Crystalline Field Splitting Research Articles

Superconductivity arising from pressure-induced emergence of a Fermi surface in the kagome-lattice chalcogenide Rb2Pd3Se4

According to the Bardeen-Cooper-Schrieffer theory, superconductivity usually needs well-defined Fermi surface(s) with strong electron-phonon coupling and moderate quasiparticle density of states. A kagome lattice can host flat bands and topological Dirac bands; meanwhile, due to the parallel Fermi surfaces and saddle points, many interesting orders are expected. Here, we report the observation of superconductivity by pressurizing a kagome compound ${\mathrm{Rb}}_{2}{\mathrm{Pd}}_{3}{\mathrm{Se}}_{4}$ using a diamond-anvil-cell. The parent compound shows an insulating behavior; however, it gradually becomes metallic and turns to a superconducting state when high pressure is applied. High-pressure synchrotron measurements show that there is no structural transition occurring during this process. The density-functional-theory calculations illustrate that the insulating behavior of the parent phase is due to the crystalline field splitting of the partial $\mathrm{Pd}\text{\ensuremath{-}}4d\phantom{\rule{0.16em}{0ex}}{t}_{\text{2g}}$ bands and the Se-derivative $4p$ band. However, the threshold of metallicity and superconductivity are reached when the Lifshitz transition occurs, leading to the emergence of a tiny Fermi surface at the $\mathrm{\ensuremath{\Gamma}}$ point. Our results point to an unconventional superconductivity and shed light on understanding the electronic evolution of a kagome material.

Successive magnetic orderings in the Ising spin chain magnet DyNi5Ge3

In this report, we investigated a new rare-earth-based one-dimensional Ising spin chain magnet $\mathrm{Dy}{\mathrm{Ni}}_{5}{\mathrm{Ge}}_{3}$ by means of magnetization, specific heat, and powder neutron diffraction measurements. Due to the crystalline electrical field splitting, the magnetic Dy ions share an Ising-like ground doublet state. Owning to the local point symmetry, these Ising moments form into two canted magnetic sublattices, which were further confirmed by the angle-dependent magnetization measurement. In zero fields, two successive antiferromagnetic phase transitions were found at temperatures ${T}_{\mathrm{N}1}=6\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{N}2}=5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, respectively. Only part of the moments are statically ordered in this intermediate state between ${T}_{\mathrm{N}1}$ and ${T}_{\mathrm{N}2}$. Powder neutron diffraction experiments at different temperatures were performed as well. An incommensurate magnetic propagation vector of ${\mathbf{k}}_{\mathbf{m}}=(0.5,0.4,0.5)$ was identified. The refined spin configurations through the irreducible representation analysis confirmed that these Ising spins are canted in the crystal $ab$ plane.

Constructing spin pathways in LaCoO3 by Mn substitution to promote oxygen evolution reaction

Designing efficient oxygen evolution reaction (OER) electrocatalysts is essential for numerous sustainable energy conversion technologies. An obstacle that impedes the development of OER electrocatalysts is the insufficient emphasis on the spin attribution of electrons. Recently, the different spin configuration of reactants and products in the OER has been recognized as the factor that slows down the reaction kinetics. In this work, Mn substitution was introduced to LaCoO3, which brought about lattice expansion and reduced crystalline field splitting energy. This led to the increase in the effective magnetic moment, which triggers the transfer of Co3+ from low to higher spin states. Thus, the hybridization of Co eg and O 2p states across the Fermi level was strengthened. Specifically, with 25 at. % Mn substitution, LaCoO3 transits from a semiconductor to a half-metal, which benefits the spin-oriented electronic transport and resultantly promotes the OER. This method paves the way for the construction of spin pathways in catalysts.

Spin Seebeck effect in nonmagnetic excitonic insulators

We propose a mechanism of the spin Seebeck effect attributed to excitonic condensation in a nonmagnetic insulator. We analyze a half-filled two-orbital Hubbard model with a crystalline field splitting in the strong coupling limit. In this model, the competition between the crystalline field and electron correlations brings about an excitonic insulating state, where the two orbitals are spontaneously hybridized. Using the generalized spin-wave theory and Boltzmann transport equation, we find that a spin current generated by a thermal gradient is observed in the excitonic insulating state without magnetic fields. The spin Seebeck effect originates from spin-split collective excitation modes although the ground state does not exhibit any magnetic orderings. This peculiar phenomenon is inherent in the excitonic insulating state, whose order parameter is time-reversal odd and yields a spin splitting for the collective excitation modes. We also find that the spin current is strongly enhanced and its direction is inverted in the vicinity of the phase transition to another magnetically ordered phase. We suggest that the present phenomenon is possibly observed in perovskite cobaltites with the $\mathrm{Gd}\mathrm{Fe}{\mathrm{O}}_{3}$-type lattice distortion.

Strong enhancement of magnetic susceptibility induced by spin-nematic fluctuations in an excitonic insulating system with spin-orbit coupling

Effects of the spin-orbit coupling (SOC) and magnetic field on excitonic insulating (EI) states are investigated. We introduce the two-orbital Hubbard model with the crystalline field splitting, which is a minimal model for discussing the exciton condensation in strongly correlated electron systems, and analyze its effective Hamiltonian in the strong correlation limit by using the mean-field theory. In the absence of the SOC and magnetic field, the ground state changes from the nonmagnetic band-insulating state to the EI state by increasing the Hund coupling. In an applied magnetic field, the magnetic moment appears in the EI state, which is continuously connected to the forced ferromagnetic state. On the other hand, in the presence of the SOC, they are separated by a phase boundary. We find that the magnetic susceptibility is strongly enhanced in the EI phase near the boundary with a small SOC. This peculiar behavior is attributed to the low-energy fluctuation of the spin nematicity inherent in the high-spin local state stabilized by the Hund coupling. The present study not only reveals the impact of the SOC for the EI state but also sheds light on the role of quantum fluctuations of the spin nematicity for the EI state.

Phase diagram and collective excitations in an excitonic insulator from an orbital physics viewpoint

Excitonic insulating system is studied from the viewpoints of the orbital physics in strongly correlated electron systems. An effective model Hamiltonian for low-energy electronic states is derived from the two-orbital Hubbard model with a finite energy difference corresponding to the crystalline field splitting. The effective model is represented by the spin operators and the pseudo-spin operators for the spin-state degrees of freedom. The ground state phase diagram is analyzed by the mean-field approximation. In addition to the low-spin state and high-spin state phases, two kinds of the excitonic insulating phases emerge as a consequence of the competition between the crystalline field effect and the Hund coupling. The excitonic transition is classified to be an Ising-like transition reflecting a spontaneous breaking of the $Z_2$ symmetry. Magnetic structures in the two excitonic insulating phases are different from each other; an antiferromagnetic order and a spin nematic order. Collective excitations in each phase are examined by using the generalized spin-wave method. The Goldstone modes in the excitonic insulating phases appear in the dynamical correlation functions for the spins and pseudo-spin operators. Both the transverse and longitudinal spin excitation modes are active in the two excitonic insulating phases in contrast to the low-spin state and high-spin state phases. Connections of the present results to the perovskite cobalt oxides are discussed.

Photoinduced Change in the Spin State of Itinerant Correlated Electron Systems

A photoinduced spin-state change in the itinerant correlated electron system is studied. A photon introduced in the low-spin band insulator induces a bound state of the high-spin state and a photoexcited hole. This bound state brings a characteristic peak in the pump-probe optical absorption spectra which are completely different from the spectra in thermal-excited states. The present results well explain the recent experiments of the ultrafast optical spectroscopy in perovskite cobaltites.

Magnetic properties of the Ag–In–rare-earth1/1 approximants

We have performed magnetic susceptibility and neutron scatteringmeasurements on polycrystalline Ag–In–RE (RE, rare-earth)1/1 approximants. In the magnetic susceptibility measurements, for most ofthe RE elements, inverse susceptibility shows linear behaviour in a widetemperature range, confirming well localized isotropic moments for theRE3 + ions. Exceptionally for the light RE elements, such as Ce and Pr, nonlinear behaviour wasobserved, possibly due to significant crystalline field splitting or valence fluctuation. ForRE = Tb, thesusceptibility measurement clearly shows a bifurcation of the field-cooled and zero-field-cooled susceptibilityat Tf = 3.7 K, suggesting a spin-glass-like freezing. On the other hand, neutron scatteringmeasurements detect significant development of short-range antiferromagnetic spincorrelations in the elastic channel, which is accompanied by a broad peak at meV in the inelastic scattering spectrum. These features have striking similarity to thosein the Zn–Mg–Tb quasicrystals, suggesting that the short-range spin freezingbehaviour is due to local high-symmetry clusters commonly seen in both systems.

Infrared spectroscopy of different phosphates structures

Infrared (IR) spectroscopic studies of mineral and synthetic phosphates have been presented. The interpretation of the spectra has been preceded by the isolated [PO 4] 3− tetrahedron spectra analyse. The K 3PO 4 saturated aqueous solution was measured in the special cell for liquids. The obtained IR results have been compared with the theoretical number of IR-active modes. The number and positions of the bands due to P–O vibrations have been established. The phase composition of the phosphates has been determined using XRD and IR spectroscopy methods. The influence of non-tetrahedral cations on the shape of the spectra and the positions of bands has been analysed and the crystalline field splitting effect has been discussed.

Dynamical Mean Field Theory for d Electrons on Cubic Lattices with Realistic Electron Hopping and Interaction

The noncrossing approximation (NCA) for solving an impurity problem of interacting electrons is applied to the dynamical mean field theory for a d -electron system on cubic lattices. Anisotropy in the hopping integrals as well as intraatomic Coulomb interactions and the crystalline field splitting of d orbitals are fully considered. Single-particle excitation spectra are calculated for various occupations of the d band and discussed with reference to the multiplet spectra obtained in the NCA calculation and the k -dependent spectra. Differences in the results of the NCA and the iterative perturbation theory are discussed.

Band calculations for 4f systems based on the dynamical mean field theory

Recent band calculations for Ce compounds based on the dynamical mean field theory(DMFT) are reported. The auxiliary impurity problem has been solved by a method namedNCAf2vc, which includes the correct exchange process of the virtual excitation, the crystalline field splitting (CFS), and the spin–orbit interaction(SOI) of the self-energy. These are necessary features in the quantitative band theory forCe compounds. The results of applications on Ce metal and Ce-monopnictides arepresented.

Crystal-field analysis for d 8 ions at D 4h symmetry sites: Electronic states in trans-NiCl 2(H 2O) 4 complex

The polarized absorption spectra of trans -NiCl 2(H 2O) 4 complex were measured by Bussière et al. [Coord. Chem. Rev. 219–221 (2001) 509–543] at low-temperature. Using the experimental spectroscopic data, semiempirical calculations of the crystal-field levels of trans-NiCl 2(H 2O) 4 chromophore are carried out, based on the Racah theory. We used idealized D 4h point group symmetry to analyse the observed crystalline-field splitting of this chromophore. As a result, Racah and crystal-field parameters have been reliably obtained. A good agreement between the theoretical and experimental energy levels of trans-NiCl 2(H 2O) 4 complex has been obtained. The region of 3T 1g/ 1E g(O h) bands is of great interest and it is useful to use the tetragonal symmetry to understand the features of this spectral region.

Crystal fields and the [formula omitted] transition in Ce

In the γ → α transition of Ce, the material undergoes an isostructural change at which the volume changes by 15% and the magnetic character changes. Recently, the transition has been described in terms of a balance between the free-energy of the magnetic moments and the characteristic energy scale of the α phase. The field-temperature dependence of the phase diagram has been predicted, and was confirmed by experiment. Inelastic neutron scattering experiments on the γ phase of Ce have shown indications of crystal field splittings, and similar experiments have determined the energy scale of the α phase. We shall examine the effects of the crystalline field splittings within the framework of NCA calculations on the single-impurity Anderson model, and examine their consequence for the phase diagram.

Crystal-field splitting of the Cr 4+ terms in LiAlO 2 oxide crystal

The absorption and excitation spectra of the tetrahedrally coordinated Cr 4+ ions doped in LiAlO 2 oxide crystal were measured by Kück and Hartung at room temperature (Chem. Phys. 240 (1999) 387). These spectra have provided evidence of the occurrence of transitions from the 3 A 2( 3 F) ground state to the crystal-field split levels 3 T 2( 3 F), 3 T 1( 3 F) and 3 T 1( 3 P) (levels are assigned to the T d symmetry, i.e., ideal tetrahedron CrO 4). The splitting of each band of the T d symmetry is due to the distortion of the ideal tetrahedron. Using the experimentally determined data from the absorption and excitation spectra, a theoretical calculation for the crystal-field levels of Cr 4+:LiAlO 2 was performed by Kück and Hartung, based on the angular overlap model theory. The calculation reveals a good agreement between the mean values of the bands, while it underestimates the splitting of each band. A detailed crystal-field analysis of electronic energy levels of Cr 4+ doped in LiAlO 2 oxide crystal based on the Racah theory is proposed in this work. The observed crystalline-field splitting of the Cr 4+ terms was accounted for by using a C 2 symmetric Hamiltonian. In turn, reliable crystal-field and Racah parameters have been obtained. This theoretical analysis confirms the observed crystalline-field splittings of the 3 F and 3 P terms of the Cr 4+ ion doped in the oxide crystal LiAlO 2.

Crystal-field analysis of the Cr4+absorption and excitation spectrum in LiGaO2oxide crystal

The absorption and excitation spectra of the tetrahedrally coordinated Cr 4+ ions doped in LiGaO 2 oxide crystal are measured by Kiick and Hartung at room temperature. Using the experimentally determined data from these spectra, a theoretical calculation for the crystal-field levels of Cr 4+ .LiGaO 2 was performed by Kiick and Hartung, based on the angular overlap model theory (AOM). The calculation reveals an important discrepancy between the theoretical and the experimental energies. A detailed crystal-field analysis of electronic energy levels of Cr 4+ doped in LiGaO 2 oxide crystal based on the Racah theory is proposed in this work. The observed crystalline-field splitting of the Cr 4+ terms was accounted for using a C 1 symmetric Hamiltonian. In turn, reliable crystal-field and Racah parameters have been obtained. This theoretical analysis confirms the observed crystalline-field splittings of the 3 F and 3 P terms of the Cr 4+ ion doped in the oxide crystal LiGaO 2 .

Bariev model for correlated hopping with crystalline field splitting

The Bethe Ansatz solution of the one-dimensional Bariev model for correlated hopping for two orbital and two spin degrees of freedom per site is used to study the evolution of the electron bands as a function of crystalline field splitting $\ensuremath{\Delta}.$ The formation of charge bound states (nonlocal Cooper pairs) leads to a charge sector with Fermi surface, while all other excitations are gapped in the absence of fields. The gap for the interband transitions is gradually closed with increasing $\ensuremath{\Delta}.$ Two critical fields ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{2}$ $({\ensuremath{\Delta}}_{1}<{\ensuremath{\Delta}}_{2})$ have to be distinguished. For two electrons per site the system is a one-component Luttinger liquid if $\ensuremath{\Delta}<{\ensuremath{\Delta}}_{1},$ a two-component Luttinger liquid for ${\ensuremath{\Delta}}_{1}<\ensuremath{\Delta}<{\ensuremath{\Delta}}_{2},$ and an insulator for $\ensuremath{\Delta}>{\ensuremath{\Delta}}_{2}.$ The critical behavior of superconducting fluctuations is also discussed.

Crystal-Field Analysis of the V3+ Excitation Spectrum in LiGaO2 and LiAlO2 Oxide Crystals

The absorption and excitation spectra of trivalent transition metal V 3+ ions doped in LiGaO 2 and LiAlO 2 oxide crystals are measured by Kuck and Jander [Opt. Mater. 13, 299 (1999)]. These spectra have provided evidence of the occurrence of transitions from the 3 A 2 ( 3 F) ground state to the crystal-field split levels 3 T 2 ( 3 F), 3 T 1 ( 3 F), and 3 T 1 ( 3 P) for V 3+ :LiGaO 2 . But only the transitions from the 3 A 2 ( 3 F) ground state to the crystal-field split levels 3 T 1 ( 3 F) and 3 T 1 ( 3 P) are observed for V 3+ :LiAlO 2 (levels are assigned to the T d symmetry, i.e. ideal tetrahedron (VO 4 ) 5- ). The splittings of each band of the T d symmetry is due to the distortion of the ideal tetrahedron. Using the experimentally determined data from the excitation spectra, a theoretical calculation for the crystal-field levels of V 3+ :LiGaO 2 and V 3+ :LiAlO 2 was performed by Kuck and Jander, based on the angular overlap model theory. The calculation reveals a good agreement between the mean values of the bands, while it underestimates the splitting of each band. A detailed crystal-field analysis of electronic energy levels of V 3+ doped in LiGaO 2 and LiAlO 2 oxide crystals based on the Racah theory is proposed in this work. The observed crystalline-field splitting of the V 3+ terms was accounted for using a C 2 symmetric Hamiltonian. In turn, reliable crystal-field and Racah parameters have been obtained. This theoretical analysis confirms the observed crystalline-field splittings of the 3 F and 3 P terms of the V 3+ ion doped in the two oxide crystals LiGaO 2 and LiAlO 2 . The crystalline-field splittings of the 3 T 2 ( 3 F) level for LiAlO 2 are deduced.

Crystal-Field Analysis of the Ce3+ Spectrum in YAlO3 Single Crystals

Infrared and ultraviolet absorption spectra arising from f → f and f → d transitions of Ce3+ in YAlO3 crystals are studied by Weber and used to derive the 4f and 5d energy levels. Excitation and fluorescence spectra of 5d → 4f emission are also studied by Weber. From these spectra, the energy-level values for the 5d and 2F7/2 multiplets are deduced, whereas the positions of the energy levels for the 2F5/2 multiplet given by Weber are uncertain. A detailed crystal-field analysis of electronic energy levels of Ce3+ doped in YAlO3 crystals is proposed in this work. The observed crystalline-field splittings of the Ce3+ multiplets were accounted for using a C1h symmetric Hamiltonian. In turn, reliable crystal-field parameters have been obtained. This theoretical analysis confirms the observed crystalline-field splittings of the 5d and 2F7/2 multiplets. The crystalline-field splittings of the 2F5/2 multiplet are deduced.

The AIPO4 polymorphs structure in the light of Raman and IR spectroscopy studies

Raman spectra of low-temperature polymorphic forms of AlPO4 (berlinite, phosphocristobalite and phosphotridymite) are presented. The interpretation of the spectra has been carried out using the model of [PO4]3− tetrahedron isolated by Al3+ cations. The theoretical number of Raman active modes has been determined using the factor group analysis. Raman and IR spectra have been compared regarding adequate selection rules. The crystalline field splitting and Davydov effects have been discussed.It has been shown that AlPO4 polymorphs, usually classified as a framework structure, because of the similarity to SiO2, should be rather treated as an orthophosphate structure. Thus the model of the oxygen bridge, commonly used for interpretation of framework structures, should not be used in the case of AlPO4.

Magnetic impurities in a correlated electron system with spin-triplet pairing

We consider an exactly solvable two-band model of electrons moving in one dimension and interacting with a δ -function spin-exchange potential. The interaction leads to the formation of spin-triplet bound states of the Cooper type (hard-core bosons that do not condensate and exist at all temperatures). Without destroying the integrability we introduce a finite concentration of mixed-valent impurities with two magnetic configurations of spin S and S− 1 2 , respectively, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the correlated host with impurities and discuss the ground state properties as a function of magnetic field, the crystalline field splitting of the bands, the concentration of the impurities and the Kondo exchange coupling. In the zero-field ground state the spin-triplet states are effectively free bosons and a threshold band splitting Δ is required to break up a triplet pair. The gap of the unpaired electron excitations is gradually reduced by the band splitting and closes at Δ . For a splitting larger than Δ a fraction of the electrons is spin-polarized. The impurities are antiferromagnetically correlated with each other and the effect of a magnetic field is to suppress these correlations as well as to gradually align the spins of the spin-triplets with the field. Spin- 1 2 impurities always enhance the gap Δ , while with impurities of higher spin the gap decreases if the coupling between the triplets and impurities is weak (small Kondo temperature), but increases otherwise. For small T K the gap is closed at a critical concentration x cr and the two electron bands have different populations. For x > x cr we obtain a zero-magnetization phase with three coexisting components, namely, itinerant ferromagnetism of unpaired electrons, antiferromagnetism of the impurities and superconducting fluctuations of ferromagnetically correlated spin triplets. The critical exponents of correlation functions are also briefly discussed in the conformal field theory limit.