intracluster hopping, opens a new perspective on the large family of lacunar spinels and cluster Mott insulators in general.

Quasimolecular orbitals in cluster Mott insulators provide a route to tailor exchange interactions, which may yield novel quantum phases of matter. We demonstrate the cluster Mott character of the lacunar spinel GaTa$_4$Se$_8$ using resonant inelastic x-ray scattering (RIXS) at the Ta $L_3$ edge. Electrons are fully delocalized over Ta$_4$ tetrahedra, forming quasimolecular $J_{\rm tet}$=3/2 moments. The modulation of the RIXS intensity as function of the transferred momentum q allows us to determine the cluster wavefunction, which depends on competing intracluster hopping terms that mix states with different character. This mixed wavefunction is decisive for the macroscopic properties since it affects intercluster hopping and exchange interactions and furthermore renormalizes the effective spin-orbit coupling constant. The versatile wavefunction, tunable via intracluster hopping, opens a new perspective on the large family of lacunar spinels and cluster Mott insulators in general.

We investigated the magnetic and magnetoelastic properties of MnSc2Se4 single crystals at low temperature under a magnetic field directed along the crystallographic [111] axis. The magnetization data at low temperature show a linear increase with magnetic field, until saturation is reached above 15 T. In ultrasound, a longitudinal acoustic mode shows a softening in field, which is absent for a transverse acoustic mode. We discuss these results using a microscopic model based on the framework of linear spin-wave theory. The magnetic and magnetoelastic data are qualitatively reproduced by considering magnon-phonon interactions arising from exchange-striction coupling between the crystal lattice and spin-wave fluctuations in the zero-temperature limit.

We present a comprehensive microscopic insight into the spin configurations within the bond-frustrated cubic spinel compound MnCr2S4 directly unveiled through extensive single-crystal neutron diffraction studies carried out in zero magnetic field and in fields up to 35 T. While our zero field results confirm the ferrimagnetic structure with an antiparallel arrangement of the magnetic Cr3+ and Mn2+ sublattices below T FiM approximate to 65 K, as well as the presence of the exotic Yafet-Kittel phase below T YK approximate to 5 K, our data measured in fields enable us to precisely determine the field-induced magnetic structures and their evolution across the phase transitions at mu 0 H 1 approximate to 11 T and mu 0 H 2 approximate to 25 T and beyond that towards mu 0 H 3 (approximate to 50 T). Additionally, combining our experimental findings with mean-field-theory calculations reveals a complex field dependence of the Mn-Mn and Mn-Cr exchange interactions across the different phases, highlighting the significant influence of spin-lattice coupling in this material.

The lack of both time-reversal and spatial inversion symmetry in polar magnets is a prerequisite for the occurrence of optical magnetoelectric effects such as nonreciprocal directional dichroism with the potential for the realization of optical diodes. In particular, antiferromagnetic materials with magnetic excitations in the THz range such as Fe2Mo3O8 are promising candidates for next-generation spintronic applications. In a combined experimental and theoretical effort we investigated the THz excitations of the polar honeycomb antiferromagnet Fe2Mo3O8 in external magnetic fields and their nonreciprocal directional dichroism, together with the temperature dependence of the electronic transitions in the mid- and near-infrared frequency range. Using an advanced single-ion approach for the Fe ions, we are able to describe optical excitations from the THz to the near-infrared frequency range quantitatively and successfully model the observed nonreciprocal directional dichroism in the THz regime.

We report a magnetization study of the rare -earth -based paramagnet KEr(MoO4)2 in a magnetic field up to 50 T. A recent observation of massive magnetostriction and rotational magnetocaloric effects in this compound triggered interest in the microscopic mechanism behind these phenomena. We combine several experimental techniques to investigate the magnetization behavior up to its saturation along three main crystallographic directions. The synergy of magnetic torque measurements and vibrating sample magnetometry allowed us to reconstruct parallel and perpendicular components of the magnetization vector, enabling us to trace its evolution up to 30 T. Our experiments reveal the magnetization saturation along all principle axes well below the value, expected from crystal electric field calculations. We argue that an externally applied magnetic field induces a distortion of the local environment of Er3+ ions and affects its crystal electric field splitting.

Antiferromagnetic FeSn is considered to be a close realization of the ideal two-dimensional (2D) kagome lattice, hosting Dirac cones, van Hove singularities, and flat bands, as it comprises Fe_3Sn kagome layers well separated by Sn buffer layers. We observe a pronounced optical anisotropy, with the low-energy optical conductivity being surprisingly higher perpendicular to the kagome planes than along the layers. This finding contradicts the prevalent picture of dominantly 2D electronic structure for FeSn. Our material-specific theory reproduces the measured conductivity spectra remarkarbly well. A site-specific decomposition of the optical response to individual excitation channels shows that the optical conductivity for polarizations both parallel and perpendicular to the kagome plane is dominated by interlayer transitions between kagome layers and adjacent Sn-based layers. Moreover, the matrix elements corresponding to these transitions are highly anisotropic, leading to larger out-of-plane conductivity. Our results evidence the crucial role of interstitial layers in charge dynamics even in seemingly 2D systems.

Quasimolecular orbitals in cluster Mott insulators provide a route to tailor exchange interactions, which may yield novel quantum phases of matter. We demonstrate the cluster Mott character of the lacunar spinel GaTa_{4}Se_{8} using resonant inelastic x-ray scattering (RIXS) at the Ta L_{3} edge. Electrons are fully delocalized over Ta_{4} tetrahedra, forming quasimolecular J_{tet}=3/2 moments. The modulation of the RIXS intensity as function of the transferred momentum q allows us to determine the cluster wave function, which depends on competing intracluster hopping terms that mix states with different character. This mixed wave function is decisive for the macroscopic properties since it affects intercluster hopping and exchange interactions and furthermore renormalizes the effective spin-orbit coupling constant. The versatile wave function, tunable via intracluster hopping, opens a new perspective on the large family of lacunar spinels and cluster Mott insulators in general.

In NiTe$_3$O$_6$ with a chiral crystal structure, we report on a giant natural optical rotation of the lowest-energy magnon. This polarization rotation, as large as 140 deg/mm, corresponds to a path difference between right and left circular polarizations that is comparable to the sample thickness. Natural optical rotation, being a measure of structural chirality, is highly unusual for long-wavelength magnons. The collinear antiferromagnetic order of NiTe$_3$O$_6$ makes this giant effect even more peculiar: Chirality of the crystal structure does not affect the magnetic ground state but is strongly manifested in the lowest excited state. We show that the dynamic magnetoelectric effect, turning this magnon to a magnetic- and electric-dipole active hybrid mode, generates the giant natural optical rotation. In finite magnetic fields, it also leads to a strong optical magnetochiral effect.

We report the magnetic properties of A -site spinel compound MnSc 2 Se 4 . The macroscopic magnetic measurements uncovers successive magnetic transitions at T N1 = 2.04 K, followed by two further transitions at T N2 =1.8 K and T N3 =1.6 K. Neutron powder diffraction reveals that both, T N2 < T < T N1 and T < T N3 , orders are associated with the propagation vector k =(3/4 3/4 0), while the magnetic structures are collinear amplitude modulated and helical, respectively. Using neutron powder spectroscopy we demonstrated the effect of substitution of S by Se on the magnetic exchange. The energy range of the spin-wave excitations is supressed due to the chemical pressure of the X - ion in MnSc 2 X 4 ( X =S, Se) spinels.

The cubic spinel FeCr2S4 has been receiving immense research interest because of its emergent phases and the interplay of spin, orbital and lattice degrees of freedom. Despite the intense research, several fundamental questions are yet to be answered, such as the refinement of the crystal structure in the different magnetic and orbital ordered phases. Here, using high-resolution synchrotron powder diffraction on stoichiometric crystals of FeCr2S4 we resolved the long sought-after cubic to tetragonal transition at ~65 K, reducing the lattice symmetry to I41/amd. With further lowering the temperature, at ~9 K, the crystal structure becomes polar, hence the compound becomes multiferroic. The elucidation of the lattice symmetry throughout different phases of FeCr2S4 provides a basis for the understanding this enigmatic system and also highlights the importance of structural deformation in correlated materials.

Recent neutron scattering experiments suggested that frustrated magnetic interactions give rise to antiferromagnetic spiral and fractional skyrmion lattice phases in MnSc$_2$S$_4$. Here, to trace the signatures of these modulated phases, we studied the spin excitations of MnSc$_2$S$_4$ by THz spectroscopy at 300 mK up to 12 T. We found a single magnetic resonance with linearly increasing frequency in field. The corresponding $g$-factor of Mn$^{2+}$ ions $g$ = 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) below 100 GHz.

We report crystal structure, magnetization, and specific heat measurements on single crystals of the hexagonal polar magnet Co2-xZnxMo3O8 magnetically diluted by replacing Co by Zn. In contrast to the transformation from the antiferromagnetic to a ferrimagnetic state observed in the isostructural Fe2Mo3O8 upon small Zn doping, a robust antiferromagnetic behavior is preserved in Zn-doped Co2Mo3O8 up to x = 0.55. The Neel temperature decreases from TN = 40 K at x = 0 to 23 K at x = 0.55, thus extrapolating to x = 1.27 (36% filling) as the percolation threshold typical for a three-dimensional, highly coordinated network. This indicates strong magnetic couplings beyond the honeycomb planes in Co2Mo3O8. A sharp peak in the specific heat and a clear cusp in the susceptibility associated with the onset of magnetic order is observed up to x = 0.55, whereas at x = 0.66 these features are broadened due to increased disorder. Interestingly, the in-plane lattice parameter, the Curie -Weiss temperature, and the magnetic entropy vary with x in a concerted but nonmonotonic manner. These obser-vations can be traced back to the observed site-selective Zn substitution. We found that in the low-doping regime (x < 0.2) Zn2+ ions primarily occupy the octahedrally coordinated sites, although they have a clear preference for occupying the tetrahedrally coordinated sites at higher doping levels. Due to the multiple interlayer exchange paths, dependent on the coordination of the Co2+ ions, this behavior is reflected in the nonmonotonic variation of the Curie-Weiss temperature and magnetic entropy with substitution.

We report crystal structure, magnetization, and specific heat measurements on single crystals of the hexagonal polar magnet ${\mathrm{Co}}_{2\text{\ensuremath{-}}x}{\mathrm{Zn}}_{x}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ magnetically diluted by replacing Co by Zn. In contrast to the transformation from the antiferromagnetic to a ferrimagnetic state observed in the isostructural ${\mathrm{Fe}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ upon small Zn doping, a robust antiferromagnetic behavior is preserved in Zn-doped ${\mathrm{Co}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ up to $x=0.55$. The N\'eel temperature decreases from ${T}_{\mathrm{N}}=40$ K at $x=0$ to 23 K at $x=0.55$, thus extrapolating to $x=1.27$ (36% filling) as the percolation threshold typical for a three-dimensional, highly coordinated network. This indicates strong magnetic couplings beyond the honeycomb planes in ${\mathrm{Co}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$. A sharp peak in the specific heat and a clear cusp in the susceptibility associated with the onset of magnetic order is observed up to $x=0.55$, whereas at $x=0.66$ these features are broadened due to increased disorder. Interestingly, the in-plane lattice parameter, the Curie-Weiss temperature, and the magnetic entropy vary with $x$ in a concerted but nonmonotonic manner. These observations can be traced back to the observed site-selective Zn substitution. We found that in the low-doping regime ($x<0.2$) ${\mathrm{Zn}}^{2+}$ ions primarily occupy the octahedrally coordinated sites, although they have a clear preference for occupying the tetrahedrally coordinated sites at higher doping levels. Due to the multiple interlayer exchange paths, dependent on the coordination of the ${\mathrm{Co}}^{2+}$ ions, this behavior is reflected in the nonmonotonic variation of the Curie-Weiss temperature and magnetic entropy with substitution.

We theoretically and experimentally study the stability of the unconventional fractional antiferromagnetic skyrmion lattice (AF-SkL) in Mn$_2$S$_4$ spinel under magnetic fields applied along the $[$1-10$]$ crystal direction. By performing numerical Monte Carlo simulations for the minimal effective spin model that we proposed in Ref. [S. Gao, et al., Nature 586, 37-41 (2020)], we show that the skyrmion lattice is aligned within the equivalent and symmetric $[$1-11$]$ or $[$1-11$]$ planes, which are equally inclined to the applied magnetic field. We attribute this behavior to the magnetic anisotropy of the host material. Neutron single crystal diffraction presents a very good agreement with the predictions of the effective model. It reveals that the topological spin texture gets destabilized at low temperatures and moderate magnetic fields and is replaced by a conical phase for B// $[$1-10$]$. The present study elucidates the central role of the magnetic anisotropy in the stabilization of antiferromagnetic skyrmionic states.

A single ferromagnetic kagome layer is predicted to realize a Chern insulator with quantized Hall conductance, which upon stacking can become a Weyl-semimetal with large anomalous Hall effect (AHE) and magneto-optical activity. Indeed, in the kagome bilayer material Fe$_3$Sn$_2$, a large AHE was detected, however, it still awaits the direct probing of the responsible band structure features by bulk sensitive methods. We measure the optical, both diagonal and Hall, conductivity spectra over a broad spectral range and identify the origin of the intrinsic AHE with the help of momentum- and band-decomposed first-principles calculations. We find that low-energy transitions, tracing "helical volumes" in momentum space reminiscent of the formerly predicted helical nodal lines, substantially contribute to the AHE, which is further increased by contributions from multiple higher-energy interband transitions. Our study also reveals that local Coulomb interactions lead to band reconstructions near the Fermi level.

We present dielectric, polarization, resistivity, specific heat, and magnetic susceptibility data on single crystals of the lacunar spinels GaNb4Se8 and GaTa4Se8, tetrahedral cluster-based materials with substantial spin-orbit coupling. We concentrate on the possible occurrence of antipolar order in these compounds, as previously reported for the isoelectronic GaNb4S8, where spin-orbit coupling plays a less important role. Our broadband dielectric-spectroscopy investigations reveal clear anomalies of the intrinsic dielectric constant at the magneto-structural transitions in both systems that are in accord with the expectations for antipolar transitions. A similar anomaly is also observed at the cubic-cubic transition of the Nb compound leading to an intermediate phase. Similar to other polar and antipolar lacunar spinels, we find indications for dipolar relaxation dynamics at low temperatures. Polarization measurements on GaNb4Se8 reveal weak ferroelectric ordering below the magneto-structural transition, either superimposed to antipolar order or emerging at structural domain walls. The temperature-dependent dc resistivity evidences essentially thermally-activated charge transport with different activation energies in the different phases. A huge step-like increase of the resistivity at the magneto-structural transition of the Ta compound points to a fundamental change in the electronic structure or the mechanism of the charge transport. At low temperatures, charge transport is governed by in-gap impurity states, as also invoked to explain the resistive switching in these compounds.

Magnetoelectric phenomena are intimately linked to relativistic effects and also require the material to break spatial inversion symmetry and time-reversal invariance. Magnetoelectric coupling can substantially affect light–matter interaction and lead to non-reciprocal light propagation. Here, we confirm on a fully experimental basis, without invoking either symmetry-based or material-specific assumptions, that the optical magnetoelectric effect in materials with non-parallel magnetization ( M ) and electric polarization ( P ) generates a trilinear term in the refractive index, δ n ∝ k ⋅ ( P × M ), where k is the propagation vector of light. Its sharp magnetoelectric resonances in the terahertz regime, which are simultaneously electric and magnetic dipole active excitations, make Co 2 Mo 3 O 8 an ideal compound to demonstrate this fundamental relation via independent variation of M , P , and k . Remarkably, the material shows almost perfect one-way transparency in moderate magnetic fields for one of these magnetoelectric resonances.