Lacunar Spinel Research Articles

Quasimolecular J_{tet}=3/2 Moments in the Cluster Mott Insulator GaTa_{4}Se_{8}.

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.

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.

Dzyaloshinskii-Moriya interactions, Néel skyrmions and V4 magnetic clusters in multiferroic lacunar spinel GaV4S8

Using ab initio density functional theory with static mean-field correlations, we calculate the Heisenberg and Dzyaloshinskii-Moriya interactions (DMI) for an atomistic spin Hamiltonian for the lacunar spinel, GaV4S8. The parameters describing these interactions are used in atomistic spin dynamics and micromagnetic simulations. The magnetic properties of the lacunar spinel GaV4S8, a material well-known from experiment to host magnetic skyrmions of Néel character, are simulated with these ab initio calculated parameters. The Dzyaloshinskii-Moriya contribution to the micromagnetic energy is a sum of two Lifshitz invariants, supporting the formation of Néel skyrmions and its symmetry agrees with what is usually expected for C3ν-symmetric systems. There are several conclusions one may draw from this work. One concerns the quantum nature of the magnetism, where we show that the precise magnetic state of the V4 cluster is crucial for understanding quantitatively the magnetic phase diagram. In particular, we demonstrate that a distributed-moment state of each V4 cluster explains well a variety of properties of GaV4S8, such as the band gap, observed Curie temperature and especially the stability of Néel skyrmions in the experimentally relevant temperature and magnetic-field range. In addition, we find that electronic correlations change visibly the calculated value of the DMI.

Resonating holes vs molecular spin-orbit coupled states in group-5 lacunar spinels

The valence electronic structure of magnetic centers is one of the factors that determines the characteristics of a magnet. This may refer to orbital degeneracy, as for jeff = 1/2 Kitaev magnets, or near-degeneracy, e.g., involving the third and fourth shells in cuprate superconductors. Here we explore the inner structure of magnetic moments in group-5 lacunar spinels, fascinating materials featuring multisite magnetic units in the form of tetrahedral tetramers. Our quantum chemical analysis reveals a very colorful landscape, much richer than the single-electron, single-configuration description applied so far to all group-5 GaM4X8 chalcogenides, and clarifies the basic multiorbital correlations on M4 tetrahedral clusters: while for V strong correlations yield a wave-function that can be well described in terms of four V4+V3+V3+V3+ resonant valence structures, for Nb and Ta a picture of dressed molecular-orbital jeff = 3/2 entities is more appropriate. These internal degrees of freedom likely shape vibronic couplings, phase transitions, and the magneto-electric properties in each of these systems.

Synthesis and Structural and Magnetic Properties of Polycrystalline GaMo4Se8

GaMo4Se8, is a lacunar spinel where skyrmions have been recently reported. This compound belongs to the GaM4X8 family, where M is a transition metal (V or Mo) and X is a chalcogenide (S or Se). In this work, we have obtained pure GaMo4Se8 in polycrystalline form through an innovative two-step synthetic route. Phase purity and chemical composition were confirmed through the Rietveld refinement of the powder XRD pattern, the sample characterisation having been complemented with SEM analysis. The magnetic phase diagram was investigated using DC (VSM) and AC magnetometry, which disclosed the presence of cycloidal, skyrmionic and ferromagnetic phases in polycrystalline GaMo4Se8.

Electronic structure and resonant inelastic x-ray scattering in GaTa4Se8

We have investigated the electronic structure of the lacunar spinel compound GaTa4Se8 within the density-functional theory (DFT) using the generalized gradient approximation while taking into account strong Coulomb correlations (GGA+U) in the framework of the fully relativistic spin-polarized Dirac linear muffin-tin orbital band-structure method. GaTa4Se8 can be classified as a Mott insulator since it was expected to be metallic from GGA band structure calculations in contradiction with the resistivity and optical measurements. Strong SOC splits the t2g-type manifold into a lower jeff = 3/2 quartet and an upper jeff = 1/2 doublet. The empty jeff = 1/2 band is well separated from the jeff = 3/2 one and almost completely given by linear combinations of d5/2 states. The partly filled jeff = 3/2 band is dominated by d3/2 states with some weight of d5/2 ones and consists of two groups of bands separated by an energy gap. The low energy jeff = 3/2 band situated at the Fermi level is very narrow, therefore even a small Hubbard U opens the energy gap. We have investigated theoretically the resonant inelastic x-ray scattering (RIXS) spectra at the Ta L2,3 edges. The calculated results are in good agreement with experimental data. We have found that the best agreement between the theory and experiment in the value of the Hubbard energy gap and RIXS spectra at the Ta L2,3 edges can be achieved for Ueff = 1.0 eV. The experimentally measured RIXS spectrum of GaTa4Se8 at the Ta L3 edge in addition to the elastic scattering peak at 0 eV possesses a sharp feature below 1 eV corresponding to transitions within the Ta t2g levels. The excitation located from 1 eV to 2 eV is due to t2g→eg transitions. The third wide very intensive structure from 2.8 eV up to 12 eV is almost completely derived from ligand-to-ligand charge transfer excitations. Such a situation is quite unique for the RIXS spectra in transition 5d metal systems. The origin of this dominant contribution as well as the electronic correlation in GaTa4Se8 is a consequence of its peculiar crystal structure which forms tetrahedral Ta4 clusters with very small intracluster Ta–Ta and Ta–Se distances and rather large distances between the Ta4 clusters. It results in the formation of localized electronic states and extremely strong Ta 5d - Se 4p hybridization which creates 5dSe states with high density of states. Such hybridization is much stronger in comparison with the corresponding 5d - O 2p hybridization in 5d transition metal oxides due to more extended Se 4p wave functions in comparison with oxygen 2p ones.

Dressed jeff-1/2 objects in mixed-valence lacunar spinel molybdates

The lacunar-spinel chalcogenides exhibit magnetic centers in the form of transition-metal tetrahedra. On the basis of density-functional computations, the electronic ground state of an Mo413+ tetrahedron has been postulated as single-configuration a12 e4 t25, where a1, e, and t2 are symmetry-adapted linear combinations of single-site Mo t2g atomic orbitals. Here we unveil the many-body tetramer wave-function: we show that sizable correlations yield a weight of only 62% for the a12 e4 t25 configuration. While spin–orbit coupling within the peculiar valence orbital manifold is still effective, the expectation value of the spin–orbit operator and the g factors deviate from figures describing nominal t5jeff = 1/2 moments. As such, our data documents the dressing of a spin–orbit jeff = 1/2 object with intra-tetramer excitations. Our results on the internal degrees of freedom of these magnetic moments provide a solid theoretical starting point in addressing the intriguing phase transitions observed at low temperatures in these materials.

Antipolar transitions in GaNb4Se8 and GaTa4Se8

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.

Bond ordering and molecular spin-orbital fluctuations in the cluster Mott insulator GaTa4Se8

For materials where spin-orbit coupling is competitive with electronic correlations, the spatially anisotropic spin-orbital wave functions can stabilize degenerate states that lead to many and diverse quantum phases of matter. Here we find evidence for a dynamical spin-orbital state preceding a ${T}^{*}$ = 50 K order-disorder spin-orbital ordering transition in the $j=3/2$ lacunar spinel ${\mathrm{GaTa}}_{4}{\mathrm{Se}}_{8}$. Above ${T}^{*}, {\mathrm{GaTa}}_{4}{\mathrm{Se}}_{8}$ has an average cubic crystal structure, but total scattering measurements indicate local noncubic distortions of ${\mathrm{Ta}}_{4}$ tetrahedral clusters for all measured temperatures $2<T<300$ K. Inelastic neutron-scattering measurements reveal the dynamic nature of these local distortions through symmetry forbidden optical phonon modes that modulate $j=3/2$ molecular orbital occupation as well as intercluster Ta-Se bonds. Spin-orbital ordering at ${T}^{*}$ cannot be attributed to a classic Jahn-Teller mechanism and, based on our findings, we propose that intercluster interactions acting on the scale of ${T}^{*}$ act to break global symmetry. The resulting staggered intercluster dimerization pattern doubles the unit cell, reflecting a spin-orbital valence bond ground state.

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.

Spin dynamics in the skyrmion-host lacunar spinel GaV4S8

In the lacunar spinel GaV4S8, the interplay of spin, charge, and orbital degrees of freedom produces a rich phase diagram that includes an unusual Neel-type skyrmion phase composed of molecular spins. To provide insight into the interactions underlying this complex phase diagram, we study the spin excitations in GaV4S8 through inelastic neutron scattering measurements on polycrystalline and single-crystal samples. Using linear spin-wave theory, we describe the spin-wave excitations using a model where V4 clusters decorate an FCC lattice. The effective cluster model includes a ferromagnetic interaction and a weaker antisymmetric Dzyaloshinskii-Moriya (DM) interaction between the neighboring molecular spins. Our work clarifies the spin interactions in GaV4S8 and supports the picture of interacting molecular clusters.

Nuclear and Electron Spin Resonance Studies on Skyrmion‐Hosting Lacunar Spinels

Magnetic resonance techniques at nuclei and electrons are applied to characterize the electronic structure and collective magnetic excitations throughout the magnetic phase diagrams of the lacunar spinels GaV4S8 and GaV4Se8 showing cycloidal, Néel‐type skyrmion lattice and ferromagnetically polarized phases. 71Ga nuclear magnetic resonance (NMR) provides a local probe of the rhombohedral distortion and the resulting uniaxial magnetic anisotropy via the detection of electric field gradients (EFGs) and hyperfine coupling at the gallium sites of these lacunar spinels. Broadband electron spin resonance (ESR) allows identifying clockwise, counterclockwise, and breathing modes of the skyrmion‐lattice phase supported by theoretical simulations.

Structural phase transition and magnetic phase diagram of the lacunar spinel GaMo4Se8

Structural phase transition and magnetic phase diagram of the lacunar spinel GaMo₄Se₈

Optical, Dielectric, and Magnetoelectric Properties of Ferroelectric and Antiferroelectric Lacunar Spinels

Lacunar spinels with a chemical formula of form a populous family of narrow‐gap semiconductors, which offer a fertile ground to explore correlation and quantum phenomena, including transition between Mott and spin‐orbit insulator states, ferro/antiferroelectricity driven by cluster Jahn‐Teller effect, and magnetoelectric response of magnetic skyrmions with polar dressing. The electronic and magnetic properties of lacunar spinels are determined to a large extent by their molecular‐crystal‐like structure. The interplay of electronic correlations with spin‐orbit and vibronic couplings leads to a complex electronic structure already on the single‐cluster level, which—together with weaker intercluster interactions—gives rise to a plethora of unconventional correlated states. This review primarily focuses on recent progresses in the field of optical, dielectric, and magnetoelectric properties on lacunar spinels. After introducing the main structural aspects, lattice dynamics and electronic structure of these compounds are discussed on the basis of optical spectroscopy measurements. Dielectric and polarization studies reveal the main characteristics of their low‐temperature ferro‐ or antiferroelectric phases as well as orbital fluctuations in their high‐temperature cubic state. Strong couplings between spin, lattice, and orbital degrees of freedom are manifested in singlet formation upon magnetostructural transitions, the emergence of various multiferroic phases, and exotic domain‐wall functionalities.

Mode Crystallography Analysis through the Structural Phase Transition and Magnetic Critical Behavior of the Lacunar Spinel GaMo4Se8.

In the lacunar spinels, with the formula AB4X8, transition-metal ions form tightly bound B4 clusters resulting in exotic physical properties such as the stabilization of Néel-type skyrmion lattices, which hold great promise for energy-efficient switching devices. These properties are governed by the symmetry of these compounds with distortion of the parent noncentrosymmetric F4̅3m space group to the polar R3m, with recent observation of a coexisting Imm2 low-temperature phase. In this study, through powder neutron diffraction, we further confirm that a metastable Imm2 coexists with the R3m phase in GaMo4Se8 and we present its structure. By applying the mode crystallography approach to the distortions together with anisotropic microstrain broadening analysis, we postulate that the formation origin of the minority Imm2 phase stems from the high compressive stress observed in the R3m phase. Bond valence sum analysis also suggests a change in electronic configuration in the transition to Imm2 which could have implications on the electrical properties of the compound. We further establish the nature of the magnetic phase transition using critical exponent analysis obtained from single-crystal magnetization measurements which shows a mixture of tricritical mean-field and 3D Heisenberg behavior [β = 0.22(4), γ = 1.19(1), and δ = 6.42(1)]. Magnetoentropic mapping performed on a single crystal reveals the signature of a positive entropy region near the magnetic phase transition which corresponds to the skyrmion phase field observed in a polycrystalline sample.

Magnetoentropic mapping and computational modeling of cycloids and skyrmions in the lacunar spinels GaV4S8 and GaV4Se8

We report the feasibility of using magnetoentropic mapping for the rapid identification of magnetic cycloid and skyrmion phases in uniaxial systems, based on the GaV4S8 and GaV4Se8 model skyrmion hosts with easy-axis and easy-plane anisotropies respectively. We show that these measurements can be interpreted with the help of a simple numerical model for the spin Hamiltonian to yield unambiguous assignments for both single phase regions and phase boundaries. In the two lacunar spinel chemistries, we obtain excellent agreement between the measured magnetoentropic features and a minimal spin Hamiltonian built on Heisenberg exchange, single-ion anisotropy, and anisotropic Dzyaloshinskii-Moriya interactions. In particular, we identify characteristic high-entropy behavior in the cycloid phase that serves as a precursor to the formation of skyrmions at elevated temperatures and is a readily-measurable signature of this phase transition. Our results demonstrate that rapid magnetoentropic mapping guided by numerical modeling is an effective means of understanding the complex magnetic phase diagrams innate to skyrmion hosts. One notable exception is the observation of an anomalous, low-temperature high-entropy state in the easy-plane system GaV$_4$Se$_8$, which is not captured in the numerical model. Possible origins of this state are discussed.

Melting of Néel skyrmion lattice

Melting of a particle lattice in two dimensional systems substantially differs from the one in three dimensions. The most prominent theory of the lattice melting in 2D, formulated by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY), describes the solid-liquid phase transition as a two-step process, where the solid phase turns into the liquid via the hexatic phase. The microscopic nature of this process lies in the excitation and unbinding of topological defects in the 2D lattice. The KTHNY melting scenario has been observed in number of 2D physical systems. Here, we theoretically analyze the melting process of a N\'eel skyrmion lattice by means of numerical simulations using a model of lacunar spinel ${\mathrm{GaV}}_{4}{\mathrm{S}}_{8}$ hosting hexagonal skyrmion lattice at low temperatures. We show that topological defects are excited in such skyrmion lattice causing its melting via the hexatic phase in agreement with the KTHNY theory.

Cooperative Cluster Jahn-Teller Effect as a Possible Route to Antiferroelectricity

We report the observation of an antipolar phase in cubic GaNb_{4}S_{8} driven by an unconventional microscopic mechanism, the cooperative Jahn-Teller effect of Nb_{4}S_{4} molecular clusters. The assignment of the antipolar nature is based on sudden changes in the crystal structure and a strong drop of the dielectric constant at T_{JT}=31 K, also indicating the first-order nature of the transition. In addition, we found that local symmetry lowering precedes long-range orbital ordering, implying the presence of a dynamic Jahn-Teller effect in the cubic phase above T_{JT}. Based on the variety of structural polymorphs reported in lacunar spinels, also including ferroelectric phases, we argue that GaNb_{4}S_{8} may be transformable to a ferroelectric state, which would further classify the observed antipolar phase as antiferroelectric.

From Semiconducting to Metallic: Jahn–Teller-Induced Phase Transformation in Skyrmion Host GaV4S8

Lacunar spinels, GaM4X8 (M = V, Nb, Mo, Ta, W; X = S, Se, Te), constitute a rare class of compounds with multiferroic properties. Recently, one member of this family, GaV4S8, received global attention due to the Néel-type skyrmions discovered in this material. Previous investigations strongly indicate the important role of the structure behind the multiferroicity, for example, the strong impact of ferroelectric transition on the exchange interactions at ∼40 K. Inspired by the delicate entanglement of lattice, spin, and charge degrees of freedom, in the present work, we aimed to use pressure to alter the structure and thus change the material’s properties to establish the inter-relation between the structural, optical, and electrical properties for a better understanding of this skyrmion host material. Upon this objective, in situ high-pressure measurements of single crystal/powder X-ray diffraction, electrical conductivity, and Raman spectroscopy were carried out by using a diamond anvil cell. These studies revealed the pressure-induced structural transformation from cubic to orthorhombic, along with a transition from semiconductor to metallic state in GaV4S8. The phase changes coincide with the variation in the optical property in this material explored by Raman spectra. We also determined the bulk modulus of the two phases of GaV4S8 by fitting the data set of unit cell volumes against pressure with the second-order birth-Murnaghan equation of state, and explained the mechanisms of phase transitions by means of the Jahn–Teller effect and the anisotropic changes in bonding lengths during compression.

Crystal and electronic structure of GaTa4Se8 from first-principles calculations

GaTa$_4$Se$_8$ belongs to the lacunar spinel family. Its crystal structures is still a puzzle though there have been intensive studies on its novel properties, such as the Mott insulator phase and superconductivity under pressure. In this work, we investigate its phonon spectra through first-principle calculations and proposed it most probably has crystal structure phase transition, which is consistent with several experimental observations. For the prototype lacunar spinel with cubic symmetry of space group $F\bar{4}3m$, its phonon spectra have three soft modes in the whole Brillouin zone, indicating the strong dynamical instability of such crystal structure. In order to find the dynamically stable crystal structure, further calculations indicate two new structures of GaTa$_4$Se$_8$, corresponding to $R3m$ and $P\bar{4}2_{1}m$, verifying that at the ambient pressure, there does exist structure phase transition of GaTa$_4$Se$_8$ from $F\bar{4}3m$ to other structures when the temperature is lowered. We also performed electronic structure calculation for $R3m$ and $P\bar{4}2_{1}m$ structure, showing that $P\bar{4}2_{1}m$ structure GaTa$_4$Se$_8$ is band insulator, and obtained Mott insulator state for $R3m$ structure by DMFT calculation under single-band Hubbard model picture when interaction parameter U is larger than 0.40 eV vs. band width of 0.25 eV. It is reasonable to assume that while lowering the temperature, $F\bar{4}3m$ structure GaTa$_4$Se$_8$ becomes $R3m$ structure GaTa$_4$Se$_8$ first, then $P\bar{4}2_{1}m$ structure GaTa$_4$Se$_8$, because of the symmetry of $P\bar{4}2_{1}m$ is lower than $R3m$ after Jahn-Teller distortion. The structure transition may explain the magnetic susceptibility anomalous at low temperature.