Lacunar Spinel Research Articles

Featureless adaptive optimization accelerates functional electronic materials design

Electronic materials that exhibit phase transitions between metastable states (e.g., metal-insulator transition materials with abrupt electrical resistivity transformations) are challenging to decode. For these materials, conventional machine learning methods display limited predictive capability due to data scarcity and the absence of features that impede model training. In this article, we demonstrate a discovery strategy based on multi-objective Bayesian optimization to directly circumvent these bottlenecks by utilizing latent variable Gaussian processes combined with high-fidelity electronic structure calculations for validation in the chalcogenide lacunar spinel family. We directly and simultaneously learn phase stability and bandgap tunability from chemical composition alone to efficiently discover all superior compositions on the design Pareto front. Previously unidentified electronic transitions also emerge from our featureless adaptive optimization engine. Our methodology readily generalizes to optimization of multiple properties, enabling co-design of complex multifunctional materials, especially where prior data is sparse.

Field-induced tricritical behavior in the Néel-type skyrmion host GaV4S8

The lacunar spinel compound ${\mathrm{GaV}}_{4}{\mathrm{S}}_{8}$ exhibits a N\'eel-type skyrmion, which holds great promise for future spintronics and ultrahigh-density magnetic memory devices. To gain more insight into the magnetic interactions, the critical behavior of ${\mathrm{GaV}}_{4}{\mathrm{S}}_{8}$ is studied by dc magnetization measurement around the Curie temperature $({T}_{\mathrm{C}})$. A set of reliable critical exponents ($\ensuremath{\beta}=0.220\ifmmode\pm\else\textpm\fi{}0.024$, $\ensuremath{\gamma}=0.909\ifmmode\pm\else\textpm\fi{}0.005$, and $\ensuremath{\delta}=5.161\ifmmode\pm\else\textpm\fi{}0.003$) is obtained by the modified Arrott plot technique, the Kouvel-Fisher method, and critical isothermal analysis. The generated critical exponents fulfill the universality class of tricritical mean-field theory, which suggests a field-induced tricritical phenomenon. Based on the scaling equations, boundaries between the skyrmion and ferromagnetic phases can be distinguished. A tricritical point is revealed at the temperature of ${T}_{\mathrm{Tr}}=12\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and field of ${H}_{\mathrm{Tr}}=60\phantom{\rule{0.16em}{0ex}}\mathrm{mT}$, which is located at the intersection point among the skyrmion, ferromagnetic, and paramagnetic phases. It is suggested that the origin of the tricritical behavior in ${\mathrm{GaV}}_{4}{\mathrm{S}}_{8}$ is related to the skyrmion state near the magnetic transition temperature ${T}_{\mathrm{C}}$.

Stability of Néel-type skyrmion lattice against oblique magnetic fields in GaV4S8 and GaV4Se8

The orientation of N\'eel-type skyrmions in the lacunar spinels GaV$_4$S$_8$ and GaV$_4$Se$_8$ is tied to the polar axes of their underlying crystal structure through the Dzyaloshinskii-Moriya interaction. In these crystals, the skyrmion lattice phase exists for externally applied magnetic fields parallel to these axes and withstands oblique magnetic fields up to some critical angle. Here, we map out the stability of the skyrmion lattice phase in both crystals as a function of field angle and magnitude using dynamic cantilever magnetometry. The measured phase diagrams reproduce the major features predicted by a recent theoretical model, including a reentrant cycloidal phase in GaV$_4$Se$_8$. Nonetheless, we observe a greater robustness of the skyrmion phase to oblique fields, suggesting possible refinements to the model. Besides identifying transitions between the cycloidal, skyrmion lattice, and ferromagnetic states in the bulk, we measure additional anomalies in GaV$_4$Se$_8$ and assign them to magnetic states confined to polar structural domain walls.

Skyrmionic order and magnetically induced polarization change in lacunar spinel compounds GaV4S8 and GaMo4S8 : Comparative theoretical study

We show how low-energy electronic models derived from the first-principles electronic structure calculations can help to rationalize the magnetic properties of two lacunar spinel compounds GaM4S8 with light (M=V) and heavy (M=Mo) transition-metal elements, which are responsible for different spin-orbit interaction strength. In the model, each magnetic lattice point was associated with the M4S4 molecule, and the model itself was formulated in the basis of molecular Wannier functions constructed for three magnetic t2 bands. The effects of rhombohedral distortion, spin-orbit interaction, band filling, and the screening of Coulomb interactions in the t2 bands are discussed in details. The electronic model is further treated in the superexchange approximation, which allows us to derive an effective spin model for the energy and electric polarization ($P$) depending on the relative orientation of spins in the bonds, and study the properties of this model by means of classical Monte Carlo simulations with the emphasis on the possible formation of the skyrmionic phase. While isotropic exchange interactions clearly dominate in GaV4S8, all types of interactions -- isotropic, antisymmetric, and symmetric anisotropic -- are comparable in the case of GaMo4S8. Particularly, large uniaxial exchange anisotropy has a profound effect on the properties of GaMo4S8. On the one hand, it raises the Curie temperature by opening a gap in the spectrum of magnon excitations. On the other hand, it strongly affects the skyrmionic phase by playing the role of a molecular field, which facilitates the formation of skyrmions, but makes them relatively insensitive to the external magnetic field in the large part of the phase diagram. We predict reversal of the magnetic dependence of $P$ in the case of GaMo4S8 caused by the reversal of direction of the rhombohedral distortion.

Magnetic phase transitions and spin density distribution in the molecular multiferroic system GaV4S8

We have carried out neutron diffraction and small angle neutron scattering measurements on a high quality single crystal of the cubic lacunar spinel multiferroic, GaV$_4$S$_8$, as a function of magnetic field and temperature to determine the magnetic properties for the single electron that is located on the tetrahedrally coordinated V$_4$ molecular unit. Our results are in good agreement with the structural transition at 44 K from cubic to rhombohedral symmetry where the system becomes a robust ferroelectric, while long range magnetic order develops below 13 K in the form of an incommensurate cycloidal magnetic structure, which can transform into a N\'eel-type skyrmion phase in a modest applied magnetic field. Below 5.9(3) K, the crystal enters a ferromagnetic phase, and we find the magnetic order parameter indicates a long range ordered ground state with an ordered moment of 0.23(1) ${\mu}_\mathrm{B}$ per V ion. Both polarized and unpolarized neutron data in the ferroelectric-paramagnetic phase have been measured to determine the magnetic form factor. The data are consistent with a model of the single spin being uniformly distributed across the V$_4$ molecular unit, rather than residing on the single apical V ion, in substantial agreement with the results of first-principles theory. In the magnetically ordered state, polarized neutron measurements are important since both the cycloidal and ferromagnetic order parameters are clearly coupled to the ferroelectricity, causing the structural peaks to be temperature and field dependent. For the ferromagnetic ground state, the spins are locked along the $[1,1,1]$ direction by a surprisingly large anisotropy.

Pressure-induced topological superconductivity in the spin\u2013orbit Mott insulator GaTa4Se8

Lacunar spinel GaTa4Se8 is a unique example of spin–orbit coupled Mott insulator described by molecular jeff = 3/2 states. It becomes superconducting at Tc = 5.8 K under pressure without doping. In this work, we show, this pressure-induced superconductivity is a realization of a new type topological phase characterized by spin-2 Cooper pairs. Starting from first-principles density functional calculations and random phase approximation, we construct the microscopic model and perform the detailed analysis. Applying pressure is found to trigger the virtual interband tunneling processes assisted by strong Hund coupling, thereby stabilizing a particular d-wave quintet channel. Furthermore, we show that its Bogoliubov quasiparticles and their surface states exhibit novel topological nature. To verify our theory, we propose unique experimental signatures that can be measured by Josephson junction transport and scanning tunneling microscope. Our findings open up new directions searching for exotic superconductivity in spin–orbit coupled materials.

Structural evolution and skyrmionic phase diagram of the lacunar spinel GaMo4Se8

In the $AB_4Q_8$ lacunar spinels, the electronic structure is described on the basis of inter- and intra-cluster interactions of tetrahedral $B_4$ clusters, and tuning these can lead to myriad fascinating electronic and magnetic ground states. In this work, we employ magnetic measurements, synchrotron X-ray and neutron scattering, and first-principles electronic structure calculations to examine the coupling between structural and magnetic phase evolution in GaMo$_4$Se$_8$, including the emergence of a skyrmionic regime in the magnetic phase diagram. We show that the competition between two distinct Jahn-Teller distortions of the room temperature cubic $F\overline{4}3m$ structure leads to the coexistence of the ground state $R3m$ phase and a metastable $Imm2$ phase. The magnetic properties of these two phases are computationally shown to be very different, with the $Imm2$ phase exhibiting uniaxial ferromagnetism and the $R3m$ phase hosting a complex magnetic phase diagram including equilibrium N\'eel--type skyrmions stable from nearly $T$ = 28 K down to $T$ = 2 K, the lowest measured temperature. The large change in magnetic behavior induced by a small structural distortion reveals that GaMo$_4$Se$_8$ is an exciting candidate material for tuning unconventional magnetic properties $via$ mechanical means.

V4tetrahedral units inAV4X8lacunar spinels: Near degeneracy, charge fluctuations, and configurational mixing within a valence space of up to 21dorbitals

This paper proposes that d-metal tetrahedra in lacunar spinel materials display correlated superpositions of multiple electron configurations, different from existing theoretical models, and discusses the basic requirements for realistic modeling of these systems.

Lattice dynamics and electronic excitations in a large family of lacunar spinels with a breathing pyrochlore lattice structure

Reproducing the electronic structure of AM$_4$X$_8$ lacunar spinels with a breathing pyrochlore lattice is a great theoretical challenge due to the interplay of various factors. The character of the M$_4$X$_4$ cluster orbitals is critically influenced by the Jahn-Teller instability, the spin-orbit interaction, and also by the magnetic state of the clusters. Consequently, to reproduce the narrow-gap semiconducting nature of these moderately correlated materials requires advanced approaches, since the strength of the inter-cluster hopping is strongly affected by the character of the cluster orbitals. In order to provide a solid experimental basis for theoretical studies, we performed broadband optical spectroscopy on a large set of lacunar spinels, with systematically changing ions at the A and M sites as well as the ligand (A=Ga, Ge, Al; M=V, Mo, Nb, Ta; X=S, Se). Our study covers the range of phonon excitations and also electronic transitions near the gap edge. In the phonon excitation spectrum a limited subset of the symmetry allowed modes is observed in the cubic state, with a few additional modes emerging upon the symmetry-lowering structural transition. All the infrared active modes are assigned to vibrations of the ligands and ions at the A sites, with no obvious contribution from the M-site ions. Concerning the electronic states, we found that all compounds are narrow-gap semiconductors ($E_\mathrm{g} = 130 - 350\,$meV) already in their room-temperature cubic state and their structural transitions induce weak, if any, changes in the band gap. The gap value is decreased when substituting S with Se and also when replacing $3d$ ions by $4d$ or $5d$ ions at the M sites.

High-field phase transitions in the orbitally ordered multiferroic GeV4S8

The high-field (H,T) phase diagram of the multiferroic lacunar spinel $\mathrm{Ge}{\mathrm{V}}_{4}{\mathrm{S}}_{8}$ has been studied by ultrasound, magnetization, and pyrocurrent experiments in magnetic fields up to 60 T. The title compound consists of molecular building blocks, with vanadium ${\mathrm{V}}_{4}$ clusters characterized by a unique electron density. These vanadium tetrahedra constitute a Jahn-Teller active entity, which drive an orbital-ordering transition at 30 K with the concomitant appearance of ferroelectricity. Ultrasound and magnetization experiments reveal sharp anomalies in magnetic fields of 46 T, which are associated with a first-order phase transition into an orbitally disordered state characterized by significant field and temperature hystereses. We report a sequence of complex magnetic, polar, and orbitally ordered states, i.e., the appearance of two orbitally ordered phases OO1 and OO2 for ${\ensuremath{\mu}}_{0}H<45\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ and $T<30\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Beyond the paraelectric phase we further evidenced three ferroelectric phases, FE1, FE2, and FE3. Finally, antiferromagnetic (AFM) order $(T<15\text{ K})$ and fully polarized ferromagnetic order $({\ensuremath{\mu}}_{0}H>60\phantom{\rule{0.16em}{0ex}}\mathrm{T})$ have been observed in $\mathrm{Ge}{\mathrm{V}}_{4}{\mathrm{S}}_{8}$. At low temperatures and for fields below 40 T, AFM order coexists with the polar phase FE3 identifying a multiferroic state. Our results demonstrate a fascinating competition of the different orders, which the material manifests in high magnetic fields and at low temperatures.

Mapping skyrmion stability in uniaxial lacunar spinel magnets from first principles

The identification of general principles for stabilizing magnetic skyrmion phases in bulk materials over wide ranges of temperatures is a prerequisite to the development of skyrmion-based spintronic devices. Lacunar spinels with the formula GaM4X8 with M=V, Mo; X=S, Se are a convenient case study towards this goal as they are some of the first bulk systems suggested to host equilibrium chiral skyrmions far from the paramagnetic transition. We derive the magnetic phase diagrams likely to be observed in these materials, accounting for all possible magnetic interactions, and prove that skyrmion stability in the lacunar spinels is a general consequence of their crystal symmetry rather than the details of the material chemistry. Our results are consistent with all experimental reports in this space and demonstrate that the differences in the phase diagrams of particular spinel chemistries are determined by magnetocrystalline anisotropy, up to a normalization factor. We conclude that skyrmion formation over wide ranges of temperatures can be expected in all lacunar spinels, as well as in a wide range of uniaxial systems with low magnetocrystalline anisotropy.

Microstructure and micromechanical properties of GaV4S8 ceramics prepared by single-step solid state synthesis

Despite the current focus on the electronic properties of GaV4S8 lacunar spinel, the microstructural and mechanical characterization of this material is scarce in the literature. In this work, we propose an effective GaV4S8 ceramics production method and provide a detailed microstructural and micromechanical characterization. Light microscopy, scanning electron microscopy and X-ray diffraction are used to describe the microstructure of the ceramic targets that can be used for thin film deposition. V2O3 was found to be the main impurity in ceramic targets and its content is discussed with respect to the sintering atmosphere control. Nanoindentation and microcantilever bending were employed to provide estimates of the indentation modulus, hardness and fracture stress of individual grains. The values of these parameters have been determined as Er = 130 ± 2 GPa, H = 8.9 ± 0.2 GPa and σc = 600 ± 57 MPa, respectively.

Polarity of domain boundaries in nonpolar materials derived from order parameter and layer group symmetry

Domain boundaries and other twin boundaries in crystalline materials are receiving increasing interest. They can carry unique functional properties, which in many cases are absent in the surrounding bulk material. One such property of domain boundaries can be their electric polarity. Phenomenological insight in the polarity of domain boundaries was so far based either on the knowledge of the order parameter and the form of Landau-Ginzburg free energy functional, or on the knowledge of the symmetry of the domain boundaries. In the present work we show on the concrete examples of potassium thiocyanate (KSCN) and lacunar spinel crystals, that the concept of the primary order-parameter can help to find the layer group describing the maximal possible symmetry of a given domain boundary. Combination of layer group and order parameter symmetries is then employed to clarify the nature of the polarity of domain boundaries.

Assessing exchange-correlation functional performance in the chalcogenide lacunar spinels GaM4Q8 (M=Mo, V, Nb, Ta; Q=S,Se)

We perform systematic density functional theory (DFT) calculations to assess the performance of various exchange-correlation potentials $V_{xc}$ in describing the chalcogenide GaM$_4$Q$_8$ lacunar spinels (M=Mo, V, Nb, Ta; Q=S, Se). We examine the dependency of crystal structure (in cubic and rhombohedral symmetries), electronic structure, magnetism, optical conductivity, and lattice dynamics in lacunar spinels at four different levels of $V_{xc}$: the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, and hybrid with fractional Fock exchange. We find that LDA significantly underperforms GGA and higher level functionals in predicting lattice constants. LDA also fails to properly describe the magnetism in the family, and for some compositions it does not find the ground state distorted crystal structure. The Perdew-Burke-Ernzerhof (PBE) and PBE revised for solids (PBEsol) GGA functionals perform reasonably well in predicting lattice constants as well as the electronic structures. We find that the GGA with an on-site Coulomb interaction (GGA$+U$) is unnecessary to produce a semiconducting state in the distorted polar $R3m$ phase. Plus Hubbard $U$ values ranging from 1$\sim$2 eV, however, improve the quantitative performance of the GGA functionals. The meta-GGA functional SCAN predicts reasonable lattice constants and electronic structures; it exhibits behavior similar to the GGA$+U$ functionals for small $U$ values. The hybrid functional HSE06 is accurate in predicting the lattice constants, but leads to a band gap of $\approx$1 eV in the rhombohedral phase, which is higher than the experimental estimation of 0.2 eV. Our findings suggest that accurate qualitative and quantitative simulations of the lacunar spinel family with DFT requires careful attention to the nuances of the exchange-correlation functional and considered spin structures.

Modeling the structural distortion and magnetic ground state of the polar lacunar spinel GaV4Se8

The lacunar spinel ${\mathrm{GaV}}_{4}{\mathrm{Se}}_{8}$ is a material whose properties are dominated by tetrahedral clusters of V atoms. The compound is known to undergo a polar distortion to a ground state structure in the $R3m$ space group, and orders ferromagnetically with a relatively small magnetic moment. We develop an understanding into the relationship between crystal structure and magnetic order in this material, and the influence of electron correlations in establishing the observed ground state using first-principles density functional theory (DFT) electronic structure calculations. Because electrons are delocalized within ${\mathrm{V}}_{4}$ clusters but localized between them, the usual approaches to simulate electron correlations---such as the use of the Hubbard $U$ in $\mathrm{DFT}+U$ schemes---do not adequately recreate the experimental ground state. We find instead that the experimental ground state of ${\mathrm{GaV}}_{4}{\mathrm{Se}}_{8}$ is well represented by the random-phase approximation to the correlation energy. Additionally, we find that magnetism and crystal structure are strongly coupled in this material, and only certain arrangements of magnetic moment within a ${\mathrm{V}}_{4}$ cluster can stabilize the observed structural distortion. In combination with the anisotropic, polar nature of the material, the strength of magnetostructural coupling indicates that application of strain could be used to tune the magnetic properties of ${\mathrm{GaV}}_{4}{\mathrm{Se}}_{8}$.

Raman scattering yields cubic crystal grain orientation

The paper proposes a fully optical method for determination of a cubic crystal grain orientation in a sample inspected by a Raman microscope. The method is based on a universal and strong polarisation anisotropy of the Raman scattering by doubly degenerate optic phonon modes and it only requires a standard Raman microscope equipped with a polarisation analysis. Explicit formulas for the orientation of the crystal grain are derived. The feasibility of the approach is demonstrated by comparing grain orientations in a polycrystalline cubic lacunar spinel GaV4S8 determined independently using electron backscatter diffraction and Raman scattering methods.

Possible emergence of a skyrmion phase in ferroelectric GaMo4S8

Polar lacunar spinels, such as GaV$_4$S$_8$ and GaV$_4$Se$_8$, were proposed to host skyrmion phases under magnetic field. In this work, we put forward, as a candidate for N\'eel-type skyrmion lattice, the isostructural GaMo$_4$S$_8$, here systematically studied via both first-principles calculations and Monte Carlo simulations of model Hamiltonian. Electric polarization, driven by Jahn-Teller distortion, is predicted to arise in GaMo$_4$S$_8$, showing a comparable size but an opposite sign with respect to that evaluated in V-based counterparts and explained in terms of different electron counting arguments and resulting distortions. Interestingly, a larger spin-orbit coupling of 4d orbitals with respect to 3d orbitals in vanadium-spinels leads to stronger Dzyaloshinskii-Moriya interactions, which are beneficial to stabilize a cycloidal spin texture, as well as smaller-sized skyrmions (radius<10 nm). Furthermore, the possibly large exchange anisotropy of GaMo4S8 may lead to a ferroelectric-ferromagnetic ground state, as an alternative to the ferroelectric-skyrmionic one, calling for further experimental verification.

Microscopic theory of electric polarization induced by skyrmionic order in GaV4S8

The lacunar spinel GaV$_{4}$S$_{8}$ was recently suggested to be a prototype multiferroic material hosting skyrmion lattice states with a sizeable polarization $\boldsymbol{P}$ coupled to magnetic order. We explain this phenomenon on the microscopic level. On the basis of density functional theory, we construct an effective model describing the behavior of magnetically active electrons in a weakly coupled lattice formed by molecular orbitals of the (V$_{4}$S$_{4}$)$^{5+}$ clusters. By applying superexchange theory combined with the Berry-phase theory for $\boldsymbol{P}$, we derive a compass model relating the energy and polarization change with the directions of spins $\boldsymbol{e}_{i}$ in magnetic bonds. We argue that, although each skyrmion layer is mainly formed by superexchange interactions in the same plane, the spin-dependence of $\boldsymbol{P}$ arises from the stacking misalignment of such planes in the perpendicular direction, which is inherent to the lacunar spinel structure. We predict a strong competition of isotropic, $\sim \boldsymbol{e}_{i}\boldsymbol{e}_{j}$, and antisymmetric, $\sim \boldsymbol{e}_{i} \times \boldsymbol{e}_{j}$, contributions to $\boldsymbol{P}$ that explains the experimentally observed effect.

Charge density functional plus U calculation of lacunar spinel GaM4Se8(M = Nb, Mo, Ta, and W)

Charge density functional plus U calculations are carried out to examine the validity of molecular Jeff = 1/2 and 3/2 states in lacunar spinel GaM4Se8 (M = Nb, Mo, Ta, and W). With LDA (spin-unpolarized local density approximation)+U, which has recently been suggested as a more desirable choice than LSDA (local spin density approximation)+U, we examine the band structure in comparison with the previous prediction based on the spin-polarized version of functional and with the prototypical Jeff = 1/2 material Sr2IrO4. It is found that the previously suggested Jeff = 1/2 and 3/2 band characters remain valid still in LDA+U calculations while the use of charge-only density causes some minor differences. Our result provides further support for the novel molecular Jeff state in this series of materials, which can hopefully motivate the future exploration toward its verification and the further search for new functionalities.

Orbital-order driven ferroelectricity and dipolar relaxation dynamics in multiferroic GaMo4S8

We present the results of broadband dielectric spectroscopy of $\mathrm{GaM}{\mathrm{o}}_{4}{\mathrm{S}}_{8}$, a lacunar spinel system that recently was shown to exhibit non canonical, orbitally driven ferroelectricity. Our study reveals complex relaxation dynamics of this multiferroic material, both above and below its Jahn-Teller transition at ${T}_{\mathrm{JT}}=47\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Above ${T}_{\mathrm{JT}}$, two types of coupled dipolar-orbital dynamics seem to compete: relaxations within cluster-like regions with short-range polar order as in relaxor ferroelectrics and critical fluctuations of only weakly interacting dipoles, the latter resembling the typical dynamics of order-disorder type ferroelectrics. Below the Jahn-Teller transition, the onset of orbital order drives the system into long-range ferroelectric order and dipolar dynamics within the ferroelectric domains is observed. The coupled dipolar and orbital relaxation behavior of $\mathrm{GaM}{\mathrm{o}}_{4}{\mathrm{S}}_{8}$ above the Jahn-Teller transition markedly differs from that of the skyrmion host $\mathrm{Ga}{\mathrm{V}}_{4}{\mathrm{S}}_{8}$, which seems to be linked to differences in the structural distortions of the two systems on the unit-cell level.